MAGNETO-TRANSPORT AND OPTICAL CONTROL OF MAGNETIZATION IN ORGANIC SYSTEMS: FROM POLYMERS TO MOLECULE-BASED MAGNETS
DISSERTATION
Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the
Graduate School of The Ohio State University
By
Kadriye Deniz Bozdag, M.S.
Graduate Program in Physics
The Ohio State University
2009
Dissertation Committee:
Arthur J. Epstein, Adviser Ezekiel Johnston-Halperin Julia S. Meyer Thomas Humanic c Copyright by
Kadriye Deniz Bozdag
2009 ABSTRACT
Organic systems can be synthesized to have various impressive properties such as
room temperature magnetism, electrical conductivity as high as conventional metals
and magnetic field dependent transport. In this dissertation, we report comprehensive
experimental studies in two different classes of organic systems, V-Cr Prussian blue
molecule-based magnets and polyaniline nanofiber networks.
The first system, V-Cr Prussian blue magnets, belongs to a family of cyano-bridged
bi-metallic compounds which display a broad range of interesting photoinduced mag-
netic properties. A notable example for optically controllable molecule-based magnets
is Co-Fe Prussian blue magnet (Tc ∼ 12 K), which exhibits light-induced changes in between magnetic states together with glassy behavior. In this dissertation, the first reports of reversible photoinduced magnetic phenomena in V-Cr Prussian blue analogs and the analysis of its AC and DC magnetization behavior are presented. Optical excitation of V-Cr Prussian blue, one of the few room temperature molecule-based magnets, with UV light (λ = 350 nm) suppresses magnetization, whereas subsequent excitation with green light (λ = 514 nm) increases magnetization. The partial recov- ery effect of green light is observed only when the sample is previously UV-irradiated.
Moreover the photoinduced state has a long lifetime at low temperatures (τ > 106 s
at T = 10 K) indicating that V-Cr Prussian blue reaches a hidden metastable state
upon illumination with UV light. The effects of optical excitation are maintained up
ii to 200 K and completely erased when the sample is warmed above 250 K. Results of detailed magnetic studies and the likely microscopic mechanisms for the photo illumination effects on magnetic properties are discussed.
The second organic system, polyaniline nanofiber networks, was synthesized via dilute polymerization and studied at low and high electric and magnetic fields for tem- peratures 2 K - 250 K for their magneto-transport behavior. We observed large mag- netoresistance (up to 55 % at H = 8 T and T = 3 K) in polymer networks composed of nanofibers with an average diameter of about 80 nm. A crossover from positive MR to negative MR is observed at ∼ 87 K. The positive and negative MR are attributed to two competing mechanisms; shrinkage of the localized electron wavefunction and suppression of quantum interference of electron wavefunctions propagating along dif- ferent current paths in the hopping process by the applied magnetic field. In addition to temperature dependence of magnetoresistance, dependencies on morphology of the nanofibers and applied electric field are observed. Detailed DC electrical transport results of various polyaniline nanofiber samples and possible mechanisms responsible for the magneto-transport behavior are discussed.
iii Dedicated to my love Doruk and my parents, Oya and Haydar Duman.
iv ACKNOWLEDGMENTS
First of all, I would like to thank my adviser Dr. Arthur J. Epstein for his support and valuable advice. His enthusiasm and motivation kept me going and inspired me for the quest for the best and novel science. It has been a real pleasure to work with him.
I would like to also thank Dr. Nan-Rong Chiou for preparing high-quality polyani- line nanofibers and Dr. Joel Miller and his students Amber C. MacConnel, William
W. Shum, Kendric J. Nelson at University of Utah for supplying me Prussian blue samples for my experiments. Without these samples, none of this work would have been possible.
I also want to thank Dr. Jung-Woo Yoo whom I have learned quite a lot in my PhD life. I am also thankful to former group members Dr. Jeremy Bergeson and Dr. Derek Lincoln who helped me in the lab anytime I needed. I also wish to thank Dr. Vladimir Prigodin for all insightful discussions. I am also grateful to all present and past group members Chia-Yi Chen, Bin Li,Chi-Yueh Kao, Austin Carter,
Lynette Mier, Timi Adetunji, June Hyoung Park, Jesse Martin, Raju Nandyala, Jen-
Chieh Wu and Yong Min who created a great and joyful environment to work in. In particular, I would like to thank Louis Nemzer and Mark Murphey for their help with latex and FIB. I also would like thank my graduate committee members Dr. Ezekiel
v Johnston-Halperin, Dr. Julia S. Meyer and Dr. Thomas Humanic. I want to thank all of my friends in Columbus who made my PhD life a lot smoother.
I gratefully acknowledge the financial support from the Department of Physics through teaching associateship and summer quarter fellowship program, Materials
Research Science and Engineering Center (MRSEC) through Center for Emergent
Materials (CEM) fellowship and DEO, AFOSR and Institue for Material Research
(IMR) through grants for research associateship, travel and facility usage.
I am also thankful to Jenny Finnell who handled and solved our administrative problems and former graduate studies chairman Dr. Thomas Humanic and secretary
Brenda Mellett for their care and help with departmental issues.
Finally, I want to thank my family; my parents Oya and Haydar and my siblings
Zumrut, Irem and Kaya for their continuous and endless support, encouragement and love despite the distance separating us. I wish to specially to thank my husband
Doruk who has been with me at all times. I always feel your encouragement, love and kindness.
vi VITA
August 7, 1980 ...... Born - Burhaniye, TURKEY
2003 ...... B.S. Physics, Bogazici University, Istanbul, TURKEY 2003-2004 ...... Graduate Teaching Associate, University of Cincinnati, Cincinnati, OHIO 2004-2006 ...... Graduate Teaching Associate, The Ohio State University, Columbus, OHIO 2007 ...... M.S. Physics, The Ohio State University, Columbus, OHIO 2007-2008 ...... Graduate Research Associate, The Ohio State University, Columbus, OHIO 2008-present ...... CEM Fellow, The Ohio State University, Columbus, OHIO
PUBLICATIONS
Research Publications
K. Deniz Bozdag, N.-R. Chiou, V. N. Prigodin, A. J. Epstein “Temperature, Mag- netic and Electric Field Dependence of Magneto-Transport for Polyaniline Nanofiber Network”. Synthetic Metals, 2009.
vii FIELDS OF STUDY
Major Field: Physics
Studies in: Magnetism in Organic Magnets Magneto-transport in Polymer Nanofibers Field Effect Transistor, Spin-valves and Spin-leds with Organic Magnets
viii TABLE OF CONTENTS
Page
Abstract ...... ii
Dedication ...... iv
Acknowledgments ...... v
Vita...... vii
LIST OF FIGURES ...... xiii
Chapters:
1. Introduction ...... 1
1.1 Optical Control of Magnetism ...... 1
1.2 Magneto-Transport in Polyaniline Nanofibers ...... 3
1.3 Outline ...... 6
2. Background on Magnetism, Molecule-Based Magnets and Photoinduced
Magnetism ...... 8
ix 2.1 Magnetism in Solids ...... 8
2.1.1 Isolated Magnetic Moments ...... 8
2.1.2 Atoms in Solids ...... 15
2.1.3 Magnetic Interactions ...... 20
2.1.4 Magnetostatic (dipole-dipole) interactions ...... 26
2.1.5 Anisotropy ...... 27
2.1.6 Domain Walls ...... 30
2.1.7 Magnetic Ordering ...... 32
2.2 Molecule-based Magnets ...... 43
2.2.1 Prussian Blue Analogs ...... 44
2.3 Photoinduced Magnetism ...... 48
2.3.1 Co-Fe Prussian Blue ...... 50
2.3.2 M[TCNE]x x ∼ 2 M = V, Mn ...... 56
3. Background on Conducting Polymers ...... 61
3.1 Conducting Polymers ...... 61
3.1.1 Electromagnetic Response ...... 71
3.1.2 Electronic Structure of Polymers ...... 75
3.1.3 Transport in Conducting Polymers ...... 82
4. Experimental ...... 96
4.1 Sample Preparation ...... 96
4.1.1 Polyaniline Nanofibers ...... 96
x 4.1.2 V-Cr Prussian Blue ...... 97
4.2 Experimental Tools ...... 98
4.2.1 Elemental Analysis ...... 98
4.2.2 Imaging and patterning: Photolithography, FIB, SEM . . . 99
4.2.3 DC conductivity ...... 103
4.2.4 DC magnetization: SQUID magnetometer ...... 104
4.2.5 AC susceptibility: PPMS susceptometer ...... 107
4.2.6 Sample Illumination: Laser and fiber optics ...... 108
4.2.7 UV-Vis Spectrometer ...... 110
4.2.8 XPS ...... 110
5. Optical Control of Magnetism in V-Cr Prussian Blue ...... 113
5.1 Magnetic Properties ...... 113
5.2 Optical Control of Magnetic Properties ...... 128
5.3 Summary and Discussion ...... 138
6. Magneto-transport in Polyaniline Nanofiber Networks ...... 139
6.1 Resistivity ...... 139
6.2 Magneto-transport ...... 146
6.2.1 Temperature Dependence ...... 146
6.2.2 Morphology Dependence ...... 150
6.2.3 Electric Field Dependence ...... 153
6.3 Summary and Discussion ...... 156
xi 7. Discussions and Future Work ...... 159
7.1 Optical Control of Magnetism ...... 159
7.2 Magneto-transport for Polyaniline Nanofiber Networks ...... 160
7.3 Future Work ...... 162
BIBLIOGRAPHY ...... 164
xii LIST OF FIGURES
Figure Page
1.1 Molecular structures of (top) emeraldine base PANI and (bottom) CSA.5
2.1 Magnetic moment versus H/T graph for spin values s = 3/2, 5/2 and
7/2 in which the data fits well to the brillouin function [47] ...... 12
2.2 Magnetic susceptibilities of diamagnetic and paramagnetic systems [43] 14
2.3 The angular distribution of d orbitals. The levels dz2 and dx2−y2 are
grouped as eg levels. The remaining levels dxz, dxz and dyz are grouped
as t2g levels [42, 46] ...... 16
2.4 The overlap of different d orbitals with the ligands. dxy orbital has
lower energy compare to dx2−y2 due to smaller overlap and electrostatic
interaction [43] ...... 17
xiii 2.5 Splitting of the d orbitals in octahedral (left) and tetrahedral (right)
crystal fields ...... 18
2.6 Electronic configuration for high-spin (HS) and low-spin (LS) states
under octahedral crystal field (left). Energy curves for LS and HS
states with respect to metal-ligand coordinate (right) [46]...... 19
2.7 Jahn-Teller lattice distortion that leads to splitting of eg and t2g levels
in MnIII (3d4) in order to reduce energy of the system [42] ...... 20
2.8 Superexchange mechanism in a magnetic oxide. The magnetic elec-
trons can be delocalized over M-O-M unit and the energy of the system
is lowered [58]...... 23
2.9 Double exchange between Mn3+ (left; 3d4) and Mn4+ (right; 3d3).
When electron hopping is possible (a) and forbidden (b) due to Hunds
rule in order to lower the energy of the system [43]...... 25
2.10 (a) Hysteresis loop for a FM-AFM bilayer with a diagram showing
magnetization at different stages (b) AFM-FM structure where only a
small number of spins are pinned (red arrows) at the interface compared
to unpinned ones (white arrows) [68, 69]...... 29
xiv 2.11 Magnetic domain structures of a rectangular ferromagnet with different
magnetostatic energies. The least magnetostatic energy is in the right
configuration [43]...... 32
2.12 Illustration of spin configuration of various magnetic orders at two
different instants: t0 and t1 [72]...... 33
2.13 The graphical solutions to Equation 2.44 at zero (left) and non-zero
(right) applied magnetic field [42]...... 35
2.14 Temperature dependence of inverse magnetic susceptibility for antifer-
romagnetic, paramagnetic and ferromagnetic systems [73]...... 36
2.15 Thermal energy is comparable to anisotropy energy. Thus the small
size magnet flips its magnetization randomly [75]...... 38
2.16 Magnetic frustration due to (a) random exchange interactions and (b)
lattice geometry[50]...... 39
2.17 Free energy diagram of a spin glass system as it cools down above the
spin-glass transition temperature [84]...... 41
xv 2.18 Schematic magnetic phase diagram of a dilute alloy EuxSr1−xS (MxA1−xB
where M is magnetic, A and B are non-magnetic ions). Transition from
both paramagnetic state (PM) and ferromagnetic state (FM) to spin
glass (SG) state is possible [76]...... 43
2.19 Schematic image of structural (a) and orbital (b) interactions in Lewis
acid-base with hexacyanometallate and paramagnetic cations [97]. . . 45
2.20 The number and type of possible exchange interactions between CrIII
and divalent transition metal ions [93]...... 47
II III 2.21 The ordering temperature of M3 Cr2 system where M is a first row transition metal [97]...... 48
2.22 The crystal structure of Co-Fe Prussian Blue Analog [109, 110] . . . . 50
2.23 Scheme of charge transfer between Fe and Co upon illumination. Due
to spin-orbit coupling, a transition into high-spin state occurs in a
fraction of Co sites [50] ...... 52
2.24 Optical control of magnetism with red (λ = 650 nm) and blue (λ = 470
nm) in Co-Fe Prussian blue [110, 50]...... 53
xvi 2.25 Schematic energy diagram of photoinduced magnetization in Co-Fe
Prussian blue [112]...... 54
2.26 Illumination effects on ns (spin concentration), M (magnetization), Tc
(quasi-critical temperature), ξ (ferrimagnetic and spin-glass correlation
lengths), τ (relaxation times), Tf (freezing temperature), ∆ (energy
barriers for rotation of cluster moments), Hc (coercive field) in cluster
glass model [50]...... 55
2.27 (a) Schematic chemical structure of tetracyanoethylene (TCNE) [109].
(b) Schematic energy diagram for V[TCNE]2 [120]...... 56
2.28 Partially reversible illumination effects on magnetism in Mn(TCNE) [15] 57
2.29 Scheme of photoinduced mechanism in Mn(TCNE) where the ligand-
metal orbital overlap is increased and exchange interactions are en-
hanced. Stronger magnetic interactions lead to better spin alignment
and increase in magnetization...... 58
2.30 Decrease in field-cooled magnetization upon illumination with λ =
457.9 nm that is around π to π∗ + U excitation [6]...... 59
2.31 Full recovery from photoinduced magnetic state upon thermal heating
to 280 K [123, 6]...... 60
xvii 3.1 Chemical structures of commonly used conjugated polymers [125] . . 62
3.2 (a) Dimerized polyacetylene structure with alternating double and sin-
gle bonds. The energy diagram of undimerized (b) and dimerized poly-
acetylene(c)...... 63
3.3 Conductivities of pristine and doped polyaniline and trans-(CH)x [19] 65
3.4 Schemes of (a) substitutional and (b) interstitial doping in inorganic
semiconductor and conducting polymer respectively...... 66
3.5 (a) Schematic picture of inhomogeneous disorder in conjugated poly-
mers (b) Schematic picture of rod-like and coil-like disorder in polymers[23]. 68
3.6 Reduced activation energy (W ) plot for various polyaniline samples
doped with CSA, hydrochloric and sulfuric acid [125]...... 69
3.7 (a)Log-log plot of W vs. T for polyacetylene (black circles) at ambient
pressure and H = 0; (black diamond) at 10 kbar and H = 0; (black
square) at ambient pressure and H = 8 T. (inset) Pressure dependence
of conductivity [136]. (b) Schematic plot of the effect of magnetic field
and pressure around metal-insulator transition in logσ−logT graph [137] 70
xviii 3.8 Temperature dependency of resistivity in PANI-CSA with metallic be-
havior (samples S1 and S2) and conventional PANI sample for com-
parison [138]...... 71
3.9 The frequency dependence of real and imaginary parts of drude re-
sponse for ω2 = 30 eV2 and ~/τ = 0.02 eV [139]...... 74
3.10 The photon energy (~ω) dependence of real and imaginary parts of
dielectric function for lorentz oscillator with resonance frequency (~ω0)
= 3.85 eV, broadening (~γ) = 2.0 eV [140]...... 75
3.11 The conjugated structure of trans-polyacetylene with dimerization co-
ordinate un [141]...... 77
3.12 The energy of dimerized polyacetylene chain with degenerate energy
minima at ±u0 [124]...... 77
3.13 The band structure (left) and density of states (right) of semiconduct-
ing polyacetylene [124]...... 79
3.14 The undimerized (a) and dimerized (b) structures of trans-polyacetylene.
(c) The structure of cis-polyacetylene. (d)The two degenerate states
(A phase, B phase) and (e) soliton in trans-polyacetylene [124]. . . . 80
xix 3.15 Band structures of positive (a), neutral (b) and negative (c) solitons [145]. 81
3.16 Chemical structures and energy of non-degenerate ground states (A
and B phases) in conducting polymers [145]...... 82
3.17 The band structure of polypyrrole for (a) low doping level (polaron) (b)
moderate doping level (bipolaron) and (c) high doping level (bipolaron
bands) [149]...... 83
3.18 The periodic potential and disorder (a) and the form of localized wave-
function (b) in Anderson metal-insulator transition. [150]...... 84
3.19 The density of states-energy plot where the Fermi level lies in the region
of localized states [ [151, 122]...... 85
3.20 Schematic image of metallic grains (well ordered regions) that are con-
nected by amorphous (poor ordered) regions [159]...... 88
3.21 Charge transfer via tunneling through resonance states around Fermi
energy between the metallic grains [159]...... 89
xx 3.22 (a)Positive magnetoresistance in polyacetylene sample. Resistivity ra-
tio increases linearly with field and saturates at a characteristic mag-
netic field where all the spins are aligned [171].(b)Wavefunction shrink-
age (positive MR) and quantum interference effect (negative MR) in
polyaniline samples [173]...... 91
3.23 Two current paths between hopping sites with different scattering paths. 92
3.24 SEM image of two nanotubes crossing at a single junction [35]. . . . . 92
3.25 Temperature dependence of resistance through (b) a single nanojunc-
tion and (c) a single nanotube [35] ...... 93
3.26 Temperature dependence of conductivity (a) in a single fiber that fol-
lows 3D VRH (b) with a room temperature conductivity of 31.4 S/cm.
Quasi-1D VRH charge transport with a room temperature conductivity
of 0.035 S/cm in nanofiber pellet [185] ...... 94
3.27 SEM image of polyaniline nanofiber in the network (left) and pellet
form (right) [24]...... 95
3.28 The temperature dependence of dc conductivity in the polyaniline
nanofiber and pellet [184]...... 95
xxi 4.1 Schematic illustration of the gold electrodes for 4-probe (left) and 2-
probe (right) measurements used for electrical measurements...... 99
4.2 An illustration of steps in photolithography process, for preparing the
conductive 4-probe electrodes ...... 101
4.3 The schematic of FIB and a liquid metal ion source [186]...... 102
4.4 The polyaniline nanofiber cluster and platinum microleads fabricated
by FIB for connecting cluster to the electrodes ...... 103
4.5 PPMS sample puck with polyaniline nanofiber network sample with
4-probe configuration ...... 104
4.6 The configuration of the superconducting detection coils which is in-
ductively connected to SQUID [187]...... 105
4.7 The SQUID configuration and output signal when the sample (mag-
netic dipole) travels through the pick up coil assembly [73]...... 106
4.8 Block diagram of an ac susceptometer (Lake Shore 7225) [189]. . . . . 109
4.9 Schematic diagram of UV-Vis spectrometer [191] ...... 111
xxii 4.10 A schematic of XPS with its basic components...... 112
5.1 Zero field cooled (ZFC) and field cooled (FC) dc magnetization of V-
Cr Prussian Blue (a) powder and (b) dispersed sample that are sealed
under vacuum in quartz tube. A sharp increase in magnetization is
observed around 350 K...... 115
5.2 The degenerate d levels of Vanadium and Chromium split into t2g and
eg levels due octahedral crystal field and all the unpaired spins of V
and Cr ions occupy the t2g level...... 116
5.3 The XPS survey spectrum of V-Cr Prussian blue...... 117
5.4 ZFC and FC magnetization at different applied magnetic fields for V-Cr
Prussian blue (a) powder and (b) dispersed sample. Strong irreversibil-
ity exists between ZFC and FC magnetization at low temperatures in
both powder and dispersed sample. The bifurcation temperature de-
pends on the applied magnetic field and decreases with increasing field. 118
5.5 Optical microscope image of dispersed sample in nujol oil...... 119
5.6 The magnetic field dependence of magnetization of (a) powder and (b)
dispersed sample at different temperatures...... 121
xxiii 5.7 The coercive fields of powder and dispersed sample at different tem-
peratures...... 122
5.8 The irreversibility of FC magnetization during heating and cooling cycles.123
5.9 Temperature dependence of in-phase (a) and out-of-phase (b) ac sus-
ceptibilities at frequencies 11 Hz ≤ f ≤ 10,000 Hz for the powder V-Cr
Prussian blue sample...... 124
5.10 Temperature dependence of in-phase (a) and out-of-phase (b) ac sus-
ceptibilities at frequencies 11 Hz ≤ f ≤ 10,000 Hz for the dispersed
sample...... 125
5.11 Schematic Argand diagram (Cole-Cole plot) [192] ...... 126
5.12 In-phase (a) and out-of-phase (b) ac susceptibilities at frequencies 11
Hz ≤ f ≤ 10000 Hz at low temperatures...... 127
5.13 Temperature dependence of mean spin relaxation time for V-Cr Prus-
sian blue...... 128
5.14 (a) The UV-Vis spectrum of V-cr Prussian blue. (b) Decrease in
FC magnetization upon excitation with UV light (intensity of light
∼ 12mW/cm2) for 60 hours...... 130
xxiv 5.15 Partial recovery of magnetization upon subsequent illumination with
green light from a photo-excited state. The light intensity is kept
around 12 mW/cm2 for both illuminations with UV and green light. . 131
5.16 Temperature (a) and field (b) dependence of dc magnetization before
illumination, after illumination for 60 hours with UV light (intensity
of light ∼ 12mW/cm2 ) and after heating the sample up to 250 K. . 132
5.17 In phase (a) and out of phase(b) ac susceptibilities for ground and pho-
toinduced states (UV light excitation with light intensity ∼ 12mW/cm2
for 60 hours) of V-Cr Prussian blue at f = 3330 Hz...... 134
5.18 Temperature dependence of ZFC and FC magnetization for V-Cr Prus-
sian blue powder sample B...... 135
5.19 In-phase (a) and out-of-phase (b) susceptibilities of V-Cr Prussian blue
powder sample B. (inset) The out-of-phase susceptibility for the dis-
persed sample B in nujol oil...... 136
xxv 5.20 (a) Decrease in FC magnetization upon illumination with UV light with
an intensity ∼ 12 mW/cm2. (b) Partial recovery of magnetization upon
subsequent illumination with green light from a photo-excited state.
The light intensity is kept around 12 mW/cm2 for both illuminations
with UV and green light...... 137
6.1 (a) SEM image of dense polyaniline nanofiber network. (b) Tempera-
ture dependence of conductivity and (inset) fitting of resistivity to 1D
VRH model...... 141
6.2 (a) SEM image of dilute polyaniline nanofiber network and (b)the tem-
perature dependence of conductance...... 143
6.3 (a) SEM image of polyaniline nanofiber micro-cluster. (b) Temperature
dependence of conductivity and (inset) fitting of resistivity to 1D VRH
model...... 144
6.4 Positive magnetoresistance (MR) at low temperatures up to 8T. . . . 148
6.5 Negative MR at intermediate temperature regime up to 8T...... 149
6.6 Temperature and magnetic field dependence of MR around the crossover
region...... 150
xxvi 6.7 MR of nanofiber network in the whole temperature regime showing
both the positive and negative MR and corresponding mechanisms. . 151
6.8 MR of polyaniline nanofiber (a) network and (b) micro-cluster at low
temperatures up to 8T...... 152
6.9 MR of polyaniline nanofiber (a) network and (b) micro-cluster at in-
termediate temperatures up to 8T...... 154
6.10 (a) MR of polyaniline nanofiber network at different applied currents
at T = 50 K. (b) IV behavior of nanofiber network and (inset) applied
current dependency of MR at constant temperature...... 155
6.11 Applied current dependency of MR at T = 50 K of polyaniline nanofiber
micro-clusters. (inset) IV behavior at the same temperature...... 156
6.12 IV behavior of polyaniline nanofiber micro-clusters at different tem-
peratures...... 157
xxvii CHAPTER 1
Introduction
Recently, organic systems have attracted remarkable attention due to their po- tential applicability in various devices (e.g. light emitting diodes, transistors, solar cells [1], memory devices [2]) and the ability to tune electrical transport, structural and magnetic properties by chemical synthesis methods. All the endeavors of chemists lead to remarkable systems including room temperature molecule-based magnet V-
Cr Prussian blue [3] and conductive polymer nanofibers [4] which are discussed and investigated in this dissertation.
1.1 Optical Control of Magnetism
Magnetic materials have been a very important part of our lives due to numer- ous technological applications including transformers, speakers and memory devices.
There is still great interest in magnetic systems to achieve smaller, faster and cheaper devices. One of the challenges in utilizing magnetism is the control of magnetic prop- erties such as coercivity, spin value, exchange interactions and anisotropy by external stimuli. A variety of molecule-based magnets exhibit magnetic bistability [5, 6] due to inherent structural disorder which leads to control of magnetic properties by external stimuli such as pressure [7] and light [8].
1 Optical control of magnetic properties have attracted significant attention since
the effect of light illumination on magnetism was first reported in 1996 by Sato et
al. [8]. Illumination with light at a certain wavelength that the organic system is sus-
ceptible to, is a promising approach for optical control of magnetism in molecule-based
magnets. However a practical device has not been realized yet since it requires both
long range magnetic order and sustained illumination effect at high temperatures.
A notable example for optically tunable molecule-based magnet is Co-Fe Prussian
blue (Tc ∼ 12 K), which exhibits reversible light-induced changes in between mag- netic states together with cluster-glass behavior. Several molecule-based systems have been developed that exhibit optically tunable magnetism such as thin films [9] and nanoparticles [10, 11] of Co-Fe Prussian blue [12], cyano-bridged cobalt-tungstate as- sembly [13] and organic based magnet Mn[TCNE]2 [14, 15]. However they all present low magnetic ordering temperature. Recently Yoo et al. introduced photoinduced magnetism in a room temperature organic-based magnet V(TCNE)2 in which the illumination effects on magnetism are reversible only upon heating the sample [6, 16].
The photoinduced magnetism in these molecule-based systems originates from vari- ous mechanisms including charge transfer between transition ions leading to a change in total number of spins, and lattice distortion that changes the exchange coupling or magnetic anisotropy.
In order to fully understand the photoinduced magnetism mechanisms, find more suitable chemical structures and overcome the challenges, we have sought novel light- tunable magnets. Our search brought the discovery of a system, V-Cr Prussian blue [3] that shows reversible photoinduced magnetic effects with a magnetic order well above room temperature.
2 In this thesis, we report optical control of magnetism in V-Cr Prussian Blue analogs that is a cyano-bridged bimetallic compound with a face-centered cubic lattice structure. In V-Cr Prussian blue, a decrease in magnetization is observed upon illuminating with UV light (λ ∼ 350 nm). Whereas illumination with green light (λ = 514nm) partially recovers the magnetization of previously illuminated system. It is noted that the system stays in the photoexcited state for long time (t > 106 s)at low temperatures (T < 100 K). However when the system is heated above 250 K, it totally recovers back to the ground state due to thermal excitations without any degradation. In our measurements, the powder Prussian blue sample was dispersed in nujol oil for better optical excitation and sealed under vacuum in quartz tube in order to prevent oxidation. In the dispersed V-Cr Prussian blue samples, a peak is observed in both ac and dc magnetic responses at T ∼ 200 K due to increased magnetic anisotropy via freezing of the nujol oil that the magnet dispersed in. In addition to high temperature peak, a peak in dc magnetization and a frequency dependent shoulder in ac susceptibility is observed at T ∼ 25 K, indicating cooperative freezing of the spins of V-Cr Prussian blue magnet and re-entrance to a spin-glass like state.
1.2 Magneto-Transport in Polyaniline Nanofibers
Polymers were known as good electrical insulators before the discovery of conduc- tive polyacetylene in 1977 [17]. After this Nobel winning discovery, there has been an increasing interest in conducting polymers due to not only their wide range control- lable conductivity but also low cost and easy synthesizing methods [18, 19]. Moreover conducting conjugated polymers exhibit exciting transport and optical properties [20].
3 These properties make them good candidates for many applications such as field ef- fect transistors, bio-sensors, photovoltaic cells, light emitting diodes and data storage devices [21].
Recently, with the need for smaller nano-scale and molecular devices, polymer nanofibers which provide tunable functionality, has attracted much attention [22].
Although the chemical structures of conducting polymer films and nanofibers are the same, their electrical, optical and mechanical properties have different charac- teristics due to effect of morphology, disorder and nano-scale confinement in those polymers [23, 24]. Various synthesizing methods [22] such as electrospinning [25], use of hard [26, 27] or soft templates [28], seeding polymerization [29] and interfacial polymerization [30] has been developed for preparing polymer nanofibers.
Studies on the transport properties of a single polymer nanofiber and nanofiber pellet have been reported [31, 32, 33, 34, 35, 36, 37, 38, 39]. However due to complex structure and morphology of polymer nanofibers, the electrical transport in these nanofibers has not been fully understood.
In order to understand the transport properties in polymer nanofibers better, we studied magnetoresistance (MR = [R(H)-R(0)]/R(0) where R(0) and R(H) are the resistances of the system within zero and non-zero magnetic fields) and dc charge transport behavior in polyaniline (PANI) nanofiber networks doped with camphor- sulfonic acid (CSA) which were synthesized via dilute chemical oxidative polymeriza- tion [4, 40]. The molecular structures of emeraldine base PANI and CSA are shown in Figure 1.1.
In this dissertation, dc electrical conductivity, magneto-transport properties and their dependencies on temperature, morphology, magnetic and electric field in PANI
4 Figure 1.1: Molecular structures of (top) emeraldine base PANI and (bottom) CSA.
nanofiber networks are discussed. In our studies with dense and dilute polyaniline nanofiber networks and nanofiber micro-clusters, we noted that charge transport is highly sensitive to the morphology of the nanofibers. As the number of interfiber contacts increases, the conductivity of the system decreases and the temperature de- pendency of the resistivity (ρ(300K)/ρ(25K); where ρ is the resistivity of the system) increases. This indicates that the system becomes more insulating and disordered with increasing interfiber crossings.
We also investigated large positive magnetoresistance (MR ∼ 55 % at H = 8 T and T = 2.5 K) at low temperatures, which decreases with increasing temperature.
Around 87.5 K a crossover from positive to negative MR was monitored and above this temperature a negative MR was observed up to 250 K. A similar temperature dependence was reported previously by Long et al. [37] on pellets of polyaniline and polypyrrole nanotubes, where nanotubes were pressed under high pressure and lost their original morphology. The effect of morphology on the magneto-transport of
5 polyaniline nanofiber networks is also investigated. MR decreases substantially with decreasing number of interfiber contacts, indicating that higher conductance and shorter hopping lengths decrease the effect of magnetic field. In our measurements we noted that magnitude of positive MR is affected by the applied electric field as well. MR increases with decreasing electric field until the linear regime is reached in the non-linear IV curves. The electric field dependency is attributed to reduction of the hopping potential barriers and hopping length by electric field that leads to decrease in the effect of magnetic field.
1.3 Outline
This dissertation is organized as follows. In chapter two, theoretical background on magnetism, molecule-based magnets and photoinduced magnetism are given. Mag- netism of individual moments, magnetic interactions between them and their coopera- tive responses to static and dynamic magnetic fields are reviewed. Moreover examples of molecular based magnets, their structures and parameters affecting their magnetic ordering are introduced. Photoinduced magnetism and previously studied systems are presented as well.
In the third chapter, π−electron systems and their structures are summarized.
The origin of conductivity in these systems, their electronic states, transport proper- ties and the effects of magnetic field are discussed in detail.
Chapter four covers the experimental techniques used in this dissertation. Prepa- ration of polyaniline nanofibers and V- Cr Prussian blue samples are explained. The
6 experimental tools which are employed for detailed magnetic studies (AC susceptome- ter, DC SQUID magnetometer), optical excitation (Ar-laser), absorption band mea- surements (UV-Vis spectrometer), investigation of chemical structure (X-ray photoe- mission spectroscopy), transport measurements (Quantum Design PPMS) and nano- imaging and lithography (scanning electron microscope and focused ion beam) are discussed.
Chapter five focuses on the magnetic properties and reversible photoinduced mag- netization in V-Cr Prussian Blue samples. Detailed experimental results and proposed mechanisms explaining the illumination effects are discussed.
Extensive experimental studies of charge transport in polyaniline nanofiber net- works are presented in chapter six. Effects of magnetic field, temperature, morphology and electric field on the electrical conductivity of nanofiber networks are reported.
Discussion and importance of our findings and possible future research are given in the final chapter.
7 CHAPTER 2
Background on Magnetism, Molecule-Based Magnets and Photoinduced Magnetism
In this section magnetic properties of isolated magnetic moments, their interac- tions with the moments of neighboring atoms and with their environment are dis- cussed. Moreover molecule based magnets, in particular Prussian blue analogs are introduced. Finally the photoinduced magnetism in various molecule-based magnets are presented.
2.1 Magnetism in Solids
2.1.1 Isolated Magnetic Moments
The magnetic moment of an isolated atom comes from the spin of the electrons and their orbital motion (angular momentum) around the nucleus. The contribution from nuclear magnetic moment can be discarded since it is 10−3 times smaller than the magnetic moment of the electron (massn masse). The quantum mechanical states of electrons is expressed by three quantum numbers n, l and m which are important for determining the magnetic moment of the atom. In addition to quantum numbers, the electron spin number (s) is also important in determining the total magnetic moment[41].
8 • The principal quantum number n (n = 1, 2,3... ) shows the spatial variation of
the wavefunction of each electronic shell.
• The orbital quantum number l (l = 0, 1 ... n-1) determines the value of the
orbital angular momentum and specifies the shape of an atomic orbital.
• The magnetic quantum number m (m = -l, -l+1 ... 0 ... l-1, l) is the projection
of the orbital angular momentum along a specified axis.
Then the total electronic magnetic moment due to electron spin and its orbital motion can be written as
µ = µl + µs = −µB(l + g0s) (2.1)
−5 where µB is the Bohr magneton (5.788310 ) which is the natural unit for describing
the atomic magnetic moments and g0 is the dimensionless g-factor that has been
experimentally determined to have the value of 2.0023 [42].
The Hamiltonian of an isolated atom is given by
Z X p2 H0 = ( i + V ) (2.2) 2m i i
which is the sum of the electron kinetic and potential energy over Z electrons in the
B×r atom. In the presence of applied magnetic field (B = O × A with A(r) = 2 ), the Hamiltonian is described by
X p2 e2 X H = Z( i + V ) + µ (L + g S) · B + (B × r )2 (2.3) 2m i B 0 8mc2 i i i
The second and third term in the Hamiltonian in addition to the original Hamiltonian
are the paramagnetic and diamagnetic terms respectively [43].
9 Diamagnetism
Diamagnetism is the tendency of inducing a magnetic moment that opposes the applied magnetic field. All materials show a diamagnetic response in magnetic filed since its due to all the electrons including the core ones in an atom. The diamagnetic
−5 −8 response is small (χdia < 10 −10 emu), negative and temperature-independent. If the material exhibits paramagnetism or has magnetic ordering (e.g. ferromagnetism), then the diamagnetic response can be neglected.
In an applied magnetic field in the z direction, the last term of Equation 2.3 can be written as a perturbation to the original Hamiltonian [44]. Then the first order correction to ground state energy is
Z e2B2 X ∆E = h0|(x2 + y2)|0i (2.4) 0 8mc2 i i i
2 2 2 If we assume a spherically symmetric atom h0|xi |0i = h0|yi |0i = 1/3h0|ri |0i. The magnetization and susceptibility defined as
1 ∂F M = − (2.5) V ∂H ∂M 1 ∂2F χ = = − (2.6) ∂H V ∂H2 thus diamagnetic susceptibility can be written as [42]
Z e2 N X χ = − h0| r2|0i. (2.7) 6mc2 V i i where N is the number of ions (each with Z electron) in a solid with volume V.
In molecules with delocalized π electrons (naphthalene and graphite), larger and anisotropic diamagnetic responses are observed. Since the electrons are mobile around the molecular ring that has larger diameter than the atomic diameter, higher currents are induced when the magnetic field is applied perpendicular to the plane of the ring.
10 Paramagnetism
When the atoms or molecules have unpaired electrons, their magnetic moments tend to align with the applied magnetic field. This induces a positive magnetic response. In the absence of magnetic field, the magnetic moments which are very weakly interacting, point at random directions in paramagnets and the system does not display magnetization [45, 46].
The total angular momentum J that is the sum of spin and orbital angular mo- mentum is written as gJ = L + g0S. And the energy of the ion in the magnetic field can be written as
E = −µ.B = jgµBB (2.8) where g is the Lande factor and given by
1hJ(J + 1) + S(S + 1) − L(L + 1)i g = 1 + . (2.9) 2 J(J + 1)
In order to calculate magnetic susceptibility, we can start from the partition function
Z. J X Z = exp(jgµBB/kBT ) (2.10) j=−J
Free energy F is −kBT lnZ and magnetization M = −N/V (∂F/∂B)T . Thus
N gµBJB M = gµBJBJ , (2.11) V kBT where BJ (x) is the Brillouin function and defined as
2J + 1 2J + 1 1 1 B (x) = coth x − coth x (2.12) J 2J 2J 2J 2J with x = gµB JB . In Figure 2.1 the magnetic moment curves for spin 3/2, 5/2 and kB T 7/2 with corresponding Brillouin functions are displayed [42]. For x << 1 Brillouin
11 function can be approximated by
J + 1 B (x) ≈ x, (2.13) J 3J
and magnetic susceptibility determined as
N (gµ )2 J(J + 1) C χ = B = (2.14) V 3 kBT T
The expression 2.14 is the Curie Law where C is known as Curie constant.
Figure 2.1: Magnetic moment versus H/T graph for spin values s = 3/2, 5/2 and 7/2 in which the data fits well to the brillouin function [47]
12 Van Vleck Paramagnetism
When the total angular momentum J is zero but spin and orbital momentum S and L are non-zero in the ground state, there is no paramagnetic contribution to
Hamiltonian in the first order since
gjµBh0|J|0i = 0 (2.15)
However the second order perturbation gives a non-zero contribution and the magnetic susceptibility is given by;
2 2 2Nµ X |h0|Lz + g0Sz|ni| χ = B (2.16) V E − E n n 0 This positive response is Van Vleck paramagnetism. Similar to diamagnetism it is small and temperature-independent.
Pauli Paramagnetism
In solids in which the conduction electron spin are responsible for the magnetic moment, the Curie paramagnetic susceptibility is not valid due to indistinguishability of the conduction electrons. However for solids in which the electrons are associated with definite positions in the crystal, the electrons can be considered as distinguishable particles.
Due to Pauli principle, the conduction electrons could not respond to an applied magnetic field since most of the orbitals at the Fermi level with parallel spin alignment are already occupied. Thus only the ones in the range of top kBT range of Fermi distribution can contribute. Since EF = kBTF then magnetic susceptibility can be written as N 3µ2 k T N 3µ2 χ = B . B = B (2.17) V kBT kBTF V kBTF 13 that is also temperature independent. In Figure 2.2 the magnetic susceptibility be- havior of diamagnetic and paramagnetic materials are shown.
Figure 2.2: Magnetic susceptibilities of diamagnetic and paramagnetic systems [43]
Hund’s Rules
In an atom it is possible to have more than one electrons. Hund’s rule are used to determine the quantum numbers that give the ground state of the multi-electron atoms [43].
14 1. The lowest energy atomic state is the one which maximizes the total value of
the S. According to Pauli Exclusion Principle two electrons of the same spin can not
be at the same place. Thus the electrons stay apart when they have parallel spins
and the Coulomb energy is minimized.
2. The maximum value of L (consistent with rule 1) gives the lowest energy state since the electrons orbiting in the same direction can avoid each other more effectively and reduce the Coulomb energy.
3. The value of the total angular momentum J is given by J = |L − S| when the shell is less than half full and by J = L + S when the shell is more than half full so that spin-orbit energy is minimized.
The third rule tries to minimize the spin-orbit interaction that is due to the weak coupling of spin and orbital angular momentums. Spin-orbit coupling is a relativistic effect and proportional to Z4 (Z is the atomic number of the atom). Hund’s third rule does not always apply especially when the spin-orbit energy is less significant than other energies such as crystal field. The Hamiltonian for spin-orbit can be written as;
Hso = λS.L (2.18)
When spin-orbit coupling is effective, L and S are not separately conversed but their total J is conserved and the states of L and S split into levels of different J values
(|L − S| < J < |L + S|).
2.1.2 Atoms in Solids
When magnetic ions are in a solid, their electronic, magnetic and structural prop- erties are significantly affected by their environment.
15 Crystal Field
Crystal field effect is the splitting of the degenerate d-orbitals that are displayed in Figure 2.3 due to electrostatic interactions between the electrons in the d-orbitals of magnetic ion and those in the ligands [48]. The d-electrons that are closer to the ligands as shown in Figure 2.4 will have a higher energy than those further due to
Coulomb repulsion. The energy splitting depends on the metal, its oxidation state and orientation with the ligands such as octahedral and tetrahedral(Figure 2.5) .
Figure 2.3: The angular distribution of d orbitals. The levels dz2 and dx2−y2 are grouped as eg levels. The remaining levels dxz, dxz and dyz are grouped as t2g levels [42, 46]
Crystal field is more effective in 3d transition metals than 4f rare-earth metals since 4f electrons lie deep inside beneath 5s and 5p and screened from the electro- static interactions. Thus crystal field (∼ 1eV ) is much larger than spin-orbit energy
16 (∼ 50meV ) in transition metals and Hund’s third rule does not apply. This high crystal field diminishes the contribution of orbital momentum to magnetic moment.
The time average of all the components of orbital angular momentum become zero and the angular momentum of non-degenerate state is quenched [49]. On the other hand, rare-earth 4f ions have smaller crystal field energy (∼ 0.01eV ) and spin orbit coupling (0.1 eV) becomes the dominant interaction and Hund’s third rule apply. De- pending on the relative direction of the spin and magnetic moments, the g-value can be larger or smaller than the spin alone contribution (g ∼ 2) due to orbital momentum contribution [42, 50].
Figure 2.4: The overlap of different d orbitals with the ligands. dxy orbital has lower energy compare to dx2−y2 due to smaller overlap and electrostatic interaction [43]
When a transition ion has more than one electron in the 3d levels (e.g in octahedral crystal field environment), first three electrons will fill the t2g levels that are the lowest energy ones. However the forth electron can fill either and doubly occupies t2g level or single occupies eg level. The competition between the Coulomb repulsion (U) due to
17 Figure 2.5: Splitting of the d orbitals in octahedral (left) and tetrahedral (right) crystal fields
having two electrons in one orbital and the crystal field splitting (∆) due to putting the electron to a higher energy orbital, determine the filling of the orbitals. In the weak crystal field case (∆ < U), as the electrons are added to the system after t2g levels are single occupied, the eg levels are filled. This will lead to high-spin state as shown in Figure 2.6. On the other hand in the strong crystal field case (∆ < U) the electrons continue to fill the single occupied t2g levels leading to a low-spin state.
When crystal field and Coulomb interaction have similar energy (|U − ∆| ∼ kBT ), it is possible to a have a crossover between low-spin and high-spin states which leads to a change in magnetic susceptibility since the number of unpaired spins alters [51].
The spin crossover can be observed upon temperature change or optical excitation
(light-induced excited spin state trapping). Figure 2.6 shows the energy of low and high spin states that are separated by an energy barrier which causes slow relaxation from the excited high-spin state to low-spin state.
18 Figure 2.6: Electronic configuration for high-spin (HS) and low-spin (LS) states under octahedral crystal field (left). Energy curves for LS and HS states with respect to metal-ligand coordinate (right) [46].
Jahn-Teller Effect
The local environment of a magnetic ion in non-linear molecules can be distorted by its magnetic properties. It is mostly encountered in octahedral complexes of the transition metals such as MnIII ions in 3d4 configuration. The electrostatic repulsion between the electron-pair on the ligands is lowered by the Jahn-Teller distortion. In
Figure 2.7 the octahedral structure and the distorted one with their energy levels are shown. The system lowers the total energy by distortion since the single occupied eg level lowers the energy and t2g levels compensate each other by both lowering and raising the energy.
19 Figure 2.7: Jahn-Teller lattice distortion that leads to splitting of eg and t2g levels in MnIII (3d4) in order to reduce energy of the system [42]
2.1.3 Magnetic Interactions
The magnetic moments not only interact with their environment but also interact with each other. The interactions which are discussed here, can lead to magnetic ordering such as ferromagnetism and antiferromagnetism in the absence of magnetic
field [45, 52].
According to Heisenberg model, two spins can interact with each other due to overlap of electron wavefunctions or by other means and its Hamiltonian is given by
X H = − JijSi.Sj (2.19) ij
20 where J is the exchange constant that gives the energy difference between singlet and
triples states and defined as J = (Es − Et)/2. Thus if J > 0, Es > Et, triplet state is
favored [53]. In exchange interactions the effective length is less than 1nm and defined
p 2 as lex ≈ A/Ms , where A is related to exchange coupling and Ms is the saturation magnetism. Exchange interactions are isotropic since the coupling only depends on the relative orientation of the spins but not on their overall direction.
Direct Exchange
When two or more atoms come closer there is a direct exchange between those due to overlap of their wavefunctions. This exchange is the most dominant form of inter- action and includes the Coulomb interactions and the isolated atom kinetic energy.
The system can lower the total energy by having antisymmetric spin wavefunctions so that electrons can wander around all the atoms and reduce their kinetic energy.
On the other hand when electrons belong to one atom, they segregate to minimize
Coulomb repulsion between them by preferring spin symmetric state (Hund’s fist rule) [54].
The exchange constant J in Heisenberg Hamiltonian (for not very large overlaps) can be written as;
2 Jab ∼ Kab − CabSab (2.20)
where Sab is the overlap integral, Cab is the Coulomb and Kab is the exchange in-
tegral. Kab exchange integral is positive and known as the potential exchange. It
favors parallel alignment of spins and leads to ferromagnetic ordering. On the other
2 hand −CabSab is usually negative and known as the kinetic exchange which favors an- tiparallel alignment of spins and antiferromagentic order. Depending on the relative
21 magnitude of these competing direct exchange terms, the resulting alignment of spins can be parallel or antiparallel.
Superexchange: Indirect exchange in ionic solids
There can also be magnetic interactions known as superexchange interactions between non-neighboring magnetic ions through a nonmagnetic ion which is located in the middle. The superexchange interaction is stronger and more long-ranged than the exponentially decayed direct exchange. In superexchange coupling delocalizing of the electrons through magnetic and non-magnetic ions lowers the kinetic energy. The exchange constant in exchange Hamiltonian is given by
−t2 J ∼ (2.21) ab U
Where t is the hopping integral in tight binding approach that is proportional to the energy conduction band and U is the Coulomb energy. In tight binding model, electrons are not treated as free particles but strongly correlated ones since Coulomb energy is comparable to the kinetic energy. As shown in Figure 2.8, delocalizing
(hopping) is only possible when the spins of the magnetic ions electrons are antipar- allel, thus Pauli exclusion principle is not broken. In other words antiferromagnetic ordering is preferred for overlapping orbitals in this interaction. However in some cases, based on the orbital symmetry, the geometry of the system superexchange can favor ferromagnetic interaction. The character of superexchange interaction can be determined by Goodenough and Kanamori rules [55, 56]. If the electron hopping does not occur due to non-overlapping orbitals of different magnetic ions then the ferromagnetic order reduce the energy by having aligned with the t2g levels (Hund’s
first rule which maximizes the S) [57].
22 Figure 2.8: Superexchange mechanism in a magnetic oxide. The magnetic electrons can be delocalized over M-O-M unit and the energy of the system is lowered [58].
RKKY: Indirect exchange in metals
In rare earth metals (partially filled 4f shells) or in dilute solid solutions of mag- netic ions in nonmagnetic metal crystal, there is an exchange coupling between the localized magnetic ions and the conduction electrons. As a result of this RKKY (Ru- derman, Kittel, Kasuya, Yosida) coupling, an interaction exists between magnetic ions which provides ferromagnetic or antiferromagnetic exchange depending on the distance between them [59, 60, 61]. As given in Equation 2, the sign of the exchange constant is oscillatory and falls off through space with 1/r3.
3 JRKKY = cos(2kF r)/r (2.22)
Due to the oscillatory nature of RKKY interaction, in solids the parallel and an- tiparallel interactions lead to competitive couplings and magnetic frustration in some sites.
23 Double Exchange
It is possible to have mixed valency of an element in some magnetic oxides such as
III IV having Mn and Mn in La1−xSrxMnO3. In transition metals five fold degeneracy
break into triply degenerate t2g and doubly degenerate eg states due to large crystal
III IV field effect. Mn has 4 electrons, 3 in the t2g and 1 in eg levels and Mn has 3 electrons in the t2g level. The electron in the eg level can lower its energy if it can hop to neighboring ion. Hopping is possible if t2g levels are parallel as stated in Hund’s
first rule (reducing Coulomb repulsion). Thus ferromagnetic alignment is preferred in double exchange interactions [43]. Moreover double exchange allows the eg electrons to hop through the solid and leads to electrical conduction.
Anisotropic Exchange (Magnetocrystalline) Interactions
In addition to the interactions discussed above which are isotropic, there are anisotropic exchange interactions. The alignment of spins not only depends on their orientation and but also depends on the direction that they are connected. Spin mag- netic moment interacts with the atomic structure of a magnetic material via spin orbit coupling and this coupling leads energy differences in magnetization along different crystal axes. The difference, anisotropy energy, is larger in low symmetry magnetic ion lattices than in high symmetry ones and it is an intrinsic property.
In the presence of spin-orbit interaction, there can be an anisotropic exchange interaction between two spins. The Hamiltonian of this anisotropic interaction which is also known as Dzyaloshinsky-Moriya interaction is given by
HDM = Dij.Si × Sj (2.23)
24 Figure 2.9: Double exchange between Mn3+ (left; 3d4) and Mn4+ (right; 3d3). When electron hopping is possible (a) and forbidden (b) due to Hunds rule in order to lower the energy of the system [43].
where Dij pseudovector related to the orbital angular momentum and vanishes in crystal field with inversion symmetry. The interaction tries to align Si andSj to be at right angles in a plane perpendicular to the D vector. However DM interaction is about an order of magnitude smaller than the isotropic exchanges, thus leads to canting of the spins in their parallel and antiparallel alignments[62, 63]. In rare- earth 4f ions have smaller crystal field energy (≈ 0.01eV ) than transition metals and spin orbit coupling (0.1 eV) becomes effective and leads to higher anisotropy than transition metals.
25 When crystal field presents in the solid, the spins prefer to lie along particular
crystalline directions. This energetic difference of spins along different axes is knows
as single ion anisotropy. The Heisenberg Hamiltonian becomes;
X X 2 H = −J Si · Sj + DSi,z. (2.24) i X H = −J Si,zSj,z. (2.25) i (XY model).The Hamiltonian is reduced to X H = −J (Si,xSj,x + Si,ySj,y). (2.26) i 2.1.4 Magnetostatic (dipole-dipole) interactions The magnetostatic interactions which have classical origin and its Hamiltonian is given by dip µi · µj − 3(µi · ˆrij)(µj · ˆrij) Hij = 3 , (2.27) rij 26 where µ is the dipole moment and ˆrij is the unit vector between them. The mag- nitude of the dipole-dipole coupling can be approximated by ∼ m2/r3 where m is the magnetic moment (≈ 106 bohr magneton in a nanomagnet) and r is the distance from the center. Dipole-dipole interactions are anisotropic and can favor parallel and antiparallel alignment of moments depending on the magnetic moment, separation arrangement [64]. 2.1.5 Anisotropy Most magnetic materials favor magnetization in a certain direction than in another direction due to an energy difference. The direction in which magnetizing requires less energy is called easy axis and the one in which magnetizing require higher energy is called hard axis. The energy difference between magnetizing along easy and hard axes is called anisotropy energy. Shape Anisotropy If magnetization suddenly stops at the boundaries instead of being parallel to the surfaces in a magnet, it diverges. This leads to poles at the surface which act like magnetic monopoles (Gauss’law for magnetism with the assumption of magnetic monopoles: ∆.H = −∆.M = 4πρm) and create a magnetic field inside the magnet op- posing the magnetization that induces it. This opposing field is called demagnetizing field and given as Hdemag = −NM where N is the shape dependent demagnetization factor. Thus Hinternal = Hexternal − Hdemag [65]. A spherical magnet has no shape anisotropy (Nx = Ny = Nz = 1/3) but a long cylindrical magnet along z, has uniaxial shape anisotropy in that direction since the poles created at the ends can be ignored (Nx = Ny = 1/2,Nz = 0). As in the case 27 of long cylinder, reducing the width of a magnet leads to stronger shape anisotropy and increase the coercive field along the long axis. Shape anisotropy is effective for magnets smaller than 20um and as magnet’s size gets larger, its importance is reduced [66]. Configuration anisotropy is to related shape anisotropy and is a result of nonuni- form demagnetization field due to sharp edges in the nanomagnet [67]. Stress Anisotropy When an external magnetic field is applied, magnet experiences a strain which changes its crystal structure. Therefore distances and interactions between magnetic ions are altered and an anisotropy in the magnetization is created. Exchange Anisotropy Due to shape or magnetocrystalline anisotropy, ferromagnets can have favorite collinear directions (easy axis). In general, the energy (magnetic field) required for magnetization reversal along the easy axis from one direction to another is the same. When the ferromagnet (FM) grown on top an antiferromagnet (AFM) and an external field is applied to bilayer structure above AFM ordering temperature (TNeel) but below FM ordering temperature (TC ), the exchange coupling existing at the interface aligns the interface spins of AFM with FM. When the temperature is reduced below TNeel, the interface spins keep their alignment and the bulk of AFM is oriented with respect to that. Therefore the reversal of ferromagnet’s magnetization requires more energy in one direction due to this coupling with AFM at the interface. This additional energy is called ”exchange bias” and shows itself as a shift in the hysteresis loop. 28 At the FM-AFM interface, only a small fraction of the uncompensated spins are pinned and lead to exchange bias. Therefore exchange bias is proportional to the number of pinned spins. AFM domain wall energy (EDW ) is also important since when it is larger (rigid AFM) than exchange energy (EEx), the maximum bias is determined by EEx and when it is smaller, the bias is determined by EDW . Exchange coupling as also affected from interfacial contamination and roughness. (a) (b) Figure 2.10: (a) Hysteresis loop for a FM-AFM bilayer with a diagram showing magnetization at different stages (b) AFM-FM structure where only a small number of spins are pinned (red arrows) at the interface compared to unpinned ones (white arrows) [68, 69]. 29 Anisotropy helps magnetic ordering where exchange interaction is not sufficient. Therefore, it affects the coercivity, remanence and hysteresis loop of a magnet. Fur- thermore, anisotropy limits the domain wall size. Magnetocrystalline and magne- tostriction constants decrease as temperature increases due to thermal fluctuations. 2.1.6 Domain Walls Both magnetic anisotropy and exchange interactions contribute to ordering in magnetic materials. Below ordering temperature, all spins are parallel in a ferromag- net on a microscopic scale. However on a larger scale all these interactions compete and results in small regions called domains that have different magnetization direc- tions. Domains are separated by a boundary called a domain wall. If the magnetiza- tion rotates parallel to the plane of the wall, it is called Bloch wall and if magnetization rotates perpendicularly, it is called Neel wall [43]. Exchange interactions favor larger domain walls, therefore neighboring spins are almost collinear and ferromagnetically coupled. However, anisotropy favors smaller domain walls so that only a few spins are not along the easy axis. Eexchange = −2JS1.S2 = −2JS1S2 cos θ (2.28) 2 2 for θ << 1 Eexchange = JS θ (2.29) If an angle of π change occurs over N atoms, then θ = Π/N and the total exchange energy per unit area (a2 where a is the lattice constant) is 2 2 2 uexchange = JS π /Na . (2.30) Similarly anisotropy energy per unit area is the anisotropy constant times the wall thickness Na uanisotropy = KNa. (2.31) 30 The equilibrium N can be found from solving δEtotal/δN = 0. As given in Equa- tions 2.34, larger exchange interactions makes the wall thicker and larger anisotropy makes it narrower. N = ΠSp2J/Ka3 (2.32) w = Na = ΠSp2J/Ka = πpA/K (2.33) √ 2 uBW = π AK where A ≈ JS (2.34) The domain walls are formed to decrease the demagnetizing field and magneto- static energy. As mentioned above, magnetic field diverges at the boundaries of a sample and creates demagnetizing fields. Since Hd = −NdM where Nd is the demag- netization constant and M is the magnetization, magnetostatic energy can be written as Z µ0 Ed = − M.Hddτ (2.35) 2 V µ E = 0 N M 2V (2.36) d 2 d Thus magnetostatic energy can be zero when the net magnetization vanishes due to closure domain structure. It has been shown that single domain magnetization can exist up to a certain √ AK radius (RSD ≈ 2 ) and RSD can be obtained from comparable values of domain Ms wall creation energy and gain in magnetostatic energy [70]. In spherical magnets it can exceed 1 micron. Domain wall width varies from 1nm for hard magnets to 100nm for soft ones and nanomagnets less than this size are single domain. It is important to note that all spins in a single domain magnet are not uniform and can have different magnetic configurations such as vortex and leaf state. However within a length of lex where exchange interactions dominate, the magnetization is uniform [71]. 31 Figure 2.11: Magnetic domain structures of a rectangular ferromagnet with different magnetostatic energies. The least magnetostatic energy is in the right configura- tion [43]. 2.1.7 Magnetic Ordering The magnetic interactions that have been discussed in the previous section can lead to magnetic ordering and cooperative behavior in solids even in the absence of magnetic field. The transition from disordered state to ordered state occurs at crit- ical temperature (Tc) and displays second-order phase transition properties. In these section various magnetic ordering states including ferromagnets, antiferromagnets, superparamagnets and spin-glasses as well as their magnetic response to temperature change and magnetic field over time are discussed. In Figure 2.12 possible spin con- figurations of various types of magnetic ordering are displayed at two different time. Ferromagnetism Ferromagnetism is a spontaneous magnetism state in which all the spins are aligned along a single unique direction below the critical temperature that is known as Curie temperature (TC ). The order parameter (the quantity which has non-zero 32 Figure 2.12: Illustration of spin configuration of various magnetic orders at two dif- ferent instants: t0 and t1 [72]. mean below Tc and zero mean above Tc in second-order phase transitions ) in ferro- magnetism is the magnetization. The spontaneous magnetization is given by N 1 X M = hµ i, (2.37) V i i where h i stands for the statistical mechanics average. In order to understand the ferromagnetism theoretically mean field theory (MFT) has been employed [45, 52]. In this approximation an effective magnetic field is defined on a given spin due to the magnetic interactions with its neighboring spins. 33 The Heisenberg Hamiltonian in the presence of applied magnetic field is given by X X Hi = −( JijSi.Sj + gµB Si.B) (2.38) i 1 X B = J S . (2.39) eff gµ ij j B i X Hi = gµB Si.(B + Beff ) (2.40) i The effective field can be expressed by Beff = λM where λ is a parameter related to the magnitude of the exchange interaction V J0 X λ = ,J = J . (2.41) N g2µ2 0 j B j and M is the magnetization given by N hS i M = i (2.42) V gµB where hSii is the mean value of neighboring spin. The magnetization can be determined by solving M = BJ (y) (2.43) Ms g µ J(B + λM) y = j B (2.44) kBT where BJ (y) is the Brillouin function, by graphical methods [42]. Figure 2.13 displays the zero and non-zero applied magnetic field graphical solutions to mean field theory. In zero applied field, for T > TC there is no spontaneous magnetization for non-zero field case it is possible to have magnetization above TC . The magnetic susceptibility 34 (a) (b) Figure 2.13: The graphical solutions to Equation 2.44 at zero (left) and non-zero (right) applied magnetic field [42]. for zero magnetic field case is given by N (gµ )2 S(S + 1) χ = B . (2.45) V 3kB T − Tc Antiferromagnetism In antiferromagnetism , below the critical temperature (known as Neel tempera- ture, TN ), the spins of two neighboring sites become antiparallel. Systems showing ferromagnetism usually considered as two interpenetrating sublattices. The order parameter is the staggered magnetization given by N 1 X M = hµ ieiQ·ri (2.46) Q V i i where the wavevector Q specifies the spatial periodicity of the antiferromagnetic state. The magnetic susceptibility in antiferromagnets is determined to be proportional to 1/(T + TN ). Curie Weiss Law states that 1 χ ∼ (2.47) T − Θ 35 Figure 2.14: Temperature dependence of inverse magnetic susceptibility for antifer- romagnetic, paramagnetic and ferromagnetic systems [73]. Figure 2.14 shows the temperature dependence of the susceptibility by using Curie Weiss Law for paramagnets (Θ = 0), ferromagnets (Θ > 0) and antiferromagnets (Θ < 0). Superparamagnetism Temperature is another important factor in ordered magnetic materials. As the temperature increases, the thermal energy (kBT ) overcomes the ordering interactions such as exchange and anisotropy energy and eventually the transition to disordered state occurs. In a bulk magnet this is a transition into paramagnetic state. In nanomagnets, as the size of the magnet decreases, the ordering energy (anisotropy energy) which depends on the size of the material becomes comparable to the thermal 36 energy. Therefore random spin flipping occurs in time and loss of magnetic order- ing is observed. The unordered state in small size particles, in which inter-particle magnetic interactions are neglected, is called superparamagnetism. In other words, there is a limit (superparamagnetic limit ≈ 10nm) for the minimum size to be a sta- ble magnet which is determined by anisotropy and thermal energies [42, 74]. The temperature which thermal fluctuations overweighs the anisotropy effect is called the blocking temperature (TB). It can be determined from the peak in the zero field cooled (ZFC) magnetization-temperature curve and strongly frequency dependent magnetic susceptibility. The total anisotropy energy can be approximated as Ea = KV where K is the total anisotropy constant and V is the volume. At finite temperature there is a probability for thermal fluctuations to change the direction of the moment and the relaxation time (τ) for the moment is given by Ea −9 τ = τ0 exp( ) where τ0 ≈ 10 s[42] (2.48) KBT Spin-glasses Spin glass is magnetic system with mixed interactions that lead to cooperative freezing of spins at a well-defined freezing temperature (Tf ) [76, 77]. Below Tf metastable, highly irreversible state without usual long-range magnetic ordering is observed. The most important two factors necessary for spin glasses are randomness and frus- tration. In spin glasses there should be randomness in either the position of the spins (site randomness) or the sign of magnetic interactions with their nearest-neighbors (bond randomness) [78]. The second prerequisite for spin glasses, frustration can be 37 Figure 2.15: Thermal energy is comparable to anisotropy energy. Thus the small size magnet flips its magnetization randomly [75]. caused by lattice topology (e.g. triangular lattice with antiferromagnetic nearest- neighbor interactions) and mixed interactions (random ferromagnetic, antiferromag- netic coupling or competing nearest-neighbor, next-nearest-neighbor interactions). Figure 2.16 shows two frustrated systems due to randomly distributed antiferro- and ferromagnetic interactions and triangular lattice geometry in a two-dimensional sys- tem with antiferromagnetic exchange. Frustrated systems display multi-degenerate, frozen ground state since no configuration of spins can satisfy all bonds and minimize the energy. The archetypal systems of metallic spin glasses due to site randomness are CuMn, AuFe, YDy, YEr magnetic alloys (known as canonical spin glasses) in which d or f magnetic ions are randomly distributed through the crystal lattice. Due to long-range oscillatory nature of RKKY exchange interactions (Equation 2.22) between magnetic 38 Figure 2.16: Magnetic frustration due to (a) random exchange interactions and (b) lattice geometry[50]. ions, both ferro- or antiferromagnetic interactions are present and for certain magnetic ion concentrations spin glass behavior is exhibited. In spin glasses there is no long- range ferromagnetism (ΣiSi = 0) or antiferromag- 1 netism ( N ΣihSiitexp(ik.Ri) = 0 as N → ∞) but hSiit 6= 0 where hit represents the time average over a long period. Transition into the spin glass state is accepted as a phase transition. Although it is an unconventional transition, it is characterized by an order parameter and critical behavior of the spin glass correlation length ξSG at the spin glass transition temperature ( Tg: Tg = Tf (f → 0)). The most commonly used order parameter was introduced in Edwards and Anderson model [79] and defined as qEA = lim lim [hSi(0) · Si(t)i]av, (2.49) t→∞ N→∞ where h i is the statistical mechanics average and [ ]av is the average over the distri- butions of random interactions in the system over long reference times. The order 39 parameter can be understood as the time correlation function, given by 2 CSG(Ri − Rj) = [hSiSji ]av, (2.50) averaged over all possible realizations of disorder in the system thus there is a non- vanishing probability that spins have the same configuration. The correlation function decays exponentially with distance as CSG(Ri − Rj) ∝ exp(−|Ri − Rj|/ξSG), (2.51) where ξSG is the spin glass correlation length. Sherrington and Kirkpatrick introduce a mean field approximation of spin glasses describing the slow dynamics of the mag- netization in spin glasses [80, 81]. Later on De Almeida and Thouless showed that in the presence of magnetic field (H), the peak temperature of ZFC magnetization linearly related to H2/3 [82]. Spin glasses can be identified experimentally by following properties due to their extremely long (macroscopic) relaxation times and free energy with many local energy minima as seen in Figure 2.17 which is supported by the study of Parisi [83]. • The magnetic susceptibility χ shows a peak at the freezing temperature (Tf ) which depends on the time scale of the experiment. In ac susceptibility, the position of the peak shifts to higher temperatures with increased frequency f of the applied ac magnetic field. • The field-cooled magnetization (Mfc) which is measured after cooling down to T < Tf in finite applied dc magnetic field and zero-field-cooled magnetization ( Mzfc) that is measured after cooling in zero applied magnetic field, and sub- sequently applying a nonzero magnetic field, displays strong irreversibility and 40 Figure 2.17: Free energy diagram of a spin glass system as it cools down above the spin-glass transition temperature [84]. history-dependence. Upon zero-field-cooling, the system finds itself in one of the local free energy minimum (Figure 2.17) and explores only a small part of the phase space due to very large energy barriers before the field was applied. On the other hand when the system field-cooled, it can explore much larger part of the phase space and find a configuration close to the equilibrium one since the energy barriers are still not too high at T ∼ Tg. • The Mfc(T ) and Mzfc(T ) curves meet at the bifurcation temperature (TB) which is strongly magnetic field dependent and for lower fields TB gets close to Tf observed in the ac susceptibility measurements. 41 • Upon field-cooling below Tf and subsequently reducing applied field to zero, spin glasses exhibit remanent magnetization, similar to ferromagnets with a slower decay time. • Below Tf spin glasses exhibit magnetic hysteresis that depends on the magnetic history and field sweeping rates. • Neutron diffraction pattern shows no magnetic Bragg peaks at any wavenumber and any temperature, indicating that no long-range spatial magnetic order is present. • The magnetic contribution to the specific heat shows a broad maximum above Tf . The transition to spin glass behavior does not have to be from paramagnetic state. In some cases, systems with long-range magnetic (ferro-, antiferro- or ferrimagnetic) order enter the spin glass state (reentrance). In Figure 2.18 a schematic phase diagram of a system (similar to alloys of transition metals and rare earths) is displayed where the horizontal and vertical axes correspond to the concentration x of the magnetic ions in the alloy and temperature respectively. Thus for certain x values, upon cooling alloys can undergo a transition from ferromagnetic to spin glass state. A number of systems exhibit magnetic properties that suggest existence of both short-range magnetic (ferro-, antiferro- or ferrimagnetic) order and spin glass-like behavior. However the colinear order is observed in small clusters (much smaller than the domain size) and limited to spins in those. Cluster glass systems (mictomagnets) are found among alloys of transition and rare-earth metals with high concentration of magnetic ions [85, 86] and molecule-based magnets [87, 88]. 42 Figure 2.18: Schematic magnetic phase diagram of a dilute alloy EuxSr1−xS (MxA1−xB where M is magnetic, A and B are non-magnetic ions). Transition from both paramag- netic state (PM) and ferromagnetic state (FM) to spin glass (SG) state is possible [76]. 2.2 Molecule-based Magnets The use and control of magnetism have always been important for its technological applications such as communication and information storage devices. Commonly used magnets are composed of transition and rare earth metal atoms and their ions. The magnetism in these metals is due to unpaired spins in the d and f orbitals. In order to fabricate these magnets high energy-intensive metallurgical methods are used. In the last few decades, a new class of magnets, molecule-based magnets that are easily processable and magnetic on a macroscopic scale, have been developed and attracted significant attention [89, 90]. In addition to their easy and cheap low temperature syntheses methods, molecule based magnets exhibit novel and controllable properties that are not observed in conventional ones. 43 By simply using chemical syntheses methods, it is possible to design a molecule- based magnet with desirable magnetic (hard or soft magnet, ordering temperature, spin values), electrical (conductor or insulator), optical (transparency) properties and dimensionalities [91, 92]. Molecule-based magnets can be bio-compatible and show interesting magnetic behavior such as spin glass , magnetic chirality and low dimensionality as well. Moreover in a variety of molecule-based magnets, magnetic properties can be controlled by external stimuli such as light [8] and pressure [7] due to magnetic bistability resulting from inherent structural disorder. In this section, two commonly studied family of molecule-based magnets; Prussian Blue analogs and M[TCNE] (M = V, Mn), their magnetic properties as well as the photoinduced magnetism phenomena are discussed. 2.2.1 Prussian Blue Analogs Prussian Blue analogs have the MxAy[B(CN)]z.nH2O formula where M is alkali metal and A and B are transition metal ions. In Prussian blue analogs the transition metals are connected by cyanide ligands (C-N) that are small and dissymmetric and create stable molecular precursors with strong metal-carbon bonds [93, 94, 95, 96]. These precursors can be used in Lewis acid-base (Figure 2.19) in order to get the ordered bimetallic systems. Depending on the relative phase of the p and d orbitals as seen Figure 2.19, bonding and antibonding levels are formed. The Na-Cl like fcc structure of Prussian blue analogs usually lead to octahedral crystal field that splits the d levels into low energy t2g levels and higher energy eg levels. Therefore electrons of transition metals occupy the t2g orbitals having π symmetry and eg levels having σ symmetry. 44 Figure 2.19: Schematic image of structural (a) and orbital (b) interactions in Lewis acid-base with hexacyanometallate and paramagnetic cations [97]. In Prussian blue analogs the main exchange interactions is the superexchange in- teraction which depends on the symmetry of the metal and ligand orbitals (Goodenough- Kanamori model). In superexchange, kinetic and potential exchange terms are im- portant in order to understand magnetic ordering. The former term is mediated by a direct pathway of overlapping orbitals and favors antiparallel spin alignment due to Pauli’s principle. The latter is between two orthogonal orbitals and favors to parallel spin alignment to reduce the Coulomb interactions (Hund’s first rule). When all the unpaired spins are in the same symmetry orbitals through which there is a direct over- lap (between t2g orbitals or eg orbitals), antiferromagnetic interactions are present. On the other hand, when unpaired spins are in the orthogonal orbitals (between t2g and eg orbitals) ferromagnetic interactions are present [98, 99, 100]. Therefore magnetic interaction between the neighboring sites can be ferromagnetic or antiferromagnetic depending on the overlap of the orbitals. According to Kahn and Briat model, the exchange constant J between site A and B in Hamiltonian 45 H = −JSASB can be expressed by J = 2k + 4βS (2.52) where k is the exchange integral (positive), β is the resonance integral (negative) and S is the overlap integral (positive). While the positive term gives ferromagnetic contribution (favoring parallel spin configuration), the negative term gives antiferro- magnetic contribution (favoring antiparallel configuration). According to Neel’s study in 1948, the ordering temperature of ferrimagnets is proportional to Tc ∼ z|J| (2.53) where z is the number of magnetic neighbors and |J| is the difference between ferro- magnetic and antiferromagnetic exchange interactions (J = |JAF −JFM |). Figure 2.20 show the number of ferromagnetic and antiferromagnetic exchange pathways between III the Cr and the divalent transition metal ions. Each unpaired spin in the t2g orbitals of the ions contribute to antiferromagnetic exchange (AF) whereas the one in the eg level contributes to ferromagnetic exchange (F) due to orbital symmetry. Figure 2.21 displays both the exchange pathways and ordering temperatures of II III III II II bimetallic systems of M3 Cr2 with Cr -CN-M unit in which M is the divalent ion of the first row transition metals. The highest ordering temperature is observed II III in V3 Cr2 since there are many exchange pathways (9 AFM) which are only an- tiferromagnetic [93, 3, 101, 97, 102, 103]. Since the magnetic properties (ordering temperature from 2 K to 350 K) can be controlled by simply changing the transition metal ions, Prussian blue analogs have a peculiar position among the molecule-based 46 Figure 2.20: The number and type of possible exchange interactions between CrIII and divalent transition metal ions [93]. 47 magnets. Prussian blue analogs are available not only in the powder form but also as a film [9] and nanoparticles embedded in polymers [11, 104, 105]. II III Figure 2.21: The ordering temperature of M3 Cr2 system where M is a first row transition metal [97]. 2.3 Photoinduced Magnetism One of the significant properties of molecule-based magnets is the ability to control their magnetic properties by external stimuli such as light due to inherent structural disorder. In molecule-based systems, there can be a transition from low-spin state to high- spin state by temperature, pressure and photo-illumination when the crystal field 48 splitting ∆ is comparable to Coulomb repulsion U (|∆ − U| ∼ KBT ). The transi- tion occurs due to large entropy gain from low-spin to high-spin states. Both higher degeneracy of high-spin state (∆S = Nkln(ΩHS/ΩLS)) and its greater vibronic en- tropy (longer metal-ligand bonds) increase the entropy of the system. The photoin- duced low-spin to high-spin transition has been known since 1984 in paramagnetic II spin crossover systems such as Fe complexes ([Fe(ptz)6](BF4)2) and termed as light- induced excited state spin state trapping (LIESST). The effect of light illumination on magnetism coexisting with magnetic ordering was first reported in Co-Fe Prussian blue by Sato and Hashimoto et al. in 1996 [8]. Since then there has been an increasing interest in optical control of magnetic prop- erties due to possible applications such as memory devices [106, 107, 108]. However a practical device has been realized yet since a system with both long range magnetic ordering and sustained reversible illumination effects at high temperatures is required. In order to overcome these challenges and fully understand the photoinduced mag- netism mechanisms, as well as to find better chemical structures, the sought for novel light-tunable magnets continues. Our research brought the discovery of a system (V-Cr Prussian blue) that shows reversible photoinduced magnetic effects with a magnetic order well above room temperature. In the next section two different class of systems, Co-Fe Prussian blue analog and organic magnets M[TCNE] (M = V, Mn), that exhibit photoinduced magnetic effects are reviewed. 49 2.3.1 Co-Fe Prussian Blue Prussian blue analogs have face-centered cubic lattice in which two transition metals ions are interconnected via C-N bridges (cyanometalate-based systems). In most of the Prussian blue analogs structural disorder exists due to vacant metal-CN groups [93]. Figure 2.22 shows the schematic structure of Co-Fe Prussian blue with the general formula of AxCoy[Fe(CN)6].nH2O. The alkali metal (A) cations such as K+, Rb+ are interstitial in the lattice and the water molecules substitute the missing C-N groups at the missing Fe(CN)6 sites. Figure 2.22: The crystal structure of Co-Fe Prussian Blue Analog [109, 110] The stoichiometry and oxidation states of the metal ions strongly depends on the experimental condition and synthesis. These variety in structure and electronic states 50 in Co-Fe Prussian blue analogs lead to different magnetic properties (diamagnetic, paramagnetic or ordered below T ∼ 25 K). In Figure 2.23 the spin distribution of ground and photo-excited states for Co-Fe Prussian blue is displayed. Initially all the II 6 0 III 6 0 spins in both Fe (t2geg, ls) and Co (t2geg, ls) are paired and give diamagnetic re- III 5 0 II 5 2 sponse. However in the excited state Fe (t2geg, ls) and Co (t2geg, hs) have unpaired spins and give magnetic response. The interaction between the unpaired spins of the III II t2g orbital of Fe and in the eg orbital of Co is ferromagnetic (potential superex- change) due to the orthogonality of the orbitals. On the other hand the interactions III II between spins of the t2g orbital of Fe and in the t2g orbital of Co is antiferromag- netic (kinetic superexchange) due to the direct overlap of the orbitals. In the excited state of Co-Fe Prussian blue, the interactions is expected to be antiferromagnetic due to dominant kinetic superexchange part [8, 5]. Upon illumination of Co-Fe Prussian blue in the spectral region of 500-750 nm, re- versible change in magnetization and magnetic properties is observed [8, 5, 111]. The ordering temperature, magnetization, remanence and the coercivity increases with red light excitation. Figure 2.24 displays the reversible optical switching of magnetization with red and blue light excitation. Intensive theoretical and experimental research on the photoinduced magnetism in Co-Fe Prussian blue reveals that the phenomena is due to light-induced electron transfer from Fe to Co. The charge transfer is then followed by a spin flip via spin-orbit coupling. During photoinduced transition the Co-N bond length changes as well and leads to a metastable state that is separated from the ground state by an energy bar- rier. Figure 2.25 shows the proposed energy diagram of photoinduced excitation and relaxation between states a and b that are separated by an energy barrier due to 51 Figure 2.23: Scheme of charge transfer between Fe and Co upon illumination. Due to spin-orbit coupling, a transition into high-spin state occurs in a fraction of Co sites [50] change in bond size. Therefore photoexcited magnetization is preserved for a long time (t > 106s) at low temperatures in Co-Fe Prussian blue. The system recovers back to ground state by blue or infrared light excitation or warming above 150 K. In Co-Fe Prussian blue analogs when the temperature is lowered to critical tem- perature (T → Tc), the interactions among spins become important and short-range ferrimagnetic ordering of magnetic moments is observed. The interacting spins creates spin clusters. The size of which increases with decreasing temperature but remain finite. Below freezing temperature the spin dynamics with in the clusters slow down enters a spin-glass like state in which the clusters’ magnetic moments are frozen in random directions. The spin glass like behavior can be explained by the random- ness in the structural disorder due to Fe(CN)6 vacancies and frustration resulting 52 Figure 2.24: Optical control of magnetism with red (λ = 650 nm) and blue (λ = 470 nm) in Co-Fe Prussian blue [110, 50]. from dipole-dipole interactions between clusters and next-nearest neighbor exchange interactions [113]. Upon illumination the number of unpaired spins increase via photoinduced charge transfer and spin flip. Therefore the critical temperature in which the short-range or- dering starts, shifts to higher temperature due to increase in the number of interacting spins. Moreover the size of the clusters become larger and the mean distance between them gets smaller. Thus the ferrimagnetic and spin-glass correlation lengths (ξ) in- creases. The freezing temperature (Tf ) and relation times (τ) which are proportional to the correlation length, increase as well. Similarly the anisotropy and magnetization 53 Figure 2.25: Schematic energy diagram of photoinduced magnetization in Co-Fe Prus- sian blue [112]. reversal energy (∆) increases upon illumination due to increase number of spins and cluster size, leading to higher coercive field (Hc) (Figure 2.26). Photoinduced magnetism effects occur only in certain Co-Fe Prussian blue sam- ples in which the concentration of Fe(CN)6 vacancies and Co/Fe stoichiometry are in specific limits. Around the missing Fe(CN)6 groups, the crystal field is lower II 5 2 due to the H2O molecules and favors the high-spin state (Co , t2geg) configura- tion. Thus systems with more vacancies have higher spin concentration. However the photoinduced effects are not observed since there is not sufficient diamagnetic moieties (FeII-CN-CoIII). On the other hand when there is low vacancy and thus 54 Figure 2.26: Illumination effects on ns (spin concentration), M (magnetization), Tc (quasi-critical temperature), ξ (ferrimagnetic and spin-glass correlation lengths), τ (relaxation times), Tf (freezing temperature), ∆ (energy barriers for rotation of cluster moments), Hc (coercive field) in cluster glass model [50]. spin concentration, photoinduced magnetization effects are suppressed as well due to the rigidity of lattice which prevents altering of the bond lengths and photoin- duced metastable state. Thus certain vacancy and Fe/Co concentration is necessary in order to observe photoinduced magnetic effects. Photoinduced magnetism is also observed in films [9] and nanoparticles [10, 114] of Co-Fe Prussian blue analogs, Co Octacyanotungstate [115, 116], Mn hexacyanoferrate [117] and Cu Octacyanomolyb- date [118, 119] that typically have low ordering temperature (Tc < 25 K). 55 2.3.2 M[TCNE]x x ∼ 2 M = V, Mn Another family of molecule-based magnets that exhibit photoinduced magnetism (PIM) and have long-range magnetic ordering is M[TCNE]x (x ∼ 2; M = V, Mn). The magnetic ordering in organic-based magnets M[TCNE]x is due to the exchange interactions between the unpaired spins in π∗ orbitals of (TCNE)− that is distributed over the whole anion and the one in the transition metal ion; Manganese, Vanadium (Figure 2.27). The origin of photoinduced magnetism has been studied in this family of magnets. Lack of change in saturation magnetization suggest that PIM is not due to change in total spin values as observed in Prussian blue analogs. (a) (b) Figure 2.27: (a) Schematic chemical structure of tetracyanoethylene (TCNE) [109]. (b) Schematic energy diagram for V[TCNE]2 [120]. In Mn(TCNE)x (ferrimagnetic ordering temperature ∼ 70 K), the magnetization can be controlled by visible light excitation [14, 15]. The reversible photoinduced magnetic effects are proposed to be originate spacial change in the [TCNE] structure 56 that enhances the exchange interactions between the spins of Mn ion and neighboring [TCNE]− anions. Figure 2.28 shows the effect of optical excitation on field cooled magnetization at T = 5 K and H = 10 Oe. Upon illumination with 2.54 eV (2.54 - 3.00 eV) argon laser line, the magnetization increases (20 %) and reaches saturation. On the other hand illumination with 2.41 eV (1.8 - 2.5 eV) laser light decreases photoinduced magnetization [121]. The system stays in the photoexcited state for a long time at low temperatures (T < 50 K) and fully recovers back to ground state after warming to 250 K. The absence of change in saturation magnetization and magnetic susceptibility in the paramagnetic regime suggest that the number of unpaired spins do not alter upon illumination. Figure 2.28: Partially reversible illumination effects on magnetism in Mn(TCNE) [15] 57 In Mn[TCNE] optical illumination changes the chemical bond lengths and an- gles, leads to lattice distortion and forms a metastable state. Figure 2.29 shows the schematic structures of ground and metastable states. Due to the altered geometry of the metastable state, the overlap integrals between the d orbitals of MnII and π∗ orbitals of [TCNE]− and exchange interactions are enhanced. Therefore upon illumi- nation both the magnetic susceptibility and charge transfer absorption increase. Figure 2.29: Scheme of photoinduced mechanism in Mn(TCNE) where the ligand- metal orbital overlap is increased and exchange interactions are enhanced. Stronger magnetic interactions lead to better spin alignment and increase in magnetization. The organic magnet V[TCNE]2 that has an ordering temperature above room temperature and exhibits photoinduced magnetism [6, 16, 122]. Upon illumination with argon laser (λ ∼ 457.9 nm), the field cooled magnetization decreases (∼ 3 % in 10 hours) at T = 10 K (Figure 2.30). In V[TCNE] the photoinduced magnetic effects are only reversible upon thermal excitation. As seen in Figure 2.31 the photoexcited magnetization fully recovers back to ground state after annealing to 250 K. 58 Figure 2.30: Decrease in field-cooled magnetization upon illumination with λ = 457.9 nm that is around π to π∗ + U excitation [6]. V[TCNE]2 have a disordered structure thus random magnetic anisotropy plays an important role in photoinduced magnetic phenomena. Optical excitation alters the overlap of metal-ligand bonds and increase the structure disorder resulting in enhanced magnetic anisotropy. Therefore a decrease in magnetization is observed in V[TCNE]2 below ∼ 90 K. 59 Figure 2.31: Full recovery from photoinduced magnetic state upon thermal heating to 280 K [123, 6]. 60 CHAPTER 3 Background on Conducting Polymers 3.1 Conducting Polymers Polymers are naturally occurring or synthetic long chain of molecules composed of many repeating structural units. Differences in synthesis, starting molecule and polymerization process leads to various polymers. The major use of polymers was electrical insulation until the discovery of conducting polymers in 1977. Alan J. Heeger, Alan G. MacDiarmid and Hideki Shrakawa were awarded with Nobel Prize in 2000 for this breakthrough [19, 17, 124]. Today conducting polymers are being used in many applications such as transistors, solar cells and light emitting diodes [21]. Conjugated Polymers In conducting polymers, the key feature for conducting is the presence of alter- nating double and single bonds along (conjugation) the polymer chain. Besides the strong chemical bond (localized σ bond) between each connected atom, there is a less strongly localized π bond in the case of double bonds. In polyacetylene which has the simplest form among all conjugated polymers (Figure 3.1), three of the four electrons in the outer shell of carbon are sp2 hybridized. These three electrons form σ bonds with the electrons of two neighboring carbon and one hydrogen atoms. The 61 left over carbon electron which occupies the pz orbital, overlaps with the π electrons of other carbon atoms and forms a π band. The chemical structures of commonly used conjugated polymers are shown in Figure 3.1. Figure 3.1: Chemical structures of commonly used conjugated polymers [125] Peierls Instability Since there is one unbounded pz electron per atom, a partially filled band is formed and metallic conduction is expected. In a periodic lattice when the conduction band is partially filled having one electron per atom and finite density of states at the Fermi level, the electron wavefunctions become delocalized. However in a conjugated 62 polymer chain, the system opens up an energy gap in the π electron band between the filled bonding states (π band) and empty anti-bonding states (π∗ band) due to lattice distortion. The energy of the system is lowered by pairing of unbounded pz electrons of successive sites along the chain, altering the bond length and forming a π bond in addition to the σ bond. As seen in Figure 3.2 the dimerization of the one-dimensional chain (Peierls instability) changes the periodicity of the lattice and unit cell and splits the metallic band into two subbands with a gap of 1.4-2 eV and wide bandwidth of ∼ 5 eV in conjugated polymer chains. Figure 3.2: (a) Dimerized polyacetylene structure with alternating double and single bonds. The energy diagram of undimerized (b) and dimerized polyacetylene(c). 63 Doped Polymers Upon doping, addition states are formed in the π − π∗ band gap of conjugated polymers and electrical conductivity increase by several orders of magnitude (from 10−10 to 105 S/cm). Since the initial study on polyacetylene doped with halogens (chlorine, bromine) and arsenic pentafluoride [17], there has been many studies on doped conducting polymers [126, 127, 128, 129, 130]. Figure 3.3 shows the conductiv- ities of polyaniline and trans-(CH)x (polyacetylene) which are comparable to metals (e.g. Au, Cu) in their doped forms. The doping process in conducting polymers differs from the one in conventional semiconductors. The doping ratio (dopant molecules to carbon atoms ratio) is orders of magnitude higher in conductive polymers than inorganic semiconductors. More- over the dopants (III/V group elements) in conventional semiconductors substitute the host atoms which are covalently bounded together and form a periodic rigid lattice structure. Thus in inorganic semiconductors electrons/holes are introduced into the lattice which constitute acceptor/donor level close to filled valance band and empty conduction band. Moreover in conducting polymers, dopants are positioned intersti- tially between the polymer chains and donate or accept charges from the polymer backbone. This introduce delocalized states in the polymer system. Figure 3.4 shows the schemes of the substitutional and interstitial doping in inorganic semiconductors and conducting polymers respectively. Several doping methods have been developed for conducting polymers such as redox doping, photo-doping, charge-injection doping and non-redox doping. The p- and/or n- redox doping which uses chemical and electrochemical processes, changes the number of electrons in the polymer backbone and can be applied to all conducting 64 Figure 3.3: Conductivities of pristine and doped polyaniline and trans-(CH)x [19] polymers. In the second type of doping, photo-doping, the polymer (e.g. trans-(CH)x) is exposed to radiation with an energy greater than the band gap, leading electrons to reach across the gap and become delocalized. The charge injection doping is commonly carried out in metal/insulator/semiconductor configuration. In this doping method, application of a potential results in a surface charge layer in the polymer and increased electrical conductivity. In the non-redox doping, the energy levels of polymers are rearranged without changing the number of electrons in the polymer backbone. This kind of doping is achieved by treating the polymer (e.g. emeraldine base polyaniline) with aqueous protonic acids such as HCl [19, 131]. 65 Figure 3.4: Schemes of (a) substitutional and (b) interstitial doping in inorganic semiconductor and conducting polymer respectively. Disorder in Conducting Polymers In addition to doping level, the electrical transport in conducting polymers de- pends on the structural disorder arising from sample quality, doping process and aging [132]. Disorder leads to localization of charge carrier wavefunctions that gets stronger as the crystallinity decreases. In conductive polymers the crystallinity is lim- ited and the best reported crystallinities are ∼ 80 − 90% for doped polyacetylene and ∼ 50% for doped polyaniline. Figure 3.5 displays the schematic picture of partially crystalline, partially disordered morphology of conducting polymers. 66 The disorder in the polymer is viewed as inhomogeneous when the localization length of the electrons in the disordered regions is comparable or smaller the crys- talline length (∼ 10A˚). In the inhomogeneous disordered model in which metallic islands surrounded by amorphous regions, charge transfer has been described as com- bination of different conduction behaviors. Electronic wavefunctions are delocalized in the metallic regions and localized in the amorphous region [23, 133]. When the polymer chains between the metallic islands are tightly coiled, free carriers are con- fined in the metallic region and transport is possible by hopping and phonon-induced delocalization or tunneling between metallic islands. On the other hand, if the poly- mer chains connecting metallic islands are sufficiently straight, then the carriers can diffuse through the disordered regions. The dimensionality of the transport is also important to model and understand the electrical transport mechanism in conductive polymers better. Three dimensionality, interchain interactions (hopping or diffusing to another chain) is necessary to avoid polymer chain breaks and defects. Because of the localization of the wavefunction in a chain due to imperfections, transport is not possible in one dimensional systems. However, due to highly anisotropic conduction behavior (σ||/σ⊥ ∼ 100), the charge transport in polymers can be thought as quasi-one dimensional. Reduced Activation Energy The room temperature conductivities of conducting polymers become comparable to conventional metals upon doping, show signatures of metallic behavior such as Pauli susceptibility, negative dielectric constant and Drude response. However the temperature dependence of conductivity varies from metals and usually decreases as the temperature is reduced. In order to better understand the insulating and 67 Figure 3.5: (a) Schematic picture of inhomogeneous disorder in conjugated polymers (b) Schematic picture of rod-like and coil-like disorder in polymers[23]. metallic transport behavior of conductive polymers, reduced activation energy W = dlnσ(T ) = dlnT is defined [134] and plotted against temperature [135]. • In metallic regime, the slope of W (T ) is positive and resistivity (ρ) is finite as T → 0. • In critical regime, W (T ) is temperature independent for a wide range of tem- perature. Resistivity follows a power law, σ(T ) = aT β where 1/3 < β < 1 indicates system is in the metallic side. 68 Figure 3.6: Reduced activation energy (W ) plot for various polyaniline samples doped with CSA, hydrochloric and sulfuric acid [125]. • In insulating regime, the slope of W (T ) is negative and resistivity follows Motts 1/(n+1) variable range hopping model (VRH) with σ = σ0exp(−T0/T ) where n is the dimensionality of the charge transfer Figure 3.6 shows the reduced activation energy vs temperature graph for different polyaniline samples that exhibit metallic behavior (positive slope) and semiconductor behavior (negative slop) [125]. The insulator to metal transition which occurs as the doping level is increased and the disorder is reduced, has been observed in many conducting polymers such as polyaniline, polyacetylene and polypyrrole. Moreover 69 the transition from metallic to insulating behavior can be observed upon changing the applied pressure and magnetic field (see Figure 3.7) (a) (b) Figure 3.7: (a)Log-log plot of W vs. T for polyacetylene (black circles) at ambient pressure and H = 0; (black diamond) at 10 kbar and H = 0; (black square) at ambient pressure and H = 8 T. (inset) Pressure dependence of conductivity [136]. (b) Schematic plot of the effect of magnetic field and pressure around metal-insulator transition in logσ − logT graph [137] Even though the room temperature conductivity is higher than the Mott min- 2 2 imum metallic conductivity, σmin = 0.002e /~a ∼ 10 S/cm (in three dimension with an interatomic spacing of a), the slope of reduced activation energy plot can be negative and resistivity can increase with decreasing temperature in a conducting polymer due disorder-induced localization of the charge carriers [132]. Recently a true metallic polyaniline sample with a room-temperature conductivity ∼ 1000 S/cm is reported [138]. Figure 3.8 displays the temperature dependence of resistivity which decreases as the temperature is lowered (down to 5 K). Moreover its infrared spectra 70 exhibits conventional Drude model behavior at the low frequencies and suggests a true metallic behavior. Figure 3.8: Temperature dependency of resistivity in PANI-CSA with metallic be- havior (samples S1 and S2) and conventional PANI sample for comparison [138]. 3.1.1 Electromagnetic Response The localization and delocalization behavior of charge carriers within a given ma- terial can be understood from its complex dielectric function. In order the understand the transport behavior in metals, the free electrons, Drude theory can be considered. 71 And the behavior of bound charge carriers can be explained by Lorentz oscillator model. Drude Theory of Metals In Drude theory when metallic atoms are brought together, the electrons become free and move through the metal (conduction electrons), whereas the ions remain immobile. In this theory, the electron-electron interaction (independent electron ap- proximation) and electron-ion interaction (free electron approximation) are neglected. The delocalized electrons collide with the ion cores for approximately every τ (relax- ation time, ∼ 10−14 s) and changes its velocity during these instantaneous collisions. The equation of motion of an electron in Drude theory, is described by[45], dp p = − − eE (3.1) dt τ Where E is the time dependent electric field (E(t) = Re(E(w)e−iωt)) with a steady- state solution of the form p(t) = Re(p(ω)e−iωt). Since the current density is j = −nep/m, it can be written as j(ω) = σ(ω)E(ω) (3.2) where σ(ω) is the frequency dependent conductivity and given by, ne2τ/m σ(ω) = (3.3) 1 − iωτ By using Maxwell equations, the Drude dielectric function is determined as, ω2 (ω) = 1 − p (3.4) Drude ω2 + iω/τ 2 2 where ωp = 4πNe /m, the plasma frequency, N is the electron density and m is the effective mass of electrons in the solid. From Equation 3.4, real and imaginary parts 72 of Drude response can be determined as, ω2τ 2 (ω) = 1 − p (3.5) r 1 + ω2τ 2 ω2τ (ω) = p (3.6) i ω(1 + ω2τ 2) Figure 3.9 shows the characteristic frequency dependence of real and imaginary parts in drude theory. When is real and negative (ω < ωp), no radiation can propagate. On the other hand when is positive (ω > ωp), radiation can propagate and the metal becomes transparent. These responses are valid in the high frequency (ωτ 1) regime. When interactions such as electron-phonon, electron-electron are taken into account, the Drude response become: ω2 = − p (3.7) r ∞ 1 + ω2τ 2 where ∞ is the high frequency term with ∞ > 1. Lorentz Model Drude model fails to explain the dielectric response of insulators in which the electrons are tightly bounded. For insulators, Lorentz model offers a simple picture for the response to time dependent electromagnetic radiation. In this model, the nucleus (more massive) is assumed to be connected to electrons (smaller mass) by a spring which would either compress or stretch due the electron-electric field interaction. Thus the electron move in harmonic motion with a damping effect by the electric field. The equation of the motion of the electron is given by, d2r dr m + mγ + mω2r = −eE. (3.8) dt2 dt 0 The second term in Equation 3.8 defines the damping term due to various scattering mechanism and spontaneous emission. The dielectric response of bound electrons to 73 Figure 3.9: The frequency dependence of real and imaginary parts of drude response for ω2 = 30 eV2 and ~/τ = 0.02 eV [139]. the oscillating electric field that is determined by a similar procedure used in Drude theory and given by, 4πNe2 1 Lorentz(ω) = 1 + 2 2 (3.9) m (ω0 − ω ) − iγω The photon energy (frequency) dependence of the real and imaginary parts of complex dielectric response are plotted in Figure 3.10. The real and imaginary parts of Lorentz 74 function can be written as, 2 2 2 4πNe ω0 − ω r(ω) = 1 + 2 2 2 2 2 (3.10) m (ω0 − ω ) − γ ω 4πNe2 γω i(ω) = 2 2 2 2 2 (3.11) m (ω0 − ω ) − γ ω Figure 3.10: The photon energy (~ω) dependence of real and imaginary parts of dielectric function for lorentz oscillator with resonance frequency (~ω0) = 3.85 eV, broadening (~γ) = 2.0 eV [140]. 3.1.2 Electronic Structure of Polymers The one dimensional electronic structure of undoped conjugated polymers can be explained by Su-Schriffer-Heeger (SSH) model. 75 Su-Schriffer-Heeger (SSH) Model The SSH model is a simple quasi-one dimensional tight-binding approach for poly- acetylene that has the simplest chemical structure among conjugated polymers (Fig- ure 3.1). The SSH model that explains the electronic structure of polyacetylene, assumes weak interchain coupling (quasi one-dimensional behavior) and bond dimer- ization due to alternating double and single bonds. In SSH model the vibrations of the carbon atoms in polyacetylene whose ionic coordinates are projected onto the chain axis (x-axis) are taken into account using quantum mechanical tight-binding approximation. On the other hand the motion of the atomic nuclei is treated classi- cally. The SSH Hamiltonian for perfectly dimerized polyacetylene (Figure 3.11) can be written as, HSSH = Hπ + Hπ−ph + Hph (3.12) The first term in Equation 3.12 is the Hamiltonian describing the hopping of the π electrons to their nearest neighbor in the undimerized chain and given by, + + Hπ = −t0Σn,s(an+1,san,s + an,san+1,s) (3.13) + where an,s and an,s are the creation and annihilation operators respectively for the π th electrons on the n (CH) group with spin 1/2 and t0 is the hopping integral. The second term in Equation 3.12 denote the electron-phonon interaction and described as, + + Hπ−ph = αΣn,s(un+1 − un)(an+1,san,s + an,san+1,s) (3.14) where α is the electron-phonon constant defining the lattice displacement and un is the displacement of the nth (CH) unit from equilibrium. In a perfectly dimerized 76 Figure 3.11: The conjugated structure of trans-polyacetylene with dimerization co- ordinate un [141]. polyacetylene, every other bond is double bond and its alternation can be written as n un = (−1) u0 with a fixed change of u0 shown in Figure 3.12. Figure 3.12: The energy of dimerized polyacetylene chain with degenerate energy minima at ±u0 [124]. 77 The last term in SSH Hamiltonian gives the phonon Hamiltonian and can be written as p2 K H = Σ n + Σ (u − u )2 (3.15) ph n 2M 2 n n+1 n where p is the nuclear momenta, m is the mass of carbon atom and K is the effective spring constant. Then the total SSH Hamiltonian can be written as, K p2 H = −Σ (t − α(u − u ))(a+ a + a+ a ) + Σ (u − u )2 + n(3.16) SSH n,s 0 n+1 n n+1,s n,s n,s n+1,s 2 n n+1 n 2M p2 = −Σ (t + (−1)n2αu)(a+ a + a+ a ) + 2NKu2 + n(3.17) n,s 0 n+1,s n,s n,s n+1,s 2M (3.18) for the polyacetylene polymer with N (CH) units. If we neglect the last kinetic energy term, Hamiltonian can be given by, c+ c v+ v 2 H = −Σk,sEk(ck,sck,s + ck,sck,s) + 2NKu (3.19) 2 2 1/2 where Ek = (k + ∆k) is the energy of the electrons with the initial electron dispersion (unperturbed band energy) k = 2t0cos(ka) and dimerization (energy gap) c+ c ∆k = 4αusin(ka) in the reduced zone with boundaries at k = ±π/2a. The ck,sck,s v+ v and ck,sck,s are the number operators counting the number of charge carriers with wavevector k and spin s in the conduction (c) and valance (v) bands. From SSH model, the band distortion that gives the minimum energy for polyacetylene is calculated as 2 u0 ∼ 0.04 A˚ with α = 4.1 eV/A˚, K = 21 eV/A˚ and t0 = 2.5 eV which is consistent with experimental results [142]. The SSH model gives an insight to understand the solitons in the two degenerate ground states of polyacetylene shown in Figure 3.14 [143, 144, 145, 146]. 78 Figure 3.13: The band structure (left) and density of states (right) of semiconducting polyacetylene [124]. Excitations in Conducting Polymers In trans-polyacetylene, there are two degenerate ground states that has the bond dimerization in the same way on different carbon atoms. Figure 3.14-d shows the chemical structures of these degenerate states; A phase and B phase. Between these two phases in a chain, there can be a domain boundary which is known as soliton (Figure 3.14-e). This elementary excitation is not an abrupt structural change be- tween phases but rather form over a finite number of atoms in order to reduce the energy. For a system with an energy gap of 1.4 eV, the soliton occurs over 14 a where a is the lattice spacing with a formation energy of 0.42 eV. When a soliton is formed, a single state occurs in the middle of the gap. This mid-gap state can accommodate at most two electrons due to the spin symmetry. In a neutral soliton, the state is single occupied and has spin 1/2. On the other 79 Figure 3.14: The undimerized (a) and dimerized (b) structures of trans-polyacetylene. (c) The structure of cis-polyacetylene. (d)The two degenerate states (A phase, B phase) and (e) soliton in trans-polyacetylene [124]. hand negative and positive solitons (charged ones) are empty or doubly occupied with no spin (the opposite spin-charge relations compared to conventional charge carriers; electrons and holes) [147]. In Figure 3.15 the neutral and charged solitons are displayed. Due to large width of solitons, their mass is on the order of electron mass and they can propagate freely within the chain. On the other hand, in most of the polymers such as cis-polyacetylene, poly(thiophene) and PPV, bond alternations on different carbon atoms result in non-degenerate ground states (see Figure 3.16). Therefore a domain boundary can not balance between the two phases that have different energies. In these polymers instead of 80 Figure 3.15: Band structures of positive (a), neutral (b) and negative (c) solitons [145]. solitons, polarons and bipolarons are formed. Polarons can be explained as a bound state of a neutral and a charged soliton whose mid-gap energy states from two states above and below the mid-gap [148]. In negative polaron (combination of negative-neutral solitons) the lower state is filled and the upper state has one electron and the total spin is 1/2. For the positive polaron (combination of positive-neutral solitons), there is single electron in the lower state with a total spin of 1/2. The theoretical calculations suggest that only the positive and negative polarons are stable. A bipolaron is formed when two charged solitons or polarons bound together, giving ± 2e charge and 0 spin. In the case of bound charged polarons, the polarons levels splits into new energy levels. The highest and lowest energy levels merges with the conduction and valance bands respectively. 81 Figure 3.16: Chemical structures and energy of non-degenerate ground states (A and B phases) in conducting polymers [145]. Figure 3.17 shows the band structure of polypyrrole at different doping levels with polaron and bipolaron energy levels and bipolaron bands. Solitons, polarons and bipolarons are excitations in conjugated polymers that al- low electrical conductivity upon doping. These excitations move along the chain and carry the lattice distortion. Optical probe of mid-gap states and magnetic measure- ments verify the theoretical model that explains these excitations. 3.1.3 Transport in Conducting Polymers Since the discovery of conducting polymers, there has been significant interest in conducting polymers. Their high and controllable conductivities, stable nature ans easy synthesizing methods made them possible candidates for many applications. However, the transport in conducting polymers is not trivial since it depends on many parameters such as the doping level, disorder, morphology, temperature and magnetic field. In this section models that explained the transport in conducting polymers as 82 Figure 3.17: The band structure of polypyrrole for (a) low doping level (polaron) (b) moderate doping level (bipolaron) and (c) high doping level (bipolaron bands) [149]. well as earlier studies on the magnetic field effect on the resistance (magnetoresis- tance) and morphology dependence (e.g. nanofiber, pellet) are discussed. Anderson Localization In a perfect lattice with periodic potentials, the wavefunctions (Bloch waves) are delocalized over the whole system. However if disorder, impurities or defects exists within the system, then wavefunctions may localized due to scattering from imperfections. Thus the transport properties highly depend on the disorder in the system and depending on its strength, metallic or insulating behavior can be observed. The transport behavior of a disordered systems can be explained by Anderson localization model that assumes isotropic electrical properties. Anderson exhibited that when the randomness in the disorder potential (W ) is comparable to or larger than the electronic bandwidth (B), the wavefunctions become localized and can be 83 described by [150], ψ(r) ∝ exp(−r/Lloc)Re(ψ0) (3.20) where Lloc is the localization length. Figure 3.18 shows the periodic potential with small disorder (B < W ) and with large random disorder (B > W ) leading to Ander- son transition and related localized wavefunction. Figure 3.18: The periodic potential and disorder (a) and the form of localized wave- function (b) in Anderson metal-insulator transition. [150]. In a disordered system, the states in the band tail become localized more easily than the ones in the center of the band [151]. The critical energy that separates the localized states in the band tail from delocalized ones in the band center is called the mobility edge (Ec). If the Fermi energy (EF ) lies in the range of extended states, then the system shows metallic behavior with a finite conductivity at low temperatures (σDC as T → 0) and positive slope in the reduced activation energy-temperature (W (T )) plot. However if the EF lies in the localized states region due to strong disorder potential, then the system show nonmetallic with σDC → 0 as T → 0) and 84 negative slope in W (T ) plot. Figure 3.19 shows density of states-energy graph. Even if there is a finite density of states at the Fermi level, the system is not metallic since EF lies in the region of localized states. When EF approaches mobility edge from the insulating side, the localization length diverges, the wavefunction becomes delocalized and the system moves from insulating to metallic side. This is known as Anderson Insulator-Metal (IM) transition. Figure 3.19: The density of states-energy plot where the Fermi level lies in the region of localized states [ [151, 122]. Mott Variable Range Hopping The transport in systems with strong disorder (disoderder energy >> bandwidth) can be explained by Mott variable range hopping (VRH) model. In Drude model, the charge carriers are accelerated by the applied electric field. In this free electron model, phonons act as a source of scattering similar to impurities and conductivity 85 decreased with increasing temperature. On the other hand in VRH model which is employed for localized charges, transport requires phonons (thermal energy) in order to hop between the sites [152, 133]. Thus the existence of phonons is crucial for the charge transport. The hopping probability from one site (n) to another (m) can be expressed by, ∆E Pnm ∝ exp(−rαRh − ) (3.21) kBT where Rh is the hopping length, α is inverse of the localization length (Lloc) and ∆E is the energy difference between the sites n and m. Therefore the hopping probability increases as the hopping length and energy difference gets smaller. The temperature dependence of conductivity can be given as 1/(d+1) σ(T ) = σ0exp(−T0/T ) (3.22) in Mott VRH where d is the dimensionality of the system and T0 is the characteristic temperature that depends on the localization length, density of states and indicates how far the system move to the insulating side. For a three-dimensional system, d 3 = 3 and T0 = 16/(kBN(EF )Lloc) where N(EF ) is the density of states at the Fermi −1/d energy. The T0 can be determined from the fitting of lnρ versus T plot. Similar transport behavior has been previously reported in many doped conducting polymers such as PANI [153] and poly(o-toluidine) (POT) [154] that conductivities of few S/cm 3 5 and T0 ∼ 10 − 10 K. The mean hopping length (Rh) and hopping energy (∆h) can be determined from (1/4) Rh = (3/8)Lloc(T0/T ) (3.23) (1/4) ∆h = (1/4)kBT (T0/T ) (3.24) 86 in 3-dimensional VRH [155]. For quasi one-dimensional hopping, the exponent in Equation 3.22 is 1/2 that can be also observed in a three-dimensional system with electron-electron interactions as suggested by Efros and Shklovskii [156, 157]. In various conducting systems crossover from Mott to Efros-Shklovskii variable range hopping at low temperatures [158, 131]. Resonance Quantum Tunneling For highly doped conducting polymers, band transport, anderson localization and Mott models fail to explain the transport mechanism. In this case, the resonance quantum tunneling model which is proposed by Epstein et al., can explain the trans- port in these metallic polymers [159]. In order to determine the charge transport in conducting polymers, first the morphology is needed to be understood. The morphol- ogy of conducting polymers includes partially crystalline and partially disordered regions [160]. The crystalline domains (metallic grains) are spatially separated by poorly conducting amorphous regions (Figure 3.20) where charge carriers are strongly localized. The transmission coefficient for direct tunneling between the metallic grains is given by −2L g = exp( ) (3.25) Lloc where L is the length of the chain. For a polymer with L = 5 nm and 50 % crys- tallinity, g ∼ 10−4, therefore direct tunneling is suppressed. On the other hand, Epstein et al. suggested that it is possible have resonance quantum tunneling between the grains. The probability of finding a resonance state is proportional to the width of the resonance state [161] which is in the center of the 87 Figure 3.20: Schematic image of metallic grains (well ordered regions) that are con- nected by amorphous (poor ordered) regions [159]. chain. Therefore the transmission coefficient in resonance tunneling can be given by g = exp(−L/Lloc) using the width of the resonance state [159]. The critical value for −2 transmission coefficient is determined as gc ∼ 10 [159, 162]. Although the critical value (10−2) is very small, due to the large number of chains (∼ 100) connecting the grains, the probability of finding a resonance state gets larger. Thus, systems with strong inter-grain coupling show metallic transport behavior. Figure 3.21 displays the inter-grain charge transfer through amorphous chains by quantum resonance tunneling granular. The energy levels inside the metallic grains are quantized and the mean energy level spacing is ∆E that depends on the number of chains and density of states [163, 164]. The energy level broadening δE depends on the number of chains, level spacing and transmission coefficient g. Thouless et al. suggested that when the level broadening is on the order of level spacing the metal insulator transition occurs [165]. In granular metals, the grains assumed to have mechanical contacts. Therefore charge transport is possible through direct tunneling which is thought as an instanta- neous process. Whereas in granular polymers, the transport is via resonance quantum 88 Figure 3.21: Charge transfer via tunneling through resonance states around Fermi energy between the metallic grains [159]. tunneling that shows a delay depending on the resonance level width. This delay in highly doped conducting polymers is identified in optical and low frequency con- ductivity measurements [166, 167]. Therefore the resonance quantum tunneling can explain the frequency dependence of the conductivity and dielectric constant in the metallic phase of highly conducting polymers [162] Magnetoresistance Conductivity of conductive polymers not only changes with temperature, doping and disorder but also changes with magnetic field [168, 169, 170]. The magnetic field dependence of the resistance can be explained by zeeman splitting, lorentz effect and quantum interference effects. In a conducting polymer where there is significant electron-electron interactions, a positive magnetoresistance can be observed due to zeeman splitting in an applied magnetic field. The zeeman effect splits the spin-up and spin-down states in energy. Due the energy difference, charge hopping is suppressed between two states with opposite spins. Hopping probability of two electrons from two single occupied states 89 whose spins are aligned parallel with the magnetic field will diminish. Similarly, hopping from doubly occupied state to unoccupied state will be suppressed in the magnetic field due the splitting of spin-up and spin-down levels. Figure 3.22(a) shows the resistivity ratio of polyacetylene sample that increases with magnetic field and saturates at a characteristic field where all the spins are aligned with the field [171, 172]. In conducting polymers positive magnetoresistance can be also observed due to Lorentz Effect. In the magnetic field the wavefunction of the charge carriers shrinks. The shrinkage leads to smaller overlap integral of wavefunction [155, 153, 154]. Thus hopping probability from one site to another site decreases and the resistivity in- creases (Figure 3.22(b)). It was reported that magnetoresistance increases with H2 (H; magnetic field) up to a critical field and then have H1/3 dependence [156, 33, 37] in this shrinkage model. A negative magnetoresistance is also observed in conducting polymers due to quantum interference of tunneling paths in hopping process [174, 173]. In weak lo- calization magnetic field alters the relative phase of the different tunneling paths involving alternative scattering (see Figure 3.23) and destroys the constructive quan- tum interference. Thus the conductivity increases with the magnetic field. Park et al. observed a change in the magnitude of magnetoresistance in poly- acetylene nanofiber systems with the applied electric field. On the other hand no change was observed in polyaniline nanofiber system [175]. This magnetoresistance phenomena was explained by the soliton (which has charge but no spin) tunneling in high electric field that leads to low magnetoresistance in polyacetylene. Similarly the absence of electric field effect in polyaniline is explained by polaron (which has both 90 (a) (b) Figure 3.22: (a)Positive magnetoresistance in polyacetylene sample. Resistivity ratio increases linearly with field and saturates at a characteristic magnetic field where all the spins are aligned [171].(b)Wavefunction shrinkage (positive MR) and quantum interference effect (negative MR) in polyaniline samples [173]. spin and charge) tunneling that leads to significant magnetoresistance in polyaniline even at high electric field. Electrical Transport in Polymer Nanofibers and Pellets Transport properties of conducting polymers have been studied intensively since the first discovery of conducting polymers. Many models have been developed and experiments have done in order to understand the transport behavior. However due to the complex structure and morphology of polymers, electrical conductivity has not been fully understood particularly in small-sized polymer microspheres [176, 177] and nanofibers [178, 179, 39, 36, 180] in which both inter-fiber and intra-fiber transport 91 Figure 3.23: Two current paths between hopping sites with different scattering paths. Figure 3.24: SEM image of two nanotubes crossing at a single junction [35]. are important. Nano-structured polymer systems have attracted great attention and investigated for many applications such as transistors [181, 182], sensors [183, 184] and memory devices [2]. In polymer nanofibers both the inter and intra-fiber conductivity determines the charge transport. Figure 3.24 shows an SEM image of two polyaniline nanofibers crossing at a junction. Long et al. reported that room-temperature resistance (RRT ∼ 30 k Ohm) through a single nanofiber is 10 times smaller than the room-temperature 92 (a) (b) Figure 3.25: Temperature dependence of resistance through (b) a single nanojunction and (c) a single nanotube [35] resistance (RRT ∼ 500 k Ohm) through fibers with a junction (Figure 3.25). This study indicates that the resistance of polymer samples is highly affected by the fiber contact resistance [35]. It is also reported that the dimensionality of the charge transport changes with morphology. The charge transport in a single polyaniline nanofiber follows three- dimensional variable range hopping (VRH) model with a room temperature conduc- tivity at ∼ 30 S/cm. On the other in nanofiber pellets the transport has quasi-1D VRH behavior with a room temperature conductivity 4 orders of magnitude smaller due to large interfiber contacts [185]. The temperature dependence of conductivity and its fitting to VRH model for both single fiber and pellet is shown in Figure 3.26. Morphology dependent conductivity in conductive polymer fibers is also reported by Adetunji et al. In polyaniline nanofibers the conductivity shows a sharp maximum 93 (a) (b) (c) Figure 3.26: Temperature dependence of conductivity (a) in a single fiber that follows 3D VRH (b) with a room temperature conductivity of 31.4 S/cm. Quasi-1D VRH charge transport with a room temperature conductivity of 0.035 S/cm in nanofiber pellet [185] at ∼ 240 K, then decreases with decreasing temperature. Both optical and frequency dependent conductivity measurements and EPR studies identify that the peak is not due to conventional metal-insulator transition but results from the fragile nature of interfiber interfaces [163, 184]. By applying high pressure to the fibers, a pellet of polyaniline was prepared in which the conductivity peak disappears as shown in Fig- ure 3.28. The absence of the peak indicate that interfiber contacts play an important role in the charge transport of polymer nanofibers. 94 Figure 3.27: SEM image of polyaniline nanofiber in the network (left) and pellet form (right) [24]. (a) (b) Figure 3.28: The temperature dependence of dc conductivity in the polyaniline nanofiber and pellet [184]. 95 CHAPTER 4 Experimental 4.1 Sample Preparation The polyaniline nanofibers and V-Cr Prussian blue samples were prepared by chemists at OSU and University of Utah respectively. The chemical synthesizes of samples by the expert chemists and their preparation for the measurements are dis- cussed in this section. 4.1.1 Polyaniline Nanofibers Polyaniline nanofibers were synthesized by Dr. Nan-Rong Chiou via dilute poly- merization following the literature procedure [4, 40]. In the chemical synthesis of polyaniline nanofibers, aniline (Aldrich) which was distilled under vacuum, ammo- nium persulfate (APS; 99.99% Aldrich) and dopant acid; camphorsulfonic acid (CSA) were used as reagents. In the preparation of polyaniline nanofibers, the solution of aniline which dissolved in a small amount of 1M HCSA dopant acid was transferred to APS/1M HCSA solution. The reaction was carried out at room temperature with no disturbance (unstirred polymerization). Throughout the reaction process, the initial concentration of aniline to total solution volume was kept at 0.1 M and the molar ratio of aniline to 96 APS was maintained at 1.5. After 1 hour, the dark-green precipitate of polyaniline nanofibers was collected to the centrifuge tube and purified with deionized water until the pH of the supernatant became ∼5 (high-speed centrifuge at 5000 rmp at 23 C). One volume of the concentrated polyaniline nanofiber suspension was redoped by 1.5 volume of 1M HCSA. One volume of the redoped suspension was centrifuged and the precipitation was washed by 1.6 volume of deionized water, followed by 0.8 volume of acetone and 0.8 volume of isopropanol. The final volume of the suspension was centrifuged again and then, the extra supernatant was discarded to form one volume of the suspension. For dc electrical measurements, PANI-CSA nanofiber suspension was placed and dried under the hood at room temperature on gold electrodes, which were previously prepared by photolithography on glass substrates and have 30 to 100 micron separa- tions. For polyaniline nanofiber micro-cluster measurements, the sample suspension was diluted with acetone and then placed and dried on electrodes in order to achieve small clusters of nanofibers. 4.1.2 V-Cr Prussian Blue V-Cr Prussian blue samples which were received in the form of powders, are highly oxygen sensitive. In order to prevent from oxidation, samples were stored and prepared for measurements in a Nitrogen glovebox from Vacuum Atmospheres Company (VAC) where oxygen and water content was maintained at low values (< 1 ppm). For the dc and ac magnetic studies of V-Cr Prussian blue, the powder samples were placed in quartz EPR tube and pressed with teflon powder to prevent spreading 97 of the sample in the tube. The tube was then sealed under vacuum in order to prevent oxidation. For photoinduced magnetism studies, the samples were prepared by dispersing V-Cr Prussian Blue powder in Nujol oil for better optical excitation. The dispersion samples were prepared by first grinding the powders in an oil in a glass jar. The mixture was then filtered through a syringe and placed in an EPR tube which was sealed under vacuum while keeping the sample in liquid nitrogen to freeze the viscous environment during sealing. In the dispersed samples, the weight of the V-Cr Prussian blue could not be determined due to mixing with oil and filtering. The UV-Vis spectroscopy samples were prepared by grinding and mixing the V- Cr Prussian blue powder with fluorolube oil (mull method). The optical studies were done on two sets of glass slides which have only the fluorolube oil (background measurement) and the mixture. 4.2 Experimental Tools Several experimental tools were used in order to characterize the samples and understand the observed magnetic and electronic phenomena. In this section the tools and techniques that were employed for this study are presented and discussed. 4.2.1 Elemental Analysis Polyaniline nanofiber samples were sent to Atlantic Microlab, Inc. for elemental analysis. Elemental analysis is a process which determines the percentage weights of carbon, hydrogen, nitrogen, and heteroatoms (halogens, sulfur) of a sample. The percentage weight help ascertain the exact structure of an unknown compound, as well as the purity of a synthesized compound. By elemental analysis, it is found that 98 polyaniline samples used in this study are 69 % doped. The presence of excess HCSA in the sample can may be attributed to drying of the PANI nanofiber dispersion. 4.2.2 Imaging and patterning: Photolithography, FIB, SEM In order to get the desired micro and nano size electrodes, various fabrication tech- niques including use of shadow mask, photolithography and Focused Ion Beam lithog- raphy were carried out. In order to characterize and verify the polymer nanofiber clusters, an electron microscope (SEM) was used. Figure 4.1: Schematic illustration of the gold electrodes for 4-probe (left) and 2-probe (right) measurements used for electrical measurements. For 2-probe electrical measurements, conductive electrodes were thermally depo- sition (5 nm Al or Ti as adhesive layer and 30 nm Au) on previously cleaned glass substrate using a shadow mask for the gold electrodes and an Al wire for the separa- tion between the electrodes. The width of the electrodes are 2mm and the separation 99 between them is ∼ 30 micron. In Figure 4.1, the schematic illustration of the elec- trodes for 4-probe and 2-probe measurements are shown. For 4-probe measurements, electrodes were patterned using photolithography which is an easy and powerful technique. In photolithography the sample is spincoated with a UV light sensitive polymer (photoresist). A mask with the desired pattern is then used to illuminate the uncovered areas on the sample which is removed selectively. After developing the film, the metals are deposited and the final lift-off process gives the desired electrodes. The photolithography process that was used in our studies was illustrated in Figure 4.2. The width and length of the electrodes that were prepared by photolithography, are 100 micron and 5 mm respectively. The separation between the electrodes changes from 30 to 100 micron, depending on the mask used. For photolithography, we used S1813 photoresist and MF 319 developer. The spincoated resist was softbaked (before illumination) at 115 C for one minute and hardbaked (after developing) at 115 C for 15 minutes. The masks were prepared by from Fine Line Imaging and Photo Sciences, Inc. The lithography process was carried out using photo-aligners (EV Group 620s) at Nanotechwest facilities. For fabrication of nano-electrodes on the polymer nanofiber clusters, a focused ion beam (FEI Helios Nanolab 600 Focused Ion Beam/Scanning Electron Microscope) was used. FIB is a direct fabrication technique by removing atoms from certain areas on the sample (milling) or depositing atoms on the desired parts of the surface (FIB-induced deposition). In FIB, highly energetic beam of ions (5-50 keV) such as inert gases or Ga+ (liquid metal ion source), collides with sample surface atoms and a momentum transfer occurs during the collision. Therefore surface atoms are ejected from the surface and a pattern with a precision around 5nm is achieved. A 100 Figure 4.2: An illustration of steps in photolithography process, for preparing the conductive 4-probe electrodes schematic diagram of FIB is displayed in Figure 4.3. For FIB-induced deposition the organometallic precursor gases were injected on the target surface through a gas nozzle. High energy ion beam decomposes the adsorbed organometallic molecules and release the metal ions which are incorporated at the sample surface. Since FIB does not require any resist or mask, it is relatively simpler than other patterning techniques. For our electrical measurements of polymer nano-clusters, diluted polymer dis- persion was placed and dried on previously deposited gold electrodes. The nanofiber 101 Figure 4.3: The schematic of FIB and a liquid metal ion source [186]. clusters were identified by an electron microscope and then, the platinum micro- electrodes were deposited between the polymer nanofiber clusters and gold electrodes. A typical SEM image of the polyaniline nanofiber microcluster and the attached Pt electrodes is displayed in Figure 4.4. The thickness and width of the Pt wires are ∼ 500 nm and 1 micron. 102 Figure 4.4: The polyaniline nanofiber cluster and platinum microleads fabricated by FIB for connecting cluster to the electrodes 4.2.3 DC conductivity The dc electrical measurements were conducted in both 2-probe and 4-probe con- figurations using a Quantum Design Physical Property Measurement System (PPMS- 9) chamber. In the PPMS which is equipped with a liquid He cryostat, the temper- ature can be controlled from 2.5 K to 300 K and magnetic fields up to 9 T can be achieved. For the electrical measurements, Keithley 2400 SourceMeter and Keithley 617 electrometer were employed since PPMS automated measurement system can only be used at low current and voltage limit. The magneto-transport studies were carried out for a wide range of temperature (2.5 K - 300 K) up to 8 T magnetic field. Labview programs were used to control the PPMS chamber and to set the measurement parameters in Keithley instruments. For electrical measurements, different source current values were used for the polyaniline 103 nanofiber network samples. For the nanofiber micro-clusters the source current value did not exceed 100 nA in order to prevent the nanofibers from destroying. Figure 4.5: PPMS sample puck with polyaniline nanofiber network sample with 4- probe configuration In Figure 4.5 the PPMS puck, sample with 4-probe configuration and electrical connections from sample to puck are shown. The PPMS sample puck which provides thermal contact with the chamber and has 12 electrical leads was used for the trans- port measurements. For the electrical studies, the samples were attached to both the gold electrodes and PPMS puck leads by thin copper wires which were fixed by pressed indium. 4.2.4 DC magnetization: SQUID magnetometer DC magnetization studies of V-Cr Prussian blue was conducted by a Quantum De- sign SQUID magnetometer (MPMS). SQUID magnetometers are magnetic flux detec- tors based on superconducting coils and Josephson junction that is a non-conducting 104 barrier linking two superconductors and allows a change in the current due to extra magnetic flux from the sample. Figure 4.6: The configuration of the superconducting detection coils which is induc- tively connected to SQUID [187]. The superconducting detection coils which are wounded in the opposite directions in order to reduce the noise and uniform background, are shown in Figure4.6. During the measurement, the sample moves through the detection coils which induces an electric current. The change in the current in the detection coils is due to moving magnetic moment of the sample, proportional to the change in the magnetic flux. Figure 4.7 shows the configuration of a MPMS and SQUID response to a sample’s magnetic dipole moving through the coils. In order to get a good symmetric response 105 curve from the SQUID, the length of the sample should be short (< 1.5 cm) and centered longitudinally in the detection coils. Figure 4.7: The SQUID configuration and output signal when the sample (magnetic dipole) travels through the pick up coil assembly [73]. The MPMS-7 system that was used in our measurements, can operate up to 7 T and at temperatures from 1.7 to 400 K with a sensitivity of 10−8 emu. When the magnet is ramped to high magnetic fields (H > 1 T), remanent field (Hrem ∼ 10 Oe) which is trapped in the magnet, can lead to uncertainty in the results. The Hrem can be avoided if the high magnetic field is removed by setting the field to smaller positive and negative fields (e.i. H0, −H0/2,,H0/4, −,H0/8, ...). 106 4.2.5 AC susceptibility: PPMS susceptometer In dc magnetic measurements, a constant magnetic field is applied to the sample and the equilibrium value of magnetization in the sample is measured. On the other hand in ac magnetic measurements, an ac magnetic field was applied to the sample and its respond to magnetic field was measured [188]. By measuring the induced moment that is time-dependent, the magnetization dynamics of the sample can be determined. At low frequencies, the ac measurement is similar to dc measurements. Magnetic moment of the sample follows MAC = (dM/dH).HAC sin(wt) (4.1) where dM/dH (slope of M(H)) is the magnetic susceptibility, HAC is the applied field and w is the frequency. At higher frequencies the magnetization of the sample may lag behind the applied field therefore ac magnetization has two components: the in-phase susceptibility (χ0) and out-of-phase susceptibility (χ00). Ac susceptibility of the V-Cr Prussian blue samples were measured by Quantum Design AC Measurement System (ACMS) option for the PPMS. The ACMS insert which fits in the PPMS chamber, contains the drive and detection coils, thermometer and sample space that lies within the uniform magnetic field region of PPMS. The ac-drive coils of ACMS provides an alternating magnetic field up to 10 Oe for a frequency range of 10-10,000 Hz. The sample which is subject to a small ac magnetic field, moves up and down smoothly longitudinally. The flux variation by the presence of the sample, is detected by the sensing coils surrounded the sample. Due to the change in flux, voltage is induced (Faraday’s Law) which is directly proportional to 107 the magnetic susceptibility of the sample. v χ = α (4.2) V fH where χ is the volume susceptibility, v is the measured RMS voltage, V is sample volume, f is the frequency and α is the calibration coefficient. Figure 4.8 shows the general schematic of ac susceptometer which has a similar di- agram with our ACMS system. The induced voltage is picked up by a phase-sensitive lock-in amplifier. Therefore both the real (χ0) and imaginary (χ00) parts of the com- 0 00 plex ac susceptibility (χac = χ − iχ ) can be determined by the in-phase (Θ = 0) and out-of-phase (Θ = π/2) signal in the driving field. Moreover, nonlinear contribu- tions to ac susceptibility can be identified by detecting the signal at integer multiples of the driving frequency. Even terms in the nonlinear susceptibility expansion (χ2, χ4,...) are observed only if spontaneous magnetization exists in the system since magnetization has no inversion symmetry with respect to the applied field[190, 78]. The induced voltage is measured by two sets of identical but counterwound coils when the sample is positioned in the center of each coils. The oppositely wounded coils prevent the signal coming from the ac field itself or unwanted external sources. 4.2.6 Sample Illumination: Laser and fiber optics For photoinduced magnetism studies, V-Cr Prussian blue samples were illumi- nated by an argon ion laser (Coherent Innova 300) and a dye laser (Cr-599) which supplies light at wavelengths from 350 nm (UV) to 650 nm (red). The samples were illuminated through fiber optic cables, which were integrated to Quantum Design squid magnetometer fiber optics sample holder (FOSH) and home- made ac susceptometer sample holder. Integrated fiber optics allow illumination of 108 Figure 4.8: Block diagram of an ac susceptometer (Lake Shore 7225) [189]. 109 the samples inside the chamber of the measurement system. The power of the laser light was measured by Coherent laser power energy meter at the top of the sample holders. The polarization of the light was random in our measurements. 4.2.7 UV-Vis Spectrometer For photoinduced magnetism studies, it is important to know the UV-Vis spectra of the sample so that the light excitation can be done with the wavelengths that the samples absorbs. We studied the UV-Vis spectra of V-Cr Prussian Blue with Varian Cary 5000 spectrophotometer. Spectrophotometer is a device that can measure the light intensity at different wavelengths including visible light, near-ultraviolet and near-infrared. Varian Cary 5000 is a dispersive double beam spectrophotometer with a deuterium lamp (190-340 nm) and a tungsten lamp (300-2500 nm). The light source in double-beam Varian Cary 5000 is split into two equal intensity beams. One beam is used as reference and the other beam passes through the sam- ple. The intensities of these light beams are measured and compared by electronic detectors. The diagram of a typical spectrometer is shown in Figure 4.9. I and I0 are the intensities of reference and sample light beams and the output spectra can be presented as transmittance (T = I/I0) or absorbance (A = logI0/I) as a function of wavelength. 4.2.8 XPS In order to find elemental composition, empirical formula and electronic state of the elements in V-Cr Prussian blue, X-ray photoelectron spectroscopy (Kratos Axis Ultra XPS) was used. XPS is a powerful quantitative spectroscopic technique which 110 Figure 4.9: Schematic diagram of UV-Vis spectrometer [191] can detect all the elements with an atomic number (Z) of 3 (lithium) and above on the surface of the sample (1 to 10 nm) and requires ultra-high vacuum (UHV) conditions. Figure 4.10 displays the basic components of an XPS and how it works. Upon illumination with a beam of X-rays, the kinetic energy and number of electrons that are emitted from the material being analyzed are measured. By measuring the kinetic energy of electrons emitted from the sample (solids, gases or liquids), the binding en- ergies of electrons are determined which reveals the elemental composition, empirical 111 Figure 4.10: A schematic of XPS with its basic components. formula, chemical state and electronic state of the elements can be determined. Ebinding = Ephoton − Ekinetic − Φ (4.3) where Ebinding is the energy required for ionization and the emission of a core (inner shell) electron, Ephoton is the energy of the X-ray photons, Ekinetic is the kinetic energy of the emitted electron and Φ is the work function of the spectrometer. 112 CHAPTER 5 Optical Control of Magnetism in V-Cr Prussian Blue Optical control of magnetism has attracted significant attention due to possible applications such as magneto-optic memory devices. Several molecule-based systems that exhibit photoinduced magnetism, have been developed. However challenges still persists for optically tunable magnets since long-ranged magnetic order and sustained reversible illumination effects are required at high temperatures. In order to over- come these challenges and find more convenient chemical structures, we sought novel molecule-based magnets. Our research introduces reversible optical control of magne- tization in V-Cr Prussian blue. In this chapter, comprehensive experimental studies along with proposed mechanisms for optical control of magnetism in room tempera- ture magnet V-Cr Prussian blue and its ac and dc magnetic properties are presented. 5.1 Magnetic Properties The Vanadium-Chromium Prussian blue sample used in this study have a mag- netic ordering temperature around ∼ 350 K. The temperature dependence of zero field cooled (ZFC) and field cooled (FC) magnetization for both V-Cr Prussian blue powder sample and dispersed sample that is ground in nujol oil for better optical ex- citation, are displayed in Figure 5.1. A sharp increase in magnetization is observed at 113 T ∼ 350 K indicates that the system has magnetic ordering around that temperature. Similar temperature dependency has been previously reported for V-Cr Prussian blue analogs [3]. The high ordering temperature observed in this sample was explained by the presence of only antiferromagnetic interactions between the unpaired spins of Vanadium and Chromium. Similar to other Prussian blue analogs such as Co-Fe Prussian blue, the two transition ions, V and Cr, are under octahedral crystal field that splits the degenerate d levels into low energy t2g and higher energy eg levels. Figure 5.2 show the spin distribution of V and Cr in non-degenerate d orbitals. All the unpaired spins occupy the low energy t2g levels and due to the symmetry of these orbitals, the interaction among them is antiferromagnetic and no ferromagnetic in- teraction exists. The presence of only antiferromagnetic interactions leads to large exchange interaction (J = |JAF − JF |) therefore the ordering temperature increases (Tc ∼ z|J| where z is the number of nearest neighbors) [3, 93]. II III III The chemical formula of V-Cr Prussian blue, K1.54V0.77V0.08[Cr (CN)6](SO4)0.163.1 H2O, was determined by X-ray Photoelectron Spectroscopy (XPS). Figure 5.3 shows the survey spectrum of V-Cr Prussian blue that is mounted using an air-free sample holder. The chemical structure of V-Cr Prussian that is synthesized for this study do not have the conventional Prussian blue analog composition. In addition to missing Cr(CN)6 groups and interstitial H2O molecules, there are SO4 groups and sites with missing V ions. Figure 5.4 shows the temperature dependence of ZFC and FC magnetization at different applied magnetic fields for the powder and dispersed V-Cr Prussian blue samples. Below T ∼ 20 K, a strong irreversibility is observed between ZFC and FC magnetization in both powder and dispersed samples. The magnitude of deviation 114 (a) (b) Figure 5.1: Zero field cooled (ZFC) and field cooled (FC) dc magnetization of V-Cr Prussian Blue (a) powder and (b) dispersed sample that are sealed under vacuum in quartz tube. A sharp increase in magnetization is observed around 350 K. 115 Figure 5.2: The degenerate d levels of Vanadium and Chromium split into t2g and eg levels due octahedral crystal field and all the unpaired spins of V and Cr ions occupy the t2g level. and the temperature that the deviation starts (bifurcation temperature) depends on the applied magnetic field and they both decreases with increasing magnetic field. In addition to the low temperature ZFC-FC deviation, an additional irreversibility and a peak in ZFC-FC magnetization is observed in the dispersed sample at T ∼ 200 K. We propose that the environment (nujol oil) in which the magnetic particles dispersed (diameter < 20 µ), freezes and fixes the magnetic particles at random positions and orientations that leads to enhanced magnetic anisotropy. Thus an additional peak and a divergence in ZFC-FC magnetization occur in the dispersed sample. The optical microscope image of the dispersed sample at room temperature is displayed in Figure 5.5 The magnetic field dependence of dc magnetization for powder and dispersed samples are displayed in Figure 5.6. From the saturation magnetization of the powder 116 Figure 5.3: The XPS survey spectrum of V-Cr Prussian blue. 117 (a) (b) Figure 5.4: ZFC and FC magnetization at different applied magnetic fields for V- Cr Prussian blue (a) powder and (b) dispersed sample. Strong irreversibility exists between ZFC and FC magnetization at low temperatures in both powder and dis- persed sample. The bifurcation temperature depends on the applied magnetic field and decreases with increasing field. 118 Figure 5.5: Optical microscope image of dispersed sample in nujol oil. sample using Equation 5.1 the total spin value per mol is determined as 0.25. Ms = NgµbSt (5.1) We also calculated the total spin value by using the chemical formula and the proposed spin values of antiferromagnetically coupled Cr and V (CrIII (1 x 3/2) - VII (0.77 x 3/2) - VIII (0.08 x 1)). The calculated total spin value is found to be 0.27 which is in good agreement with our experimental result. We observed that the coercive field of the powder sample reduces with increasing temperature and reaches low values (Hc ∼ 2 Oe) around T ∼ 100 K. On the other hand, the coercive field of the dispersed sample decreases more slowly and reaches low values around ∼ 200 K. Figure 5.7 summarizes the change of coercive field with temperature for both the powder and dispersed samples. Larger coercive fields of the dispersed V-Cr Prussian blue sample also suggest increased magnetic anisotropy in 119 the systems that is proposed to result from fixing of the magnetic particles at random orientations and positions via freezing of the nujol oil. FC magnetization of dispersed V-Cr Prussian blue sample also exhibits strong ir- reversibility between the magnetization measurements during heating and cooling of the dispersed V-Cr Prussian blue sample. The magnetization that is measured while heating the sample has higher values than the magnetization measured while cooling the sample between 50 K and 200 K. During cooling of the sample at around 200 K due to the freezing of the Nujol oil in which V-Cr Prussian blue was ground, the mag- netic anisotropy is increased and it become harder for spins to respond the magnetic field. On the other hand at low temperatures (T = 10 K) due to small thermal excita- tions and spin-glass like behavior of V-Cr Prussian blue (will be discussed later), the spins can be aligned with the magnetic field. The system responds to magnetic field easily and exhibit higher magnetization. The irreversibility in magnetization during heating and cooling of the sample is attributed to increased magnetic anisotropy in the dispersed sample via freezing of the oil that changes the magnetic response to both static and dynamic magnetic field. Below 50 K, V-Cr Prussian blue enters a spin-glass like behavior and the spin dynamics of the system gets slower. Therefore cooling and heating cycles merge below 50 K. More detailed studies are needed to be done in order to better understand this magnetization phenomena. Figure 5.9 and 5.10 shows the temperature dependence of in-phase (χ0) and out- of-phase (χ00) ac susceptibilities of V-Cr Prussian blue powder and dispersed samples for frequencies 11 Hz ≤ f ≤ 10,000 Hz. A frequency dependent shoulder at around 20 K is observed for both powder and dispersed samples that coincides with bifurcation temperature of ZFC-FC dc magnetization. Moreover similar to dc magnetization, an 120 (a) (b) Figure 5.6: The magnetic field dependence of magnetization of (a) powder and (b) dispersed sample at different temperatures. 121 Figure 5.7: The coercive fields of powder and dispersed sample at different tempera- tures. addition peak exists at T ∼ 200 K in the dispersed V-Cr Prussian blue samples due to increased magnetic anisotropy. No frequency dependency of ac susceptibility is expected for a system with long- ranged magnetic ordering when the spin relaxation process is much faster than the experimental time scale (1/f). The in-phase (χ0) and out-of-phase (χ00) ac suscepti- bilities for frequencies 11 Hz ≤ f ≤ 10,000 Hz at low temperatures for dispersed V-Cr Prussian blue samples, are displayed in Figure 5.12. The frequency dependency of both susceptibility components and the peak indicates that the spin relaxation process slows down and becomes comparable with the experimental time scale. For a system with a single relaxation time constant τ, the frequency dependent ac susceptibility 122 Figure 5.8: The irreversibility of FC magnetization during heating and cooling cycles. can be given by χ − χ χ = χ + 0 s (5.2) S 1 + (iωτ) where χ0 and χs are the isothermal (ω = 0) and adiabatic (ω → ∞) susceptibilities respectively. From Equation 5.2, χ0 and χ00 can be obtained as 0 2 2 χ = χ0/(1 + ω τ ) (5.3) 00 2 2 χ = χ0ωτ/(1 + ω τ ) (5.4) The plot of χ0 against χ00 gives the Argand diagram (Cole-Cole plot) [193] from which the spin relaxation times can be determined. The Argand diagram gives a semicircular shape (Figure 5.11) for a system with a single relaxation time but deviates from the semicircle shape when the system is not characterized by a single relaxation 123 (a) (b) Figure 5.9: Temperature dependence of in-phase (a) and out-of-phase (b) ac suscep- tibilities at frequencies 11 Hz ≤ f ≤ 10,000 Hz for the powder V-Cr Prussian blue sample. 124 (a) (b) Figure 5.10: Temperature dependence of in-phase (a) and out-of-phase (b) ac suscep- tibilities at frequencies 11 Hz ≤ f ≤ 10,000 Hz for the dispersed sample. 125 Figure 5.11: Schematic Argand diagram (Cole-Cole plot) [192] time. The characteristic mean spin relaxation times (τc) were determined by using χ0 + χs χ = χS + 1−α (5.5) 1 + (iωτc) where α is the uncertainty width of relaxation time. Through obtaining χ0 and χ00 the τc at each temperature can be calculated from χ − χ cos(πα/2) χ00 = 0 s (5.6) 2 cosh[(1 − α)ln(ωτc)] + sin(πα/2) Figure 5.13 displays the temperature dependence of mean spin relaxation time for the dispersed sample in nujol oil. Below T ∼ 25 K, the relaxation time starts to increase showing that the spin dynamics of the system slows down. In addition to the increased spin relaxation time, frequency dependent ac susceptibility as well as the ZFC-FC dc magnetization irreversibility and magnetic field dependent bifurcation 126 (a) (b) Figure 5.12: In-phase (a) and out-of-phase (b) ac susceptibilities at frequencies 11 Hz ≤ f ≤ 10000 Hz at low temperatures. 127 temperature indicate that the system undergoes cooperative freezing of the spin and a spin-glass like state is reached at low temperatures. The V-Cr Prussian blue magnet that is ferrimagnetic below T < 350 K, forms spin clusters of domains which have local magnetic ordering but are interacting weakly with the neighboring clusters. When the system cools down below T < 25 K, the weakly interacting clusters start to freeze and the V-Cr Prussian blue enters a cluster-glass state. Figure 5.13: Temperature dependence of mean spin relaxation time for V-Cr Prussian blue. 5.2 Optical Control of Magnetic Properties The UV-Vis absorption spectrum of V-Cr Prussian blue is displayed in Fig- ure 5.14(a). For optical excitations of the dispersed V-Cr Prussian blue sample multi-line UV light (λ = 350nm) and single-line green light (λ = 514nm) were used. 128 Figure 5.14(b) shows the decrease in FC magnetization at T = 10 K and H = 10 Oe upon illumination with UV light with an intensity of ∼ 12mW/cm2 for 60 hours. The change in magnetization is around ∼ 2 % that is substantially smaller (∼ 10 fold) than that for other reported Prussian blue analogs such as Co-Fe Prussian blue. The V-Cr Prussian blue sample sustains the illumination effects after the light excitation stops for a long time (t > 106 s) which is similar to previously reported lifetimes of Co-Fe Prussian Blue [8]. The long lifetime of the photoinduced state indicates that upon illumination the system reaches a metastable state. The V-Cr Prussian blue recovers back from the photoinduced state partially when the sample is optically excited by green light (Figure 5.15). The reversible optical excitation effects on magnetism were previously reported for Co-Fe Prussian blue analogs [110]. The effect of green light is only observed when the V-Cr Prussian blue sample is previously excited by UV-light also indicating a hidden photoinduced metastable state. The V-Cr Prussian blue fully recovers back from the photoinduced state to initial ground state without any degradation by heating the sample above 250 K. The full recovery is attributed to strong thermal activation that relaxes the system back to ground state from the metastable state. The full recovery of temperature and field dependence of dc magnetization upon heating for the dispersed V-Cr Prussian blue sample is shown in Figure 5.16. In the field dependence of magnetization upon illumi- nation along with magnetization suppression, a decrease in saturation magnetization (Ms) is observed. The decrease in Ms indicates that the total number spins decrease in the system. In conventional Prussian blue analogs the photoinduced magnetization is explained by charge transfer between the transition ions that are under octahedral 129 (a) (b) Figure 5.14: (a) The UV-Vis spectrum of V-cr Prussian blue. (b) Decrease in FC magnetization upon excitation with UV light (intensity of light ∼ 12mW/cm2) for 60 hours. 130 Figure 5.15: Partial recovery of magnetization upon subsequent illumination with green light from a photo-excited state. The light intensity is kept around 12 mW/cm2 for both illuminations with UV and green light. crystal field. The spins of transition ions occupy the t2g and eg levels and charge transfer between them changes the total spin value. However this charge transfer model can not explain the photoinduced magnetic effects in V-Cr Prussian blue since the total spin value stays unchanged upon optical excitation in contradiction with our experimental results. Moreover the change in the dc magnetization (∼ 2 % after 60 hours ) upon illumination is much smaller than the change reported for Co-Fe Prussian blue analogs suggesting that the photoinduced effects are not occurring in the bulk sample but only occurring in restricted regions of the sample. We propose that due to the unique disorder in our V-Cr Prussian blue samples likely around the 131 (a) (b) Figure 5.16: Temperature (a) and field (b) dependence of dc magnetization be- fore illumination, after illumination for 60 hours with UV light (intensity of light ∼ 12mW/cm2 ) and after heating the sample up to 250 K. 132 missing V ions but incorporating SO4 molecules, the V and Cr ions are under unusual (non-octahedral) crystal field. Thus d orbitals of V and Cr do not simply split into t2g and eg levels but have two degenerate low-energy d levels and upon excitation the following reversible reaction is proposed to proceed. CrIII (S = 1/2),V II (S = 1/2) ↔ CrII (S = 0),V III (S = 1) (5.7) Total spin value (magnetization) decreases with this proposed reversible reaction since the spins of V and Cr are antiferromagnetically coupled and the magnetization is in the direction of the spins of the Cr. Figure 5.17 displays the temperature dependence of ac susceptibilities χ0 and χ00 for the ground and photoinduced states at 3330 Hz. Upon illumination with UV light for 60 hours both χ0 and χ00 substantially as much as 25 % and 40 % respectively and their peak temperatures shifts to lower values. Within the spin cluster glass model proposed for V-Cr Prussian blue, reduction in ac magnetization and shift of peak temperatures to lower values suggest that the number of unpaired spins decrease upon illumination. The decrease in spin value reduces the size of the spin clusters and slows down the spin dynamics. The temperature dependence of χ0 and χ00 exhibit a shoulder at T ∼ 200 K similar to the high temperature peak in dc magnetization for the dispersed V-Cr Prussian blue samples, can be explained by freezing of the oil that enhances the magnetic anisotropy of dispersed V-Cr Prussian blue samples. We also studied a second Prussian Blue sample with a different chemical formula (sample B). The temperature dependence of ZFC and FC magnetization at various applied magnetic fields and ac susceptibility are shown in Figure 5.18 and Figure 5.19 respectively. Both the divergence of ZFC and FC magnetization and frequency de- pendent shoulder of ac susceptibility occurs at around T ∼ 70 K that is higher than 133 (a) (b) Figure 5.17: In phase (a) and out of phase(b) ac susceptibilities for ground and photoinduced states (UV light excitation with light intensity ∼ 12mW/cm2 for 60 hours) of V-Cr Prussian blue at f = 3330 Hz. 134 Figure 5.18: Temperature dependence of ZFC and FC magnetization for V-Cr Prus- sian blue powder sample B. the temperature for the first V-Cr Prussian blue sample suggesting higher structural disorder in the sample. Similar illumination effects are observed in dispersed V-Cr Prussian blue sample B. Figure 5.20 displays the decrease in FC magnetization upon illumination with UV light with an intensity of ∼ 12 mW/cm2 and partial recovery from the photo- excited state by illuminating with green light with an intensity of ∼ 12 mW/cm2. In addition to the dispersed V-Cr Prussian blue sample with different structural disorder, photoinduced magnetism effects are observed in the powder V-Cr Prussian blue sample that was ground on a transparent sticky tape and mounted into the MPMS holder in the air. 135 (a) (b) Figure 5.19: In-phase (a) and out-of-phase (b) susceptibilities of V-Cr Prussian blue powder sample B. (inset) The out-of-phase susceptibility for the dispersed sample B in nujol oil. 136 (a) (b) Figure 5.20: (a) Decrease in FC magnetization upon illumination with UV light with an intensity ∼ 12 mW/cm2. (b) Partial recovery of magnetization upon subsequent illumination with green light from a photo-excited state. The light intensity is kept around 12 mW/cm2 for both illuminations with UV and green light. 137 5.3 Summary and Discussion Reversible optical control of magnetism in one of the few room temperature molecule-based magnets, V-Cr Prussian blue is reported. In V-Cr Prussian blue both dc and ac magnetization can be manipulated upon optical excitation with multi-line UV light (λ = 350 nm) that suppresses magnetization and single-line green light (λ = 514 nm) that partially recovers back to ground state from photoinduced state. V-Cr Prussian blue reaches a hidden metastable state upon illumination suggested by the long lifetime of the photoinduced state ( t > 106 s) and the recovery effect of green light that only occurs after illumination with UV light. Moreover the illumination effects are sustained up to 200 K in this room temperature molecule-based magnet and completely erased when the sample is heated above 250 K. The photoinduced phenomena in V-Cr Prussian blue is proposed to originate from decrease in the to- tal number of spins via charge transfer between V and Cr ions around the unique disordered regions that leads to two degenerate low-energy d levels. The disorder is likely around the missing V ions and incorporating additional SO4 molecules. The detailed studies of V-Cr Prussian in response to static and dynamic magnetic field reveals that V-Cr Prussian blue is ferrimagnetic even above room temperature and exhibits a spin-glass like reentrance behavior the temperature decreases (T < 25 K). 138 CHAPTER 6 Magneto-transport in Polyaniline Nanofiber Networks Recently there has been an increasing interest in devices based on nanofibers [22] and small-molecules [194, 195] such as nano-scaled transistors, memory devices and bio-sensors. In order to develop these novel applications, the transport properties of nanofibers and nanofiber networks are needed to be understood. However due to the complex structure and morphology of nanofibers, the electrical transport has not been fully understood. In this chapter the electrical charge transport properties of dense and dilute polyaniline (PANI) nanofiber networks and nanofiber micro-clusters are discussed. Moreover we report the effect of magnetic field, temperature, morphology and electric field on the transport properties. 6.1 Resistivity Polyaniline nanofibers used for this study are doped with camphorsulfonic acid (CSA) and synthesized via dilute chemical oxidative polymerization [40]. Detailed chemical synthesis of PANI nanofibers are given in chapter 4 of this dissertation. Figure 6.1(a) displays the scanning electron microscopy (SEM) image of dense PANI nanofiber (have an average diameter of 80 nm) networks. The electrical transport 139 measurements were done using 4-probe measurements with photolithographically pat- terned gold electrodes on a glass substrate that have a separation of 30-100µ. Figure 6.1(b) shows the temperature dependence of electrical conductivity in dense PANI nanofiber networks. The room temperature conductivity is ∼ 0.3 S/cm. As the temperature is decreased from room temperature an increase in the conductivity is observed up to ∼ 240 K. At this temperature a sharp peak in the conductivity is observed and below 240 K the conductivity decreases with decreasing temperature. Similar conductivity behavior (peak in the temperature-conductivity curve) observed in the conventional films of highly conducting polyaniline that goes through metal to insulator (MI) transition [196, 197, 23, 136]. However the room temperature conduc- tivity in these conventional polymer films that exhibit the MI transition is greater than Mott’s minimum metallic conductivity (σMOTT ∼ 100 S/cm). In our PANI nanofiber samples the conductivity is much smaller than Mott’s minimum conductiv- ity (0.3 S/cm 100 S/cm), suggesting that the observed peak in the conductivity is not due to MI transition. Detailed studies on the anomalous behavior of PANI nanofibers are reported by Timi et al. using EPR and FTIR [163]. It is reported that the conductivity peak is not due to conventional metal-insulator transition but can be explained by the fragile nature of conductance at the interface of the nanofiber crossings [24]. The charge transport in PANI nanofiber networks is affected by the transport through the nanofibers and the transport at the interfiber crossings. The fit of temperature dependence of conductivity for PANI nanofiber dense net- works to quasi-1D variable range hopping (VRH) is given in the inset of Figure 6.1(b). 140 (a) (b) Figure 6.1: (a) SEM image of dense polyaniline nanofiber network. (b) Temperature dependence of conductivity and (inset) fitting of resistivity to 1D VRH model. 141 The quasi-1D VRH is described by: T ρ(T ) = ρ ( 0 )1/2 (6.1) 0 T where T0 is the characteristic temperature that shows the effective energy barrier between the localized states. T0 is determined by the disorder and how much the system is in the insulating side. From Equation 6.1 T0 is calculated as ∼ 2850 K which is in the range (∼ 103 − 105 K) of previously reported systems such as doped PANI [153] and poly(o-toluidine) (POT) [154]. Figure 6.2 shows the SEM image of dilute PANI nanofiber networks and the temperature dependence of conductance that is measured on gold electrodes with 4-probe measurement configuration. The conductivity in dilute nanofiber networks could not be determined since the width of the sample in which the charge transport occurs varies a lot. It is noted that the peak in the conductance at T ∼ 240 K decreases substantially in dilute nanofiber that has fewer interfiber crossings. Thus we proposed that the number of interfiber contacts affects the charge transport in PANI nanofiber networks. The conductivity peak at 240 K is due to interfiber crossings and reduces with decreasing number of interfiber contacts. In addition to dense and dilute PANI nanofiber networks, we also studied the transport properties of PANI nanofiber micro-clusters. Figure 6.3(a) displays the SEM image of PANI micro-clusters and the Pt electrodes that are deposited on top the fibers using Focused Ion Microscopy (FIB). The electrical transport measurements in PANI micro-clusters were done using 2-probe configuration at low applied currents (I < 100 nA) in order to avoid destruction of the nanofiber micro-clusters. The temperature dependence of electrical conductivity of the PANI nanofiber micro-clusters is given in Figure 6.3(b).The room temperature conductivity is ∼ 3.8 142 (a) (b) Figure 6.2: (a) SEM image of dilute polyaniline nanofiber network and (b)the tem- perature dependence of conductance. 143 (a) (b) Figure 6.3: (a) SEM image of polyaniline nanofiber micro-cluster. (b) Temperature dependence of conductivity and (inset) fitting of resistivity to 1D VRH model. 144 S/cm that is more than an order of magnitude greater than the conductivity of dense polyaniline nanofiber networks (σ ∼ 0.3 S/cm). The high room temperature conduc- tivity in nanofiber micro-clusters also indicates that the interfiber contacts play an important role in determining the transport properties. We propose that nanofiber crossings have large resistances and when charge transport is through nanofiber con- tacts the total resistance of the system increases. From the fit of lnρ - T −1/2, it is determined that the transport in PAN nanofiber cluster also follows quasi-1D VRH. The characteristic temperature T0 which indi- cates how insulating the sample is, determined as ∼ 45 K from Equation 6.1. The much smaller value of T0 compared to that for dense nanofiber networks indicates that the transport in nanofiber micro-clusters is less resistive. Moreover the peak at T ∼ 240 K in the temperature dependent conductivity totally vanishes in PANI nanofiber clusters suggesting that the peak originates from the nanofiber-nanofiber contacts. It is also noted that σ(300K)/σ(25K) ratio that shows the temperature dependence of conductivity is much weaker (∼ 103) in nanofiber micro-clusters than the dense nanofiber networks. We propose that as the interfiber contact increase, the conductivity decreases and the system moves more into the insulating regime. Timi et al. proposed a model based on the pellets and films of PANI nanofiber networks which is also supported by our experimental studies on the dense networks and micro-clusters of PANI [24]. In this model, the charge transport is determined by two competing mechanisms. These mechanisms are phonon-assisted charge con- duction in the nanofiber networks and the nature of conduction at the interface of nanofiber crossing. For temperatures below 240 K, the phonon-activated transport dominates, the system follows quasi-1D VRH and the conductivity decreases with 145 decreasing temperature. Within this temperature range the fragile nature of the in- terfiber contacts remains same and does not alter the conductivity behavior of the polyaniline nanofiber networks. On the other hand at higher temperatures (T > 240 K), the nature of the interfiber contacts changes and dominates the transport behav- ior. As the temperature decreases from room temperature, the nanofiber contactsare enhanced and become tighter and rigid. Thus the resistance of the system decreases with better interfiber contacts. Since the contribution from the change in interfiber contact nature dominates, the resistance decreases down to 240 K. 6.2 Magneto-transport We have also studied the charge transport of PANI nanofiber networks and micro- clusters under magnetic field for low and high electric fields in a large temperature range (from 2.5 K to 250 K). Comprehensive experimental studies and proposed mechanism explaining the magneto-transport properties of PANI nanofiber networks are discussed in this section. 6.2.1 Temperature Dependence At low temperatures the resistance of the polyaniline nanofiber networks increases when a magnetic field is applied to the system. Figure 6.4 shows the change in re- sistance with applied magnetic field at different temperatures (T < 15 K) in PANI nanofiber networks. Large positive magnetoresistance (MR) up to 55 % at H = 8 T in dense nanofiber networks is observed and attributed to the shrinkage of the localized electron wavefunction due to Lorentz effect. Due the shrinkage of the wavefunction, the hopping probability from one localized site another decreases and within the vari- able range hopping mechanism, an increase in the resistance of the PANI nanofibers 146 is observed. For quasi-1D VRH, the magnetoresistance is expressed by Efros and Shklovskii [156] and given by: ρ(H) L T ln[ ] = 0.0015( c )4( 0 )3/2 ∼ H2 (6.2) ρ0 LH T 1/2 where Lc is the localization length, LH is the magnetic length ((c~/eH) ) and T0 is the characteristic temperature determined from Equation 6.1 in quasi-1D VRH. Sim- ilar positive MR is also reported for other systems including CdSe [198] and polymer nanotubes [33] in which the MR was also attributed to shrinkage of wavefunction. The effect of magnetic field that shrinks the electron wavefunction, is valid when LH is larger Lc. Thus even at H = 8 T, since LH = 9nm is larger than Lc = 3 nm, no saturation of magnetization is expected and observed in our measurements. We also noted the magnitude of MR decreases with increasing temperature (MR = 55 % at 2.5 K and MR = 20 % at 5 K). The decrease in MR with increasing temperature is explained by thermal activations (phonon). At higher temperatures, the hopping probability gets larger (hopping length get shortened), thus the effect of shrinkage of wavefunction due to magnetic field decreases. For intermediate temperature regime, the effect of magnetic field on resistance changes its direction. Upon applying a magnetic field, the resistance of PANI nanofiber networks decreases for temperatures ∼ 87 K to 250 K. The negative MR behavior in dense nanofiber networks at different temperatures is shown in Figure 6.5. The nega- tive MR is attributed to destruction of quantum interference of electron wavefunctions along possible current paths. In quasi-1D VRH there can be more than one current paths along which the hopping process occurs. These wavefunctions through different paths interfere constructive in the absence of magnetic field and increases the resistiv- ity. However when a magnetic field is applied, the quantum interference of different 147 Figure 6.4: Positive magnetoresistance (MR) at low temperatures up to 8T. electron wavefunctions between two localized states is destroyed due to change in their phase factors and the conductivity is enhanced (Nguyen-Spivak-Shklvskii mech- anism) [174]. The negative MR has a linear dependence on the applied magnetic field and can be expressed by: ρ(H) 2πΦ ln[ ] = ln[1 + |sin( )|] ∼ |H| (6.3) ρ0 φ0 where Φ is the flux between different current paths in magnetic field and Φ0 is the quantum flux unit (hc/e). Similar negative MR behavior has been reported for InO [199] and n-type GaAs [200] and CdSe [201] systems. In dense polyaniline nanofiber networks a crossover from positive to negative MR is observed at T ∼ 87.5 K. Figure 6.6 shows the MR at around the crossover region. We 148 Figure 6.5: Negative MR at intermediate temperature regime up to 8T. propose that the two MR mechanisms that leads to positive and negative MR coexist and compete with each other. At low temperatures (below 87 K) the shrinkage effect dominates and positive MR is observed. With increasing temperature due to decrease in hopping length the effect of shrinkage reduces. Above the crossover temperature the suppresion of quantum interference of different electron wavefunctions in the hopping process become effective and negative MR is observed. Therefore at a given temperature and applied magnetic field, the MR behavior mechanism is determined by the dominant MR mechanism. Figure 6.7 displays the both positive and negative MR in the whole temperature range and summarizes the mechanisms that corresponds to the observed MR effects. 149 Figure 6.6: Temperature and magnetic field dependence of MR around the crossover region. Within the limits of our measurements we did not observe any MR above 250 K. Below 2.5 K MR measurements were not accurate since the temperature could not be stabilized when the magnetic field was swept from -8 T to 8 T. 6.2.2 Morphology Dependence In addition to dense polyaniline nanofiber networks, we studied the MR in nanofiber micro-clusters. The magnetoresistance exhibits similar behavior (positive MR at low temperatures and negative MR at high temperatures) suggesting that both shrinkage effect and destruction of quantum interference due to magnetic field are also effective in a system with fewer interfiber contacts. However differences (magnitude of MR 150 Figure 6.7: MR of nanofiber network in the whole temperature regime showing both the positive and negative MR and corresponding mechanisms. and crossover temperature) are also observed in the magneto-transport behavior. Fig- ure 6.8 displays the positive MR for both the dense nanofiber networks and nanofiber micro-clusters. The magnitude of MR decreases substantially (from 55 % to 5 % at 2.5 K) in the nanofiber micro-clusters that have fewer interfiber contacts. Thus the interfiber crossings affect not only the temperature dependence of dc charge trans- port (peak around 240 K) but also the magnetic field dependency. With decreasing interfiber contact the conductivity of the system increases and the transport mainly includes hopping through a nanofiber that is easier than the transport through the in- terface of nanofiber crossings. Therefore the effect of localized wavefunction shrinkage decreases and magnitude of positive MR reduces. A decrease in the negative MR (from 0.2 % to 0.08 %) is also observed in nanofiber micro-clusters (see Figure 6.9). The decrease in the MR is also attributed to decreased resistance and enhanced conductance with fewer interfiber contacts which diminishes the effect of magnetic field. Between 50 K to 100 K no significant MR is observed 151 (a) (b) Figure 6.8: MR of polyaniline nanofiber (a) network and (b) micro-cluster at low temperatures up to 8T. 152 in the nanofiber micro-clusters, proposed to due to low magnitude of MR that could not be detected with our measurement system. 6.2.3 Electric Field Dependence In addition to the morphology dependence, the magnitude of positive MR in dense polyaniline nanofiber networks also depends on the applied electric field. Fig- ure 6.10(a) shows the magnitude of MR in dense network samples at T = 50 K for different source current values in 4-probe measurements. The IV curve of the same system at T = 50 K and zero applied magnetic field, is displayed in Figure 6.10(b). The numbers in Figure 6.10(b) (a) and (b) (1-6) represent a current value in the IV curve and the corresponding MR at that applied current. The IV curve exhibits strong non-linearity which we propose to originate from reduction in the hopping activation energy and hopping length. Thus as the applied current increases the conductivity of the polyaniline nanofiber network enhances. The effect of the applied electric field (current) on magnetoresistance can be also explained with the same model. when high electric field is applied, the hopping length is reduced and the shrinkage of electron wavefunction by magnetic field becomes less effective and MR decreases. The positive MR is only sensitive to the applied electric field in the non-linear regime of the IV curve also indicating the correlation between the conductivity and magnetoresistance. We have also studied the electric field dependency of MR with in smaller steps of applied current both in the negative and positive range. Symmetric current depen- dency is observed around the zero applied current and almost independent current dependency on MR in the linear part of IV curve in the dense polyaniline nanofiber networks (see Figure 6.11). 153 (a) (b) Figure 6.9: MR of polyaniline nanofiber (a) network and (b) micro-cluster at inter- mediate temperatures up to 8T. 154 (a) (b) Figure 6.10: (a) MR of polyaniline nanofiber network at different applied currents at T = 50 K. (b) IV behavior of nanofiber network and (inset) applied current dependency of MR at constant temperature. 155 Figure 6.11: Applied current dependency of MR at T = 50 K of polyaniline nanofiber micro-clusters. (inset) IV behavior at the same temperature. The IV curve of polyaniline nanofiber micro-clusters exhibits substantially smaller nonlinearity even at low temperatures (T = 2.5 K) compared to nanofiber networks samples. The lack of nonlinearity in the micro-cluster samples indicates that interfiber contacts are also important for determining the IV behavior. Thus we propose that the nanofiber crossings have large resistance and with the application of high electric field, the resistance of nanofiber contacts decreases and a nonlinear IV is observed. 6.3 Summary and Discussion Our study discussed here provides a deep understanding of the transport prop- erties for polyaniline nanofiber networks. We propose that interfiber contacts plays 156 Figure 6.12: IV behavior of polyaniline nanofiber micro-clusters at different temper- atures. an important role in determining the transport properties of polyaniline nanofiber networks. The dense nanofiber network that has large number of interfiber contacts have larger resistance and stronger temperature dependent conductivity compared to the nanofiber micro-clusters. Moreover the peak at T ∼ 240 K diminishes in the temperature dependence of conductivity that follows quasi-1D VRH, as the number of interfiber contacts decreases. Moreover detailed experimental studies indicate that the magneto-transport be- havior in polyaniline nanofiber networks that depends on the temperature, magnetic 157 and electric field and nanofiber network morphology. Two competing MR mecha- nisms that are dominant at different temperature and magnetic field ranges leads to positive MR at low temperatures and negative MR in the intermediate temper- ature range. The positive MR is attributed to the shrinkage of wavefunction with the applied magnetic field that reduces the hopping probability. In the positive MR regime, the magneto-transport is affected by the applied electric field in the nonlinear region of the IV curve. We propose that the dependency of electric field is due to reduction of the hopping potential barriers and hopping length that decreases the effect of magnetic field. The negative MR observed in the intermediate tempera- tures (90K < T < 250K) is explained by the destruction of quantum interference among different wavefunctions through possible current paths between the two lo- calized states by the applied magnetic field. The MR of the polyaniline nanofiber networks also depends on the morphology of the nanofiber networks. Both in the polyaniline nanofiber networks and nanofiber micro-clusters positive MR at low tem- peratures and negative MR at higher temperatures are observed. However the mag- nitude of MR is substantially smaller in the micro-clusters that have fewer interfiber contacts. We propose that with fewer interfiber crossings the conductivity is enhanced and the effect of magnetic field on the resistance decreases. 158 CHAPTER 7 Discussions and Future Work 7.1 Optical Control of Magnetism Comprehensive experimental studies of magnetic properties and reversible optical control of magnetism in V-Cr Prussian blue are presented. V-Cr Prussian blue is one of the few room temperature molecule-based magnets with a magnetic ordering tem- perature of ∼ 350 K. As the temperature decreases below 25 K, a strong irreversibility and temperature dependent bifurcation temperature are observed. Moreover both the in-phase and out-of-phase ac susceptibilities exhibit frequency dependent shoulder at around same temperature (T ∼ 25 K) indicating that the spin dynamics of the system slows down. We suggest V-Cr Prussian blue re-enters a spin-glass like state involving individual spins and clusters of spins below 25 K. In the dispersed V-Cr Prussian blue samples that were ground in Nujol oil, an additional peak is observed at T ∼ 200 K in its magnetic respond to static and dynamic magnetic fields. We propose that the high temperature peak in magnetization curve is due to increased magnetic anisotropy in V-Cr Prussian blue. Freezing of the oil in which V-Cr Prussian blue was ground and dispersed, fixes magnetic particles at random positions and orientations and leads to enhanced magnetic anisotropy. 159 Optical control of magnetism was studied in the V-Cr Prussian blue samples dis- persed in Nujol oil for better optical excitation. Upon illumination with UV light (350 nm) the system reaches a metastable photoinduced state in which both dc mag- netization and ac susceptibility decrease. Upon subsequent illumination with green light (514 nm), the system partially recovers back to the ground state and the mag- netization increases. Total recovery from the photoinduced state occurs when the sample is heated above 250 K. Due to thermal activations, the system relaxes back to the ground state without any degradation. The effects of optical illumination are maintained for a long time ( > 106 s) at low temperatures (T = 10 K) and disappears around T = 200 K. We propose that the light-induced magnetism phenomenon in V-Cr Prussian blue is due to change in total number of spins via charge transfer be- tween V and Cr ions. In the ordered regions of V-Cr Prussian blue V and Cr ions are under octahedral crystal field splitting however with in the charge-transfer model the number of spins remains constant in contradiction with our experiments. Moreover the magnitude of photoinduced change is much smaller than that for previously re- ported Prussian blue systems such as Co-Fe Prussin blue. Therefore we suggest that photoinduced charge transfer only occurs in restricted regions of V-Cr Prussian blue that is likely around the missing V ions but incorporating SO4 molecules. 7.2 Magneto-transport for Polyaniline Nanofiber Networks Extensive studies of charge transport in polyaniline nanofiber networks and its de- pendency on magnetic field, temperature, morphology and electric field are reported. The charge transport in polyaniline nanofiber networks follow quasi-1D variable range 160 hopping with an anomalous peak at ∼ 240 K that diminishes with decreasing num- ber of interfiber contacts. The peak in the temperature dependence of conductivity is attributed to two competing transport mechanisms: the phonon-assisted hopping within the nanofiber system and the nature of transport at the interface of inter- fiber crossings. As the temperature is lowered from room-temperature to 240 K, the interfiber contacts looses their rigidity and the large resistance resulting from the interfiber crossing decreases. Thus the conductivity of the system increases. On the other hand, below 240 K the nature of the interfiber contacts do not alter more and thus the phonon-activated hopping process dominates the transport behavior and conductivity decreases with decreasing temperature. It is also noted that the room-temperature conductivity enhances and temperature dependence of conductiv- ity decreases in the nanofiber micro-cluster samples where there are fewer interfiber crossings. Therefore we propose that the interfiber contacts play an important role in determining the charge transport in polyaniline nanofiber networks and act as additional high resistance whose nature is fragile and changes with temperature. Magneto-transport for polyaniline nanofiber networks were studied at low and high magnetic and electric for temperature 2.5 K - 250 K. Both positive and negative MR are observed due to two competing mechanisms that are dominant at different temperature and magnetic field regimes. At low temperatures (< 87 K) positive MR that is attributed to shrinkage of localized electron wavefunction, is observed in polyaniline nanofiber networks. At around 87 K, a crossover from positive to negative MR is observed. Above the crossover temperature negative MR that is attributed to destruction of quantum interference of different wavefunction during hopping from one site another, is observed. Similar MR behavior is also studied in the nanofiber 161 micro-clusters in which there are fewer interfiber contacts. However the magnitude of both positive and negative MR are smaller than that of dense nanofiber networks. We propose that with fewer interfiber contacts the resistance of the system and hopping length are decreased. Thus the effect of magnetic field (MR) is reduced. Moreover we observed that the magnitude of positive MR depends on applied electric field. With increasing applied current in the nonlinear regime of the IV curve, the MR decreases while the temperature is kept constant. We propose that the change is in the MR is due to reduction of the hopping potential barriers and hopping length by the applied electric field that decreases the effect of magnetic field. 7.3 Future Work The reversible optical control of magnetism in room-temperature molecule-based magnet V-Cr Prussian is demonstrated below 200 K. However, in order to achieve a practical magneto-optic memory device, the photoinduced effects should be main- tained at room temperature. In V-Cr Prussian blue, the photoinduced magnetism is proposed to originate from the charge transfer around the unique disordered regions likely around missing V ions and additional SO4 molecules. Therefore photoinduced effects at room temperatures might be achieved in the variations of V-Cr Prussian blue samples that have different structural disorder. Moreover the change in dc mag- netization is around ∼ 2 % upon illumination for a long time (60 hours). Faster optical excitation responses is also necessary for practical applications and can be obtained by controlling the disorder in our samples. Thus as a future study, new V-Cr Prussian blue samples with various structural disorder and composition should be synthesized and studied for their photoinduced magnetism. Furthermore, novel 162 forms V-Cr Prussian blue such as films and nanoparticles and other molecule-based magnets should be investigated for reversible optical control of magnetism. In this dissertation, the nature of electrical transport and the effect of interfiber contacts on the charge transport of polyaniline nanofiber networks are exhibited. As a future study, electrical conductance in a single nanofiber can be investigated so that the transport through a single fiber can be also determined. However in order to study a single fiber, first longer nanofibers are needed to be synthesized thereby nanofibers can be placed separately on the substrate and electrodes can be deposited on top of the single fibers using FIB. For future study, transport properties of other conducting polymer nanofibers and other forms should be studied and compared in order to better understand the overall charge transport and the effect of nano-scale confinement. 163 BIBLIOGRAPHY [1] N. Sariciftci, L. Smilowitz, A. Heeger, and F. Wudl, “Photoinduced electron transfer from conducting polymers onto buckminsterfullerene,” Science 258 (1992) 1474. [2] R. J. Tseng, J. Huang, J. Ouyang, R. 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