Spin and Charge Ordering in Organic Conductors Investigated by Electron Spin Resonance Takahisa D

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2008 Spin and Charge Ordering in Organic Conductors Investigated by Electron Spin Resonance Takahisa D. Tokumoto

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FLORIDA STATE UNIVERSITY

COLLEGE OF ARTS AND SCIENCES

SPIN AND CHARGE ORDERING IN ORGANIC CONDUCTORS

INVESTIGATED BY ELECTRON SPIN RESONANCE

TAKAHISA D. TOKUMOTO

A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy

Degree Awarded: Summer Semester, 2008

The members of the Committee approve the Dissertation of Takahisa D. Tokumoto defended on June 30, 2008.

James S. Brooks Professor Directing Dissertation

Johan van Tol Professor Co-Directing Dissertation

Naresh S. Dalal Outside Committee Member

Irinel Chiorescu Committee Member

Mark A. Riley Committee Member

Pedro U. Schlottmann Committee Member

ACKNOWLEDGEMENTS

I would like to express my gratitude to both of supervisors, Dr. James S. Brooks and Dr. Johan van Tol, for their supports and encouragements. I have really enjoyed and learned a lot from their way of conducting research, passions for science, willingness for teaching, patience for arguments. I would also like to appreciate the every member of the Brooks group, BT&T, especially, Dr. Eun Sang Choi, Dr. Hengbo Cui, Dr. David Graf, Dr. Yugo Oshima, and Dr. Jin Gyu Park for encouragements and guidances, and the every member of the EMR group. I am grateful to the committee members, Dr. Irinel Chiorescu, Dr. Naresh Dalal, Dr. Mark Riley, and Dr. Pedro Schlottmann, who have willingly spared their time to give suggestions and corrections. I am also indebted to Dr. Shinya Uji, Dr. Stuart Brown, Dr. Tadashi Kawamoto, Dr. Hitoshi Ohata, and Dr. Motoi Kimata for helpful discussions. In this dissertation, I have worked on three organic systems. Without these high quality samples and insightful discussions, this dissertation could not be ﬁnished. I would like to thank Drs. Akiko and Hayao Kobayashi and the rest of their groups and also Dr. Hisashi

Tanaka for λ-(BETS)2FexGa1−x mixed crystals. I would like to thank Dr. Junichi Yamada 3+ 3+ and the rest of his group for β-(BDA-TTP)2MCl4(M = Fe , Ga ). I would like to thank

Dr. Papavassiliou and the rest of his group for τ-(P-(S,S)-DMEDT)2(AuBr2)1+y. I wish to thank Florida State University and National High Magnetic Field Laboratory for giving me the best opportunity to learn physics as a graduate student. I would like to extend my sincerest thanks to my parents, Madoka and Michiko, my brother and sister, Masanori and Yuki, my grandmother Tomiko and my late grandfather Shouji for their unconditional love.

iii TABLE OF CONTENTS

List of Figures ...... vi

Abstract ...... ix

1. Introduction to Organic Conductors ...... 1

2. Electron Spin Resonance ...... 6 2.1 Spin Hamiltonian: Quantum description ...... 6 2.2 Bloch equation and resonance phenomena: classical description...... 9 2.3 c.w. ESR ...... 11 2.4 Pulsed ESR ...... 13 2.5 A basic theory of AFMR ...... 15

3. Experimental ...... 23 3.1 Experimental realizations ...... 23 3.2 Detection methods ...... 23 3.3 Multi Vector Network Analyzer ...... 25 3.4 Quasi-optical spectrometers ...... 25 3.5 BWO spectrometer ...... 27 3.6 Far Infrared Laser spectrometer up to 1.2 THz...... 29

4. π d CORRELATED SPIN SYSTEMS ...... 32 4.1− Introduction to π d interaction ...... 32 4.2 Estimation of exchange− interaction, J ...... 33 4.3 λ-(BETS)2FexGa1−xCl4 ...... 34 3+ 3+ 4.4 β-(BDA-TTP)2MCl4(M=Fe , Ga ) ...... 45

5. ITINERANT SPIN SYSTEM ...... 60 5.1 Introduction to a τ phase organic conductor...... 60 5.2 Crystal structure of τ-(P-(S,S)-DMEDT-TTF)2(AuBr2)1(AuBr2)y .... 63 5.3 Physical properties of τ-P...... 64 5.4 Motivation of this work ...... 66 5.5 Results and discussions ...... 67 5.6 Summary and what’s next? ...... 73

6. CONCLUSION ...... 74

iv REFERENCES ...... 76

BIOGRAPHICAL SKETCH ...... 82

v LIST OF FIGURES

1.1 Chemical formula of TMTSF molecule...... 1

1.2 Crystal structure of TMTSF2PF6...... 2 1.3 A variety of phases of donor stacking...... 3

2.1 A schematic diagram of energy levels and resonance conditions...... 10

2.2 Lineshapes. (a)Black line: Absorption (Lorentzian), Gray line: Dispersion. (b)Inhomogeneous broadening (Gaussian) (c) Derivative of Dysonian lineshape for a metallic material...... 13

∗ 2.3 A schematic diagram of T2 and T2 measurements...... 14

2.4 A schematic diagram of T1 measurement...... 15 2.5 A schematic diagram of antiferromagnetic order and its susceptibility picture. 18

2.6 Antiferromagnetic resonance modes with the ﬁeld along the easy axis. .... 20

2.7 The frequency dependence of antiferromagnetic resonance...... 21

3.1 A schematic diagram of detection methods...... 24

3.2 A schematic diagram of induction mode detection...... 26

3.3 A schematic diagram of quasi-optical setup...... 27

3.4 Sample holder conﬁgurations...... 28

3.5 BWO information...... 29

3.6 A transmission type rotational sample holder...... 30

3.7 A schematic diagram of a far infrared laser...... 31

4.1 Chemical formula of BETS molecule...... 34

4.2 Crystal structure of λ-(BETS)2FeCl4...... 35

vi 4.3 Calculated band structure and Fermi surface of λ-(BETS)2FeCl4...... 36

4.4 Global phase diagram (no magnetic ﬁeld) of λ-(BETS)2FexGa1−xCl4. .... 38

4.5 Global magnetic phase diagram of λ-(BETS)2FexGa1−xCl4 for magnetic ﬁelds parallel to the c axis...... 39

4.6 The schematic diagram of Jaccarino-Peter eﬀect through the exchange interaction...... 40

4.7 AFMR of λ-(BETS)2FexGa1−xCl4 at x =0.5...... 41

4.8 Temperature dependence of a resistance ratio of λ-(BETS)2FexGa1−xCl4 at x =0.4 at B = 0...... 42

4.9 Simultaneous ESR and magneto-transport measurement of λ-(BETS)2Fe0.5Ga0.5Cl4. 43 4.10 Temperature dependence of the ESR transmission signal...... 44

4.11 Chemical formula of the conventional ET and novel BDA-TTP molecules. .. 45

4.12 Crystal structure of β-(BDA-TTP)2FeCl4...... 46

3+ 4.13 Temperature-Pressure phase diagram of β-(BDA-TTP)2MCl4 (M = Fe , Ga3+)...... 47

4.14 Angle dependent ESR signals of β-(BDA-TTP)2GaCl4 at room temperature in b c plane...... 49 −

4.15 Complete angular dependence of the g value of β-(BDA-TTP)2GaCl4. .... 50

4.16 Temperature dependence of magnetic properties of β-(BDA-TTP)2GaCl4. .. 51

4.17 Temperature dependence of echo detected ESR of β-(BDA-TTP)2GaCl4 impurities...... 52

4.18 T1, T2 measurements of β-(BDA-TTP)2GaCl4...... 53

4.19 Complete angular dependence of the g value of β-(BDA-TTP)2FeCl4 at room temperature with 240 GHz...... 54

4.20 Temperature dependent a c plane lineshapes of β-(BDA-TTP) FeCl at 9.3 − 2 4 GHz...... 55

4.21 Temperature dependence of magnetic properties of β-(BDA-TTP)2FeCl4. .. 56 4.22 Temperature dependent Raman signals...... 57

vii 4.23 Frequency dependence of β-(BDA-TTP)2FeCl4 at 1.5 K along the a, b, and c axes...... 58

5.1 The chemical structure of (S,S)-DMBEDT-TTF...... 60

5.2 The chemical structure of P-(S,S)-DMEDT-TTF...... 61

5.3 A conducting layer of a τ phase organic conductor...... 61

5.4 Calculated Fermi surface, a band structure, and a τ phase donor structure with its transfer integrals in the conducting plane...... 62

5.5 A crystal structure of a τ-P...... 63

5.6 Temperature/magnetic ﬁeld dependent resistivity of τ-P...... 64

5.7 Schematic high ﬁeld phase diagram and cantilever torque magnetization signal of the τ-P...... 66

5.8 Temperature dependent spectra of τ-P at intermediate frequencies with the ﬁeld along the c axis...... 68

5.9 Temperature dependent resonance ﬁeld of τ-P with the ﬁeld along the c axis. 69

5.10 Temperature dependent (a) 240 GHz spectra and (b) resonance ﬁeld of τ-P with the ﬁeld along the a axis...... 70

5.11 Field direction dependent resonance ﬁeld of τ-P at 240 GHz at 5 K...... 71

5.12 Ultra high ﬁeld cw ESR spectra of τ-P. (a) Frequency dependence. (b) Temperature dependence...... 72

5.13 Deviation for the resonance ﬁeld from g=2, paramagnetic, resonance ﬁeld τ-P. 72

viii ABSTRACT

This dissertation presents systematic studies on ordered states of organic conductors investigated mainly by Electron Spin Resonance (ESR). First, we describe an introduction to organic conductors. Organic conductors are based on conducting layers of highly planar donor molecules, separated by insulating layers of acceptors. The donor arrangements in the conducting layers determine the three simple parameters, transfer integral t between the donor molecules, onsite Coulomb interaction U and next neighboring Coulomb interaction V . Depending on the values of the above three parameters, a variety of ground states is realized and hence the organic conductors has become a main stream of condensed matter physics. Among many ground states, the main focus is on magnetic orders in this dissertation. Therefore we have employed ESR to probe local magnetic structures. And we cover a basic theory of ESR in paramagnetic/antiferromagnetically ordered states and the experimental realizations. Next, after an introduction to a system with an exchange interaction between d magnetic moments embedded at acceptor sites and π spins at donor molecules is given, we discuss the effectiveness of systematic studies on isostructural magnetic and non-magnetic acceptor based organic conductors. Then, we go over one of the “exchange coupled” 3+ 3+ materials, β-(BDA-TTP)2MCl4 (M=Fe ,Ga ). We examine the origins of the Metal- Insulator transition and the long range antiferromangetic order in the magnetic acceptor based material, where we found the critical importance of the quantum fluctuations of π spins. Finally, we delineate the magnetic order of alternating easy axes of a class of an organic conductor, τ-(P-(S,S)-DMEDT)2(AuBr2)1+y, at low temperature/field by ESR. We briefly discuss the origin of this unprecedented magnetic structure in terms of the unstoichiometric ratio of donors to acceptors and the tetragonal symmetry of the unit cell. Then, we report the results of the ultra high field ESR to probe the magnetic structure changes around a hysteretic field induced metal insulator transition.

ix CHAPTER 1

Introduction to Organic Conductors

Although they look complicated, the physical properties of organic conductors can be described by four simple parameters: transfer integral t between donor molecules, a bandwidth W calculated by tight binding model based on the t, an onsite Coulomb repulsion U, and a nearest neighbor site Coulomb repulsion V . This introduction is designed to give readers a concise view of organic conductors in terms of those parameters and explain why they keep attracting so much attention. Figure 1.1 shows the chemical formula of TMTSF (tetramethyl tetraselena fulvalene),one of the conventional organic donors, TCF (tetrachalcogenafulvalene). Most of organic donors are highly planar so that they stack on each other to form a conducting path along the column. Most of conventional organic conductors consists of a combination of organic donors

Figure 1.1: Chemical formula of TMTSF molecule. Hydrogen atoms are omitted at the fringe.

(D) and inorganic anions or acceptors (A) with a 2:1 ratio (D2A). Charge transfer from the TCF donor molecules to the inorganic anions leads to one de-localized hole per donor pair, yielding a 1/4 ﬁlled hole (π) band.

1 A schematic view along the conducting donor column in the crystal structure of a quasi- one dimensional organic conductor, TMTSF2PF6, is shown in Figure 1.2. The donors stack in a certain way with a tendency of overlaps of molecular (π) orbitals, and form a conduction band. Anions form insulating layers, separating the quasi-one dimensional donor stacking columns or planes. When the side -by-side overlap between donors is relatively weak, the conduction remains quasi one dimensional along the direction of the stacking. When side- by-side overlap, and interaction between stacking columns, becomes strong, the conduction becomes quasi two dimensional in the stacking plane. For the latter, because of the two

Figure 1.2: Crystal structure of TMTSF2PF6. Carbon (C), Selenium (Se), Phosphorus (P), and Fluorine (F), are represented by balls in red, light yellow, blue, and green, respectively.

dimensionality, a stacking of planar donors can take a variety of patterns as shown in Figure 1.3, where Greek letter is assigned for each symmetry. The value of transfer integral, t, reﬂects the overlap of π orbitals of the donor molecules and is an index of the bandwidth. The anisotropic overlap of donors results in anisotropic tis. Hence, organic conductors have anisotropic or low dimensional electronic band structure resulting in anisotropic conduction. The energy dispersion, E = E 2t cos(k x ), is 0 − i i i Xi

2 Figure 1.3: A variety of phases of donor stacking. After [1]

calculated by a mean field tight binding model. The bandwidth, W is defined as 4ti in each direction. At room temperature, these parameters are usually sufficient to describe the behavior. Most of the organic charge transfer salts are conducting. When temperature goes down, thermal excitation gets suppressed, and one can no longer ignore the interaction between the conduction electrons and the interaction between the conduction electron and the lattice. At low temperature, for weakly correlated systems, with those additional interactions, nesting of the Fermi surface (Fermiology) can lead to density waves (charge and/or spin), which is peculiar in one dimension, exhibiting instability in the Fermi surface, and can lead to superconducting state and magnetic order. Quantum oscillations are also observable under a high magnetic field at low temperatures. One of the strongest research driving forces in condensed matter physics research is to find a new superconductor. Although it was almost neglected for a long time, an insulating ground state finally starts to draw a keen attention for a newly proposed mechanism concerning not

3 only the onsite Coulomb repulsion, U, but also the nearest neighbor Coulomb repulsion, V . Here naively speaking, U is determined by the size of the donor, and V is determined by the distance between donors. D2A type conductors are 1/4 filled, unless the donors are forming dimers (1/2 filled band.). When the system has a 1/2 band filling, depending on U and W , it may become a conventional Mott insulator with evenly spaced charges. Still some 1/4 filled conductors actually become insulating at low temperatures. And a next neighboring Coulomb repulsion, V , then plays a key role. When the energy gain by V is larger than that of U, a charge ordered insulating state appears. As mentioned above, in the early stage of organic conductor research, and even now, the development of a donor is somewhat devoted towards the realization of higher Tc superconductivity. To avoid the one dimensional metallic instability, smaller peripheral hydrogen atoms are replaced by a larger peripheral group such as methyl group to reduce the stacking strength between planes. Also, it is designed to reduce U. To achieve a stronger correlation (U/W ), the system prefers a lower W . In fact, the unit cells of high Tc organic superconductors are relatively large. By changing the combinations of donors and acceptors, crystal structure symmetries, applying pressure, and/or magnetic field, we can change those (t, W , U, V ) parameters. As a result, organic conductors can exhibit a large variety of ground states such as superconducting state, insulating state (Mott insulating state, charge ordered state), magnetically ordered states, and Fermiology in low dimensions such as charge and spin density waves[2]]. Hence, anisotropic low dimensional organic conductors based on conventional TCF (tetrachalcogenafulvalene) donors, such as Bechgaard salts, ET (bis(ethylenedithio)- tetrathiofulvalene) salts, and BETS (bis(ethylenedithio)- tetraselenafulvalene) salts have become mainstream in condensed matter physics. That said, a question of “what kind of unusual magnetic order can the system have?” arises when localized magnetic moments are embedded in addition to the existing π spins or when a band filling is unusual due to unstoichiometric ratio of donor to anion. To answer the question, we performed several experiments mainly of Electron Spin Resonance (ESR) to probe the local magnetic structures. In this dissertation, we first describe a basic theory of ESR with a brief review of the resonance in magnetically ordered states in Chapter 2. Then we cover the experimental setups utilized in this thesis work in Chapter 3. Finally we describe the studies of two very different classes of organic conductors. The first study (Chapter 4) is on λ-

4 3+ 3+ (BETS)2FexGa1−xCl4 alloys and β-(BDA-TTP)2MCl4(M = Fe , Ga ) alloys to reveal the magnetism caused by a so-called “π-d exchange interactions” between spins in the conducting π -electron system and the intentionally added d-electron spins at anion sites in insulating layers. The second study (Chapter 5) is devoted for the study on a τ-phase organic conductor, which has an unstoichiometric donor to anion ratio, reported to exhibit some kind of magnetic ordering at low temperature and, moreover, a ﬁeld induced metal to insulator transition with an unknown origin.

5 CHAPTER 2

Electron Spin Resonance

In Chapter 2, we ﬁrst describe basic concepts and theories of continuous (c.w.) and pulsed electron spin resonance for paramagnetic spin systems. Then we discuss antiferromagnetic resonance (AFMR) theory for coupled spin systems.

2.1 Spin Hamiltonian: Quantum description

Energy states of paramagnetic species of an eﬀective electron spin S are often described by the so called the Pryce spin Hamiltonian

= + (2.1) H0 HEZ HZF S derived by Abragam and Pryce [3]. is the effective spin Hamiltonian because it only H0 contains effective electron spin operators. is the electron Zeeman interaction and HEZ HZF S is the zero-field splitting. Here we assume no nuclear spins and no exchange interactions between electrons.

2.1.1 Electron Zeeman interaction

The interaction between the electron spin and the external ﬁeld B0 is described in terms of the electron Zeeman interaction. Rigorously speaking, we must take orbital angular momentum into consideration. Then this Hamiltonian is given by

+ = µ B0(L + g S)+ λLS (2.2) HZ HLS B e where λLS is the spin-orbit interaction with the coupling constant λ. In conjugated organic molecule crystals, strong ligand ﬁeld approximation is applicable where the coupling constant λ is small enough to be treated as perturbation. Although

6 diagonal components of L are quenched due to its low symmetry, L still has off-diagonal components in molecular orbital basis. Therefore, the deviation of the principal g values from free electron value and their orientation dependence come from second order perturbation through an interaction of ground state and excited states admixing orbital angular momentum L. Putting them all together into an effective g tensor, the effective Zeeman term is described as

= + = µ B0gS (2.3) HEZ HZ HLS B where

g = ge1 +2λΛ, (2.4) and <ψ0 Li ψn >< ψn Lj ψ0 > Λij = | | | | . (2.5) ǫ0 ǫn Xn6=0 − This indicates that larger deviations of the principal g values are obtained when the energy differences between ground state and excited states become smaller and/or the spin- orbit coupling becomes larger. The principal axes frame is taken as the molecular frame and all interaction tensors are described with respect to this frame. For cubic and axial symmetries, gx = gy = gz and gx = gy = g⊥, gz = gk, respectively. For any non-axial system, such as a system with orthorhombic symmetry, g = g = g . For conjugated organic radicals x 6 y 6 z without localized magnetic moments, the shape/framework of the molecule is planar with in-plane σ bonds which are sp2 hybrids, while the out-of-plane pz of the C and S atoms are responsible for the weaker π bonding between adjacent atoms and form the π molecular orbitals. In most cases, the LUMO and HOMO orbitals of these conjugated systems are π molecular orbitals. For charge transfer salts such as organic conductors, a charge is taken from the Highest Occupied Molecular Orbital of a donor leaving an available spin on the molecule. The eigendirections are deduced from the symmetry of the molecule, usually taken perpendicular to the plane and along the long and short axis, and corresponding eigenvalues tell the nature of the orbitals. Since the coupling constant λ is small, the deviation of principal g values from free electron value remains very small. An exception arises when the molecule contains 4d orbitals such as Se in BETS molecule because of the larger λ, which is proportional to Z4 where Z is effective nuclear charge. And the principal g values show significant deviations.

7 2.1.2 Zero-ﬁeld splitting

For a spin system with spin S>1/2 and non cubic symmetry, dipole-dipole coupling between the electron spins removes the (2S+1)-fold degeneracy of the ground state. Since the interaction is ﬁeld independent, this is called zero-ﬁeld splitting. This term is described in second order as = SDS˜ (2.6) HZF S where D is a dipole splitting tensor. By taking D principal directions, the is written HZF S as 1 = D S2 + D S2 + D S2 = D[S2 S(S +1)]+ E(S2 S2), (2.7) HZF S x x y y z z z − 3 x − y where D = 3 D and E = Dx−Dy . D = E = 0 for cubic. D =0, E = 0 for axial, D =0, E =0 2 z 2 6 6 6 for orthorhombic or lower symmetry.

2.1.3 Resonance condition

First, we consider here N non-interacting electrons under magnetic field B0 along z direction. 1 Under the field, a degenerated energy level of S = 2 system split into two Zeeman levels. Quantum mechanically speaking, transitions between lower energy level and higher level are induced by applying an oscillating (a frequency at ν Hertz) electromagnetic field perpendicular to the static magnetic field B0. This resonance condition is satisfied at + − hν = gµBB0(See Figure 2.1(a)). Assign n , n for the number of spins in lower energy state (the direction of magnetic moment is along the static field) and higher energy state (the direction is opposite to the field), respectively. Then, we have following equations.

N = n+ + n− (2.8)

− gµ B n − B = e kT (2.9) n+ where k is Boltzmann constant and T is the temperature of the system. From the equations above, n+ and n− are calculated as

+ N n = gµ B (2.10) − B 1+ e kT

gµ B − B − Ne kT n = gµ B (2.11) − B 1+ e kT

8 Since transition probabilities, W , from lower energy level to higher energy level and from higher to lower are the same, a net absorption of the applied electromagnetic wave is proportional to the difference of n+ and n−, n (=n+ n−). − gµ B − B n (1 e kT ) = − gµ B (2.12) − B N 1+ e kT Hence, at room temperature (300 K) with a 9.3 GHz alternating field, one out of one thousand electrons absorbs the energy (a typical organic conductor has spins of the order of 1020−21). It is quite natural to assume exponential decays as relaxation mechanisms. And because of a spin-lattice relaxation, an excited electron gets back to the lower energy level by transferring absorbed energy to the environment, the lattice, at a mean life-time of T1. Taking n as the thermal equilibrium population difference, dn = 2W n + n0−n . Therefore, 0 dt − T1 n0 in steady state with simple assumptions, n = 1+2WT1 .

In c.w. ESR experiments, we keep 2WT1 very small to have the population difference close to the equilibrium values. At room temperature, this T1 value varies depending on the spin species and their environment. The other relaxation process we have to consider is spin-spin relaxation (the characteristic time is defined as T2). Due to this relaxation, an effective field on each individual electron from the others has some deviation, resulting in a finite linewidth of the resonance from the Heisenberg uncertainty principle. For S = 1 system, we may have to consider zero-field splitting parameter. Figure 2.1(b) shows D = 0 system where resonances for the transition between S = 1 and S = 0 and z − z between Sz = 0 and Sz = 1 are observed at the same field. Figure 2.1(c) shows the D>0 system with separate resonance fields. As obvious from the figure, the size of the resonance peaks depends on the population difference of the each energy level at the resonance field.

2.2 Bloch equation and resonance phenomena: classical description.

Although the spin Hamiltonian is useful to describe the energy levels of the system and resonance ﬁelds, the observable is an ensemble of the magnetic moments of the spins

(µ), a bulk magnetization (M = µi), for most spin resonance measurements. Hence Xi the classical treatment, Bloch equation, is suﬃcient enough to describe the motion of the ensemble in the applied magnetic ﬁeld.

9 1 Figure 2.1: A schematic diagram of energy levels and resonance conditions. (a) S = 2 ,(b) S =1,D = 0, (c) S =1,D>0.

10 Bloch equation is written as dM = γ[M B0] (2.13) dt × ω where γ is gyromagnetic ratio deﬁned as γ = . By taking longitudinal and transverse B0 relaxation time as T1 and T2, respectively, the Bloch equation is then modiﬁed as

dMx,y Mx,y = γ[M B0]x,y (2.14) dt × − T2

dMz Mz M0 = γ[M B0]z − (2.15) dt × − T1 where M0 is the magnetization at thermal equilibrium. 2.3 c.w. ESR

iωt Taking B0 as (B1e , 0,B0) where ω is an eﬀective frequency, the transverse parts of modiﬁed Bloch equation become,

Mx iωMx = γMyB0 (2.16) − T2

iωt My iωMy = γ(MzB1e MxB0) (2.17) − − T2 By solving this, we have γ2B B M eiωt M = 1 0 z (2.18) x 2 2 1 2 γ H0 +(iω + T2 ) 1 iωt γB1Mz(iω + )e M = T2 (2.19) y 2 2 1 2 γ B0 +(iω + T2 ) Since M becomes constant at resonance, h zi d M M M h zi = γB M eiωt h z − 0i =0 (2.20) dt − 1 y − T 1 2 2 1 2 2 2 1 γ B1 T1( )(γ H0 + ω + 2 ) Mz 2T2 T2 h i Mz M0 = Mz M0 = 2 (2.21) 2 2 2 1 2 ω h − i h i− − (γ B0 ω + 2 ) +4 2 − T2 T2 Hence, 2 2 2 2 1 2 2 (4ω + T2 (γ B0 + 2 ω ) )M0 T2 − Mz = 2 2 2 2 1 2 (2.22) γ B1 T1T2(γ B0 + 2 +ω ) h i 2 2 2 2 1 2 2 T2 4ω + T2 (γ B0 + 2 ω ) + T2 − 2

11 2 2 where γ B1 T1T2 is defined as a saturation factor. Resonance condition is satisfied where M is minimum where, h zi 2 2 2 1 ω = γ B0 + 2 (2.23) T2 Then Mz turns out to be h i M M 0 (2.24) z 1 2 2 h i≈ 1+ 4 γ H1 T1T2 Experimentally, the response to the electromagnetic field is detected as ac susceptibility along the x axis, χ(ω) = χ′ iχ”. χ′ and χ”‘ are proportional to a dispersion and an x − x x x absorption of the applied electromagnetic wave. By putting the calculated M in the h zi equation of Mx, χx(ω) becomes

Mx ′ ” = χx(ω) iχx(ω) (2.25) Hx − 2 2 2 2 2 1 2 χ0γ H0 T2 (γ H0 + 2 ω ) ′ T2 − χx(ω)= (2.26) 2 2 2 2 1 2 2 1 2 2 2 2 1 2 4ω + T2 (γ H0 + 2 ω ) + γ H1 T1T2(γ H0 + 2 + ω ) T2 − 2 T2 2 2 ” 2χ0γ H0 T2ω χx(ω)= (2.27) 2 2 2 2 1 2 2 1 2 2 2 2 1 2 4ω + T2 (γ H0 + 2 ω ) + γ H1 T1T2(γ H0 + 2 + ω ) T2 − 2 T2 M0 where χ0 = H0 In an actual c.w. experiment, we adjust the power of the oscillating field, so γ2H2T T 1 1 2 ≪ ′ ”‘ 1 is satisfied as mentioned above. Therefore, χx and χx become 2 2 2 2 2 ′ χ0γ H0 (γ H0 ω ) χ = − 2 (2.28) x 2 2 2 2 ω (γ H0 ω ) +4 2 − T2 2χ γ2H2( γ ) ” 0 0 T2 χ = 2 (2.29) x 2 2 2 2 ω (γ H0 ω ) +4 2 − T2 The equations above show that the lineshape of the absorption becomes Lorentzian, as shown in Figure 2.2(a), when the local field is homogeneous in the above condition. Naively speaking, T2 value is estimated from the full linewidth at half height. Also T1 can be 2 2 estimated by setting γ H1 T1T2 = 4. At the resonance, the absorption intensity become half then. Inhomogeneous broadening can be observed as a Gaussian lineshape due to a distribution of local fields on each spin (See Figure 2.2(b)). Also the skin effect of highly conducting materials can modify the lineshape from a simple Lorentzian to a Dysonian with an A asymmetry ( B )(See Figure 2.2(c)). Actual shapes are often observed as derivatives of Lorentzian, Gaussian, or Dysonian due to a usage of magnetic field modulation coils.

12 Figure 2.2: Lineshapes. (a)Black line: Absorption (Lorentzian), Gray line: Dispersion. (b)Inhomogeneous broadening (Gaussian) (c) Derivative of Dysonian lineshape for a metallic material.

2.4 Pulsed ESR

Although, c.w. ESR is more sensitive to the signals, pulsed ESR can measure the relaxation time (T1,T2) more accurately for the spin system with suﬃciently long T1, and T2. The motion of spins is well described in a rotating frame (x′ and y′ ) in the same frequency with the applied electromagnetic ﬁeld along x axis in the laboratory frame. The measurements procedure and motions of spins under spin-spin relaxation process, T2 processes, are displayed in Figure 2.3. Those under spin-lattice relaxation process, T1 process, are exhibited in Figure 2.4. Unlike the c.w. ESR measurements, the pulsed manipulations of spins require a rotation of the entire ensemble of spins in the pulsed ESR measurements. Therefore the thermal equilibrium is broken during the pulse manipulations.

2.4.1 T2 measurements

For measuring the T2, Hahn echo method is usually employed. Typical conﬁgurations are shown in Figure 2.3. First, the ensemble is at thermal equilibrium (Figure 2.3(c)). Then, π a 2 pulse is applied along x direction in a laboratory frame. Figure 2.3(a), (b) show pulse sequences and magnetization signals on the x′ y′ plane in the rotating frame, respectively. −

13 π The motion of the ensemble during the 2 pulse is shown in the rotating frame in Figure 2.3(d). Just after the pulse, it starts splitting due to a time-independent distribution of the local fields on each spin (See Figure 2.3(e) for the motion of each spin at τ after the first pulse.), ∗ resulting in a free induction (FI) decay in the magnetization with a coefficient, T2 . This FI decay is the Fourier transform of the spectrum convoluted by the excitation band associated with the pulses. Since it took τ to spread, it will take another τ to get back to align for an echo after the application of π pulse (See Figure 2.3(f), (g), and (h)). And the peak height of this echo changes when τ changes. This decay reflects the spin-spin interaction with a characteristic time, T2, which is associated with a change in the local field of the spins.

∗ Figure 2.3: A schematic diagram of T2 and T2 measurements. (a) Pulse sequences. (b) Corresponding signals. The dotted line illustrates the T2 decay relaxation. (c) The spin π ensembles, the magnetization, in thermal equilibrium, just before the 2 pulse. (d) The π ′ ′ ensemble, just after the 2 pulse. (e) Motions of spins on the x y plane in the rotating frame, corresponding to Free Induction (FI) decay. (f) The spins,− just after the π pulse at t = τ. (g) The spin echo with the center around t =2τ. These ﬁgures are after [4]

14 2.4.2 T1 measurement

The pulse sequences, following magnetizations, and general form of T1 decay are displayed Figure 2.4(a), while the actual motion in the rotating frame are shown in Figure 2.4(b), (c), (d), and (e). The π pulse gives the transition from Figure 2.4(b) to (c). The longer you wait π (say t0) before the 2 pulse, the smaller the magnetization becomes due to the spin-lattice relaxation. By plotting the head of the free induction decays, the T1 decay is calculated.

Figure 2.4: A schematic diagram of T1 measurement. (a) Pulse sequences, the resulting free induction decays, and T1 decay. (b) The spin ensembles, the magnetization just before the π pulse. (c) The spin ensembles, the magnetization just after the π pulse. (d) The relaxed spin ensembles, the magnetization, in thermal equilibrium, t0 after the π pulse. (e) The signal, π just after the 2 pulse.

2.5 A basic theory of AFMR

2.5.1 Antiferromagnetic state

One of the fundamental phenomena in condensed matter physics is an onset of spontaneous order at low temperatures. In particular, antiferromagnetic order is most commonly observed in organic conductors. Above a critical temperature, Tc (N`eel temperature, TN , for an antiferromagnet), magnetization, M does not have any preferred directions (paramagnetic) in zero ﬁeld when averaged over time, resulting in a complete translational and rotational

15 symmetry. Below TN , the system is no longer in a paramagnetic state. For a simple case,

M form a coupled spin system of two sublattices, M1, and M2. In the mean field theory, the exchange term on M1 is defined as the field created by M2 and vice versa. Therefore it is energetically favorable for neighboring spins to have opposite spin. Then, the most favorable direction of the sublattices (an easy axis) is determined by an anisotropic energy term, which reflects the crystal (discrete) symmetry. Therefore, the order parameter is M on each sublattice in this antiferromagnetically ordered state. The temperature susceptibility starts showing a magnetic field direction dependence below TN . The susceptibility parallel to the easy axis, χk(T ), shows a kink at TN and decreases down to zero, while the susceptibility perpendicular to the easy axis, χ⊥, becomes almost constant at the onset of the AFM order. See Figure 2.5 (a) for an uniaxial anisotropic energy case. Magnetization in antiferromagnetic state stays zero when the field is applied along the easy axis below a critical field(Figure 2.5 (b)). At the critical field, the direction of the spins flops from parallel to perpendicular to the easy axis when the Zeeman term matches the anisotropic term. Above this spin flop field, spins start aligning to the field when the applied magnetic field increases(Figure 2.5 (d)). The more general case will be described in detail in the next section.

2.5.2 Antiferromagnetic Resonance

In the antiferromagnetic state, the spins cannot be considered independently and interactions between the spins play a critical role. To describe the dynamics of these spins, the mean field approximation is applied for temperatures far from the Tc where the magnetic order is fully developed[5, 6, 7]. Near the Tc (in this case, Nèel temperature, TN ), more delicate theories such as the dynamic scaling theory may be required to deal with correlations and fluctuations [8].

For coupled spin systems of two sublattices with each magnetic moment, M1, and

M2 where M = M and M = M , here we consider zero temperature bi-axial | 1| 0 | 2| 0 antiferromagnetic order, following Date’s derivation[4]. For further information and a treatment with ﬁnite temperature, see Nagamiya’s paper[9].

In the presence of two spins, S1 and S2, an exchange energy is deﬁned as,

H = JS1 S2. (2.30) E − · In the ordered system like our case here, the interaction between the two sublattices is

16 described by the mean field theory, where HE1 is the mean field on the M1 sublattice due to the M2 sublattice and HE2 field is the mean field of M1 on M2. Then, they are defined as H = AM (2.31) E1 − 2 H = AM (2.32) E2 − 1 where A = 2Z|J|S when the interactions are only valid with nearest Z neighboring spins. J gµB is the exchange interaction constant between the neighboring spins. Assuming that x, y, and z axes are easy, 2nd easy, and hard axes, respectively, the anisotropic energy is then described as 1 1 U = K (β2 + β2)+ K (γ2 + γ2) (2.33) A 2 1 1 2 2 2 1 2 where K2>K1 and direction cosines of M1, M2 are (α1,β1,γ1), (α2,β2,γ2), respectively. From U through the equation U = M H , each component of H and H are A A − · A A1 A2 calculated. For example, (H ) = K2 γ . A1 z − M0 1 In this section, we only consider the AFM order in the H H limit. Figure 2.5(a) A ≪ E shows the temperature dependence of the magnetic susceptibility above and below the antiferromagnetic ordering temperature, TN . Below TN , the susceptibilities split depending on the applied field. χ// and χ⊥ for the field along and perpendicular to the easy axis. When the field is applied perpendicular to the easy axis (See Figure 2.5(b)), the M1 and M2 are tilted from the easy axis with an angle θ. Then, χ⊥i is written as

2M0 sin θ 1 χ⊥i = = (2.34) Ki H0 A + 2 2M0 where K = K for H y), K for H z). When the anisotropy is really small, χ i 1 0k 2 0k ⊥ 1 becomes A . When the field is applied along the easy axis, the spin flop transition occurs 2HAHE at Hsf = χ . Below Hsf , each spin is along the easy axis (see Figure 2.5(c)) with 1− // r χ⊥ M1 = M2. At the spin-flop transition, it becomes energetically favorable for the spins to − change the orientation and magnetic moments flop. Above the field, the magnetic moments start aligning to the applied field (see Figure 2.5(d)). With the additional electromagnetic wave applied to the system, those spins, therefore M 1 and M 2 oscillate around the equilibrium points. The Bloch equations are dM 1 = γ[M H ] (2.35) dt 1 × 1 17 Figure 2.5: A schematic diagram of antiferromagnetic order and its susceptibility picture. (a)Temperature dependent susceptibility, χk : green line, χ⊥ : light blue line, (b) M1 (blue vector) and M2 (red vector) at the equilibrium positions with the applied field (gray vector) perpendicular to the easy axis (black line),(c) M1 and M2 at the equilibrium positions with the applied field parallel to the easy axis below the spin flop field, (d) M1 and M2 at the equilibrium positions with the applied field parallel to the easy axis above the spin flop field.

dM 2 = γ[M H ] (2.36) dt 2 × 2 where H = H + H AM (2.37) 1 0 A1 − 2 and H = H + H AM (2.38) 2 0 A2 − 1 By deﬁning

M = M 1 + M 2 (2.39) and M ′ = M M , (2.40) 1 − 2 18 the Bloch equation can be written as

1 dM 1 1 ′ = [M H0]+ [M (H + H )] + [M (H H )] (2.41) γ dt × 2 × A1 A2 2 × A1 − A2

′ 1 dM ′ 1 1 ′ = [M (H0 AM)] + [M (H H )] + [M (H + H )] (2.42) γ dt × − 2 × A1 − A2 2 × A1 A2

′ Since H AM can be rewritten in terms of M and M as 0 − ′ ′ χk αM (M · H0) H0 AM =(H0k + H0⊥) A(χkH0k+χ⊥H0⊥)=(1 )Hk = 2 (2.43) − − − χ⊥ 4M0

′ where (α =1 χk ), we take a variation of M and M by assuming a small oscillation around − χ⊥ the equilibrium points. See Figure 2.6(a) and (b). Neglecting any term which includes Mx,y,z, we have iω δM = [H δM]+ γ − 0 ×

K2 K1 ′ ′ ′ ′ ( − 2 (M zδM y + M yδM z), − 2M0 K2 ′ ′ ′ ′ 2 (M xδM z + M zδM x), 2M0 K1 ′ ′ ′ ′ 2 (M yδM x + M xδM y)) (2.44) − 2M0 ′ ′ iω ′ αM (M · H0) ′ δM = 2 A[M δM] (2.45) γ − 4M0 − × For H

iω K2 ′ δMy = H0δMz + δM z (2.46) γ M0

iω K1 ′ δMz = H0δMy δM y (2.47) γ − − M0

iω δM ′ = αH δM ′ +2AM δM (2.48) γ y 0 z 0 z

iω δM ′ = αH δM ′ 2AM δM (2.49) γ z 0 y − 0 y

19 Figure 2.6: Antiferromagnetic resonance modes with the field along the easy axis. (a) ω+ mode below the spin flop field. (b) ω− mode below the spin flop field. (c) ω1 mode above the spin flop field. It oscillates along easy axis. (d) ω2 mode, spin flop mode, above the spin flop field. It oscillates making a circle on x y plane. −

By reforming this into an eigen equation, we have iω H 0 K2 − γ 0 M0 H iω K1 0 0 γ M0 − − − iω =0 (2.50) 0 2AM0 γ αH0 − iω 2AM0 0 αH0 − − − γ

By solving the equation above, we have 2 ω± 1 2 2 2 2 4 2 2 2 ( ) = (1 + α )H + C1 + C2 (1 α ) H +2(1+ α) (C1 + C2)H +(C1 C2) γ 2 0 ± q − 0 0 − (2.51) where C1 =2AK1 and C2 =2AK2.

When H0>Hsf , H0//xˆ M (2M sin θ, 0, 0) and M ′ = (0, 2M cos θ, 0). See Figure 2.6(c) and (d). ≈ 0 0 iω K2 K1 ′ δMx = − cos θδM z (2.52) γ − M0

20 iω δM = H δM (2.53) γ y 0 z

iω K1 ′ δMz = H0δMy cos θδM x (2.54) γ − − M0 iω δM ′ = 2AM cos θδM (2.55) γ x − 0 z iω δM ′ =0 (2.56) γ y iω δM ′ =2AM cos θδM (2.57) γ z 0 x The eigen function yields

Figure 2.7: The frequency dependence of antiferromagnetic resonance. Black lines for B k an easy axis. Green for B a 2nd easy axis. Blue for B a hard axis. Dotted gray line is for a paramagnetic resonance.k k

ω ( 1 )2 =(C C ) cos2 θ C C (2.58) γ 2 − 1 ≈ 2 − 1 ω ( 2 )2 = H2 C cos2 θ H2 C (2.59) γ 0 − 1 ≈ 0 − 1

21 When H0 perpendicular to the easy axis, with similar assumptions, for H0//yˆ ω ( 1 )2 = C (2.60) γ 2 ω ( 2 )2 = H2 + C (2.61) γ 0 1

H0//zˆ ω ( 1 )2 = C (2.62) γ 1 ω ( 2 )2 = H2 + C (2.63) γ 0 2 The frequency dependence of resonance ﬁeld is plotted in Figure 2.7. Figure 2.7 is for a bi-axial system. If the system is a uniaxial system, then the gap between √C1 and √C2 is closed and the curves (ω1 and ω2 modes) for the easy axis become straight. In Figure 2.7, the temperature is assumed to be zero. Since the antiferromagnetic order below TN is BCS type. So the order grows while temperature goes down. Therefore temperature dependence of the resonance ﬁeld/g value shows larger deviation from paramagnetic values when temperature goes down below TN .

22 CHAPTER 3

Experimental

3.1 Experimental realizations

For the work described in this thesis, a variety of instruments was used, each with their own detection methods. Those details are given in this chapter.

3.2 Detection methods

3.2.1 Homodyne detection method

A schematic diagram of Homodyne detection method is shown in Figure 3.1(a).

Electromagnetic waves are generated by a source at the frequency of ν1. It is then split into two. One goes to the sample and the other serves as the reference signal. Returning signals from the sample and reference signals are mixed together at the mixer. Therefore a signal is detected as a change in DC voltage with a phase modulation. The advantage lies in simple circuit components and a phase control.

3.2.2 Heterodyne detection method

A schematic diagram of Heterodyne detection method is shown in Figure 3.1(b). Although a Homodyne detection method is widely employed in many commercially available ESR 1 system, it has an intrinsic f noise, which tends to become more important at higher 1 frequencies. To reduce the f noise, we use a source at ν1 and a local oscillator source with a frequency ν2. At the mixer, they are mixed and a wave with intermediate frequency (IF) comes out at ν ν . We detect the intensity of the IF frequency. In the purely | 1 − 2| Heterodyne detection method, the phase information is lost.

23 Figure 3.1: A schematic diagram of detection methods. (a) Homodyne, (b) Heterodyne, (c) Superheterodyne method.

3.2.3 Superheterodyne detection method

A schematic diagram of Superheterodyne detection method is shown in Figure 3.1(c). By having two more mixers, one for ν ν and the other for DC, it is possible to acquire | 1 − 2| 1 both a phase control function and a reduction of f noise.

3.2.4 X-band(9.3-9.7 GHz)

This machine is used for high sensitivity measurements at a single, relatively low frequency. We use a commercially available Brucker X-band Elesys e580 system for c.w. (9.3 GHz) and pulsed (9.7 GHz) ESR experiments with ﬂow Helium cryostat (from 4 K to room temperature) where homodyne detection method is employed. A sample is set on a quartz rod in a rectangular cavity for cw measurements and a cylindrical dielectric resonator for pulsed measurements. In cw, ﬁeld modulation at 100 kHz is used to improve signal to noise. Angle dependence of ESR signal can be measured by rotating the quartz rod.

24 3.3 Multi Vector Network Analyzer

This spectrometer was used in the Q to W GHz range and provides a high frequency range at a medium sensitivity. We have used a commercially available ABMillimetre MVNA with superheterodyne detection method with a home-built probe of rectangular waveguides and a cylindrical cavity. A sample is set in the cavity. A 4Helium bath cryostat is employed to achieve a temperature range between 1.3 K and room temperature.

3.4 Quasi-optical spectrometers

A quasi-optical design is employed to optimize sensitivity and minimize losses. With circular corrugated waveguides, quasi-optical techniques, and the radiation propagating parallel to the magnetic ﬁeld, it becomes possible to use a “induction-mode detection”, where the magnetic dipolar absorption of only one of the two circular components of the incident linearly polarized radiation results in the generation of a cross-polarized signal and a co-polarized reference. This separation of the signal from the reference minimizes both the phase noise and the phase drift, and signiﬁcantly improves sensitivity (See Figure 3.2(b)). A schematic diagram of quasi-optical setup is drawn in Figure 3.3: Since it employs a quadrature “superheterodyne detection” scheme, the quasi-optical setup requires two Gunn diodes (LO Gunn-diode and a signal Gunn-diode) and two millimeter-wave (single-ended)

Schottky mixers and two 6 GHz balanced mixers. The source millimeter TE01 waves are generated by a phase-locked Gunn diode at G2 (120 GHz or 240 GHz with a doubler). A corrugated horn transforms the TE01 mode in the single-moded waveguide into an HE11 mode, which is a linear combination of TE11 and TM11 modes (See Figure 3.2(a)), where the circular corrugated horn enables an almost lossless transition to the TEM00 free space mode. Then, the radiation enters the quasi-optical millimeter-wave bridge (dotted region in Figure). In the bridge, it passes through a variable attenuator (0-30 dB) and a circulator, a 45◦ Faraday rotator in between a pair of wire-grid polarizers, which serves as an isolator. After it goes through a Martin-Puplett interferometer (a polarization converter) the radiation enters the oversized corrugated waveguide to a sample on a mirror. The returning radiation is split into two components by a wire grid polarizer. The cross-polarized signal beam is led to the signal Schottky diode mixer (M2). The co-polarized reference beam goes back to the circulator and then led to the reference Schottky diode mixer (M1). The second Gunn diode

25 Figure 3.2: A schematic diagram of induction mode detection. (a) Propagating mode in a corrugated wave guide,(b) Induction mode. These ﬁgures are after [10]

(G1) operating at a 6 GHz frequency below the source frequency is added at those single- ended mixers (signal and LO enter through the same port). The resulting 6 GHz intermediate frequency (IF) signals from M1 and M2 are amplified by low-noise amplifiers, pass through variable attenuators, and are quadraturely mixed down to dc by 6 GHz mixers. A phase shifter in the reference channel allows for phase tuning. A signal is observed in general as a mixture of absorption and dispersion. Therefore , the availability of two quadrature signals makes data phase correction possible. Finally, the signals are led to a pair of lock-in amplifiers. The sample is mounted on a sample holder inside a Helium flow cryostat at the end of the corrugated waveguide. A modulation coil for c.w. ESR is integrated in the sample holder. A single crystal is put on a mirror, or on a single-axis rotator. (See Figure 3.4.) A more complete description of this spectrometer can be found in ref[11]. While this instrument provides high sensitivity, it only operates at a limited number of frequencies (120, 240, 336

26 Figure 3.3: A schematic diagram of quasi-optical setup. G1: LO Gunn diode, G2: Signal Gunn diode, FR: Faraday rotator, MP: Martin-Puplett interferometer, S1, S2: quadrature signal outputs, M1, M2: millimeter-wave single-ended Schottky mixers, M3, M4: 6 GHz balanced mixers. After [11]

GHz).

3.5 BWO spectrometer

For even higher frequencies in the range of 300-800 GHz, we need a Back Wave Oscillator (BWO) spectrometer. BWO is a tube source. A schematic diagram of the tube is shown in Figure 3.5 III. By changing the voltage, we can control an output frequency. Important parameters and formula are shown for the frequency-voltage correspondence relation of a particular tube in Figure 3.5 IV and V. A calibration curve is also shown in Figure 3.5 VI. It can cover 230 - 900 GHz by changing tubes. As shown in Figure 3.5 VII, the tube has favorable frequencies so that we have to carefully choose a speciﬁc frequency for experiments (for example, we choose a peak voltage in Figure 3.5 VII and calculate frequency by the

27 Figure 3.4: Sample holder conﬁgurations. (a) c.w. ESR of a solid sample. (b) A single with single axis rotation. S denotes the sample position. M designates the position of a mirror. The position of the ﬁeld modulation coils is given by the areas with a diagonal cross. After [11]

equation in Figure 3.5 IV.). The tube consists of a heater, the modulation comb, an anode, and an external magnet. Plasma is ejected and accelerated from the heater, then repelled and accelerated from the anode while the external magnet keeps it in an axial orientation in the tube. The energy is released when the plasma changes the direction at the anode. This energy is emitted in submillimeter waves, which is subsequently led to a sample in a transmission mode. By changing the voltage, we can vary the frequency. We used an InSb hot-electron bolometer as a detector for multi-frequency setups because of its large frequency range of 50-1200 GHz. The detector is magnetically tuned using a rare earth magnet. InSb normally is sensitive up to 600 GHz. By applying an inhomogeneous magnetic field, which results in a gradient of magnetic field, this stabilizes the 4th Landau level, creating a cyclotron resonance band. Due to the inhomogeneous field, InSb acquires broad band absorption up to 2.5 THz. Since it is a transmission ESR, the signal and reference travel through the same path, making it a virtual homodyne detection system although the phase cannot be easily controlled. For angular dependence, a rotational sample holder is designed and built for this BWO experiment and also for higher frequency experiment with a far infrared laser as a source. By rotating the side screw, the ring shape sample stage rotates in a single-axis way, where the axis is perpendicular to the applied magnetic field. (See Figure 3.6.)

28 Figure 3.5: BWO information sheet. See text for a further explanation. After an instruction book of the BWO equipments.

3.6 Far Infrared Laser spectrometer up to 1.2 THz.

The available power of BWO’s decreases with frequency and for frequency above 800 GHz, we have used a Far Infrared Laser (FIRL). As a source, we used an integrated CO2 and FIR laser system, FIRL100 from Edinburgh Instruments Ltd.

The CO2 laser uses a ﬁlling gas in a water-cooled discharge tube consists of carbon dioxide

(CO2) (6 %), nitrogen (N2) (18 %), and helium (He) (the balance). To have a laser (light ampliﬁcation by stimulated emission of radiation), we have to achieve a population inversion by a few steps. First, electron impact excites the energy levels of vibration modes of nitrogen. Then, the gained energy is transferred to the vibration modes of carbon dioxide, resulting in the desired population inversion. Finally the laser transitions occur between vibration-rotation bands of a carbon dioxide molecule, and the rotational structure of the P and R bands is selected by a tuning element in the laser cavity.

The CO2 resonator consists of a partially reﬂecting output coupling mirror (ZnSe) and a

29 Figure 3.6: A transmission type rotational sample holder. See text for a further explanation.

blazed diﬀraction grating. The output coupler is attached on a piezo-electric transducer. By rotating the diﬀraction grating, a particular rotational line of a vibrational transition can be selected. Hence, we can tune the wavelength/frequency of the output laser. By changing the cavity length, we can optimize the output power.

The CO2 pump laser provides wavelength in the range of 9-11 µm, corresponding to about 30000 GHz. These wavelength are subsequently used to excite a low pressure ( 1 ∼ mbar) molecular gas (CH3OH, CD3OH, CH3I etc...). This can create population inversion between rotational levels of the molecules, which then can lead to lasing between these levels.

In this manner, various discrete FIR frequencies can be obtained. We have used CD3OD

(10R16 for 847.036 GHz) and CD3OH (10P8 for 1044.18 GHz and 10R36 for 1182.4 GHz). The cavity for the Far Infrared laser comprises a input Brewster window (ZnSe) which forms a vacuum seal at one end of the laser, a ﬂat chromium gold coated stainless steel input mirror at one end of the laser and a specially optimized dichroic output coupler from which the FIR power is extracted. A water-cooled oversized brass waveguide of 36 mm inside diameter is

30 Figure 3.7: A schematic diagram of a far infrared laser. After the instruction book of FIRL100.

used.

31 CHAPTER 4

π d CORRELATED SPIN SYSTEMS −

In this Chapter 4, we explore the interplay of dimensionality and interactions involving the onset of an internal ﬁeld and/or 3D magnetic order in related “π d” materials, λ- − 3+ 3+ (BETS)2FexGa1−xCl4 and β-(BDA-TTP)2MCl4(M=Fe , Ga ). To fully understand the role of π d interactions in these materials, we compare the iso-structural systems with a − − 5 − magnetic anion (FeCl4 , S= 2 ) and their non-magnetic analog (GaCl4 , S=0). 4.1 Introduction to π d interaction − Organic conductors are the subject of superconductivity, magnetism, and fermiology in lower dimensions due to the anisotropic overlapping of donor molecules’ π orbitals [2]. Recently the mechanisms that produce insulating ground states and the nature of magnetic interactions correlated with itinerant and/or localized conduction electrons have shown that experiments on these materials complement fully the theory of extended Hubbard model systems and vice versa [12, 13, 14, 15]. Joining ladder systems, transition metal oxides, and the cuprates [16], organic conductors have stimulated the investigation of the competition between Wigner crystallization [15], charge order [17, 18], Mott transitions [19], spin frustration [20], Fermi and non-Fermi liquid behavior [21], unconventional superconductivity [22], and antiferromagnetic order [23]. Magnetic order may arise in quasi-two dimensions in the organic donor lattice from band ﬁlling (Mott type) [13, 14] due to strong electron-electron correlation, Fermi surface nesting spin density wave (low dimensional metallic instability) [24], and/or in three dimensions from explicit inclusion of localized d-electron sites in the insulating anion layer. In the latter case, a ”π d” interaction is introduced between the donor π conduction − electrons at donor sites and the localized d electrons at insulating anion sites. Although

32 the three dimensional antiferromagnetic order of π spins at donor sites arises at low temperature from the strong electron-electron correlation or the quasi low dimensional conduction instability, those interaction between the π spins are essentially restricted in the donor stacking plane. Also, there might be a linear direct d d interaction in insulating − layers, if any, usually due to the geometrical overlap of d spin orbitals, which is also confined in one or two dimensionality. Therefore, the π d interaction between the π spins at the donor planes and localized − d spins at insulating layers is indispensable to have three dimensional long range magnetic order of localized d spins. A dramatic example of the effects of the π d interaction includes the observation of − magnetic field induced superconductivity [25, 26, 27] and evidence for the Fulde-Ferrell-

Larkin-Ovchinnikov ground state [27] in λ-(BETS)2FeCl4 as well as the onset of the long range three dimensional antiferromagnetic order in the absence of the π spins due to singlet formation on the donor sites as shown in β-(BDA-TTP)2FeCl4. In the following sections, we discuss those two “π d” related systems, ﬁrst λ-(BETS) Fe Ga Cl (where x =0.6), − 2 x 1−x 4 3+ 3+ and second β-(BDA-TTP)2MCl4(M=Fe , Ga ).

4.2 Estimation of exchange interaction, J

Before proceeding to each system in detail, a brief explanation on the estimation of an exchange interaction is given here. The exchange interaction, J, is estimated by t2 J = 2 i , (4.1) − n∆ Xi where t is a transfer integral, n is the number of the combinations, and ∆ is an energy gap, which will be explained later. Transfer integrals are calculated by the intermolecular overlap of molecular orbitals based on the crystal structure. For Jπ−d, the energy gap between − HOMO of a donor molecule and t2g level of FeCl4 is estimated by the extended Huckel calculation of each energy level. Since Fe3+ has five d-orbitals (five unpaired spins in each orbital), J is acquired by the average of the five π d interactions. Hence, it is written π−d − as 2 5 J = t2. (4.2) π−d −5∆ i π−d Xi=1

33 For Jπ, the energy gap ∆ is the onsite Coulomb repulsion Uπ. So it is written as

2 2tπ Jπ = . (4.3) − Uπ

For Jd, it is written as 2 25 J = t2. (4.4) d −25U i d Xi=1 More details can be found in references[28, 29].

4.3 λ-(BETS)2FexGa1 xCl4 − 4.3.1 BETS donor molecule

The chemical formula of the BETS donor (cation) molecule is shown in Figure 4.1, where BETS stands for bis(ethylenedithio)tetraselenafulvalene. The axes correspond to

Figure 4.1: Chemical formula of BETS molecule. Hydrogen atoms at fringe are omitted.

the principal axes of the molecule. As indicated by red circles, the central S atoms of a conventional ET molecule are replaced by Se atoms in the BETS molecule. This has the eﬀect of increasing the intermolecular overlap of π orbitals.

4.3.2 Crystal structure of λ-(BETS)2FeCl4

Combined with an acceptor (anion), FeCl4, crystals of (BETS)2FeCl4 can take either λ or κ phases. The unit cell of λ-(BETS)2FeCl4 crystal has a triclinic symmetry, with P 1¯ space group, a = 16.164, b = 18.538, c = 6.593A˚, α = 98.40,β = 96.67,γ = 112.52◦. It contains two crystallographically independent BETS cations, where centers of the molecules

34 at (a, b, c) = (0.60, 0.00, 0.15) for BETS1, (0.10, 0.00, 0.05) for BETS2, and one FeCl − − 4 anion with the center at (0.21, 0.47, 0.88). Since it has P 1¯ space group, only the inversion operation is allowed. The crystal structure is shown in the Figure 4.2, illustrating the

Figure 4.2: Crystal structure of λ-(BETS)2FeCl4. Hydrogen (H), Carbon (C), Sulfur (S), Selenium (Se), Iron (Fe), and Chloride (Cl), are represented by balls in blue, black, orange, purple, red, and green, respectively.

separation of conducting layers of BETS donor molecules and insulating layers of FeCl4.

35 4.3.3 Physical Properties of λ-(BETS)2FexGa1 xCl4: Quantum − chemical estimations and experimental values.

The eﬀective exchange interactions between π spins (Jπ), between d spins (Jd), and between π and d spins (Jπ−d) are estimated by the quantum calculations as followed.

Upon the calculation of the effective exchange interaction Jπ, 8 inter-donor molecular exchange interaction are calculated first. One of them is about -2600 K, which is at least 3 times larger than the other exchange interactions. Therefore it is considered that dimers are forming between the strong exchange interaction and π spins are assumed to be localized at each dimer. Then the inter-dimer interactions are estimated. By adding the cooperative interactions and frustrating ones, a significantly large Jπ (-448 K) is calculated, which indicates a strong antiferromagnetic coupling in the π system. The calculated energy band structure (Figure 4.3(a)) and Fermi surface (Figure 4.3(b)) also suggest the spin density wave π (SDW) antiferromagnetic ground state with a nesting vector q = (0, c ), which bridges across quasi-one dimensional Fermi surfaces. Jd (-0.64 K) is calculated from direct interactions of

Figure 4.3: Calculated band structure (a) and Fermi surface (b) of λ-(BETS)2FeCl4. After [28].

− FeCl4 anions through Cl-Cl contacts, one between the crystallographically independent one at (x,y,z) = (0.21, 0.47, 0.88) and ( x, 1 y, 2 z), and the other between (x,y,z) and − − − (x, y, z + 1), resulting in ladder-like chains of d spins along the c axis. − − Jπ−d (-14.62 K) consists of seven overlaps between Cl orbital of FeCl4 anion and BETS molecular orbital, two for molecule 1, and ﬁve for molecule 2. The largest one (-14.14 K) is obtained by the interaction through a short Se (molecule 2) -Cl contact. This exceptionally

36 high value is intrinsic to a λ phase donor arrangement, where a strong dimerization of BETS molecules with a large displacement between the dimers is realized, supposedly resulting in this strong π d interaction. From this J , the maximum of the internal ﬁeld is estimated − π−d Jπ−dSd as = 33 T. And the estimated N`eel temperature is TN =6.22 K. gµB Considering all together, the quantum chemical calculations predict simultaneous antiferromagnetic ground state of both π spin system of BETS molecules and d spin system of

FeCl4 anions below 6.22 K with the internal field of 33 T at maximum by the application of high magnetic field. The experimentally determined global phase diagram of ground states in zero magnetic field, Figure 4.4, confirms the onset of an antiferromagnetic insulating (AFI) ground state from the paramagnetic metallic (PM) state in the pure Fe compound (π d material) below − 8.5 K while the Ga compound (non π d material) exhibits a superconducting (SC) ground − state below 5.8 K. For x between 0.35 and 0.5, the alloys show PM-SC-AFI phase transitions. The global diagram under magnetic fields parallel to the c axis (Figure 4.5) shows the shift of the superconducting state to a higher field with 3d magnetic moments increase, i.e. the π d interaction increase. At the maximum concentration (for the pure Fe compound − at x = 1.0), the center of the field induced superconducting state (FISC state) agrees with the quantum chemically calculated value, 33 T. It is noteworthy that there are no significant differences in Fermi surfaces/band structures between magnetic and non-magnetic anion analogs, both experimentally and theoretically. Yet, despite the similarity in Fermi surface, the Ga compound becomes a superconductor below 5.8 K, suggesting an crucial role played by the strong Jπ−d for the onset of the AFM order in the Fe compound. Although there remain unresolved issues for the AFM order at low temperature, the quantum chemical calculations are recognized as an effective way for estimating the physical properties of alloys of λ-(BETS)2FexGa1−xCl4.

4.3.4 Field Induced Superconductivity

The above mentioned FISC state is well explained by Fischer’s two-dimensional expansion of the Jaccarino-Peter compensation mechanism [31, 32], where the magnetic interaction between the conduction π electrons on the BETS molecules and the localized d magnetic moments in the insulating layers plays a role.

37 Figure 4.4: Global phase diagram (no magnetic ﬁeld) of λ-(BETS)2FexGa1−xCl4. After [30].

A schematic diagram is shown in Figure 4.6. In the paramagnetic (PM) phase, the localized 3d moments in the anion layers are aligned along the external magnetic ﬁeld, B.

Through a negative exchange interaction Jπ−d between the 3d and the π spins, the π spins experience an internal magnetic field (Bint) up to 33 T (Bmax) formed by the 3d moments antiparallel to the applied external magnetic field. Therefore, the effective field on the π spins approaches to zero around Bmax since the exchange field on π spins is compensated by the applied field. This is called the Jaccarino-Peter compensation mechanism. There are two mechanisms to account for the destruction of superconductivity. One is the Zeeman effect and the other is the orbital effect. Under the condition above, the Zeeman effect is not present. When the applied magnetic field is parallel to the BETS molecule conducting layers, the orbital effect is suppressed due to the highly quasi two dimensionality of the electronic state.

38 Figure 4.5: Global magnetic phase diagram of λ-(BETS)2FexGa1−xCl4 for magnetic ﬁelds parallel to the c axis. After [30].

Ergo, superconductivity can be achieved by the application of high magnetic ﬁelds.

4.3.5 The motivation of the work

The theory explains the FISC state well, and the exchange field is estimated by quantum chemical calculations [28], as well as the splitting of the observed Shubnikov-de Haas oscillation frequencies [33, 34]. Yet, there was no experimental evidence of the internal field, and hence, of the J-P compensation mechanism. Assuming the separation of the ESR signals from π and d, the effective ESR frequency for separated π spin system in the high field regime around B , ω = gµ B + B , could give the experimental value of the exchange | int| B | int| field [34]. Therefore, the motivation of this work is to probe the local magnetic field and measure directly the internal field on the π electrons by ESR while monitoring the resistivity of the sample simultaneously for the observation of FISC state and the examination of the

39 Figure 4.6: The schematic diagram of Jaccarino-Peter eﬀect through the exchange interaction.

validity of the compensation mechanism.

4.3.6 Experimental methods

A simultaneous Electron Spin Resonance and magneto-transport measurement was employed. Resistivity was measured in a conventional four terminal method with a lock-in amplifier. 10 µm width annealed gold wires are attached on a surface of an a c conducting − plane by carbon paste. A transmission BWO is adopted for c.w. ESR in a 25 T high homogeneity magnet here at National High Magnetic Field Laboratory. The sample is placed in the Voigt configuration, where the dc magnetic field is perpendicular to the propagation of the electromagnetic wave, and a metallic foil is placed around the sample to cut off any background radiation. To bring down the center of the FISC state below 25 T, we used a single FexGa1−x alloy crystal from the x = 0.4 batch. The ESR probe does not have a rotational function. Hence, the angle of the sample to the applied field is fixed.

4.3.7 Results and Discussions: λ-(BETS)2Fe0.5Ga0.5Cl4.

Figure 4.7 shows the temperature dependence of the AFMR signal with ESR frequency at 44.9 GHz while the magnetic field was applied along a axis. From the temperature dependence of the resonance field, it is concluded that this reflects the separation of the

40 clustered paramagnetic d magnetic moments surrounded by GaCl s and π d exchange 4 − coupled antiferromagnets. This means that the Jπ−d interaction in this compound is suﬃcient enough to couple π and d spins.

Figure 4.7: AFMR of λ-(BETS)2FexGa1−xCl4 at x =0.5.

Therefore it was impossible to detect the exchange field by ESR in the metallic state as originally proposed without uncoupled π spins. Later, the internal field was experimentally confirmed to be about 32 T by NMR, where nuclear spins are separable from electronic spins and hence suitable for the detection of the internal field on the donor molecule [35, 36]. The temperature dependence of the resistance ratio to the room temperature resistance of a λ-(BETS)2FexGa1−xCl4 single crystal from the x = 0.4 batch is shown in Figure 4.8. Although x =0.4 sample is reported to have the PM-SC-AFI transitions, our sample showed no onset of the superconducting state. This implies a deviation of the x value of the crystal from 0.4. By comparing the obtained TN , 5.3 K, to the value on the zero field global

41 4 10

3 10

2 10 RT

R/R 1 10

0 10

-1 10 2 4 6 8 2 4 6 8 2 1 10 100 T (K)

Figure 4.8: Temperature dependence of a resistance ratio of λ-(BETS)2FexGa1−xCl4 at x =0.4 at B = 0.

phase diagram (Figure 4.4), we conclude that x is about 0.5, where the phase diagram only presents the PM-AFI transition. Crystals of λ-(BETS)2FexGa1−xCl4 alloys are prepared electrochemically from 10% ethanol-containing chlorobenzene solutions of BETS and mixed (Et N)(FeCl ) and (Et N)(GaCl ) supporting electrolytes with the ratio of x :1 x. Usually, 4 4 4 4 − the x value is estimated by an initial ratio of the starting solution and it can fluctuate as we have seen especially when x is around 0.5. For the exact measurement of the x value, EPMA (electron probe microanalysis) and/or X-ray refinements of the atomic population of the anion site are required [37]. Signals from the simultaneous c.w. ESR and magneto-transport measurement are shown in Figure 4.9. It was taken at 1.7 K with 403 GHz electromagnetic wave emission while the magnetic field is set to be along the sample’s c axis. Resistance exhibits no change at the resonance field, and only shows a monotonic increase with a magnetic field raise. As discussed in the experimental section 3, only a fraction of the spins absorb the electromagnetic wave

42 in the c.w. ESR measurement, which could explain no hint of the magnetic resonance in resistance.

403 GHz 1.7 K 28.5 B // c*

28.0

27.5 R ( Ω

27.0 )

26.5 EMR signal resistance 26.0 Transmission (arb. unit)

12 14 16 18 B (T)

Figure 4.9: Simultaneous ESR and magneto-transport measurement of λ- (BETS)2Fe0.5Ga0.5Cl4.

Also there is no sign of the FISC state, which indicates the deviation of the applied magnetic ﬁeld from the a c conducting plane. It is reported for pure FeCl compound that − 4 0.5 degree deviation from the plane destroys the FISC state. Figure 4.10 shows the ESR signals at several temperatures. The inset is g value temperature dependence, which shows a monotonic increase down to 2.5 K. Below 2.5 K, it shows an abrupt shift to lower values.

The cantilever-based magneto-torque measurements of the pure FeCl4 compound at 3 T on the b c plane is reported to show an abrupt change of the magnetic easy axis from the − b axis to 30 degree from the c axis with the development of magnetic ordering through Jπ−d interaction below TN in an antiferromagnetic insulating state, where a π electron localized at a BETS dimer [38, 39, 40]. Then, the g value along the c axis would appear to show the steep decrease reﬂecting the easy axis shift. Assuming the same nature, this steep change in

43 eeomn fteculn below coupling the of development hsidctsta ml hnei h lcrncparamet electronic the in change small a that indicates This of alloys the for reported iue41:Tmeauedpnec fteERtransmissio ESR the the of of dependence dependence Temperature 4.10: Figure h ne eo 2 below inset the ftees xs nldrcin ntematm,teground the meantime, the In direction. analog, final isostructural axis’ easy the of re ol espotdb pcfi esrmn,wihind which measurement, specific a the by supported be could order vlto fthe of evolution .. uueeprmn proposals. experiment Future 4.3.8 state. metallic the smnindaoe h atlvrbsdmgeotru me magneto-torque cantilever-based the above, mentioned As π pnAModrat order AFM spin J . π ol niaeteosto h antcodrthrough order magnetic the of onset the indicate could K 5 g − d λ value. opigb h butcag fmgei ayai below axis easy magnetic of change abrupt the by coupling -(BETS) Transmission (arb. units) λ T -(BETS) N g value B //c* 403 GHz 2.06 2.07 2.08 2.09 2.10 u not but 10 2 GaBr T 2.0 2 N FeBr z T Cl ugsstegaulosto the of onset gradual the suggests d 3.0 (K) antcmmns[ moments magnetic 4 − x 12 z Cl 4.0 hwaS oisltrtasto at transition insulator to SC a show , 44 4 B − x (T) for x 14 0 = 4.3 K . 4 r nue h aitoso not on variations the induces ers , 41 0 . inl ne:Temperature Inset: signal. n .Smlreouin r also are evolutions Similar ]. n 0 and 5 1.7 K 16 2.1 K 3.0 K 2.6 K ctstesde ne of onset sudden the icates tt ftenon-magnetic the of state srmn vdne the evidences asurement . d with 7 antcmoments’ magnetic x J z dependence π − 0 = T d N vnin even . This . [ 8 42 ]. only Jπ−d but also Jπ. ESR would be a perfect tool to conduct a systematic study of the role of the antiferromagnetic coupling upon the onset of superconductivity and magnetism.

3+ 3+ 4.4 β-(BDA-TTP)2MCl4(M=Fe , Ga )

Recently, organic conductors based on non-TCF donors (BDY-TTP: [bis-fused 1,3-dithiol- 2-ylidene]-1,3,4,6-tetrathiapentalene) have been developed with the strategy that relieving the tight intermolecular cohesion will lead to superconductivity [43].

From this family of compounds, we explore the interplay of dimensionality and interactions involving the onset of 3D magnetic order in the magnetic and non-magnetic analogs

β-(BDA-TTP)2FeCl4 and β-(BDA-TTP)2GaCl4, which follows the contents of a published paper citeref:Takahisa.

4.4.1 BDA-TTP donor molecule

By reversing the TCF C=C bridge and ring C=C bonding, the BDY donors consequently acquire more structural freedom in the fringe aromatic ring, which allows looser packing of the donor molecules. The chemical formulas of the conventional ET and novel BDA-TTP molecules are shown in Figure 4.11.The hydrogen atoms at the fringes are omitted. The axes correspond to the principal axes of the molecules. The looser packing leads to a smaller

Figure 4.11: Chemical formula of the conventional ET and novel BDA-TTP molecules.

transfer integral and smaller bandwidth, and hence a larger density of the states. Indeed,

45 superconductivity has been observed in some of those organic charge transfer conductors, and one of these, β-(BDA-TTP)2SbF6 (where BDA-TTP is [2,5-bis(1,3-dithian-2-ylidene)- 1,3,4,6-tetrathiapentalene]), is reported to have the largest eﬀective cyclotron mass (12.4 ± 1.1 me) yet found in organic conductors [44].

4.4.2 Crystal structure of β-(BDA-TTP)2FeCl4

− Combined with an acceptor (anion), FeCl4 , crystals of (BDA-TTP)2FeCl4 take a β phase

(See Chapter 1.). The unit cell of β-(BDA-TTP)2FeCl4 crystal has monoclinic symmetry, ◦ with a P 21/a space group with a = 12.452(7), b = 38.72(1), c = 7.731(4) A˚, β = 91.17(4) . It contains two crystallographically independent BDA-TTP cation molecules centered at

(a, b, c)=(0.23, 0.03, 0.92) for BDA-TTP1, (0.72, 0.03, 0.67) for BDA-TTP2, and one FeCl4 anion at (0.89, 0.25, 0.38). Due to the inversion symmetry, the unit cell contains four donor

Figure 4.12: Crystal structure of β-(BDA-TTP)2FeCl4. Hydrogen (H), Carbon (C), Sulfur (S), Iron (Fe), and Chloride (Cl), are represented by balls in blue, black, orange, red, and green, respectively.

1 molecules. The FeCl4 anions are located on the a glide plane at y = 4 and form linear chains of d magnetic moments along a axis through the Cl-Cl contacts. As shown in Figure 4.12, the structure consists of conducting layers of slightly dimerized BDA-TTP donor molecules, separated by insulating layers of FeCl4.

4.4.3 Physical Properties of β-(BDA-TTP)2MCl4: Estimated exchange interactions and experimental values.

From quantum chemical calculations, Jd is estimated as -0.86 K between neighboring d moments in a spin chain along a axis. Jπ−d is estimated at -1.49 K from the sum of − ﬁve overlaps between the Cl orbitals of the FeCl4 anions and the surrounding BDA-TTP

46 molecular orbitals. The small value is due to the inert trimethylene groups on the terminals. Jπ−dSd From this Jπ−d, the maximum of the internal ﬁeld is estimated as = 2 T. The N`eel gµB temperature, TN , is estimated as 5 K assuming that the π electrons are itinerant [29].

Therefore, the quantum chemical calculations evaluate β-(BDA-TTP)2FeCl4 as a large

Jd and a small Jπ−d system compared with the λ-(BETS)2FeCl4. Both Fe and Ga compounds show a metal-insulator transition with a transition temperature, TMI , around 113 K at ambient pressure. The zero ﬁeld temperature - pressure phase diagrams are nearly identical as shown in Figure 4.13. By applying pressure, both materials show a pressure induced superconducting state above 4.5 kbar.

120 Metal 100 (a. u.) 80 χ

(K) 60 0 50 100 150 T T (K) 40 Insulator

0 Superconductor 0 1 2 3 4 5 6 7 8 P (kbar)

3+ Figure 4.13: Temperature-Pressure phase diagram of β-(BDA-TTP)2MCl4 (M = Fe , 3+ Ga ). Inset: Temperature dependent magnetic susceptibility of β-(BDA-TTP)2FeCl4. After a reference [45].

The absence of splitting in the Shubnikov-de Haas oscillations in a pressure-dependent

Fermi surface study also indicates that Jπ−d is relatively small [45, 29]. Hence, the experimental observations support the calculated small Jπ−d.

47 4.4.4 The motivation of the work

Although the small value of the Jπ−d is theoretically and experimentally indicated, the eﬀect of the various exchange interactions upon the magnetic properties in β-(BDA-

TTP)2FeCl4, evident in both pressure dependent magneto-transport[45] and magnetic measurements (the onset of the long range order antiferromagnetic ground state below 8.5 K) [46], still remains an important question. To compare the π d material, β-(BDA- − TTP) FeCl , and the non- π d material, β-(BDA-TTP) GaCl , we report here a study of 2 4 − 2 4 their magnetic properties.

4.4.5 Experimental methods.

3+ 3+ β-(BDA-TTP)2MCl4 (M = Fe , Ga ) single crystals were grown by electrochemical methods [47, 46]. X-band ESR measurements were performed on a Bruker Elexsys 580 spectrometer (9.3-9.7 GHz), and higher frequency ESR was carried out on a millimeter vector network analyzer (40-100 GHz) [48] and a home-built superheterodyne quasioptical spectrometer (240 GHz) with a helium ﬂow cryostat [11]. Magnetic torque measurements utilized an atomic force microscopy (AFM) cantilever method [49], and a SQUID magne- tometer was used for susceptibility measurements. Raman spectroscopy was performed with a Renishaw inVia Raman microscope with a liquid nitrogen ﬂow system.

4.4.6 Results and Discussion.

Magnetic properties of β-(BDA-TTP)2GaCl4 at room temperature.

We first consider β-(BDA-TTP)2GaCl4 where the only spin component is due to the π electron donor system. The room temperature ESR spectrum as a function of magnetic field orientation in the b c plane is shown for 9.3 GHz (X-band), and 240 GHz in Figure 4.14(a), − 4.14(b), respectively. Although general angular dependences are similar, due to the much higher Zeeman interaction resolution at high frequencies, the spectra at 240 GHz reveal two components that are attributed to the equivalent but differently oriented layers of donor molecules as shown in Figure 4.12. The signals are symmetry-related by the a c mirror plane and overlap in this − plane. In Figure 4.15, the complete orientation dependence of the g values in the b c, c a, − − a b planes is shown, which allows the determination of the principal values and directions −

48 Figure 4.14: Angle dependent ESR signals of β-(BDA-TTP)2GaCl4 at room temperature in b c plane: (a) taken at 9.3 GHz, (b) taken at 240 GHz. −

of the associated g tensors. The directions of the principal axes of the two symmetry related g tensors are very close to the molecular axes of the donor molecule in neighboring layers (see Figure 4.12), which have an alternating stacking direction of the donor molecules. The observed principal values gx, gy, and gz are 2.0091, 2.0064, 2.0020, close to reported values for a similar donor molecule [50]. If an appreciable interplane coupling between the donor planes exists, and is of the order of ∆gµBB or larger, one would expect to see a single averaged signal. In this case, each layer gives rise to its own separate signal with its g tensor reﬂecting the orientation of donor molecules within the plane. We thus conclude that the π exchange interaction between neighboring donor layers is vanishingly small.

Temperature dependence of magnetic properties of β-(BDA-TTP)2GaCl4.

In Figure 4.16(a), the temperature dependent magnetic susceptibility measured at 0.3 T shows a sharp drop in χ at TMI . The b-axis susceptibility (ESR) of β-(BDA-TTP)2GaCl4, obtained from the integrated intensity of the 9.3 GHz spectra, is shown in Figure 4.16(b).

The χ (ESR) also shows a sharp drop of almost 2 orders of magnitude at TMI . Since constant-ﬁeld χ is proportional to the magnetization, the abrupt change indicates a ﬁrst order transition (∆ 400 K). The g value along the b axis also shows a sudden change at ∼ TMI (Figure 4.16(c)).

49 2.008

2.006 value g

2.004

2.002 b c a b

Figure 4.15: Complete angular dependence of the g value of β-(BDA-TTP)2GaCl4.

At low temperatures the spin susceptibility gradually increases following the Curie-Weiss law at 9.3 GHz and 240 GHz, respectively. We ascribe this to various paramagnetic impurities related to structural defects in the crystal since the signal at 9.3 GHz splits into several peaks at 240 GHz (Figure 4.17). Although intensities of some of the split signals increase monotonically when temperature goes down, the others, for example the signals around 8.48 T, seem to be due to the excited states since they disappear at 5K, possibly due to S=1 triplets. As shown in Figure 4.18(a), pulsed ESR measurements show the exponential increase of the spin-lattice relaxation time T1 below 20 K (1.5 ms at 5 K) while the spin-memory relaxation time T2 is more less temperature independent of the order of 1.5 µs. Figure 4.18(d), and (e) show the magnetization signals of T1, T2 measurements at 240 GHz at 5 K, respectively. Estimated T1 is about 0.8 ms and T2 is about 1.5 µs, at the same order of the T2 at 9.3 GHz. The T1 decrease with the increase of the frequency/field is explained by the enhancement of a one phonon mode excitation by higher frequency. If temperature dependence of T2 at 240 GHz is taken and shows temperature independence again, the frequency/field independence of T2 will indicate that the relaxation mechanism is based on hyperfine coupling relaxation, but not on electron-electron dipole interaction. This relatively long T2 corresponds to a homogenous linewidth, and indicates that electron spin- spin interactions are very small. The estimated spin concentration is less than 1018 cm−3.

50 500 2 (a) 100 χ (emu)x10 4

(0) Resistance ratio (left) 2 400 R χ (right) 10 (T)/

4 -6 R

2 300 1 600 (b) 500 400 (a. u.) 300 200

(ESR) 100 χ B//b 0 2.0115 (c)

2.0110

2.0105 g value 2.0100 B//b 2.0095 0 50 100 150 200 250 300 T (K)

Figure 4.16: Temperature dependence of magnetic properties of β-(BDA-TTP)2GaCl4. (a) Left axis: Resistance ratio of β-(BDA-TTP)2GaCl4. Right axis: χ from dc SQUID measurements. (b) χ and (c) g value from ESR along the b axis.

From these observations we conclude that the compound is predominantly nonmagnetic at low temperatures, and that at TMI , the system undergoes a transition from a paramagnetic metal to a nonmagnetic S = 0 insulator.

Magnetic properties of β-(BDA-TTP)2FeCl4.

We now turn to the magnetic properties of β-(BDA-TTP)2FeCl4. Figure 4.19 shows a orientation dependence of the g value of β-(BDA-TTP)2FeCl4 at room temperature at 240

GHz. Unlike β-(BDA-TTP)2GaCl4 (Figure 4.14(b)), only a single resonance line is observed with the principal axes reﬂects the crystal symmetry. The FeCl4 anions are located on the a c mirror plane and the principal axis with lowest g value is perpendicular to this plane, − while the other principal axes are roughly in between the a and c directions. This indicates that there is suﬃcient Jπ−d spin-exchange interaction to obtain a single exchange-narrowed

51 n eoe Lorentzian. transition, and becomes metal-insulator and plane the conducting Below the important. along becomes is ﬁeld electric oscillating muiis ne:Teapiuecnrs ftesgasab signals the of contrast amplitude The Inset: impurities. edi epniua othe whe to lineshapes perpendicular Dysonian is shown the ﬁeld as observed shape sometimes Dysonian a we to samples, Lorentzian ideal an from deviate ie hc ie oe on nteecag neato o interaction exchange the on bound lower a gives which line, neape h us w iesoaiyi em ftecond Chapter the of in m terms mentioned magnetic in As dimensionality the two of quasi terms the example, in an layers donor of dimensionality two h hne nteERsga ttemtlisltrtransit metal-insulator the at signal ESR the in changes the iue41:Tmeauedpnec feh eetdERof ESR detected echo of dependence Temperature 4.17: Figure ieit ln the along linewidth hscs h S inli oiae ytecnrbto fro contribution the by dominated is signal ESR the case this h eprtr eedneo h cssetblt ln t along susceptibility dc the of dependence temperature The rmtero eprtr S inlo h acmon,w ha we compound, Ga the of signal ESR temperature room the From a , b and ,

2 Pulsed detected ESR signals (a. u.) hntesml smtli,telnsaeo h inlcan signal the of lineshape the metallic, is sample the when , c xsa 4 H S r hw nFigure in shown are ESR GHz 240 at axes a 8.53 8.48 − 115K 110 K c 8.54 odcigpae nti iuto,teresulting the situation, this In plane. conducting 8.52 8.55 52 B (T) 8.56 105 K 85 K 65 K v n below and ove 45 K 25 K h yoinsaedisappears shape Dysonian the o r esdramatic. less are ion 5 K h kndpho h sample the of depth skin the re ∆ order f 8.60 he ciiyi h ecompound. Fe the in uctivity h = S the m mns eew hw as show, we Here oments. h siltn magnetic oscillating the n c nFigure in xs n the and axis, β -(BDA-TTP) gµ 4.21 esontequasi the shown ve 2 5 B T Fe , B MI 4.20 nieteGa the Unlike . 0 . 3+ ≈ g o larger For . 0m.In mK. 40 ausand values pn,and spins, 2 GaCl 4 Figure 4.18: T1, T2 measurements of β-(BDA-TTP)2GaCl4. (a) Temperature dependence of T1, T2 relaxation time at 9.3 GHz. Left axis: Spin-lattice relaxation time, T1. Right axis: Spin-spin (spin memory) relaxation time, T2 at 9.3 GHz. Open symbols for T1 and closed symbols for T2. (b) T1 magnetization signals at 9.3 GHz at various temperatures. (c) T2 magnetization signals at 9.3 GHz at various temperatures. The colors represent the temperature of the measurements. (d) T1 Relaxation time measurement signals at 240 GHz at 5 K. (e) T2 Relaxation time measurement signals at 240 GHz at 5 K.

compound, there is no signiﬁcant change at TMI in dc susceptibility data in Figure 4.21(a).

However, at TMI the g values in Figure 4.21(b) show slight changes that are consistent with the extinction of the donor contribution due to the formation of a π electron spin singlet.

Also, since the exchange narrowing due to Jπ−d interaction vanishes at TMI , the linewidths get broader as shown in Figure 4.21(c).

Metal-Insulator transition and charge order.

As the formation of spin-singlet states suggests a dimerization of neighboring donor molecules, it is likely that the MI transition is accompanied by a change in the crystal structure. The local donor environment was probed by temperature dependent Raman spectra of both the Ga and Fe compounds (Figure 4.22). Nearly identical temperature

53 2.015

2.014 value

g 2.013

2.012 c a c

bb c a b

Figure 4.19: Complete angular dependence of the g value of β-(BDA-TTP)2FeCl4 at room temperature with 240 GHz. Inset: c a c rotation. − −

dependent Raman spectra are seen in both cases, including similar changes in the spectrum −1 passing through TMI . The peaks around 1500 cm originate from Raman active modes associated with the C = C bonds. Below TMI , these peaks begin to resolve into additional peaks and shoulders, and other peaks at lower wave numbers either appear or change form. While we cannot make speciﬁc assignments to the modes in question at this time, it is clear that Raman data indicate a lowering of symmetry and a change in the local environment at

TMI .

The transition at TMI for β-(BDA-TTP)2GaCl4 is strikingly similar to that reported for the charge order transition in α-ET2I3 [51, 52]. In both cases, it is a transition from a paramagnetic metal to a nonmagnetic (spin-singlet) insulator. Moreover, as in α-ET2I3,

Raman data show a significant shift at and below TMI . In the case of α-ET2I3, horizontal stripes of donors alternate between charge rich and charge poor configurations [51, 53]. Although earlier x-ray measurements did not show a lowering of symmetry at the MI transition [54], recent synchrotron data [55] confirm a change of symmetry from P 1¯ to P 1 at the MI transition for αET2I3. For β-(BDA-TTP)2MCl4, there is weak dimerization of the

54 ucpiiiydw o5Kfiswl oaBne-ihrcref curve Bonner-Fisher a [Figure to K well -1.05(2) fits of K interaction 5 to down susceptibility au f-.6K[ K -0.86 of value iue42:Tmeauedependent Temperature 4.20: Figure ar.Rpre -a aaaoeadblwteM transition MI the below local and the above enhance data x-ray can Reported which pairs. temperature, room at even donors GHz. niermgei re in order temp Antiferromagnetic low the resolve low to and necessary K), be 95 will (above measurements observed x-ray been the yet in has changes symmetry comparable in change and direction, stacking the along hwsmlrcagsi atc osat saeosre in observed are as constants lattice in changes similar show h xstruhteitrainC-lcnat.Teaniso [ The K contacts. 5 Cl-Cl inter-anion the through axis a the TTP) ial,w ou ntentr fteA neato in interaction AF the of nature the on focus we Finally, 43 2 FeCl ofim the confirms ] 4 xiistpclatfroantcrsnne(FR behav (AFMR) resonance antiferromagnetic typical exhibits 29 for ] a J xsa h ieto ftecan.Below chains. the of direction the as axis

d Signal Intensity (arb. unit) opigbtenteF pn,wihi nyapeibealo appreciable only is which spins, Fe the between coupling 2500 β -(BDA-TTP) 4.21 a a] hsi ngo gemn ihteestimated the with agreement good in is This (a)]. 3000 − c Field (G) ln iehpsof lineshapes plane 55 2 3500 FeCl 110K 130K 4 . 4000 α rp ntessetblt above susceptibility the in tropy -ET rtr symmetry. erature ierlage.Hwvrno However angles. dihedral [ β β 56 2 zto fcag ndonor on charge of ization r1 hiswt nAF an with chains 1D or -(BDA-TTP) -(BDA-TTP) I 3 in ] eprtr synchrotron temperature ihtelretchange largest the with , T β N -(BDA-TTP) o [Figure ior ≃ K, 5 2 2 FeCl FeCl β 4 -(BDA- 4 4.21 The . 2 t9.3 at FeCl (b) ng 4 140 χ 2 (a) Resistance ratio (left) 100 χ (right) B//c 120 (emu)x10

4 100 2 80 (295) 10 R 60 )/

4 -6 T 40 ( 0 5 10 15 20 25 2 R 20 1 0 2.06 (b) 2.008 B//b B//a 2.04 2.006 B//b 100 120 140 B//c 2.02

g value TN 2.00 TMI

1.98 (c) 0.1 B a 8 B//b // 6 B//b B c 4 100 120 140 //

Linewidth (T) 0.01 8 6

0 50 100 150 200 250 300 T (K)

Figure 4.21: Temperature dependence of magnetic properties of β-(BDA-TTP)2FeCl4. (a) Left axis: Resistance ratio of β-(BDA-TTP)2FeCl4 near TMI . Right axis: Magnetic susceptibility of β-(BDA-TTP)2FeCl4. Dotted line: Curie-Weiss law: solid line: Bonner- Fisher ﬁt (see text). Inset: Magniﬁed view of the susceptibility around the peak. (b) g values of β-(BDA-TTP)2FeCl4 at 240 GHz along the a, b, and c axes. Inset: g value change along b at TMI . (c) Linewidths of β-(BDA-TTP)2FeCl4 at 240 GHz along the a, b, and c axes. Inset: Linewidth along b at TMI .

and 4.21(c)] with the easy axis along c: Here gc decreases and ga and gb increase with broadened linewidths. Figure 4.23 summarizes the frequency dependence of the ESR signals at 1.5 K, which exhibit biaxial AFMR behavior with the easy axis along c. The spin ﬂop

ﬁeld, Bsf , is estimated to be 0.77 T, very close to the value of 0.8 T obtained by cantilever magnetic torque measurements at 0.3 K (inset of Figure 4.23). We conclude that β-(BDA-

TTP)2FeCl4 undergoes a transition to anisotropic three dimensional antiferromagnetic order below TN . To explain these magnetic properties the diﬀerent exchange interactions in this system need to be considered. They have been analyzed theoretically [29]: a direct J ( -0.86 d ≈ K) interaction is expected along the a axis, while in the b and c directions the exchange is mediated by Jπ and Jπ−d couplings, with an estimate for the latter of the order of -1.5

56 (a) Ga (b) Fe

93K 93K

103K 103K

T MI TMI 113K 113K Raman Spectrum

123K 123K

1200 1300 1400 1500 1200 1300 1400 1500 -1 -1 wave number (cm ) wave number (cm )

Figure 4.22: Temperature dependent Raman signals: (a) β-(BDA-TTP)2GaCl4; (b) β-(BDA- TTP)2FeCl4.

K. The observation of antiferromagnetically coupled quasi-1D spin chains along the a axis down to 5 K illustrates the apparent absence of a substantial Jπ−d interaction. This is in line with the formation of the singlet state in the donor system below TMI and the associated quenching of the Jπ−d interaction. However, this raises the question why then the Fe system forms a 3D AF ordered state at T 5 K. At least a small interaction ( -0.3 K) [57] must N ≃ ≈ exist along the b and c axes, where, along b, the Fe ions are separated by the donor layers over the very large distance of 20 A˚. At this distance, the magnetic dipolar interaction is 1 ∼ mK and can be excluded as a possible mechanism. At these temperatures it is unlikely that spin excitations play a role in the gapped donor system, but quantum spin fluctuations will mix in some higher spin character into the ground singlet. The existence of Jπ−d interaction above TMI also indicates that at least some of the iron spin must be admixed into the delocalized donor molecular orbitals, even in the formal singlet state. Recent theoretical and experimental work has shown that, for spin singlet conjugated linker molecules, exchange can take place over quite large distances [58, 59]. The role of the spin fluctuations in the Fe3+ spin chains, the quantum spin fluctuations in the donor layers, and the superexchange

57 4 +5°

c axis

3 (a.u.) τ -5° 0.0 0.5 1.0 1.5 Field (T) a-axis (T) 2 b-axis

ω/γ c-axis

hard axis 1 2nd easy axis B easy axis above sf

B =0.77T 0 sf 0 1 2 3 4 B (T)

Figure 4.23: Frequency dependence of β-(BDA-TTP)2FeCl4 at 1.5 K along the a, b, and c axes. Inset: Magnetic ﬁeld direction dependence of the AFM cantilever (torque) signal at 2.5 ◦ intervals.

through the donor layers should be accessible via quantum chemical calculations. Based on the experimental evidence above, we conclude that the combination of these factors leads 5 3+ to a small but suﬃcient exchange between the S = 2 Fe spins along b and c to cause the observed 3D AF ordering.

4.4.7 Proposals for future work and concluding remarks

Although the origin of the Metal-Insulator transition of β-(BDA-TTP)2MCl4 (M= Fe, Ga) seems to be the charge order of π donor systems, there is no direct evidence obtained yet. As mentioned above, temperature dependent synchrotron x-ray measurements will be required to resolve the symmetry breaking. Precise temperature dependent Raman spectroscopy will also be a help for a comparison between β-(BDA-TTP)2MCl4 (M= Fe, Ga) and BDA-TTP, the donor molecule itself. A prediction of a pattern of the charge order should be done by quantum chemical calculations. In this work, we have shown that the ﬁrst order Metal-Insulator transition at 113

58 K in both these compounds involves the formation of a spin-singlet state in the donor layers, which is likely associated with charge order. However, we have also shown that 3D antiferromagnetic ordering of the Fe spins in the anion layers is observed at relatively high temperature of 5 K, in spite of the large separation ( 20A˚) of the anion layers by the ∼ spin-singlet donor layers. This experimental observation posed the question: In the absence of a π spin system, what is the mechanism providing the necessary coupling over these unusually large distance? Our main contribution in this chapter is to point out as follows: A mixing into a triplet state is induced by quantum ﬂuctuations even in a spin singlet state at a donor. Since the π orbital is spread all over the donor, as long as the orbitals of d spins overlap with the π orbital of the donor, the triplet exchanges the d spins no matter large the distance between the d spins. In simple words, as long as the orbitals overlap, exchange interactions between the spins at quite large distances can happen. This mechanism in turn explains why π spin systems, which are separated by non magnetic anion layers, can have a long range antiferromagnetic order. For a solid proof, quantum chemical calculations will be required.

59 CHAPTER 5

ITINERANT SPIN SYSTEM

Chapter 4 discussed the magnetism in systems with exchange interactions between localized d magnetic moments and π spins. In this Chapter 5, we discuss the magnetism in an itinerant spin system, a τ phase organic conductor, τ-(P-(S,S)-DMEDT-TTF)2(AuBr2)1(AuBr2)y. 5.1 Introduction to a τ phase organic conductor.

Finding a novel superconducting material has always been one of the strongest driving forces in material science. In the organic community, a particular class of organic conductors, κ phase conductors, where a layer of donor molecules consists of orthogonal mixed-valence dimers, is well known for superconductivity with a relatively high Tc [60, 61, 62]. One of the κ phase superconductors is κ-((S,S)-DMBEDT-TTF)2ClO4, which is based on the unsymmetrical donor molecule S,S-dimethyl-bis(ethylene)dithio-tetrathiafulvalene. See

Figure 5.1: The chemical structure of (S,S)-DMBEDT-TTF.

Figure 5.1 for a donor structure. This organic conductor has a superconducting transition temperature Tc at 2.6 K under a pressure of 5.8 kbar [63].

60 By replacing two sulfur atoms of the ethylenedithio moiety by nitrogen as shown in Figure 5.2, a new donor, (P-(S,S)-DMEDT-TTF), pyrazino-(S,S)-dimethyl-ethylenedithio- tetrathiafuluvalene is formed, which maintains the same molecular shape and size of ((S,S)- DMBEDT-TTF).

Figure 5.2: The chemical structure of P-(S,S)-DMEDT-TTF.

This donor only forms a crystal with linear acceptors such as (AuBr2). Due to intermolecular S–N and S–S interactions between the neighboring donors with a support of the linear acceptor in the middle of the donor planes, the donor stacking of (P-(S,S)-DMEDT- TTF) is transformed into a new lamellar-type phase as shown in Figure 5.3 of a conducting layer. Unlike conventional organic conductors, where there are alternating layers of donors

Figure 5.3: A conducting layer of a τ phase organic conductor: View down along a c axis.

and acceptors, in this case the conducting layers are a mixture of donors and acceptors. The intermolecular distances of S1–S2 and S2–N are within or close to the van der Waals radii,

61 leading to a large overlap of the two neighboring donor orbitals. As a result, the transfer integral, which is a barometer of the easiness for electrons to move between donor molecules, between perpendicular molecules, t1, is 10 times larger than the transfer integral between parallel ones, t2 [64]. From the conﬁguration of each donor and the value of the transfer

Figure 5.4: Calculated (a) Fermi surface, (b) band structure, and (c) τ phase donor structure and its transfer integrals calculated between neighboring donor molecules of the conducting plane. In (a) and (b), the dashed line represents y = 0 and the solid line represents y 0.75. After [65]. ∼

integrals between them, an electronic band structure of a single conducting layer has been calculated with the extended Huckel tight binding method and Fermi surface for y 0.75 is ∼ estimated [66] as in Figure 5.4.

62 5.2 Crystal structure of τ-(P-(S,S)-DMEDT-TTF)2(AuBr2)1(AuBr2)y

Figure 5.3 and Figure 5.5 shows the crystal structure of τ -(P,(S,S)-DMEDT)2(AuBr2)1+y. Here after it is named τ-P. The unit cell is highlighted by blue dotted lines with the dimensions a = 7.3546 and c = 67.977 A˚ [66]. As “τ” implies, the crystal structure sustains the tetragonal symmetry of the conducting layers along the c axis. Between the conducting

Figure 5.5: A crystal structure of a τ-P. View down along a a axis.

′ layers, an AuBr2 anion forms an insulating layer located at a =0, c =0.125 along the a axis.

The symmetry group is I4122 [66]. Each conducting layer is connected by simple symmetry ′ 1 matrices such as “90 degree in-plane rotation from the a axis to the a axis and 2 unit cell translation along the a′ axis” as well as insulating layers.

It is noteworthy that the ratio of the donor, (P-(S,S)-DMEDT), to the acceptor, AuBr2, is unstoichiometric (2:1+y) due to the uncertain vacancies of the AuBr2 in the insulating

63 layers. From an element analysis and other methods, the y value is estimated to be around 0.75 [66]. Since the number of electrons per donor depends on the y value, a variation of y value represents a Fermi energy change. The band structure calculation predicts that the system becomes conducting for y between 0.6 and 1. Indeed, at y around 0.75, an in-plane resistivity shows a metallic behavior below 95 K while it is almost constant above 95 K. The inter-plane resistivity shows a semiconducting behavior [66, 67]. The ratio of inter-plane and in-plain resistivities at room temperature is about four orders of magnitude, also indicating the strong quasi two dimensionality [66, 67]. 5.3 Physical properties of τ-P. 5.3.1 Transport properties at zero and low/intermediate magnetic ﬁeld

Figure 5.6(a) shows the inter-plane resistivity as a function of temperature indicating a non- metallic behavior with a kink around 12 K [67]. Despite the non-metallic behavior, when a

Figure 5.6: Temperature/magnetic field dependent resistivity of τ-P. (a) Temperature dependent resistivity (zero magnetic field). (b) magneto-resistivity. The field is applied along the interplane c axis. After [67].

magnetic ﬁeld is applied, it shows a negative magnetoresistivity and starts exhibiting two Shubnikov-de Haas (SdH) oscillations below 1.4 K above 20 T with a large hysteresis as shown in Figure 5.6. The material remains metallic up to 35-38 T.

64 Two Shubnikov-de Haas frequencies can be distinguished. The highest frequency of 516

T is dominant, and corresponds to an eﬀective mass of 4.4 me, and a lower frequency of 186 T corresponds to 7.5 me. The observation of SdH oscillation is the signature of coherence of the in-plane transport properties and reﬂects a closed Fermi surface. Therefore the observation of two SdH frequencies contradicts the calculated Fermi surface based on the room temperature crystal structure, which has only one closed orbit. Neither a lattice distortion nor a super- lattice was yet reported by previous low temperature X-ray measurements.

5.3.2 Magnetic properties at low/intermediate magnetic ﬁeld

Field dependent SQUID magnetization show a slight kink with the field along the c axis below 12 K, while they show more gradual changes with the field along the a and a′ axes at any temperature range [68]. Temperature dependent SQUID magnetization data show a monotonic increase of the magnetization with the field along the c axis, while the data show peaks with the field along the a and a′ axes around 12 K [68]. Although there are disagreements between field dependence and temperature dependence, the magnetization data indicate the onset of antiferromagnetic behavior below 12 K [68]. Proton NMR on a 1 single crystal (field along c axis) shows the linewidth broadening with T1 divergence below 20 K, which usually is a signature of magnetic order [35]. When the paramagnetic spin system undergoes a magnetic ordering, randomly fluctuated spins become static passing through the 1 NMR frequency range, interfering T1 measurement, resulting in the T1 divergence. From the theoretical point of view, ferromagnetic order is predicted due to the flat band structure as shown in Figure 5.4 [69]. When the band is flat, all the electrons have more or less the same velocity. To avoid building coulomb energy, spins of those electrons tend to align. Previous measurements and magnetic properties indicate the possibility of magnetic ordering at low temperatures, low fields.

5.3.3 Physical properties at high ﬁeld

Moreover, when an even higher magnetic ﬁeld is applied, the material shows a metal- insulator transition above 38 T, accompanied by hysteresis as shown in Figure 5.7. This T H phase diagram is plotted by way of magnetocaloric eﬀect, Tunnel Diode Oscillator, − and transport measurements. The transport measurements show that this M-I transition is very sensitive to pressure ( 1 kbar). Hysteretic behavior is also observed in the magnetization

65 Figure 5.7: Schematic high field phase diagram and cantilever torque magnetization signal of the τ-P. (a) Schematic high field phase diagram of the τ-(P-(S,S)-DMEDT- TTF)2(AuBr2)1(AuBr2)y. The threshold field for the high field phase boundaries is based on magnetoresistance and ac skin-depth measurements in pulsed fields, and magnetocaloric measurements in dc fields. Arrows indicate the up-sweep and down-sweep data. (b) Cantilever torque magnetization signal from τ-P-racemic. at 0.5 K. The overall background signal depends on the orientation of the cantilever with respect to field. The inset shows detailed behavior of the hysteresis in the magnetization in the field induced MI transition region. The arrows indicate the direction of the field sweep. The double arrow indicates reversible behavior between the upper and lower threshold limits. After [70]

measurements as shown in Figure 5.7 [64, 65]. Angular dependent torque measurement shows that this ﬁeld induced M-I transition is nearly isotropic. Thermopower studies indicate that a magnetic ﬁeld dependent gap opens up at the M-I transition. All the measurements on this system illustrate the hysteretic M-I transition.

5.4 Motivation of this work

As a summary of previously reported physical properties, τ-(P-(S,S)-DMEDT-

TTF)2(AuBr2)1(AuBr2)y shows the kink in zero ﬁeld resistivity around 12 K. It also exhibits hysteretic negative magneto-resistivity with Shubnikov-de Haas oscillations below 1 K. The negative magneto-resistivity is usually a signature of magnetic interaction. Below 12 K, SQUID and NMR display the onset of some kind of magnetic order (possibly antiferromagnetic order). It also presents the hysteretic Metal-Insulator transition that occurs above 38 T

66 and below 13 K. Therefore the question here is “Does magnetism play a role in the behavior of this material?” And the motivation of this work is to find an answer by characterizing the precise magnetic structure in the above described regions. ESR is a ideal tool for probing the local magnetic fields. To cover a vast range of the field/frequency required for this series of experiments (from 0.3 T up to 45 T / from 9.3 GHz up to 1.2 THz), we have employed several ESR experimental setups.

5.5 Results and discussions

5.5.1 Low temperature and low magnetic ﬁeld ESR

First, temperature dependent X-band (9.3GHz) measurements between 0.1 to 0.5 T below 20 K down to 4 K did not yield any signals, in contrast with the previous reports [66]. However, using a non-field-modulated resonant cavity perturbation detection by Millimeterwave Vector Network Analyzer (MVNA) at 91.3 GHz, with the field parallel to the c axis, we observed two peaks (resonances), which start shifting to lower fields below 12 K as shown in Figure 5.8(a). This temperature dependence of the resonance field shifts is a typical Antiferromagnetic Resonance (AFMR) behavior when the field is applied along a non-easy axis, and can explain why no signals were observed at X-band. To identify the origin of the two signals we tried to do the frequency dependence with the vector analyzer. Then, we performed quasi-optical non-cavity field-modulated reflection ESR with a home build 120/240 GHz superheterodyne equipment with a helium flow cryostat [11]. In Figure 5.8(b) are the temperature dependent ESR spectra with the field applied along the c axis at 240 GHz. Again the spectra show two peaks, which seem to follow AFMR temperature dependence when a magnetic field is applied along a non-easy axis. The difference from the previous in-cavity measurement is fine structures appearing on a shoulder of the lower field resonance at low temperatures. Figure 5.9(a) and Figure 5.9(b) show the temperature dependence of the resonance fields at 240 GHz and 120 GHz, respectively. Although 120 GHz and 240 GHz resonance fields shift to lower field when the temperature decreases, higher field resonances along c axis only show the gradual deviation from g = 2, paramagnetic, field. The resonance fields for free (paramagnetic) g = 2 electrons are 4.282 and 8.564 T at 120 and 240 GHz, respectively. The effective g values, which usually describe

67 Figure 5.8: Temperature dependent spectra of τ-P at intermediate frequencies with the ﬁeld along the c axis. (a) MVNA spectra. (b) 240 GHz quasi-optics Spectra.

the environments around spins, stay almost constant when the spins are paramagnetic. When spins have some kind of magnetic order, the g values start changing systematically as the order grows. In a simple AFMR mode far below the Nèel temperature, the “non-easy axis” g values are higher than 2 while the “easy axis” g value is lower than 2 when the applied magnetic field is above spin flop field. Although the temperature dependence of the resonance field follows the “non-easy axis” AFMR mode, for the higher field resonances for 120 GHz as well as 91.3 GHz, the g values are lower than 2. When the field is applied in the conducting plane (along a or a′ axis), this temperature dependence of the resonance field changes completely. Those spectra are shown in Figure 5.10(a). Instead of two peaks, two additional peaks are recognizable. The resonance fields from Figure 5.10(a) are plotted in Figure 5.10(b). Except the lowest field signal, all resonance fields seem to follow the “easy axis” AFMR mode. The connections between the “B c” two peaks and the “B a” four peaks are revealed k k

68 Figure 5.9: Temperature dependent resonance ﬁeld of τ-P with the ﬁeld along the c axis. (a) At 240 GHz. (b) At 120 GHz.

by the angle dependent measurement at 4 K as two sets of “symmetry related” signals, as shown in Figure 5.11. Previously reported temperature dependent magnetization data may indicate that each conducting plane has a preferable easy axis of Antiferromagnetic order along the a or a′ axes [68]. With this assumption, the c axis is the hard axis. Therefore, when it is rotated from out of plane to in plane (from B c to B a), the applied magnetic k k field is getting aligned to one of the easy axes, the a axis, while staying perpendicular to the other easy axis, the a′ axis. As a consequence, when the field is tilted from the c axis to the a axis, overlapped signals of each set split into two separate signals, one with the easy axis along the a axis and the other with the easy axis along the a′ axis, resulting in total four peaks for two sets. Although the a′ easy axis stays perpendicular to the field during the “out of plane (B c) to in plane (B a)” rotation, the positions of the signals of each k k set from the a′ easy axis are not constant. So it is reasonable to take the c axis as a hard axis, and take the a′ axis as an intermediate axis for the a easy axis signals. When the field is in the plane revolved from the a easy axis to the a′ easy axis, the signals merge at 45 degrees from both the a and the a′ easy axes. The alternating two fold symmetries can be explained by the local two fold symmetry of AuBr2 anion insulating layers provided that Au has a spin. In fact, Au3+ has a spin with S = 1. But, due to this linear shape, it is unlikely

69 Figure 5.10: Temperature dependent (a) 240 GHz spectra and (b) resonance ﬁeld of τ-P with the ﬁeld along the a axis.

that Au is trivalent and hence has a spin. If then we assume that spins are located on donor sites in the conducting plane, spins are in a frustrated situations due to its tetragonal symmetry and it is impossible to have an easy axis in any direction on the plane. Since the y value in the insulating plane is about 0.75, one out of four anions in the insulating plane are missing. These defects might break the frustration on the conducting planes, resulting in an alternating easy axes structure with two fold symmetry. Upon the symmetry breaking, we can expect slight changes in the crystal structure. Hence the precise determination of the crystal structure below 12 K is required for the further understanding. Although this description of two easy axes, which are attributed from the diﬀerent conducting planes, explains very well the behavior of a set of signals to the ﬁeld, it remains to be solved that we observed the two sets of the symmetry related signals. Although the two sets’ angle dependent ESR responses are symmetrically analogous in general, they are not identical. We suggest that this could be due to an interaction between four sublattices, two along a easy axis and two along a′ easy axis.(Figures)

70 Figure 5.11: Field direction dependent resonance ﬁeld of τ-(P-(S,S)-DMEDT- TTF)2(AuBr2)1(AuBr2)y at 240 GHz at 5 K:

5.5.2 Low temperature and ultra high magnetic ﬁeld ESR

Now we turn to the ﬁeld-induced hysteretic Metal-Insulator transition around 38 T. The state above BMI can only be studied in hybrid and/or pulsed magnetic ﬁelds, presenting a challenge to determine the mechanism leading to the MI state. To explore the possibility of the magnetic ordering below and above the BMI , we employed a FIRL as a ESR source at 847.036 GHz(CD3OD:10R16), at 1044.18 GHz(CD3OH:10P8), at 1182.4 1GHz

(CD3OH:10R36) in the hybrid magnet at NHMFL. The sample is set in a transmission configuration with a marker (no field dependence in the intensity, linewidth, and resonance field) on the top and field is applied along the c interplane axis. Hence a spectrum consists of two spectra, broad signal from the sample and sharp reference from a marker. Figure 5.12(a) shows the frequency dependence of the ESR spectra at 1.3 K at the metallic state, the M-I transition region, and the insulating state, respectively. The signal in the metallic state is wider and smaller compared to those in the insulating state, following the general features expected for the M-I transition. Unusual phenomena are found for the spectra field at 37.2 T, which corresponds to the center of the M-I transition region from the comparison of the

71 signal from the sample and the reference from the marker as the broadest linewidth. The

Figure 5.12: Ultra high ﬁeld cw ESR spectra of τ-P. (a) Frequency dependence. (b) Temperature dependence.

reason of the small reference from marker is unknown. This reduction of the reference signal is also observed in Figure 5.12(b), the temperature dependence of the signal, when the sample is approaching to the M-I transition( 13 K) with monotonic shifts of the resonance fields ∼ to higher field. Figure 5.13 shows the deviation of the resonance field from the paramagnetic

1.2

1.0

0.8 B ∆ 0.6

0.4

0.2

0.0 0 400 800 1200 Frequency (GHz)

Figure 5.13: Deviation for the resonance ﬁeld from g=2, paramagnetic, resonance ﬁeld τ-P.

ﬁeld. Since the reference signal from a marker does not have any frequency or temperature

72 dependence, the deviation is obtained by comparison between the sample signal and the reference signal. The deviations are exponential decrease to zero and becomes negative (g < 2) at 42.244 T in the field induced insulating state. Although this reduction of the deviation at higher field is reasonably understood by the alignment of the spins to the applied field, the temperature dependence in Figure 5.12(b) shows that the g values are re-approaching to 2.

5.6 Summary and what’s next?

At least two ESR lines emerge and shift to higher g values with decreasing temperature below T = 12 K at low field /frequencies when the field is along the c axis. Multiple ESR lines shift systematically with rotation of in-plane magnetic field, which indicates the alternating two easy axes structure in the conducting plane at intermediate field/ frequencies. Multiple ESR lines approach g = 2, and even go below g = 2 near 45 T. ESR line intensity anomalies are found in the hysteretic transition region. ESR intensities are consistent with metal vs. insulator conditions. No strong evidence is obtained for a (ferro)magnetic phase transition at BMI . As a next step to solve the field induced Metal-Insulator mystery, a high field X-ray in the 35 to 50 T range is suitable to decide whether the transition is a structural transition or not. For the experimental requirement, 4.2 K should be low enough. We have many descriptive experiments, but no real model. Therefore, a development of a theory is necessary to explain the two easy axes model and the hysteretic field induced metal-insulator transition.

73 CHAPTER 6

CONCLUSION

We have worked on two completely diﬀerent systems. One is the system with the exchange interaction, “Jπ−d”, between localized d magnetic moments embedded at acceptors and π spins located on the donors. Due to the exchange interaction, a variety of magnetic ground states, such as ﬁeld induced superconducting state, is expected. For λ-

(BETS)2Fe0.5Ga0.5Cl4, we performed a simultaneous resistivity and ESR measurement and pointed out the possibility of development of the magnetic order even in the field induced 3+ 3+ metallic state. For β-(BDA-TTP)2MCl4 (M = Fe , Ga ), we compared the iso-structural systems, a system with the magnetic acceptor(FeCl4) and a system with the non-magnetic acceptor(GaCl4) for the full understanding of the effect of the exchange interaction mainly by ESR. At the metal-insluator transition, ESR showed the formation of π spin singlets in both Fe and Ga compounds. With the help of the Raman spectroscopy, we concluded that the spin singlets are probably accompanied by charge ordering in the donor sites. In fact, Fe compound exhibits one dimensional spin chain characteristic down to 5 K, where it becomes a long range ordered antiferromagnet. This raises an important question, “In the absence of a π spin system, what is the mechanism providing the necessary coupling over these unusually large distance?” Our answer to the question is that a mixing into a triplet state is induced by quantum fluctuations even in a spin singlet state at a donor. Since the π orbital is spread all over the donor, as long as the orbitals of d spins overlap with the π orbital of the donor, the triplet exchanges the d spins no matter large the distance between the d spins. Hence, as long as the orbitals overlap, exchange interactions between the spins at quite large distances can happen. As a future work, it is interesting to measure ESR in the pressure induced metallic state where the Jπ−d is expected. Also, to determine whether the origin of the metal-insulator is charge order or not, temperature dependent syncrotron

74 x-ray may be required. And the other system is one of the τ phase organic conductors, where conducting layers consist of asymmetric donors and linear acceptors and hold a tetragonal symmetry and unstoichiometric donor/acceptor ratio. We investigated the low/intermediate magnetic order of τ-(P-(S,S)-DMEDT)2(AuBr2)1+y by ESR and confirmed the alternating two easy axes on conducting planes with an additional set of resonances. Also we examined the origin of the hysteretic field induced metal-insulator transition by ultra high field ESR based on far infra red laser. Although we succeeded to conduct the experiment, there is no observation of the significant changes in the local magnetic structures, suggesting a different origin. For future works, cantilever base magneto-torque measurements may be required to determine the spin flop fields and X-ray in pulse field may help to unveil the still unknown origin of the field induced metal-insulator transition.

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78 [39] M. Tokumoto, H. Tanaka, T. Otsuka, H. Kobayashi, and A. Kobayashi. Observation of spin-ﬂop transition in antiferromagnetic organic molecular conductors using AFM micro-cantilever. Polyhedron, 24:2793, 2005. 4.3.7

[40] H. Tanaka, S. Hara, M. Tokumoto, H. Cui, H. Kobayashi, and A. Kobayashi. Obser- vation of Antiferromagnetic Spin-Flop Transition in λ-type BETS Salts Using AFM Microcantilever. Journal of Low Temperature Physic, 142:605, 2006. 4.3.7 [41] H. Akiba, S. Nakano, Y. Nishio, K. Kajita, H. Kobayashi, and A. Kobayashi. Speciﬁc heat measurement in λ-(BETS) systems - superconductivity and antiferromagnetism - . Spring Meeting of Physical Society of Japan, 2008. 4.3.8

[42] H. Kobayashi, H. Akutsu, E. Arai, H. Tanaka and A. Kobayashi. Electric and magnetic properties and phase diagram of a series of organic superconductors λ- (BETS)2GaXzY4−z [BETS=bis(ethylenedithiotetraselenafulvalene; X, Y = F, Cl, Br; 0

[44] E. S. Choi, E. Jobilong, A. Wade, E. Goetz, J. S. Brooks, J. Yamada, T. Mizutani, T. Kinoshita, and M. Tokumoto. Fermiology and superconductivity studies on the non-tetrachalcogenafulvalene-structured organic superconductor β-(BDA-TTP)2SbF6. Physical Review B, 67:174511, 2003. 4.4.1

[45] E. S. Choi, D. Graf, J. S. Brooks, J. Yamada, H. Akutsu, K. Kikuchi, and M. Tokumoto. Pressure-dependent ground states and fermiology in β-(BDA-TTP)2MCl4 (M = Fe, Ga). Physical Review B, 70:024517, 2004. 4.13, 4.4.3, 4.4.4

[46] J. Yamada, T. Toita, H. Akutsu, S. Nakatsuji, H. Nishikawa, I. Ikemoto and K. Kikuchi. The crystal structure and physical properties of β-(BDA-TTP)2FeCl4 [BDA-TTP = 2,5-bis(1,3-dithian-2-ylidene)-1,3,4,6-tetrathiapentalene]. Chemical Communications, 2001:2538, 2001. 4.4.4, 4.4.5

[47] J. Yamada, T. Toita, H. Akutsu, S. Nakatsuji, H. Nishikawa, I. Ikemoto, K. Kikuchi, E. S. Choi, D. Graf and J. S. Brooks. A new organic superconductor, β-(BDA-TTP)2GaCl4[BDA-TTP = 2,5-(1,3-dithian-2-ylidene)-1,3,4,6- tetrathiapentalene]. Chemical Communications, 2003:2230, 2003. 4.4.5

[48] S.Hill, N.S. Dalal, and J.S Brooks. A multifrequency-resonator-based system for high-sensitivity high-ﬁeld epr investigations of small single crystals. Applied Magnetic Resonance, 16:237, 1999. 4.4.5

[49] E. Ohmichi and T. Osada. Torque magnetometry in pulsed magnetic ﬁelds with use of a commercial microcantilever. Review of Scientiﬁc Instruments, 73:3022, 2002. 4.4.5

79 [50] N. Kinoshita, M. Tokumoto, H. Anzai and G. Saito. Anisotropy in ESR g Factors and Linewidths for α- and β-(BEDT-TTF)2I3. Journal of the Physical Society of Japan, 54:4498, 1985. 4.4.6

[51] T. Takahashi, Y. Nogami, and K. Yakushi. Charge ordering in organic conductors. Journal of the Physical Society of Japan, 75:051008, 2006. 4.4.6

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[53] H. Seo, J. Merino, H. Yoshioka and M. Ogata. Theoretical aspects of charge ordering in molecular conductors. Journal of the Physical Society of Japan, 75:051009, 2006. 4.4.6

[54] Y. Nogami, S. Kagoshima, T. Sugano and G. Saito. X-ray evidence for structural changes in the organic conductors, α-(BEDT-TTF)2I3, α-(BEDT-TTF)2IBr2 and β- (BEDT-TTF)2I3. Synthetic Metals, 16:367, 1986. 4.4.6 [55] T. Kakiuchi, Y. Wakabayashi, H. Sawa, T. Takahashi, and T. Nakamura. Charge ordering in α-(BEDT-TTF)2I3 by synchrotron x-ray diﬀraction. Journal of the Physical Society of Japan, 76:113702, 2007. 4.4.6 [56] K. Kikuchi, H. Nishikawa, I. Ikemoto, T. Toita, H. Akutsu, S. Nakatsuji, and J. Yamada. Tetrachloroferrate (iii) salts of BDH-TTP [2,5-Bis(1,3-dithiolan- 2-ylidene)-1,3,4,6-tetrathiapentalene] and BDA-TTP [2,5-bis(1,3-dithian-2-ylidene)- 1,3,4,6-tetrathiapentalene]: Crystal structures and physical properties. Journal of Solid State Chemistry, 168:503, 2002. 4.4.6

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80 transition temperature yet observed (inductive onset Tc = 11.6 K, resistive onset = 12.5 K). Inorganic Chemistry, 29:2555, 1990. 5.1 [62] J.M. Williams, A.M. Kini, H.H. Wang, K.D. Carlson, U. Geiser, L.K. Montgomery, G.J. Pyrka, D.M. Watkins, J.M. Kommers, S.J. Boryschuk, A.V. Strieby Crouch, W.K. Kwok, J.E. Schirber, D.L. Overmyer, D. Jung, and M.-H. Whangbo. From semiconductor-semiconductor transition (42 K) to the highest-TC organic superconductor, kappa-(ET)2Cu[N(CN)2]Cl (TC = 12.5 K). Inorganic Chemistry, 29:3272, 1990. 5.1

[63] J. S. Zambounis, C. W. Mayer, K. Hauenstein, B. Hilti, W. Hofherr, Jurgen Pfeiﬀer, Markus B¨urkle, Grety Rihs. Crystal structure and electrical properties of κ-((S,S)- DMBEDT-TTF)2ClO4. Advanced Materials, 4:33, 1991. 5.1 [64] D.E. Graf. Graf’s thesis, Magnetic Field-Dependent Electronic Structures of Low- Dimensional Organic Materials, and references there in. Florida State University Dessetation, 2005. 5.1, 5.3.3

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81 BIOGRAPHICAL SKETCH

Takahisa D. Tokumoto

Education [2003 2008] Florida State University, Doctor of Philosophy in Physics, Dissertation: “Spin − and charge ordering in organic conductors investigated by Electron Spin Resonance” [1999 2001] M. S. degree in Science, The University of Tokyo, Japan, Thesis: “Analysis − of synapse formation by transneuronal marker WGA” [1995 1999] B. S. in Science, The University of Tokyo, Japan −

Academic Awards and Honors [2005] Phi Kappa Phi, Florida State University, for excellent scholastic achievement. [2007] Golden Key, Florida State University, for excellent academic achievement.

List of publications 1. T. Tokumoto, J. S. Brooks, Y. Oshima, L.-C. Brunel. E. S. Choi, D. Graf, G. Pa- pavassiliou, J. van Tol, Exotic antiferromagnetic states in a tau-phase organic conductor, manuscript in preparation. 2. J. S. Brooks, R. Vasic, A. Kismarahardja, E. Steven, T. Tokumoto, P. Schlottmann, and S. Kelly, Debye relaxation in high magnetic ﬁelds, to be published in Phys. Rev. B 3. T. Tokumoto, J. S. Brooks, Y. Oshima, L.-C. Brunel. E. S. Choi, T. Kaihatsu, J. Yamada, J. van Tol, Antiferromagnetic d-electron exchange via a spin-singlet π-electron ground state in an organic conductor, Phys. Rev. Lett., 100, 147602 (2008) 4. K. Jeon, L. Lumata, T. Tokumoto, E. Steven, J. S. Brooks, and R. G. Alamo, Low electrical conductivity threshold and crystalline morphology of single-walled carbon nanotubes -

82 high density polyethylene nanocomposites characterized by SEM, Raman spectroscopy and AFM, Polymer, 48, 4751 (2007) 5. L. Channels, T. Tokumoto, E. Jobiliong, J. S. Brooks, S. Nellutla, and N. S. Dalal, Dielectric, Electron Paramagnetic Resonance and Transport Properties of Spanish Moss, J. Low Temp. Phys., 142, 663 (2006) 6. Y. Oshima, T. Tokumoto, J. S. Brooks, H. Akutsu, J. Yamada, Electron spin resonance study of the organic conductor β-(BDA-TTP)2FeCl4, J. Low Temp. Phys., 142, 1573 (2006) 7. S. Uji, T. Terashima, M. Nishimura, Y. Takahide, T. Konoike, K. Enomoto, H. Cui, H. Kobayashi, A. Kobayashi, H. Tanaka, M. Tokumoto, E. S. Choi, T. Tokumoto, D. Graf, and J. S. Brooks, Vortex dynamics and the Fulde-Ferrell-Larkin-Ovchinnikov state in a magnetic-ﬁeld-induced organic superconductor, Phys. Rev. Lett., 97, 157001 (2006) 8. T. Tokumoto, J. S. Brooks, D. Graf, E. S. Choi, N. Biskup, D. L. Eaton, J. E. Anthony and S. A. Odom, Persistent photo-excited conducting states in functionalized pentacene, Synth. Met., 152, 449 (2005) 9. J. S. Brooks, T. Tokumoto, E. S. Choi, D. Graf, N. Biskup, D. L. Eaton, J. E. Anthony and S. A. Odom, Persistent photoexcited conducting states in functionalized pentacene, J. Appl. Phys., 96, 3312 (2004) 10. J. S. Brooks, R. Vasic, T. Tokumoto, D. Graf, O. H. Chung, J. E. Anthony, and S. A. Odom, Transport and melt processing in functionalized pentacene with ’organic wire connections’, Current Appl. Phys., 4, 479-483 (2004) 11. T. Tokumoto, E. Jobiliong, E. S. Choi, Y. Oshima, and J. S. Brooks, Electric and thermoelectric transport probes of metal-insulator and two-band magnetotransport behavior in graphite, Solid State Commun., 129, 599 (2004) 12. T. Tokumoto, J. S. Brooks, R. Clinite, X. Wei, J. E. Anthony, D. L. Eaton, and S. R. Parkin, Photoresponse of the conductivity in functionalized pentacene compounds, J. Appl. Phys., 92 (9), 5208-5213 (2002)

List of talks 1. High ﬁeld ESR study on a tau phase organic conductor - from GHz to THz -, APS March meeting, New Orleans, March 10th (2008) 2. Antiferromagnetic d-electron exchange via a spin-singlet pi-electron ground state in an organic conductor, 36th Southeast Magnetic Research Conference, Tuscaloosa, AL,

83 November 9-11 (2007) 3. Coexistence of a spin singlet state and an exchange interaction, International Symposium on Crystalline Organic Metals, Superconductors and ferromagnets (ISCOM), Spain, 09/24- 09/29 (2007) 4. High ﬁeld ESR study of the π d interaction eﬀect in β-(BDA-TTP) MCl (M = Fe, − 2 4 Ga), APS March meeting, Colorado, March 6th (2007) 5. Multiple spin sites in an organic conductor without magnetic ions, American Physical Society March Meeting, Baltimore, MD, March 13-17 (2006) 6. Persistent photo-induced conducting states in functionalized pentacene, International Conference of Synthetic Metals (ICSM), Wollongong, NSW, Australia, June (2004)

List of posters

1. ESR Study of the Organic Conductor, β-(BDA-TTP)2MCl4 (M = Fe,Ga), 35th South- eastern Magnetic Resonance Conf., Gainesville, FL, November 3-5 (2006) 2. Observation of the exchange narrowing in the π d correlated organic conductors, Physical − Phenomena at High Magnetic Fields - V, Tallahassee, FL, 08/05/05 (2005) 3. What is the origin of multiple spin sites in an organic conductor without magnetic ions?, 34th Southeastern Magnetic Resonance Conference, Emory Univ. at Atlanta, GA, November 11-13 (2005)