Magnetism and Interactions Within the Single Domain Limit
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Accomplishments in Nanotechnology
U.S. Department of Commerce Carlos M. Gutierrez, Secretaiy Technology Administration Robert Cresanti, Under Secretaiy of Commerce for Technology National Institute ofStandards and Technolog}' William Jeffrey, Director Certain commercial entities, equipment, or materials may be identified in this document in order to describe an experimental procedure or concept adequately. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment used are necessarily the best available for the purpose. National Institute of Standards and Technology Special Publication 1052 Natl. Inst. Stand. Technol. Spec. Publ. 1052, 186 pages (August 2006) CODEN: NSPUE2 NIST Special Publication 1052 Accomplishments in Nanoteciinology Compiled and Edited by: Michael T. Postek, Assistant to the Director for Nanotechnology, Manufacturing Engineering Laboratory Joseph Kopanski, Program Office and David Wollman, Electronics and Electrical Engineering Laboratory U. S. Department of Commerce Technology Administration National Institute of Standards and Technology Gaithersburg, MD 20899 August 2006 National Institute of Standards and Teclinology • Technology Administration • U.S. Department of Commerce Acknowledgments Thanks go to the NIST technical staff for providing the information outlined on this report. Each of the investigators is identified with their contribution. Contact information can be obtained by going to: http ://www. nist.gov Acknowledged as well, -
Magnetism, Magnetic Properties, Magnetochemistry
Magnetism, Magnetic Properties, Magnetochemistry 1 Magnetism All matter is electronic Positive/negative charges - bound by Coulombic forces Result of electric field E between charges, electric dipole Electric and magnetic fields = the electromagnetic interaction (Oersted, Maxwell) Electric field = electric +/ charges, electric dipole Magnetic field ??No source?? No magnetic charges, N-S No magnetic monopole Magnetic field = motion of electric charges (electric current, atomic motions) Magnetic dipole – magnetic moment = i A [A m2] 2 Electromagnetic Fields 3 Magnetism Magnetic field = motion of electric charges • Macro - electric current • Micro - spin + orbital momentum Ampère 1822 Poisson model Magnetic dipole – magnetic (dipole) moment [A m2] i A 4 Ampere model Magnetism Microscopic explanation of source of magnetism = Fundamental quantum magnets Unpaired electrons = spins (Bohr 1913) Atomic building blocks (protons, neutrons and electrons = fermions) possess an intrinsic magnetic moment Relativistic quantum theory (P. Dirac 1928) SPIN (quantum property ~ rotation of charged particles) Spin (½ for all fermions) gives rise to a magnetic moment 5 Atomic Motions of Electric Charges The origins for the magnetic moment of a free atom Motions of Electric Charges: 1) The spins of the electrons S. Unpaired spins give a paramagnetic contribution. Paired spins give a diamagnetic contribution. 2) The orbital angular momentum L of the electrons about the nucleus, degenerate orbitals, paramagnetic contribution. The change in the orbital moment -
Thermal Fluctuations of Magnetic Nanoparticles: Fifty Years After Brown1)
THERMAL FLUCTUATIONS OF MAGNETIC NANOPARTICLES: FIFTY YEARS AFTER BROWN1) William T. Coffeya and Yuri P. Kalmykovb a Department of Electronic and Electrical Engineering, Trinity College, Dublin 2, Ireland b Laboratoire de Mathématiques et Physique (LAMPS), Université de Perpignan Via Domitia, 52, Avenue Paul Alduy, F-66860 Perpignan, France The reversal time (superparamagnetic relaxation time) of the magnetization of fine single domain ferromagnetic nanoparticles owing to thermal fluctuations plays a fundamental role in information storage, paleomagnetism, biotechnology, etc. Here a comprehensive tutorial-style review of the achievements of fifty years of development and generalizations of the seminal work of Brown [W.F. Brown, Jr., Phys. Rev., 130, 1677 (1963)] on thermal fluctuations of magnetic nanoparticles is presented. Analytical as well as numerical approaches to the estimation of the damping and temperature dependence of the reversal time based on Brown’s Fokker-Planck equation for the evolution of the magnetic moment orientations on the surface of the unit sphere are critically discussed while the most promising directions for future research are emphasized. I. INTRODUCTION A. THERMAL INSTABILITY OF MAGNETIZATION IN FINE PARTICLES B. KRAMERS ESCAPE RATE THEORY C. SUPERPARAMAGNETIC RELAXATION TIME: BROWN’S APPROACH II. BROWN’S CONTINUOUS DIFFUSION MODEL OF CLASSICAL SPINS A. BASIC EQUATIONS B. EVALUATION OF THE REVERSAL TIME OF THE MAGNETIZATION AND OTHER OBSERVABLES III. REVERSAL TIME IN SUPERPARAMAGNETS WITH AXIALLY-SYMMETRIC MAGNETOCRYSTALLINE ANISOTROPY A. FORMULATION OF THE PROBLEM B. ESTIMATION OF THE REVERSAL TIME VIA KRAMERS’ THEORY C. UNIAXIAL SUPERPARAMAGNET SUBJECTED TO A D.C. BIAS FIELD PARALLEL TO THE EASY AXIS IV. REVERSAL TIME OF THE MAGNETIZATION IN SUPERPARAMAGNETS WITH NONAXIALLY SYMMETRIC ANISOTROPY 1) Published in Applied Physics Reviews Section of the Journal of Applied Physics, 112, 121301 (2012). -
Magnetic Force Microscopy of Superparamagnetic Nanoparticles
Magnetic Force Microscopy of Superparamagnetic Nanoparticles for Biomedical Applications Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Tanya M. Nocera, M.S. Graduate Program in Biomedical Engineering The Ohio State University 2013 Dissertation Committee: Gunjan Agarwal, PhD, Advisor Stephen Lee, PhD Jessica Winter, PhD Anil Pradhan, PhD Copyright by Tanya M. Nocera 2013 Abstract In recent years, both synthetic as well as naturally occurring superparamagnetic nanoparticles (SPNs) have become increasingly important in biomedicine. For instance, iron deposits in many pathological tissues are known to contain an accumulation of the superparamagnetic protein, ferritin. Additionally, man-made SPNs have found biomedical applications ranging from cell-tagging in vitro to contrast agents for in vivo diagnostic imaging. Despite the widespread use and occurrence of SPNs, detection and characterization of their magnetic properties, especially at the single-particle level and/or in biological samples, remains a challenge. Magnetic signals arising from SPNs can be complicated by factors such as spatial distribution, magnetic anisotropy, particle aggregation and magnetic dipolar interaction, thereby confounding their analysis. Techniques that can detect SPNs at the single particle level are therefore highly desirable. The goal of this thesis was to develop an analytical microscopy technique, namely magnetic force microscopy (MFM), to detect and spatially localize synthetic and natural SPNs for biomedical applications. We aimed to (1) increase ii MFM sensitivity to detect SPNs at the single-particle level and (2) quantify and spatially localize iron-ligated proteins (ferritin) in vitro and in biological samples using MFM. -
Phonon Dynamics in a Single Nanomagnet
ARTICLE https://doi.org/10.1038/s41467-019-10545-x OPEN Strongly coupled magnon–phonon dynamics in a single nanomagnet Cassidy Berk 1, Mike Jaris1, Weigang Yang1, Scott Dhuey2, Stefano Cabrini2 & Holger Schmidt1 Polaritons are widely investigated quasiparticles with fundamental and technological sig- nificance due to their unique properties. They have been studied most extensively in semi- conductors when photons interact with various elementary excitations. However, other fi 1234567890():,; strongly coupled excitations demonstrate similar dynamics. Speci cally, when magnon and phonon modes are coupled, a hybridized magnon–phonon quasiparticle can form. Here, we report on the direct observation of coupled magnon–phonon dynamics within a single thin nickel nanomagnet. We develop an analytic description to model the dynamics in two dimensions, enabling us to isolate the parameters influencing the frequency splitting. Fur- thermore, we demonstrate tuning of the magnon–phonon interaction into the strong coupling regime via the orientation of the applied magnetic field. 1 School of Engineering, University of California Santa Cruz, 1156 High Street, Santa Cruz, CA 95064, USA. 2 Molecular Foundry, University of California Berkeley, 67 Cyclotron Road, Berkeley, CA 94720, USA. Correspondence and requests for materials should be addressed to C.B. (email: [email protected]) NATURE COMMUNICATIONS | (2019) 10:2652 | https://doi.org/10.1038/s41467-019-10545-x | www.nature.com/naturecommunications 1 ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-019-10545-x agnonics is an extremely active research area which ab Mexploits the wave nature of magnons, the quanta of spin Spins waves, in order to advance data storage, communica- tion, and information processing technology. -
Two-Dimensional Field-Sensing Map and Magnetic Anisotropy Dispersion
PHYSICAL REVIEW B 83, 144416 (2011) Two-dimensional field-sensing map and magnetic anisotropy dispersion in magnetic tunnel junction arrays Wenzhe Zhang* and Gang Xiao† Department of Physics, Brown University, Providence, Rhode Island 02912, USA Matthew J. Carter Micro Magnetics, Inc., 617 Airport Road, Fall River, Massachusetts 02720, USA (Received 22 July 2010; revised manuscript received 24 January 2011; published 22 April 2011) Due to the inherent disorder in local structures, anisotropy dispersion exists in almost all systems that consist of multiple magnetic tunnel junctions (MTJs). Aided by micromagnetic simulations based on the Stoner-Wohlfarth (S-W) model, we used a two-dimensional field-sensing map to study the effect of anisotropy dispersion in MTJ arrays. First, we recorded the field sensitivity value of an MTJ array as a function of the easy- and hard-axis bias fields, and then extracted the anisotropy dispersion in the array by comparing the experimental sensitivity map to the simulated map. Through a mean-square-error-based image processing technique, we found the best match for our experimental data, and assigned a pair of dispersion numbers (anisotropy angle and anisotropy constant) to the array. By varying each of the parameters one at a time, we were able to discover the dependence of field sensitivity on magnetoresistance ratio, coercivity, and magnetic anisotropy dispersion. The effects from possible edge domains are also discussed to account for a correction term in our analysis of anisotropy angle distribution using the S-W model. We believe this model is a useful tool for monitoring the formation and evolution of anisotropy dispersion in MTJ systems, and can facilitate better design of MTJ-based devices. -
Module 2C: Micromagnetics
Module 2C: Micromagnetics Debanjan Bhowmik Department of Electrical Engineering Indian Institute of Technology Delhi Abstract In this part of the second module (2C) we will show how the Stoner Wolfarth/ single domain mode of ferromagnetism often fails to match with experimental data. We will introduce domain walls in that context and explain the basic framework of micromagnetics, which can be used to model domain walls. Then we will discuss how an anisotropic exchange interaction, known as Dzyaloshinskii Moriya interaction, can lead to chirality of the domain walls. Then we will introduce another non-uniform magnetic structure known as skyrmion and discuss its stability, based on topological arguments. 1 1 Brown's paradox in ferromagnetic thin films exhibiting perpendicular magnetic anisotropy We study ferromagnetic thin films exhibiting Perpendicular Magnetic Anisotropy (PMA) to demonstrate the failure of the previously discussed Stoner Wolfarth/ single domain model to explain experimentally observed magnetic switching curves. PMA is a heavily sought after property in magnetic materials for memory and logic applications (we will talk about that in details in the next module). This makes our analysis in this section even more relevant. The ferromagnetic layer in the Ta/CoFeB/MgO stack, grown by room temperature sput- tering, exhibits perpendicular magnetic anisotropy with an anisotropy field Hk of around 2kG needed to align the magnetic moment in-plane (Fig. 1a). Thus if the ferromagnetic layer is considered as a giant macro-spin in the Stoner Wolfarth model an energy barrier equivalent to ∼2kG exists between the up (+z) and down state (-z) (Fig. 1b). Yet mea- surement shows that the magnet can be switched by a field, called the coercive field, as small as ∼50 G, which is 2 orders of magnitude smaller than the anisotropy field Hk, as observed in the Vibrating Sample Magnetometry measurement on the stack (Fig. -
Magnetic Hysteresis
Magnetic hysteresis Magnetic hysteresis* 1.General properties of magnetic hysteresis 2.Rate-dependent hysteresis 3.Preisach model *this is virtually the same lecture as the one I had in 2012 at IFM PAN/Poznań; there are only small changes/corrections Urbaniak Urbaniak J. Alloys Compd. 454, 57 (2008) M[a.u.] -2 -1 M(H) hysteresesof thin filmsM(H) 0 1 2 Co(0.6 Co(0.6 nm)/Au(1.9 nm)] [Ni Ni 80 -0.5 80 Fe Fe 20 20 (2 nm)/Au(1.9(2 nm)/ (38 nm) (38 Magnetic materials nanoelectronics... in materials Magnetic H[kA/m] 0.0 10 0.5 J. Magn. Magn. Mater. Mater. Magn. J. Magn. 190 , 187 (1998) 187 , Ni 80 Fe 20 (4nm)/Mn 83 Ir 17 (15nm)/Co 70 Fe 30 (3 nm)/Al(1.4nm)+Ox/Ni Ni 83 Fe 17 80 (2 nm)/Cu(2 nm) Fe 20 (4 nm)/Ta(3 nm) nm)/Ta(3 (4 Phys. Stat. Sol. (a) 199, 284 (2003) Phys. Stat. Sol. (a) 186, 423 (2001) M(H) hysteresis ●A hysteresis loop can be expressed in terms of B(H) or M(H) curves. ●In soft magnetic materials (small Hs) both descriptions differ negligibly [1]. ●In hard magnetic materials both descriptions differ significantly leading to two possible definitions of coercive field (and coercivity- see lecture 2). ●M(H) curve better reflects the intrinsic properties of magnetic materials. B, M Hc2 H Hc1 Urbaniak Magnetic materials in nanoelectronics... M(H) hysteresis – vector picture Because field H and magnetization M are vector quantities the full description of hysteresis should include information about the magnetization component perpendicular to the applied field – it gives more information than the scalar measurement. -
EM4: Magnetic Hysteresis – Lab Manual – (Version 1.001A)
CHALMERS UNIVERSITY OF TECHNOLOGY GOTEBORÄ G UNIVERSITY EM4: Magnetic Hysteresis { Lab manual { (version 1.001a) Students: ........................................... & ........................................... Date: .... / .... / .... Laboration passed: ........................ Supervisor: ........................................... Date: .... / .... / .... Raluca Morjan Sergey Prasalovich April 7, 2003 Magnetic Hysteresis 1 Aims: In this laboratory session you will learn about the basic principles of mag- netic hysteresis; learn about the properties of ferromagnetic materials and determine their dissipation energy of remagnetization. Questions: (Please answer on the following questions before coming to the laboratory) 1) What classes of magnetic materials do you know? 2) What is a `magnetic domain'? 3) What is a `magnetic permeability' and `relative permeability'? 4) What is a `hysteresis loop' and how it can be recorded? (How you can measure a magnetization and magnetic ¯eld indirectly?) 5) What is a `saturation point' and `magnetization curve' for a hysteresis loop? 6) How one can demagnetize a ferromagnet? 7) What is the energy dissipation in one full hysteresis loop and how it can be calculated from an experiment? Equipment list: 1 Sensor-CASSY 1 U-core with yoke 2 Coils (N = 500 turnes, L = 2,2 mH) 1 Clamping device 1 Function generator S12 2 12 V DC power supplies 1 STE resistor 1, 2W 1 Socket board section 1 Connecting lead, 50 cm 7 Connecting leads, 100 cm 1 PC with Windows 98 and CASSY Lab software Magnetic Hysteresis 2 Introduction In general, term \hysteresis" (comes from Greek \hyst¶erÄesis", - lag, delay) means that value describing some physical process is ambiguously dependent on an external parameter and antecedent history of that value must be taken into account. The term was added to the vocabulary of physical science by J. -
Vibrational Coherences in Manganese Single-Molecule Magnets After
1 Vibrational coherences in manganese single-molecule magnets 2 after ultrafast photoexcitation 3 Florian Liedy1, Robbie McNab1, Julien Eng2, Ross Inglis1, Tom J. Penfold2, Euan K. 4 Brechin1, J. Olof Johansson1,* 5 1EaStCHEM School of Chemistry, University of Edinburgh, David Brewster Road, EH9 3FJ, 6 Edinburgh, UK 7 2 Chemistry - School of Natural and Environmental Sciences, Newcastle University, 8 Newcastle upon Tyne, NE1 7RU, UK 9 *Email: [email protected] 10 11 Abstract 12 Single-Molecule Magnets (SMMs) are metal complexes with two degenerate magnetic ground 13 states arising from a non-zero spin ground state and a zero-field splitting. SMMs are promising 14 for future applications in data storage, howeVer, to date the ability to manipulate the spins 15 using optical stimulus is lacking. Here, we have explored the ultrafast dynamics occurring after 16 photoexcitation of two structurally related Mn(III)-based SMMs, whose magnetic anisotropy is 17 closely related to the Jahn-Teller distortion, and demonstrate coherent modulation of the axial 18 anisotropy on a femtosecond timescale. Ultrafast transient absorption spectroscopy in solution 19 reVeals oscillations superimposed on the decay traces with corresponding energies 20 around 200 cm−1, coinciding with a vibrational mode along the Jahn-Teller axis. Our results 21 provide a non-thermal, coherent mechanism to dynamically control the magnetisation in 22 SMMs and open up new molecular design challenges to enhance the change in anisotropy in 23 the excited state, which is essential for future ultrafast magneto-optical data storage devices. 24 25 1 1 Single-Molecule Magnets (SMMs), molecules that show magnetic hysteresis below a certain 2 blocking temperature1, show great promise for future applications in data storage devices2-4 3 because their small size and well-defined magnetic properties can reduce the size of data bits 4 and therefore increase storage density. -
Magnetic Materials: Hysteresis
Magnetic Materials: Hysteresis Ferromagnetic and ferrimagnetic materials have non-linear initial magnetisation curves (i.e. the dotted lines in figure 7), as the changing magnetisation with applied field is due to a change in the magnetic domain structure. These materials also show hysteresis and the magnetisation does not return to zero after the application of a magnetic field. Figure 7 shows a typical hysteresis loop; the two loops represent the same data, however, the blue loop is the polarisation (J = µoM = B-µoH) and the red loop is the induction, both plotted against the applied field. Figure 7: A typical hysteresis loop for a ferro- or ferri- magnetic material. Illustrated in the first quadrant of the loop is the initial magnetisation curve (dotted line), which shows the increase in polarisation (and induction) on the application of a field to an unmagnetised sample. In the first quadrant the polarisation and applied field are both positive, i.e. they are in the same direction. The polarisation increases initially by the growth of favourably oriented domains, which will be magnetised in the easy direction of the crystal. When the polarisation can increase no further by the growth of domains, the direction of magnetisation of the domains then rotates away from the easy axis to align with the field. When all of the domains have fully aligned with the applied field saturation is reached and the polarisation can increase no further. If the field is removed the polarisation returns along the solid red line to the y-axis (i.e. H=0), and the domains will return to their easy direction of magnetisation, resulting in a decrease in polarisation. -
Tailored Magnetic Properties of Exchange-Spring and Ultra Hard Nanomagnets
Max-Planck-Institute für Intelligente Systeme Stuttgart Tailored Magnetic Properties of Exchange-Spring and Ultra Hard Nanomagnets Kwanghyo Son Dissertation An der Universität Stuttgart 2017 Tailored Magnetic Properties of Exchange-Spring and Ultra Hard Nanomagnets Von der Fakultät Mathematik und Physik der Universität Stuttgart zur Erlangung der Würde eines Doktors der Naturwissenschaften (Dr. rer. nat.) genehmigte Abhandlung Vorgelegt von Kwanghyo Son aus Seoul, SüdKorea Hauptberichter: Prof. Dr. Gisela Schütz Mitberichter: Prof. Dr. Sebastian Loth Tag der mündlichen Prüfung: 04. Oktober 2017 Max‐Planck‐Institut für Intelligente Systeme, Stuttgart 2017 II III Contents Contents ..................................................................................................................................... 1 Chapter 1 ................................................................................................................................... 1 General Introduction ......................................................................................................... 1 Structure of the thesis ....................................................................................................... 3 Chapter 2 ................................................................................................................................... 5 Basic of Magnetism .......................................................................................................... 5 2.1 The Origin of Magnetism .......................................................................................