Band Theory of Magnetism in Metals

Total Page：16

File Type：pdf, Size：1020Kb

Band Theory of Magnetism Ian McDonald in Metals Northeastern University Boston, Ma 03/24/15 Contents • Free atoms vs solids Band Theory • Density of States • Ferromagnetism of Magnetism • Slater-Pauling Curve in Metals Application of band theory to magnetic materials was first performed by Stoner, Mott & Slater (1933-1936) 03/24/15 1 Electronic structure of free atoms vs solids • Atoms separated by large distances (free atoms) • Electrons occupy well-defined energy levels – Pauli exclusion principle = 2 electrons per energy level • Atoms in close proximity (solids) • Electron clouds overlap • Energy levels split to accommodate 4 electrons that would be at each energy level B.D. Cullity. “Introduction to Magnetic Materials” Wiley. pg. 135. 2009. 1 Electronic structure of free atoms vs solids • In transition elements, 3d and 4s levels split the most because they’re farther from the nucleus (i.e. interact first) • Lower levels (2p, 2s, 1s) less split because closer to nucleus • More electrons = more splitting • These levels are so closely spaced that they can be approximated into an energy band. • Electrons become delocalized (itinerant) B.D. Cullity. “Introduction to Magnetic Materials” Wiley. pg. 135. 2009. 2 Practical Example of Band Theory • 1 mg of Fe contains ~1019 atoms. • Pauli exclusion principle requires each separate energy level in the free atom must necessarily be split into 1019 levels in the solid. • N(E) – defines the density of energy levels at a given energy • N(E) dE is the number of available energy levels between E and E + dE B.D. Cullity. “Introduction to Magnetic Materials” Wiley. pg. 135. 2009. 3 Density of States • 3d band has a much larger density because there are five 3d levels per atom each with a capacity of 10 electrons whereas only one 4s with 2 electrons • Area under the curve is equal to the total available number of energy levels in a band. • Fermi level shows topmost filled energy level B.D. Cullity. “Introduction to Magnetic Materials” Wiley. pg. 135. 2009. 4 Density of States • Imagine 3d band split into two sections (spin up / spin down) • And these two bands as two connected tanks of water • Fermi energy is the water level • Filled energy bands cannot contribute a magnetic moment because opposing spins cancel out H.S. Nalwa. “Handbook of Thin Film Materials” Academic Press. pg. 520. 2002. 5 Spin up VS Spin down • An electron may reverse its spin 0 through exchange interaction (Stoner criterion) • Exchange force acts like a dam allowing for spin imbalance resulting in a magnetic moment +2 • This only happens if the levels are very close together S. Chikazumi. “Physics of Magnetism” Wiley & Sons. Pg. 74. 1964. 6 Ferromagnetism in Solids Non-magnetic Ferromagnetic N = N N > N H.S. Nalwa. “Handbook of Thin Film Materials” Academic Press. pg. 520. 2002. 7 Slater-Pauling Curve μ = (10.6-n3d)μβ B.D. Cullity. “Introduction to Magnetic Materials” Wiley. pg. 135. 2009. 8 Summary Requirement for ferromagnetism from 3d band 1) Partially filled bands so there’s available energy levels for unpaired spin to move into. 2) Density of states in the band must be high so that change in spin orientation will produce only small change in energy. 3) Interatomic distance must facilitate exchange forces • Only Fe, Co, and Ni meet all requirements • RE-elements have spontaneous magnetization due to spin unbalance in 4f band .

Copy Link

Recommended publications

Coexistence of Superparamagnetism and Ferromagnetism in Co-Doped
Available online at www.sciencedirect.com ScienceDirect Scripta Materialia 69 (2013) 694–697 www.elsevier.com/locate/scriptamat Coexistence of superparamagnetism and ferromagnetism in Co-doped ZnO nanocrystalline films Qiang Li,a Yuyin Wang,b Lele Fan,b Jiandang Liu,a Wei Konga and Bangjiao Yea,⇑ aState Key Laboratory of Particle Detection and Electronics, University of Science and Technology of China, Hefei 230026, People’s Republic of China bNational Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei 230029, People’s Republic of China Received 8 April 2013; revised 5 August 2013; accepted 6 August 2013 Available online 13 August 2013 Pure ZnO and Zn0.95Co0.05O films were deposited on sapphire substrates by pulsed-laser deposition. We confirm that the magnetic behavior is intrinsic property of Co-doped ZnO nanocrystalline films. Oxygen vacancies play an important mediation role in Co–Co ferromagnetic coupling. The thermal irreversibility of field-cooling and zero field-cooling magnetizations reveals the presence of superparamagnetic behavior in our films, while no evidence of metallic Co clusters was detected. The origin of the observed superparamagnetism is discussed. Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Dilute magnetic semiconductors; Superparamagnetism; Ferromagnetism; Co-doped ZnO Dilute magnetic semiconductors (DMSs) have magnetic properties in this system. In this work, the cor- attracted increasing attention in the past decade due to relation between the structural features and magnetic their promising technological applications in the field properties of Co-doped ZnO films was clearly of spintronic devices [1]. Transition metal (TM)-doped demonstrated. ZnO is one of the most attractive DMS candidates The Zn0.95Co0.05O films were deposited on sapphire because of its outstanding properties, including room- (0001) substrates by pulsed-laser deposition using a temperature ferromagnetism.
[Show full text]
Solid State Physics 2 Lecture 5: Electron Liquid
Physics 7450: Solid State Physics 2 Lecture 5: Electron liquid Leo Radzihovsky (Dated: 10 March, 2015) Abstract In these lectures, we will study itinerate electron liquid, namely metals. We will begin by re- viewing properties of noninteracting electron gas, developing its Greens functions, analyzing its thermodynamics, Pauli paramagnetism and Landau diamagnetism. We will recall how its thermo- dynamics is qualitatively distinct from that of a Boltzmann and Bose gases. As emphasized by Sommerfeld (1928), these qualitative di↵erence are due to the Pauli principle of electons’ fermionic statistics. We will then include e↵ects of Coulomb interaction, treating it in Hartree and Hartree- Fock approximation, computing the ground state energy and screening. We will then study itinerate Stoner ferromagnetism as well as various response functions, such as compressibility and conduc- tivity, and screening (Thomas-Fermi, Debye). We will then discuss Landau Fermi-liquid theory, which will allow us understand why despite strong electron-electron interactions, nevertheless much of the phenomenology of a Fermi gas extends to a Fermi liquid. We will conclude with discussion of electrons on the lattice, treated within the Hubbard and t-J models and will study transition to a Mott insulator and magnetism 1 I. INTRODUCTION A. Outline electron gas ground state and excitations • thermodynamics • Pauli paramagnetism • Landau diamagnetism • Hartree-Fock theory of interactions: ground state energy • Stoner ferromagnetic instability • response functions • Landau Fermi-liquid theory • electrons on the lattice: Hubbard and t-J models • Mott insulators and magnetism • B. Background In these lectures, we will study itinerate electron liquid, namely metals. In principle a fully quantum mechanical, strongly Coulomb-interacting description is required.
[Show full text]
Study of Spin Glass and Cluster Ferromagnetism in Rusr2eu1.4Ce0.6Cu2o10-Δ Magneto Superconductor Anuj Kumar, R
Study of spin glass and cluster ferromagnetism in RuSr2Eu1.4Ce0.6Cu2O10-δ magneto superconductor Anuj Kumar, R. P. Tandon, and V. P. S. Awana Citation: J. Appl. Phys. 110, 043926 (2011); doi: 10.1063/1.3626824 View online: http://dx.doi.org/10.1063/1.3626824 View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v110/i4 Published by the American Institute of Physics. Related Articles Annealing effect on the excess conductivity of Cu0.5Tl0.25M0.25Ba2Ca2Cu3O10−δ (M=K, Na, Li, Tl) superconductors J. Appl. Phys. 111, 053914 (2012) Effect of columnar grain boundaries on flux pinning in MgB2 films J. Appl. Phys. 111, 053906 (2012) The scaling analysis on effective activation energy in HgBa2Ca2Cu3O8+δ J. Appl. Phys. 111, 07D709 (2012) Magnetism and superconductivity in the Heusler alloy Pd2YbPb J. Appl. Phys. 111, 07E111 (2012) Micromagnetic analysis of the magnetization dynamics driven by the Oersted field in permalloy nanorings J. Appl. Phys. 111, 07D103 (2012) Additional information on J. Appl. Phys. Journal Homepage: http://jap.aip.org/ Journal Information: http://jap.aip.org/about/about_the_journal Top downloads: http://jap.aip.org/features/most_downloaded Information for Authors: http://jap.aip.org/authors Downloaded 12 Mar 2012 to 14.139.60.97. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions JOURNAL OF APPLIED PHYSICS 110, 043926 (2011) Study of spin glass and cluster ferromagnetism in RuSr2Eu1.4Ce0.6Cu2O10-d magneto superconductor Anuj Kumar,1,2 R. P. Tandon,2 and V. P. S. Awana1,a) 1Quantum Phenomena and Application Division, National Physical Laboratory (CSIR), Dr.
[Show full text]
Ferromagnetic State and Phase Transitions
Ferromagnetic state and phase transitions Yuri Mnyukh 76 Peggy Lane, Farmington, CT, USA, e-mail: [email protected] (Dated: June 20, 2011) Evidence is summarized attesting that the standard exchange field theory of ferromagnetism by Heisenberg has not been successful. It is replaced by the crystal field and a simple assumption that spin orientation is inexorably associated with the orientation of its carrier. It follows at once that both ferromagnetic phase transitions and magnetization must involve a structural rearrangement. The mechanism of structural rearrangements in solids is nucleation and interface propagation. The new approach accounts coherently for ferromagnetic state and its manifestations. 1. Weiss' molecular and Heisenberg's electron Its positive sign led to a collinear ferromagnetism, and exchange fields negative to a collinear antiferromagnetism. Since then it has become accepted that Heisenberg gave a quantum- Generally, ferromagnetics are spin-containing materials mechanical explanation for Weiss' "molecular field": that are (or can be) magnetized and remain magnetized "Only quantum mechanics has brought about in the absence of magnetic field. This definition also explanation of the true nature of ferromagnetism" includes ferrimagnetics, antiferromagnetics, and (Tamm [2]). "Heisenberg has shown that the Weiss' practically unlimited variety of magnetic structures. theory of molecular field can get a simple and The classical Weiss / Heisenberg theory of straightforward explanation in terms of quantum ferromagnetism, taught in the universities and presented mechanics" (Seitz [1]). in many textbooks (e. g., [1-4]), deals basically with the special case of a collinear (parallel and antiparallel) spin arrangement. 2. Inconsistence with the reality The logic behind the theory in question is as follows.
[Show full text]
Band Ferromagnetism in Systems of Variable Dimensionality
JOURNAL OF OPTOELECTRONICS AND ADVANCED MATERIALS Vol. 10, No. 11, November 2008, p.3058 - 3068 Band ferromagnetism in systems of variable dimensionality C. M. TEODORESCU*, G. A. LUNGU National Institute of Materials Physics, Atomistilor 105b, P.O. Box MG-7, RO-77125 Magurele-Ilfov, Romania The Stoner instability of the paramagnetic state, yielding to the occurence of ferromagnetism, is reviewed for electron density of states reflecting changes in the dimensionality of the system. The situations treated are one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) cases and also a special case where the density of states has a parabolic shape near the Fermi level, and is half-filled at equilibrium. We recover the basic results obtained in the original work of E.C. Stoner [Proc. Roy. Soc. London A 165, 372 (1938)]; also we demonstrate that in 1D and 2D case, whenever the Stoner criterion is satisfied, the system evolves spontaneously towards maximum polarization allowed by Hund's rules. For the 3D case, the situation is that: (i) when the Stoner criterion is satisfied, but the ratio between the Hubbard repulsion energy and the Fermi energy is between 4/3 and 3/2, the system evolves towards a ferromagnetic state with incomplete polarization (the polarization parameter is between 0 and 1); (ii) when , the system evolves towards maximum polarization. This situation was also recognized in the original paper of Stoner, but with no further analysis of the obtained polarizations nor comparison with experimental results. We apply the result of calculation in order to predict the Hubbard interaction energy.
[Show full text]
Condensed Matter Option MAGNETISM Handout 1
Condensed Matter Option MAGNETISM Handout 1 Hilary 2014 Radu Coldea http://www2.physics.ox.ac.uk/students/course-materials/c3-condensed-matter-major-option Syllabus The lecture course on Magnetism in Condensed Matter Physics will be given in 7 lectures broken up into three parts as follows: 1. Isolated Ions Magnetic properties become particularly simple if we are able to ignore the interactions between ions. In this case we are able to treat the ions as effectively \isolated" and can discuss diamagnetism and paramagnetism. For the latter phenomenon we revise the derivation of the Brillouin function outlined in the third-year course. Ions in a solid interact with the crystal field and this strongly affects their properties, which can be probed experimentally using magnetic resonance (in particular ESR and NMR). 2. Interactions Now we turn on the interactions! I will discuss what sort of magnetic interactions there might be, including dipolar interactions and the different types of exchange interaction. The interactions lead to various types of ordered magnetic structures which can be measured using neutron diffraction. I will then discuss the mean-field Weiss model of ferromagnetism, antiferromagnetism and ferrimagnetism and also consider the magnetism of metals. 3. Symmetry breaking The concept of broken symmetry is at the heart of condensed matter physics. These lectures aim to explain how the existence of the crystalline order in solids, ferromagnetism and ferroelectricity, are all the result of symmetry breaking. The consequences of breaking symmetry are that systems show some kind of rigidity (in the case of ferromagnetism this is permanent magnetism), low temperature elementary excitations (in the case of ferromagnetism these are spin waves, also known as magnons), and defects (in the case of ferromagnetism these are domain walls).
[Show full text]
The Spinor Bose-Einstein Condensate: a Dipolar Magnetic Superfluid
Ψ TThhee SSppiinnoorr BBoossee--EEiinnsstteeiinn CCoonnddeennssaattee:: AA DDiippoollaarr MMaaggnneettiicc SSuuppeerrfflluuiidd Dan Stamper-Kurn UC Berkeley, Physics Lawrence Berkeley National Laboratory, Materials Sciences Ψ Spinor gases mF = 2 Energy mF = 1 F=2 mF = 0 magnetically Optically m = -1 F trappable trapped F=2 m = -2 spinor gas F mF = -1 F=1 mF = 0 Optically mF = 1 trapped F=1 spinor gas B What do we want to know? ≈ χ χ χ ’ ≈ ρ ρ ρ ’ + + + + − +1,+1 +1,0 +1,−1 ∆ σ ,σ σ ,π σ ,σ ÷ ∆ ÷ ρ = ρ ρ ρ χ = ∆ χ + χ χ − ÷ ∆ 0,+1 0,0 0,−1 ÷ π ,σ π ,π π ,σ ∆ρ ρ ρ ÷ ∆ ÷ « −1,+1 −1,0 −1,−1 ◊ ∆χ − + χ − χ − − ÷ « σ ,σ σ ,π σ ,σ ◊ FC F = cosθ spin F m=1 coh erences y φ “orientation” x nematicity N m=2 coh erences “alignment” θ θ iφ −iφ ’ R∆e cos m =1 − e sin m = −1 ÷ « 2 2 ◊ + F′ = 2 1 1 1 12 2 2 y F =1 z x in this case small signal 2 (# photons/pixel) = + ( + + ε ) S Nγ 1 A ( 1) Fy Fy ⁄ ∝ n2D Direct imaging of Larmor precession m 0 0 3 l a n g i s t s a r t n y o F c 0.5 - ~ e s a h p 0 k a e time (50 s/frame) P Aliased sampling: 2 x 20 kHz – Observed rate = 38.097(15) kHz Spinor gas magnetometry B N atoms F F F φ Probe: t = 0 t = τ N N 0 0 N N B 0 1 N N 0 0 t = 0 t = τ > 1 ’ 1 1 Area-resolving: ∆B = ∆ ÷× = S × ∆ µ ÷ A « g B DTcoh n2 D ◊ Ttotal A Ttotal A Ψ Experimental demonstration Clarify fundamental and technical limits on precision single-particle and collective light scattering, experimental tricks unbiased phase estimation methods Measure background noise confirm areal and temporal scaling of sensitivity Measure localized magnetic field quantum-mechanical diffusion of magnetization actually measure limits to dynamic range magnetic background field with uncontrolled long-range inhomogeneities actually measure fictitious Z eeman shift from focused, off- resonance laser Ψ %F&ield“ measurements B AC Stark shift = “Fictitious” magnetic field Comparing atoms & SQUIDs Existing low freq.
[Show full text]
Phase Transitions in Condensed Matter Hans-Henning Klauss
Phase Transitions in Condensed Matter Spontaneous Symmetry Breaking and Universality Hans-Henning Klauss Institut für Festkörperphysik TU Dresden 1 References [1] Stephen Blundell, Magnetism in Condensed Matter, Oxford University Press [2] Igot Herbut, A Modern Approach to Critical Phenomena, Cambridge University Press [3] Eugene Stanley, Introduction to Phase Transitions and Critical Phenomena, Oxford Science Pub. [4] Roser Valenti, Lecture Notes on Thermodynamics, U Frankfurt [5] Matthias Vojta, Lecture Notes on Thermal and Quantum Phase Transitions, Les Houches 2015 [6] Thomas Palstra, Lecture Notes on Multiferroics: Materials and Mechanisms, Zuoz 2013 2 Outline • Phase transitions in fluids - Phase diagram, order parameter and symmetry breaking - Microscopic van-der-Waals theory universality • Magnetic phase transitions in condensed matter - Ferromagnetic phase transition - Interacting magnetic dipole moments “spins” - Weiss model for ferromagnetism, phase diagram - Landau theory • Consequences of symmetry breaking - Critical phenomena and universality - Excitations, Nambu-Goldstone-, Higgs-modes • More complex ordering phenomena - Multiferroics, competing order - [Quantum phase transitions] 3 Introduction • What is a thermodynamic phase? - Equilibrium state of matter of a many body system - Well defined symmetry - Thermodynamic potential changes analytically for small parameter changes (temperature, pressure, magnetic field) • What is a phase transition? - Point in parameter space where the equilibrium properties of a system change qualitatively. - The system is unstable w.r.t. small changes of external parameters 4 Introduction • What is a thermodynamic phase? - Equilibrium state of matter (many body system) Phase diagram of water - Well defined symmetry - Thermodynamic potentials change analytically for small parameter changes (temperature, pressure, magnetic field) • What is a phase transition? - Point in parameter space where the equilibrium properties of a system change qualitatively.
[Show full text]
Ferromagnetism, Paramagnetism, and a Curie-Weiss Metal in an Electron-Doped Hubbard Model on a Triangular Lattice
PHYSICAL REVIEW B 73, 235107 ͑2006͒ Ferromagnetism, paramagnetism, and a Curie-Weiss metal in an electron-doped Hubbard model on a triangular lattice J. Merino,1 B. J. Powell,2 and Ross H. McKenzie2 1Departamento de Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid, Madrid 28049, Spain 2Department of Physics, University of Queensland, Brisbane, Qld 4072, Australia ͑Received 4 January 2006; revised manuscript received 27 April 2006; published 8 June 2006͒ Motivated by the unconventional properties and rich phase diagram of NaxCoO2 we consider the electronic and magnetic properties of a two-dimensional Hubbard model on an isotropic triangular lattice doped with electrons away from half-ﬁlling. Dynamical mean-ﬁeld theory ͑DMFT͒ calculations predict that for negative intersite hopping amplitudes ͑tϽ0͒ and an on-site Coulomb repulsion, U, comparable to the bandwidth, the system displays properties typical of a weakly correlated metal. In contrast, for tϾ0 a large enhancement of the effective mass, itinerant ferromagnetism, and a metallic phase with a Curie-Weiss magnetic susceptibility are found in a broad electron doping range. The different behavior encountered is a consequence of the larger noninteracting density of states ͑DOS͒ at the Fermi level for tϾ0 than for tϽ0, which effectively enhances the mass and the scattering amplitude of the quasiparticles. The shape of the DOS is crucial for the occurrence of ferromagnetism as for tϾ0 the energy cost of polarizing the system is much smaller than for tϽ0. Our observation of Nagaoka ferromagnetism is consistent with the A-type antiferromagnetism ͑i.e., ferromagnetic ͒ layers stacked antiferromagnetically observed in neutron scattering experiments on NaxCoO2.
[Show full text]
Observation of Spin Glass State in Weakly Ferromagnetic Sr2fecoo6 Double Perovskite R
Observation of spin glass state in weakly ferromagnetic Sr2FeCoO6 double perovskite R. Pradheesh, Harikrishnan S. Nair, C. M. N. Kumar, Jagat Lamsal, R. Nirmala et al. Citation: J. Appl. Phys. 111, 053905 (2012); doi: 10.1063/1.3686137 View online: http://dx.doi.org/10.1063/1.3686137 View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v111/i5 Published by the American Institute of Physics. Additional information on J. Appl. Phys. Journal Homepage: http://jap.aip.org/ Journal Information: http://jap.aip.org/about/about_the_journal Top downloads: http://jap.aip.org/features/most_downloaded Information for Authors: http://jap.aip.org/authors Downloaded 16 May 2013 to 134.94.122.141. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://jap.aip.org/about/rights_and_permissions JOURNAL OF APPLIED PHYSICS 111, 053905 (2012) Observation of spin glass state in weakly ferromagnetic Sr2FeCoO6 double perovskite R. Pradheesh,1 Harikrishnan S. Nair,2 C. M. N. Kumar,2 Jagat Lamsal,3 R. Nirmala,1 P. N. Santhosh,1 W. B. Yelon,4 S. K. Malik,5 V. Sankaranarayanan,1,a) and K. Sethupathi1,a) 1Low Temperature Physics Laboratory, Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India 2Ju¨lich Center for Neutron Sciences-2/Peter Gru¨nberg Institute-4, Forschungszentrum Ju¨lich, 52425 Ju¨lich, Germany 3Department of Physics and Astronomy, University of Missouri-Columbia, Columbia, Missouri 65211, USA 4Materials Research Center and Department of Chemistry, Missouri University of Science and Technology, Rolla, Missouri 65409, USA 5Departmento de Fisica Teo´rica e Experimental, Natal-RN, 59072-970, Brazil (Received 30 September 2011; accepted 18 January 2012; published online 1 March 2012) A spin glass state is observed in the double perovskite oxide Sr2FeCoO6 prepared through sol-gel technique.
[Show full text]
Magnons in Ferromagnetic Metallic Manganites
Magnons in Ferromagnetic Metallic Manganites Jiandi Zhang1,* F. Ye2, Hao Sha1, Pengcheng Dai3,2, J. A. Fernandez-Baca2, and E.W. Plummer3,4 1Department of physics, Florida International University, Miami, FL 33199, USA 2Center for Neutron Scattering, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA 3Department of physics & Astronomy, the University of Tennessee, Knoxville, TN 37996, USA 4Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA * Electronic address: [email protected] ABSTRACT Ferromagnetic (FM) manganites, a group of likely half-metallic oxides, are of special interest not only because they are a testing ground of the classical double- exchange interaction mechanism for the “colossal” magnetoresistance, but also because they exhibit an extraordinary arena of emergent phenomena. These emergent phenomena are related to the complexity associated with strong interplay between charge, spin, orbital, and lattice. In this review, we focus on the use of inelastic neutron scattering to study the spin dynamics, mainly the magnon excitations in this class of FM metallic materials. In particular, we discussed the unusual magnon softening and damping near the Brillouin zone boundary in relatively narrow band compounds with strong Jahn-Teller lattice distortion and charge/orbital correlations. The anomalous behaviors of magnons in these compounds indicate the likelihood of cooperative excitations involving spin, lattice, as well as orbital degrees of freedom. PACS #: 75.30.Ds, 75.47.Lx, 75.47.Gk, 61.12.-q Contents 1. Introduction 2. Magnons in double exchange (DE) magnet 3. Neutron as a probe for magnon excitations 4. Magnons in high-TC manganites 5.
[Show full text]
Heisenberg and Ferromagnetism
GENERAL I ARTICLE Heisenberg and Ferromagnetism S Chatterjee Heisenberg's contributions to the understanding of ferromagnetism are reviewed. The special fea tures of ferrolnagnetism, vis-a-vis dia and para magnetism, are introduced and the necessity of a Weiss molecular field is explained. It is shown how Heisenberg identified the quantum mechan ical exchange interaction, which first appeared in the context of chemical bonding, to be the es sential agency, contributing to the co-operative ordering process in ferromagnetism. Sabyasachi Chatterjee obtained his PhD in Though lTIagnetism was known to the Chinese way back condensed matter physics in 2500 BC, and to the Greeks since 600 BC, it was only from the Indian Institute in the 19th century that systematic quantitative stud of Science, Bangalore. He ies on magnetism were undertaken, notably by Faraday, now works at the Indian Institute of Astrophysics. Guoy and Pierre Curie. Magnetic materials were then His current interests are classified as dia, para and ferromagnetics. Theoretical in the areas of galactic understanding of these phenomena required inputs from physics and optics. He is two sources, (1) electromagnetism and (2) atomic the also active in the teaching ory. Electromagnetism, that unified electricity and mag and popularising of science. netiSlTI, showed that moving charges produce magnetic fields and moving magnets produce emfs in conductors. The fact that electrons (discovered in 1897) reside in atoms directed attention to the question whether mag netic properties of materials had a relation with the mo tiOll of electrons in atoms. The theory of diamagnetism was successfully explained to be due to the Lorentz force F = e[E + (l/c)v x H], 011 an orbiting electron when a magnetic field H is ap plied.
[Show full text]