Chapter One Introduction
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Arxiv:Cond-Mat/0106646 29 Jun 2001 Landau Diamagnetism Revisited
Landau Diamagnetism Revisited Sushanta Dattagupta†,**, Arun M. Jayannavar‡ and Narendra Kumar# †S.N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700 098, India ‡Institute of Physics, Sachivalaya Marg, Bhubaneswar 751 005, India #Raman Research Institute, Bangalore 560 080, India The problem of diamagnetism, solved by Landau, continues to pose fascinating issues which have relevance even today. These issues relate to inherent quantum nature of the problem, the role of boundary and dissipation, the meaning of thermodynamic limits, and above all, the quantum–classical crossover occasioned by environment- induced decoherence. The Landau diamagnetism provides a unique paradigm for discussing these issues, the significance of which is far-reaching. Our central result connects the mean orbital magnetic moment, a thermodynamic property, with the electrical resistivity, which characterizes transport properties of material. In this communication, we wish to draw the attention of Peierls to term diamagnetism as one of the surprises in the reader to certain enigmatic issues concerning dia- theoretical physics4. Landau’s pathbreaking result also magnetism. Indeed, diamagnetism can be used as a demonstrated that the calculation of diamagnetic suscep- prototype phenomenon to illustrate the essential role of tibility did indeed require an explicit quantum treatment. quantum mechanics, surface–boundary, dissipation and Turning to the classical domain, two of the present nonequilibrium statistical mechanics itself. authors had worried, some years ago, about the issue: Diamagnetism is a material property that characterizes does the BV theorem survive dissipation5? This is a natu- the response of an ensemble of charged particles (more ral question to ask as dissipation is a ubiquitous property specifically, electrons) to an applied magnetic field. -
Density of States Information from Low Temperature Specific Heat
JOURNAL OF RESE ARC H of th e National Bureau of Standards - A. Physics and Chemistry Val. 74A, No.3, May-June 1970 Density of States I nformation from Low Temperature Specific Heat Measurements* Paul A. Beck and Helmut Claus University of Illinois, Urbana (October 10, 1969) The c a lcul ati on of one -electron d ensit y of s tate va lues from the coeffi cient y of the te rm of the low te mperature specifi c heat lin ear in te mperature is compli cated by many- body effects. In parti c ul ar, the electron-p honon inte raction may enhance the measured y as muc h as tw ofo ld. The e nha nce me nt fa ctor can be eva luat ed in the case of supe rconducting metals and a ll oys. In the presence of magneti c mo ments, add it ional complicati ons arise. A magneti c contribution to the measured y was ide ntifi e d in the case of dilute all oys and a lso of concentrated a lJ oys wh e re parasiti c antife rromagnetis m is s upe rim posed on a n over-a ll fe rromagneti c orde r. No me thod has as ye t bee n de vised to e valu ate this magne ti c part of y. T he separati on of the te mpera ture- li near term of the s pec ifi c heat may itself be co mpli cated by the a ppearance of a s pecific heat a no ma ly due to magneti c cluste rs in s upe rpa ramagneti c or we ak ly ferromagneti c a ll oys. -
Unusual Quantum Criticality in Metals and Insulators T. Senthil (MIT)
Unusual quantum criticality in metals and insulators T. Senthil (MIT) T. Senthil, ``Critical fermi surfaces and non-fermi liquid metals”, PR B, June 08 T. Senthil, ``Theory of a continuous Mott transition in two dimensions”, PR B, July 08 D. Podolsky, A. Paramekanti, Y.B. Kim, and T. Senthil, ``Mott transition between a spin liquid insulator and a metal in three dimensions”, PRL, May 09 T. Senthil and P. A. Lee, ``Coherence and pairing in a doped Mott insulator: Application to the cuprates”, PRL, Aug 09 Precursors: T. Senthil, Annals of Physics, ’06, T. Senthil. M. Vojta, S. Sachdev, PR B, ‘04 Saturday, October 22, 2011 High Tc cuprates: doped Mott insulators Many interesting phenomena on doping the Mott insulator: Loss of antiferromagnetism High Tc superconductivity Pseudogaps, non-fermi liquid regimes , etc. Stripes, nematics, and other broken symmetries This talk: focus on one (among many) fundamental question. How does a Fermi surface emerge when a Mott insulator changes into a metal? Saturday, October 22, 2011 High Tc cuprates: how does a Fermi surface emerge from a doped Mott insulator? Evolution from Mott insulator to overdoped metal : emergence of large Fermi surface with area set by usual Luttinger count. Mott insulator: No Fermi surface Overdoped metal: Large Fermi surface ADMR, quantum oscillations (Hussey), ARPES (Damascelli,….) Saturday, October 22, 2011 High Tc cuprates: how does a Fermi surface emerge from a doped Mott insulator? Large gapless Fermi surface present even in optimal doped strange metal albeit without Landau quasiparticles . Mott insulator: No Fermi surface Saturday, October 22, 2011 High Tc cuprates: how does a Fermi surface emerge from a doped Mott insulator? Large gapless Fermi surface present also in optimal doped strange metal albeit without Landau quasiparticles . -
United States Patent Application 20110255645 Kind Code A1 Zawodny; Joseph M
( 1 of 1 ) United States Patent Application 20110255645 Kind Code A1 Zawodny; Joseph M. October 20, 2011 Method for Producing Heavy Electrons Abstract A method for producing heavy electrons is based on a material system that includes an electrically-conductive material is selected. The material system has a resonant frequency associated therewith for a given operational environment. A structure is formed that includes a non-electrically-conductive material and the material system. The structure incorporates the electrically-conductive material at least at a surface thereof. The geometry of the structure supports propagation of surface plasmon polaritons at a selected frequency that is approximately equal to the resonant frequency of the material system. As a result, heavy electrons are produced at the electrically-conductive material as the surface plasmon polaritons propagate along the structure. Inventors: Zawodny; Joseph M.; (Poquoson, VA) Assignee: USA as represented by the Administrator of the National Aeronautics and Space Administration Washington DC Family ID: 44788191 Serial No.: 070552 Series 13 Code: Filed: March 24, 2011 Current U.S. Class: 376/108 Class at Publication: 376/108 Current CPC Class: G21B 3/00 20130101; Y02E 30/18 20130101 International Class: G21B 1/00 20060101 G21B001/00 Goverment Interests STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT [0002] The invention was made by an employee of the United States Government and may be manufactured and used by or for the Government of the United States of -
Chapter 6 Antiferromagnetism and Other Magnetic Ordeer
Chapter 6 Antiferromagnetism and Other Magnetic Ordeer 6.1 Mean Field Theory of Antiferromagnetism 6.2 Ferrimagnets 6.3 Frustration 6.4 Amorphous Magnets 6.5 Spin Glasses 6.6 Magnetic Model Compounds TCD February 2007 1 1 Molecular Field Theory of Antiferromagnetism 2 equal and oppositely-directed magnetic sublattices 2 Weiss coefficients to represent inter- and intra-sublattice interactions. HAi = n’WMA + nWMB +H HBi = nWMA + n’WMB +H Magnetization of each sublattice is represented by a Brillouin function, and each falls to zero at the critical temperature TN (Néel temperature) Sublattice magnetisation Sublattice magnetisation for antiferromagnet TCD February 2007 2 Above TN The condition for the appearance of spontaneous sublattice magnetization is that these equations have a nonzero solution in zero applied field Curie Weiss ! C = 2C’, P = C’(n’W + nW) TCD February 2007 3 The antiferromagnetic axis along which the sublattice magnetizations lie is determined by magnetocrystalline anisotropy Response below TN depends on the direction of H relative to this axis. No shape anisotropy (no demagnetizing field) TCD February 2007 4 Spin Flop Occurs at Hsf when energies of paralell and perpendicular configurations are equal: HK is the effective anisotropy field i 1/2 This reduces to Hsf = 2(HKH ) for T << TN Spin Waves General: " n h q ~ q ! M and specific heat ~ Tq/n Antiferromagnet: " h q ~ q ! M and specific heat ~ Tq TCD February 2007 5 2 Ferrimagnetism Antiferromagnet with 2 unequal sublattices ! YIG (Y3Fe5O12) Iron occupies 2 crystallographic sites one octahedral (16a) & one tetrahedral (24d) with O ! Magnetite(Fe3O4) Iron again occupies 2 crystallographic sites one tetrahedral (8a – A site) & one octahedral (16d – B site) 3 Weiss Coefficients to account for inter- and intra-sublattice interaction TCD February 2007 6 Below TN, magnetisation of each sublattice is zero. -
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. -
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. -
Structural Chemistry and Metamagnetism of an Homologous Series of Layered Manganese Oxysulfides Zolta´Na.Ga´L,† Oliver J
Published on Web 06/10/2006 Structural Chemistry and Metamagnetism of an Homologous Series of Layered Manganese Oxysulfides Zolta´nA.Ga´l,† Oliver J. Rutt,† Catherine F. Smura,† Timothy P. Overton,† Nicolas Barrier,† Simon J. Clarke,*,† and Joke Hadermann‡ Contribution from the Department of Chemistry, UniVersity of Oxford, Inorganic Chemistry Laboratory, South Parks Road, Oxford, OX1 3QR, U.K., and Electron Microscopy for Materials Science (EMAT), UniVersity of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp, Belgium Received February 7, 2006; E-mail: [email protected] Abstract: An homologous series of layered oxysulfides Sr2MnO2Cu2m-δSm+1 with metamagnetic properties is described. Sr2MnO2Cu2-δS2 (m ) 1), Sr2MnO2Cu4-δS3 (m ) 2) and Sr2MnO2Cu6-δS4 (m ) 3), consist of 2+ MnO2 sheets separated from antifluorite-type copper sulfide layers of variable thickness by Sr ions. All three compounds show substantial and similar copper deficiencies (δ ≈ 0.5) in the copper sulfide layers, and single-crystal X-ray and powder neutron diffraction measurements show that the copper ions in the m ) 2 and m ) 3 compounds are crystallographically disordered, consistent with the possibility of high two-dimensional copper ion mobility. Magnetic susceptibility measurements show high-temperature Curie- Weiss behavior with magnetic moments consistent with high spin manganese ions which have been oxidized to the (2+δ)+ state in order to maintain a full Cu-3d/S-3p valence band, and the compounds are correspondingly p-type semiconductors with resistivities around 25 Ω cm at 295 K. Positive Weiss temperatures indicate net ferromagnetic interactions between moments. Accordingly, magnetic susceptibility measurements and low-temperature powder neutron diffraction measurements show that the moments within a MnO2 sheet couple ferromagnetically and that weaker antiferromagnetic coupling between sheets leads to A-type antiferromagnets in zero applied magnetic field. -
Condensation of Bosons with Several Degrees of Freedom Condensación De Bosones Con Varios Grados De Libertad
Condensation of bosons with several degrees of freedom Condensación de bosones con varios grados de libertad Trabajo presentado por Rafael Delgado López1 para optar al título de Máster en Física Fundamental bajo la dirección del Dr. Pedro Bargueño de Retes2 y del Prof. Fernando Sols Lucia3 Universidad Complutense de Madrid Junio de 2013 Calificación obtenida: 10 (MH) 1 [email protected], Dep. Física Teórica I, Universidad Complutense de Madrid 2 [email protected], Dep. Física de Materiales, Universidad Complutense de Madrid 3 [email protected], Dep. Física de Materiales, Universidad Complutense de Madrid Abstract The condensation of the spinless ideal charged Bose gas in the presence of a magnetic field is revisited as a first step to tackle the more complex case of a molecular condensate, where several degrees of freedom have to be taken into account. In the charged bose gas, the conventional approach is extended to include the macroscopic occupation of excited kinetic states lying in the lowest Landau level, which plays an essential role in the case of large magnetic fields. In that limit, signatures of two diffuse phase transitions (crossovers) appear in the specific heat. In particular, at temperatures lower than the cyclotron frequency, the system behaves as an effectively one-dimensional free boson system, with the specific heat equal to (1/2) NkB and a gradual condensation at lower temperatures. In the molecular case, which is currently in progress, we have studied the condensation of rotational levels in a two–dimensional trap within the Bogoliubov approximation, showing that multi–step condensation also occurs. -
Arxiv:2010.01933V2 [Cond-Mat.Quant-Gas] 18 Feb 2021 Tigated in Refs
Finite temperature spin dynamics of a two-dimensional Bose-Bose atomic mixture Arko Roy,1, ∗ Miki Ota,1, ∗ Alessio Recati,1, 2 and Franco Dalfovo1 1INO-CNR BEC Center and Universit`adi Trento, via Sommarive 14, I-38123 Trento, Italy 2Trento Institute for Fundamental Physics and Applications, INFN, 38123 Povo, Italy We examine the role of thermal fluctuations in uniform two-dimensional binary Bose mixtures of dilute ultracold atomic gases. We use a mean-field Hartree-Fock theory to derive analytical predictions for the miscible-immiscible transition. A nontrivial result of this theory is that a fully miscible phase at T = 0 may become unstable at T 6= 0, as a consequence of a divergent behaviour in the spin susceptibility. We test this prediction by performing numerical simulations with the Stochastic (Projected) Gross-Pitaevskii equation, which includes beyond mean-field effects. We calculate the equilibrium configurations at different temperatures and interaction strengths and we simulate spin oscillations produced by a weak external perturbation. Despite some qualitative agreement, the comparison between the two theories shows that the mean-field approximation is not able to properly describe the behavior of the two-dimensional mixture near the miscible-immiscible transition, as thermal fluctuations smoothen all sharp features both in the phase diagram and in spin dynamics, except for temperature well below the critical temperature for superfluidity. I. INTRODUCTION ing the Popov theory. It is then natural to ask whether such a phase-transition also exists in 2D. The study of phase-separation in two-component clas- It is worth stressing that, in 2D Bose gases, thermal sical fluids is of paramount importance and the role of fluctuations are much more important than in 3D, as they temperature can be rather nontrivial. -
Pauli Paramagnetism of an Ideal Fermi Gas
Pauli paramagnetism of an ideal Fermi gas The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation Lee, Ye-Ryoung, Tout T. Wang, Timur M. Rvachov, Jae-Hoon Choi, Wolfgang Ketterle, and Myoung-Sun Heo. "Pauli paramagnetism of an ideal Fermi gas." Phys. Rev. A 87, 043629 (April 2013). © 2013 American Physical Society As Published http://dx.doi.org/10.1103/PhysRevA.87.043629 Publisher American Physical Society Version Final published version Citable link http://hdl.handle.net/1721.1/88740 Terms of Use Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. PHYSICAL REVIEW A 87, 043629 (2013) Pauli paramagnetism of an ideal Fermi gas Ye-Ryoung Lee,1 Tout T. Wang,1,2 Timur M. Rvachov,1 Jae-Hoon Choi,1 Wolfgang Ketterle,1 and Myoung-Sun Heo1,* 1MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA 2Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA (Received 7 January 2013; published 24 April 2013) We show how to use trapped ultracold atoms to measure the magnetic susceptibility of a two-component Fermi gas. The method is illustrated for a noninteracting gas of 6Li, using the tunability of interactions around a wide Feshbach resonance. The susceptibility versus effective magnetic field is directly obtained from the inhomogeneous density profile of the trapped atomic cloud. The wings of the cloud realize the high-field limit where the polarization approaches 100%, which is not accessible for an electron gas. -
Semimetallic Antiferromagnetism in the Half-Heusler Compound Cumnsb
PHYSICAL REVIEW B 71, 184103 ͑2005͒ Semimetallic antiferromagnetism in the half-Heusler compound CuMnSb T. Jeong,1 Ruben Weht,2 and W. E. Pickett1 1Department of Physics, University of California, Davis, California 95616, USA 2Departamento de Física, CNEA, Avda. General Paz y Constituyentes, 1650-San Martín, Argentina ͑Received 17 September 2004; revised manuscript received 5 January 2005; published 20 May 2005͒ The half-Heusler compound CuMnSb, the first antiferromagnet ͑AFM͒ in the Mn-based class of Heuslers and half-Heuslers that contains several conventional and half metallic ferromagnets, shows a peculiar stability of its magnetic order in high magnetic fields. Density functional based studies reveal an unusual nature of its unstable ͑and therefore unseen͒ paramagnetic state, which for one electron less ͑CuMnSn, for example͒ would be a zero gap semiconductor ͑accidentally so͒ between two sets of very narrow, topologically separate bands of Mn 3d character. The extremely flat Mn 3d bands result from the environment: Mn has four tetrahedrally coordinated Cu atoms whose 3d states lie well below the Fermi level, and the other four tetrahedrally coordi- nated sites are empty, leaving chemically isolated Mn 3d states. The AFM phase can be pictured heuristically as a self-doped Cu1+Mn2+Sb3− compensated semimetal with heavy mass electrons and light mass holes, with magnetic coupling proceeding through Kondo and/or anti-Kondo coupling separately through the two carrier types. The ratio of the linear specific heat coefficient and the calculated Fermi level density of states indicates a large mass enhancement m* /mϳ5, or larger if a correlated band structure is taken as the reference.