Condensed Matter Option MAGNETISM Handout 1
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Canted Ferrimagnetism and Giant Coercivity in the Non-Stoichiometric
Canted ferrimagnetism and giant coercivity in the non-stoichiometric double perovskite La2Ni1.19Os0.81O6 Hai L. Feng1, Manfred Reehuis2, Peter Adler1, Zhiwei Hu1, Michael Nicklas1, Andreas Hoser2, Shih-Chang Weng3, Claudia Felser1, Martin Jansen1 1Max Planck Institute for Chemical Physics of Solids, Dresden, D-01187, Germany 2Helmholtz-Zentrum Berlin für Materialien und Energie, Berlin, D-14109, Germany 3National Synchrotron Radiation Research Center (NSRRC), Hsinchu, 30076, Taiwan Abstract: The non-stoichiometric double perovskite oxide La2Ni1.19Os0.81O6 was synthesized by solid state reaction and its crystal and magnetic structures were investigated by powder x-ray and neutron diffraction. La2Ni1.19Os0.81O6 crystallizes in the monoclinic double perovskite structure (general formula A2BB’O6) with space group P21/n, where the B site is fully occupied by Ni and the B’ site by 19 % Ni and 81 % Os atoms. Using x-ray absorption spectroscopy an Os4.5+ oxidation state was established, suggesting presence of about 50 % 5+ 3 4+ 4 paramagnetic Os (5d , S = 3/2) and 50 % non-magnetic Os (5d , Jeff = 0) ions at the B’ sites. Magnetization and neutron diffraction measurements on La2Ni1.19Os0.81O6 provide evidence for a ferrimagnetic transition at 125 K. The analysis of the neutron data suggests a canted ferrimagnetic spin structure with collinear Ni2+ spin chains extending along the c axis but a non-collinear spin alignment within the ab plane. The magnetization curve of La2Ni1.19Os0.81O6 features a hysteresis with a very high coercive field, HC = 41 kOe, at T = 5 K, which is explained in terms of large magnetocrystalline anisotropy due to the presence of Os ions together with atomic disorder. -
Arxiv:2005.03138V2 [Cond-Mat.Quant-Gas] 23 May 2020 Contents
Condensed Matter Physics in Time Crystals Lingzhen Guo1 and Pengfei Liang2;3 1Max Planck Institute for the Science of Light (MPL), Staudtstrasse 2, 91058 Erlangen, Germany 2Beijing Computational Science Research Center, 100193 Beijing, China 3Abdus Salam ICTP, Strada Costiera 11, I-34151 Trieste, Italy E-mail: [email protected] Abstract. Time crystals are physical systems whose time translation symmetry is spontaneously broken. Although the spontaneous breaking of continuous time- translation symmetry in static systems is proved impossible for the equilibrium state, the discrete time-translation symmetry in periodically driven (Floquet) systems is allowed to be spontaneously broken, resulting in the so-called Floquet or discrete time crystals. While most works so far searching for time crystals focus on the symmetry breaking process and the possible stabilising mechanisms, the many-body physics from the interplay of symmetry-broken states, which we call the condensed matter physics in time crystals, is not fully explored yet. This review aims to summarise the very preliminary results in this new research field with an analogous structure of condensed matter theory in solids. The whole theory is built on a hidden symmetry in time crystals, i.e., the phase space lattice symmetry, which allows us to develop the band theory, topology and strongly correlated models in phase space lattice. In the end, we outline the possible topics and directions for the future research. arXiv:2005.03138v2 [cond-mat.quant-gas] 23 May 2020 Contents 1 Brief introduction to time crystals3 1.1 Wilczek's time crystal . .3 1.2 No-go theorem . .3 1.3 Discrete time-translation symmetry breaking . -
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 -
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. -
Solid State Physics II Level 4 Semester 1 Course Content
Solid State Physics II Level 4 Semester 1 Course Content L1. Introduction to solid state physics - The free electron theory : Free levels in one dimension. L2. Free electron gas in three dimensions. L3. Electrical conductivity – Motion in magnetic field- Wiedemann-Franz law. L4. Nearly free electron model - origin of the energy band. L5. Bloch functions - Kronig Penney model. L6. Dielectrics I : Polarization in dielectrics L7 .Dielectrics II: Types of polarization - dielectric constant L8. Assessment L9. Experimental determination of dielectric constant L10. Ferroelectrics (1) : Ferroelectric crystals L11. Ferroelectrics (2): Piezoelectricity L12. Piezoelectricity Applications L1 : Solid State Physics Solid state physics is the study of rigid matter, or solids, ,through methods such as quantum mechanics, crystallography, electromagnetism and metallurgy. It is the largest branch of condensed matter physics. Solid-state physics studies how the large-scale properties of solid materials result from their atomic- scale properties. Thus, solid-state physics forms the theoretical basis of materials science. It also has direct applications, for example in the technology of transistors and semiconductors. Crystalline solids & Amorphous solids Solid materials are formed from densely-packed atoms, which interact intensely. These interactions produce : the mechanical (e.g. hardness and elasticity), thermal, electrical, magnetic and optical properties of solids. Depending on the material involved and the conditions in which it was formed , the atoms may be arranged in a regular, geometric pattern (crystalline solids, which include metals and ordinary water ice) , or irregularly (an amorphous solid such as common window glass). Crystalline solids & Amorphous solids The bulk of solid-state physics theory and research is focused on crystals. -
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 . -
Lecture 3: Fermi-Liquid Theory 1 General Considerations Concerning Condensed Matter
Phys 769 Selected Topics in Condensed Matter Physics Summer 2010 Lecture 3: Fermi-liquid theory Lecturer: Anthony J. Leggett TA: Bill Coish 1 General considerations concerning condensed matter (NB: Ultracold atomic gasses need separate discussion) Assume for simplicity a single atomic species. Then we have a collection of N (typically 1023) nuclei (denoted α,β,...) and (usually) ZN electrons (denoted i,j,...) interacting ∼ via a Hamiltonian Hˆ . To a first approximation, Hˆ is the nonrelativistic limit of the full Dirac Hamiltonian, namely1 ~2 ~2 1 e2 1 Hˆ = 2 2 + NR −2m ∇i − 2M ∇α 2 4πǫ r r α 0 i j Xi X Xij | − | 1 (Ze)2 1 1 Ze2 1 + . (1) 2 4πǫ0 Rα Rβ − 2 4πǫ0 ri Rα Xαβ | − | Xiα | − | For an isolated atom, the relevant energy scale is the Rydberg (R) – Z2R. In addition, there are some relativistic effects which may need to be considered. Most important is the spin-orbit interaction: µ Hˆ = B σ (v V (r )) (2) SO − c2 i · i × ∇ i Xi (µB is the Bohr magneton, vi is the velocity, and V (ri) is the electrostatic potential at 2 3 2 ri as obtained from HˆNR). In an isolated atom this term is o(α R) for H and o(Z α R) for a heavy atom (inner-shell electrons) (produces fine structure). The (electron-electron) magnetic dipole interaction is of the same order as HˆSO. The (electron-nucleus) hyperfine interaction is down relative to Hˆ by a factor µ /µ 10−3, and the nuclear dipole-dipole SO n B ∼ interaction by a factor (µ /µ )2 10−6. -
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. -
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. -
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. -
A Short Review of Phonon Physics Frijia Mortuza
International Journal of Scientific & Engineering Research Volume 11, Issue 10, October-2020 847 ISSN 2229-5518 A Short Review of Phonon Physics Frijia Mortuza Abstract— In this article the phonon physics has been summarized shortly based on different articles. As the field of phonon physics is already far ad- vanced so some salient features are shortly reviewed such as generation of phonon, uses and importance of phonon physics. Index Terms— Collective Excitation, Phonon Physics, Pseudopotential Theory, MD simulation, First principle method. —————————— —————————— 1. INTRODUCTION There is a collective excitation in periodic elastic arrangements of atoms or molecules. Melting transition crystal turns into liq- uid and it loses long range transitional order and liquid appears to be disordered from crystalline state. Collective dynamics dispersion in transition materials is mostly studied with a view to existing collective modes of motions, which include longitu- dinal and transverse modes of vibrational motions of the constituent atoms. The dispersion exhibits the existence of collective motions of atoms. This has led us to undertake the study of dynamics properties of different transitional metals. However, this collective excitation is known as phonon. In this article phonon physics is shortly reviewed. 2. GENERATION AND PROPERTIES OF PHONON Generally, over some mean positions the atoms in the crystal tries to vibrate. Even in a perfect crystal maximum amount of pho- nons are unstable. As they are unstable after some time of period they come to on the object surface and enters into a sensor. It can produce a signal and finally it leaves the target object. In other word, each atom is coupled with the neighboring atoms and makes vibration and as a result phonon can be found [1]. -
Magnetism Some Basics: a Magnet Is Associated with Magnetic Lines of Force, and a North Pole and a South Pole
Materials 100A, Class 15, Magnetic Properties I Ram Seshadri MRL 2031, x6129 [email protected]; http://www.mrl.ucsb.edu/∼seshadri/teach.html Magnetism Some basics: A magnet is associated with magnetic lines of force, and a north pole and a south pole. The lines of force come out of the north pole (the source) and are pulled in to the south pole (the sink). A current in a ring or coil also produces magnetic lines of force. N S The magnetic dipole (a north-south pair) is usually represented by an arrow. Magnetic fields act on these dipoles and tend to align them. The magnetic field strength H generated by N closely spaced turns in a coil of wire carrying a current I, for a coil length of l is given by: NI H = l The units of H are amp`eres per meter (Am−1) in SI units or oersted (Oe) in CGS. 1 Am−1 = 4π × 10−3 Oe. If a coil (or solenoid) encloses a vacuum, then the magnetic flux density B generated by a field strength H from the solenoid is given by B = µ0H −7 where µ0 is the vacuum permeability. In SI units, µ0 = 4π × 10 H/m. If the solenoid encloses a medium of permeability µ (instead of the vacuum), then the magnetic flux density is given by: B = µH and µ = µrµ0 µr is the relative permeability. Materials respond to a magnetic field by developing a magnetization M which is the number of magnetic dipoles per unit volume. The magnetization is obtained from: B = µ0H + µ0M The second term, µ0M is reflective of how certain materials can actually concentrate or repel the magnetic field lines.