Magnetic monopoles in spin ice
|
|
- Aubrey Palmer
- 6 years ago
- Views:
Transcription
1 Magnetic monopoles in spin ice Claudio Castelnovo Oxford University Roderich Moessner MPI-PKS Dresden Shivaji Sondhi Princeton University Nature 451, 42 (2008)
2 The fundamental question astroparticle physics scale (metres) cosmology astrophysics our world nuclear physics? string theory
3 The fundamental question scale (metres) astroparticle physics cosmology astrophysics our world nuclear physics emergent phenomena many body physics complexity? string theory
4 Collective phenomena and complexity Complementary questions: What are the fundamental building blocks of matter, and how do they interact? high energy+particle physics Given building blocks and interactions: what is the resulting collective behaviour? many-body physics and complexity
5 Outline frustrated Ising models and the (spin) ice model the spin ice compounds zero-point entropy long-range (dipolar) interactions survival of the ground-state degeneracy excitations: magnetic monopoles and their properties Is spin ice ordered?
6 Conventional vs frustrated Ising models Consider classical Ising spins, pointing either up or down: σ i = ±1 Simple exchange (strength J): H = Jσ i σ j J < 0: ferromagnetic spins align J > 0: antiferromagnetic spins antialign... but only where possible: frustration = What happens instead??
7 Frustration leads to (classical) degeneracy Not all terms in H = ij σ iσ j can simultaneously be minimised But we can rewrite H:? H = J 2 ( q i=1 σ i ) 2 + const which can be minimised for tetrahedron: i σ i = 0 N gs = ( 4 ) = 6 ground states 2 Degeneracy is hallmark of frustration
8 Zero-point entropy on the pyrochlore lattice Pyrochlore lattice = corner-sharing tetrahedra H pyro = J 2 ( σ i ) 2 tet i tet Pauling estimate of ground state entropy S 0 = ln N gs : ( ) N/2 6 N gs = 2 N S 0 = ln 3 2 microstates vs. constraints; N spins, N/2 tetrahedra
9 Pauling entropy in spin ice Anderson 1956; Harris+Bramwell 1997 Ho 2 Ti 2 O 7 (and Dy 2 Ti 2 O 7 ) are pyrochlore Ising magnets Pauling entropy measured Ramirez as predicted
10 Mapping from ice to spin ice In ice, water molecules retain their identity Hydrogen near oxygen spin pointing in /takagi/matuhirasan/SpinIce.jpg axes non-collinear everything seems to hang together
11 The real (dipolar) Hamiltonian of spin ice Siddharthan+Shastr The nearest-neighbour model H nn for spin ice is not correct Leading term is dipolar energy (µ 0 µ 2 /4πa 3 > J): H = H nn + µ 0 4π ij µ i µ j 3( µ i ˆr ij )( µ i ˆr ij ) r 3 ij Both give same entropy (!!!) Gingras et al. Wrong model right answer... WHY???
12 The dumbell model Dipole pair of opposite charges (µ = qa): Sum over dipoles sum over charges: +q H ij = 2 v(r mn ij ) µ = q a m,n=1 v q 2 /r is the usual Coulomb interaction (regularised): v(r mn ij ) = { µ0 q m i qn j /(4πrmn ij ) i j v o ( µ a )2 = J 3 + 4D 3 ( ) i = j,
13 Origin of the ice rules Choose a = a d, separation between centres of tetrahedra Resum tetrahedral charges Q α = r m i α qm i : H mn ij v(r ij,mn ) αβ V (r αβ ) = { µ0 Q α Q β r αβ α β 4π 1 v 2 oq 2 α α = β Ice configurations (Q α 0) degenerate Pauling entropy!
14 Excitations: dipoles or charges? Ground-state no net charge Excited states: flipped spin dipole excitation same as two charges? one dipole Q=0 two charges
15 Excitations: dipoles or charges? Ground-state no net charge Excited states: flipped spin dipole excitation same as two charges? Q=0 one dipole two charges Fractionalisation in d = 1
16 Excitations in spin ice: dipolar or charged? Single spin-flip (dipole µ) two charged tetrahedra (charges q m = 2µ/a d ) Are charges independent? Fractionalisation in d = 3?
17 Deconfined magnetic monopoles Dumbell Hamiltonian gives E(r) = µ 0 4π q 2 m r magnetic Coulomb interaction
18 Deconfined magnetic monopoles Dumbell Hamiltonian gives E(r) = µ 0 4π q 2 m r magnetic Coulomb interaction deconfined monopoles
19 Deconfined magnetic monopoles Dumbell Hamiltonian gives E(r) = µ 0 4π q 2 m r magnetic Coulomb interaction deconfined monopoles charge q m = 2µ/a = (2µ/µ b )(αλ C /2πa d )q D q D /8000 monopoles in H, not B
20 Intuitive picture for monopoles Simplest picture does not work: disconnect monopoles N S N Next best thing: no string tension between monopoles: S N S N S Two monopoles form a dipole: connected by tensionless Dirac string Dirac string is observable q m q D /8000 not in conflict with quantisation of e
21 Experiment I: Stanford monopole search Monopole passes through superconducting ring magnetic flux through ring changes e.m.f. induced in the ring countercurrent q m is set up Works for both fundamental cosmic and spin ice monopoles signal-noise ratio a problem
22 Experiment I: Stanford monopole search Monopole passes through superconducting ring magnetic flux through ring changes e.m.f. induced in the ring countercurrent q m is set up Works for both fundamental cosmic and spin ice monopoles signal-noise ratio a problem How do we know if a particle is elementary?
23 Experiment II: interacting Coulomb liquid Monopoles form a two-component liquid any characteristic collective behaviour? interaction strength Γ (q 2 m / r )/T exp[ cv 0/T]/T vanishes at both high and low T
24 Experiment II: interacting Coulomb liquid Monopoles form a two-component liquid any characteristic collective behaviour? interaction strength Γ (q 2 m / r )/T exp[ cv 0/T]/T vanishes at both high and low T solution: [111] magnetic field acts as chemical potential can tune r and T separately B
25 Liquid-gas transition in spin ice in a [111] field H nn predicts crossover to maximally polarised state dipolar H: first-order transition with critical endpoint Fisher et al. observed experimentally Hiroi+Maeno groups confirmed numerically
26 Kagome ice: dimensional reduction in a field Ising axes are not collinear [111] field pins one sublattice of spins B
27 Kagome ice: dimensional reduction in a field Ising axes are not collinear [111] field pins one sublattice of spins B Other sublattices form kagome lattice
28 Kagome ice: dimensional reduction in a field Ising axes are not collinear [111] field pins one sublattice of spins Other sublattices form kagome lattice Kagome lattice: two-dimensional How many dimensions are there? B
29 Conventional order and disorder Gas-crystal (e.g. rock salt): Paramagnet-ferromagnet (e.g. fridge magnet) In between: critical points Anything else???
30 Is spin ice ordered or not? No order as in ferromagnet deconfined monopoles
31 Is spin ice ordered or not? No order as in ferromagnet deconfined monopoles Not disordered like a paramagnet ice rules
32 Is spin ice ordered or not? No order as in ferromagnet deconfined monopoles Not disordered like a paramagnet ice rules conservation law Consider magnetic moments µ i as (lattice) flux vector field Ice rules µ = 0 = µ = A
33 Is spin ice ordered or not? No order as in ferromagnet deconfined monopoles Not disordered like a paramagnet ice rules conservation law Consider magnetic moments µ i as (lattice) flux vector field Ice rules µ = 0 = µ = A Local constraint emergent gauge structure Bow-tie motif in neutron scattering Algebraic (but not critical!) correlations
34 Bow-ties in neutron scattering proton correlations in water ice I h Li et al. spin correlations in kagome ice Fennell+Bramwell
35 Emergent particles and new order in spin ice Spin ice is an interesting model system (and material!) frustrated magnet with ground-state entropy dimensional reduction in a field; emergent gauge structure
36 Emergent particles and new order in spin ice Spin ice is an interesting model system (and material!) frustrated magnet with ground-state entropy dimensional reduction in a field; emergent gauge structure Magnetic monopoles as excitations magnetic Coulomb law (felt by external test particle) fractionalisation/deconfinement in 3d material would show up in monopole search: q m q D /8000
37 Thanks Claudio Castelnovo Oxford John Chalker Oxford Karol Gregor Caltech Peter Holdsworth ENS Lyon Sergei Isakov ETH Zürich Ludovic Jaubert ENS Lyon Kumar Raman UC Riverside Shivaji Sondhi Princeton Alessandro Canossa
38 Picture credits Iceberg: Levitation: math.ucr.edu/home/baez/physics/general/levitation/levitation.html Field lines: NaCl:
Magnetic Monopoles in Spin Ice
Magnetic Monopoles in Spin Ice Claudio Castelnovo University of Oxford Roderich Moessner Max Planck Institut Shivaji Sondhi Princeton University Nature 451, 42 (2008) ISIS Seminars, Rutherford Appleton
More informationMagnetic Monopoles in Spin Ice
Magnetic Monopoles in Spin Ice Claudio Castelnovo University of Oxford Roderich Moessner Max Planck Institut Shivaji Sondhi Princeton University Nature 451, 42 (2008) 25 th International Conference on
More informationMagnetic Monopoles in Spin Ice
Magnetic Monopoles in Spin Ice Claudio Castelnovo University of Oxford Roderich Moessner Max Planck Institut Shivaji Sondhi Princeton University Nature 451, 42 (2008) International Conference on Highly
More informationGeometry, topology and frustration: the physics of spin ice
Geometry, topology and frustration: the physics of spin ice Roderich Moessner CNRS and LPT-ENS 9 March 25, Magdeburg Overview Spin ice: experimental discovery and basic model Spin ice in a field dimensional
More informationSTATISTICAL PHYSICS OF GEOMETRICALLY FRUSTRATED MAGNETS
STATISTICAL PHYSICS OF GEOMETRICALLY FRUSTRATED MAGNETS Classical spin liquids, emergent gauge fields and fractionalised excitations John Chalker Physics Department, Oxford University Outline Geometrically
More informationMagnetic Monopoles in Spin Ice
Magnetic Monopoles in Spin Ice Tim Herfurth Institut für Theoretische Physik Goethe-Universität Frankfurt July 6th, 2011 Outline 1 Spin Ice Water Ice What is Spin Ice? 2 Magnetic Monopoles Origin of Magnetic
More informationDynamics and Thermodynamics of Artificial Spin Ices - and the Role of Monopoles
Dynamics and Thermodynamics of Artificial Spin Ices - and the Role of Monopoles Gunnar Möller Cavendish Laboratory University of Cambridge Roderich Moessner Max Planck Institute for the Physics of Complex
More informationGEOMETRICALLY FRUSTRATED MAGNETS. John Chalker Physics Department, Oxford University
GEOMETRICLLY FRUSTRTED MGNETS John Chalker Physics Department, Oxford University Outline How are geometrically frustrated magnets special? What they are not Evading long range order Degeneracy and fluctuations
More informationMagnetoelastics in the frustrated spinel ZnCr 2 O 4. Roderich Moessner CNRS and ENS Paris
Magnetoelastics in the frustrated spinel ZnCr 2 O 4 Roderich Moessner CNRS and ENS Paris CEA Saclay, June 2005 Overview Neutron scattering experiments on ZnCr 2 O 4 Modelling magnetism on the B sublattice
More informationTopological phases and the Kasteleyn transition
Topological phases and the Kasteleyn transition Peter Holdsworth Ecole Normale Supérieure de Lyon 1. Ice and Spin-Ice, collective paramagnets 2. Topologically constrained states 3. Monopole excitations
More informationTutorial on frustrated magnetism
Tutorial on frustrated magnetism Roderich Moessner CNRS and ENS Paris Lorentz Center Leiden 9 August 2006 Overview Frustrated magnets What are they? Why study them? Classical frustration degeneracy and
More informationSpin liquids in frustrated magnets
May 20, 2010 Contents 1 Frustration 2 3 4 Exotic excitations 5 Frustration The presence of competing forces that cannot be simultaneously satisfied. Heisenberg-Hamiltonian H = 1 J ij S i S j 2 ij The ground
More informationThe AC Wien effect: non-linear non-equilibrium susceptibility of spin ice. P.C.W. Holdsworth Ecole Normale Supérieure de Lyon
The AC Wien effect: non-linear non-equilibrium susceptibility of spin ice P.C.W. Holdsworth Ecole Normale Supérieure de Lyon 1. The Wien effect 2. The dumbbell model of spin ice. 3. The Wien effect in
More informationThe monopole physics of spin ice. P.C.W. Holdsworth Ecole Normale Supérieure de Lyon
The monopole physics of spin ice P.C.W. Holdsworth Ecole Normale Supérieure de Lyon 1. The dumbbell model of spin ice. 2. Specific heat for lattice Coulomb gas and spin ice 3. Spin ice phase diagram and
More informationParamagnetic phases of Kagome lattice quantum Ising models p.1/16
Paramagnetic phases of Kagome lattice quantum Ising models Predrag Nikolić In collaboration with T. Senthil Massachusetts Institute of Technology Paramagnetic phases of Kagome lattice quantum Ising models
More informationDegeneracy Breaking in Some Frustrated Magnets. Bangalore Mott Conference, July 2006
Degeneracy Breaking in Some Frustrated Magnets Doron Bergman Greg Fiete Ryuichi Shindou Simon Trebst UCSB Physics KITP UCSB Physics Q Station Bangalore Mott Conference, July 2006 Outline Motivation: Why
More informationA study of the effect of perturbations in spin ice systems: site dilution, weak exchange, quantum and finite-size effects
A study of the effect of perturbations in spin ice systems: site dilution, weak exchange, quantum and finite-size effects by Taoran Lin A thesis presented to the University of Waterloo in fulfillment of
More informationSpin liquids and frustrated magnetism. J. T. Chalker Theoretical Physics. Oxford University, 1, Keble Road, Oxford, OX1 3NP
Spin liquids and frustrated magnetism J. T. Chalker Theoretical Physics. Oxford University, 1, Keble Road, Oxford, OX1 3NP 1 Preface Lecture Notes Acknowledgements I am very grateful to all my collaborators
More informationChapter 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
More informationGeometrical frustration, phase transitions and dynamical order
Geometrical frustration, phase transitions and dynamical order The Tb 2 M 2 O 7 compounds (M = Ti, Sn) Yann Chapuis PhD supervisor: Alain Yaouanc September 2009 ann Chapuis (CEA/Grenoble - Inac/SPSMS)
More informationarxiv: v1 [physics.comp-ph] 27 Sep 2018
Comparison of diluted antiferromagnetic Ising models on frustrated lattices in a magnetic field arxiv:89.278v [physics.comp-ph] 27 Sep 28 Konstantin Soldatov,2, Alexey Peretyatko, Konstantin Nefedev,2,
More informationA Theory of Water and Ionic Solution, with Particular Reference to Hydrogen
A Theory of Water and Ionic Solution, with Particular Reference to Hydrogen and Hydroxyl Ions, J. D. Bernal and R. H. Fowler, J. Chem. Phys. 1 (1933) 515-548. Ice-I h : a = 7.82 Å ; c = 7.36 Å P6 3 cm
More informationFrustration and ice. Similarities with the crystal structure of ice I h : the notion of spin ice.
Frustration and ice The cubic (Fd-3m) structure of pyrochlore (CaNa)Nb 2 O 6 F [A 2 B 2 O 7 or A 2 B 2 O 6 Oʹ] The A site often has lone-pair cations (Pb 2+ or Bi 3+ ). Polar materials in this structure
More informationDegeneracy Breaking in Some Frustrated Magnets
Degeneracy Breaking in Some Frustrated Magnets Doron Bergman Greg Fiete Ryuichi Shindou Simon Trebst UCSB Physics KITP UCSB Physics Q Station cond-mat: 0510202 (prl) 0511176 (prb) 0605467 0607210 0608131
More informationLone pairs in the solid state: Frustration
Lone pairs in the solid state: Frustration Bi 2 Ti 2 O 6 O, the pyrochlore analogue of perovskite PbTiO 3, is cubic down to 2 K. [Hector, Wiggin, J. Solid State Chem. 177 (2004) 139] Question: Is the absence
More informationRICHARD MASON. A thesis submitted to The University of Birmingham for the degree of DOCTOR OF PHILOSOPHY
TRANSFER FUNCTION APPROACHES TO THE ONE-DIMENSIONAL THERMODYNAMICS OF CLASSICAL MAGNETS, AND THE LONG-RANGE DIPOLE INTERACTION IN RARE-EARTH PYROCHLORES by RICHARD MASON A thesis submitted to The University
More informationMagnetic Ordering of Dipolar Spin Ice in Moderate [111] Field
Magnetic Ordering of Dipolar Spin Ice in Moderate [111] Field by Brian Yee A thesis presented to the University of Waterloo in fulfilment of the thesis requirement for the degree of Master of Science in
More informationSpin Ice and Quantum Spin Liquid in Geometrically Frustrated Magnets
Spin Ice and Quantum Spin Liquid in Geometrically Frustrated Magnets Haidong Zhou National High Magnetic Field Laboratory Tallahassee, FL Outline: 1. Introduction of Geometrically Frustrated Magnets (GFM)
More informationJung Hoon Kim & Jung Hoon Han
Chiral spin states in the pyrochlore Heisenberg magnet : Fermionic mean-field theory & variational Monte-carlo calculations Jung Hoon Kim & Jung Hoon Han Department of Physics, Sungkyunkwan University,
More informationArtificial spin ice: Frustration by design
Artificial spin ice: Frustration by design Peter Schiffer Pennsylvania State University Joe Snyder, Ben Ueland, Rafael Freitas, Ari Mizel Princeton: Bob Cava, Joanna Slusky, Garret Lau Ruifang Wang, Cristiano
More informationThe Coulomb phase in frustrated systems
The Coulomb phase in frustrated systems Christopher L. Henley, [Support: U.S. National Science Foundation] Waterloo/Toronto, March 2010 1 Outline 1. Examples: lattices/models/materials w/ Coulomb phase
More informationWORLD SCIENTIFIC (2014)
WORLD SCIENTIFIC (2014) LIST OF PROBLEMS Chapter 1: Magnetism of Free Electrons and Atoms 1. Orbital and spin moments of an electron: Using the theory of angular momentum, calculate the orbital
More informationFrustrated diamond lattice antiferromagnets
Frustrated diamond lattice antiferromagnets ason Alicea (Caltech) Doron Bergman (Yale) Leon Balents (UCSB) Emanuel Gull (ETH Zurich) Simon Trebst (Station Q) Bergman et al., Nature Physics 3, 487 (007).
More informationSPT: a window into highly entangled phases
SPT: a window into highly entangled phases T. Senthil (MIT) Collaborators: Chong Wang, A. Potter Why study SPT? 1. Because it may be there... Focus on electronic systems with realistic symmetries in d
More informationZero Point Entropy in Stuffed Spin Ice
1 Zero Point Entropy in Stuffed Spin Ice G.C. Lau 1, R.S. Freitas 2, B.G. Ueland 2, B.D. Muegge 1, E.L. Duncan 1, P. Schiffer 2, and R.J. Cava 1 1 Department of Chemistry, Princeton University, Princeton
More informationSPIN LIQUIDS AND FRUSTRATED MAGNETISM
SPIN LIQUIDS AND FRUSTRATED MAGNETISM Classical correlations, emergent gauge fields and fractionalised excitations John Chalker Physics Department, Oxford University For written notes see: http://topo-houches.pks.mpg.de/
More informationSpin Hamiltonian and Order out of Coulomb Phase in Pyrochlore Structure of FeF3
Spin Hamiltonian and Order out of Coulomb Phase in Pyrochlore Structure of FeF3 Farhad Shahbazi in collaboration with Azam Sadeghi (IUT) Mojtaba Alaei (IUT) Michel J. P. Gingras (UWaterloo) arxiv: 1407.0849
More informationDirac Strings and Magnetic Monopoles in Spin Ice Dy 2 Ti 2 O 7
Dirac Strings and Magnetic Monopoles in Spin Ice Dy 2 Ti 2 O 7 D.J.P. Morris 1, D.A. Tennant 1,2, S.A. Grigera 3,4, B. Klemke 1,2, C. Castelnovo 5, R. Moessner 6, C. Czternasty 1, M. Meissner 1, K.C. Rule
More informationMagnetic Relaxation in Spin Ice Compounds : Spin Flip Dynamic Driven by a Thermal Bath
Master Science de la matière Stage 2014 2015 École Normale Supérieure de Lyon Jouffrey Victor Université Claude Bernard Lyon I M2 Physique Magnetic Relaxation in Spin Ice Compounds : Spin Flip Dynamic
More informationMean-field theory for confinement transitions and magnetization plateaux in spin ice
Mean-field theory for confinement transitions and magnetization plateaux in spin ice Stephen Powell School of Physics and Astronomy, The University of Nottingham, Nottingham, NG7 2RD, United Kingdom We
More informationCritical speeding-up in magneto-electric spin-ice
Kolymbari, Crete, 16.09.2015 Joachim Hemberger II. Physikalisches Institut, Universität zu Köln, 50937 Köln Critical speeding-up in magneto-electric spin-ice Dy 2 Ti 2 O 7 Crete, 16.09.2015) Joachim Hemberger
More informationNumerical diagonalization studies of quantum spin chains
PY 502, Computational Physics, Fall 2016 Anders W. Sandvik, Boston University Numerical diagonalization studies of quantum spin chains Introduction to computational studies of spin chains Using basis states
More informationSmall and large Fermi surfaces in metals with local moments
Small and large Fermi surfaces in metals with local moments T. Senthil (MIT) Subir Sachdev Matthias Vojta (Augsburg) cond-mat/0209144 Transparencies online at http://pantheon.yale.edu/~subir Luttinger
More informationOrdering and Defects in Artificial Magnetic Square Ice: Thermodynamic and Field-Driven Processes
Ordering and Defects in Artificial Magnetic Square Ice: Thermodynamic and Field-Driven Processes Jason Phillip Morgan School of Physics and Astronomy University of Leeds Submitted in accordance with the
More informationQuantum Phase Transition
Quantum Phase Transition Guojun Zhu Department of Physics, University of Illinois at Urbana-Champaign, Urbana IL 61801, U.S.A. (Dated: May 5, 2002) A quantum system can undergo a continuous phase transition
More informationThe Phase Transition of the 2D-Ising Model
The Phase Transition of the 2D-Ising Model Lilian Witthauer and Manuel Dieterle Summer Term 2007 Contents 1 2D-Ising Model 2 1.1 Calculation of the Physical Quantities............... 2 2 Location of the
More informationLow-temperature properties of classical geometrically frustrated antiferromagnets
PHYSICAL REVIEW B VOLUME 58, NUMBER 18 1 NOVEMBER 1998-II Low-temperature properties of classical geometrically frustrated antiferromagnets R. Moessner and J. T. Chalker Theoretical Physics, Oxford University,
More informationQuantum spin systems - models and computational methods
Summer School on Computational Statistical Physics August 4-11, 2010, NCCU, Taipei, Taiwan Quantum spin systems - models and computational methods Anders W. Sandvik, Boston University Lecture outline Introduction
More informationSpin Systems. Frustrated. \fa. 2nd Edition. H T Diep. World Scientific. University of Cergy-Pontoise, France. Editor HONG SINGAPORE KONG TAIPEI
BEIJING HONG Frustrated Spin Systems 2nd Edition H T Diep University of Cergy-Pontoise, France Editor \fa World Scientific NEW JERSEY LONDON SINGAPORE SHANGHAI KONG TAIPEI CHENNAI CONTENTS Preface of the
More informationOrbital order and Hund's rule frustration in Kondo lattices
Orbital order and Hund's rule frustration in Kondo lattices Ilya Vekhter Louisiana State University, USA 4/29/2015 TAMU work done with Leonid Isaev, LSU Kazushi Aoyama, Kyoto Indranil Paul, CNRS Phys.
More informationDirect observation of the ice rule in artificial kagome spin ice
1/31/2008 Direct observation of the ice rule in artificial kagome spin ice Yi Qi 1, T. Brintlinger 1,2, and John Cumings 1* 1 Department of Materials Science and Engineering 2 Center for Nanophysics and
More informationarxiv: v1 [cond-mat.dis-nn] 12 Nov 2014
Representation for the Pyrochlore Lattice arxiv:1411.3050v1 [cond-mat.dis-nn] 12 Nov 2014 André Luis Passos a, Douglas F. de Albuquerque b, João Batista Santos Filho c Abstract a DFI, CCET, Universidade
More informationCritical Spin-liquid Phases in Spin-1/2 Triangular Antiferromagnets. In collaboration with: Olexei Motrunich & Jason Alicea
Critical Spin-liquid Phases in Spin-1/2 Triangular Antiferromagnets In collaboration with: Olexei Motrunich & Jason Alicea I. Background Outline Avoiding conventional symmetry-breaking in s=1/2 AF Topological
More informationA Monte Carlo Implementation of the Ising Model in Python
A Monte Carlo Implementation of the Ising Model in Python Alexey Khorev alexey.s.khorev@gmail.com 2017.08.29 Contents 1 Theory 1 1.1 Introduction...................................... 1 1.2 Model.........................................
More informationSpin Frustration in Some Magnetic Compounds
Vol. 106 (2004) ACTA PHYSICA POLONICA A No. 5 Proceedings of the School Superconductivity and Other Phenomena in Perovskites, Warsaw 2004 Spin Frustration in Some Magnetic Compounds A. Szytu la a,, L.
More informationQuantum magnetism and the theory of strongly correlated electrons
Quantum magnetism and the theory of strongly correlated electrons Johannes Reuther Freie Universität Berlin Helmholtz Zentrum Berlin? Berlin, April 16, 2015 Johannes Reuther Quantum magnetism () Berlin,
More informationPhase Transitions in Condensed Matter Spontaneous Symmetry Breaking and Universality. Hans-Henning Klauss. Institut für Festkörperphysik TU Dresden
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
More informationSome open questions from the KIAS Workshop on Emergent Quantum Phases in Strongly Correlated Electronic Systems, Seoul, Korea, October 2005.
Some open questions from the KIAS Workshop on Emergent Quantum Phases in Strongly Correlated Electronic Systems, Seoul, Korea, October 2005. Q 1 (Balents) Are quantum effects important for physics of hexagonal
More informationAn intermediate state between the kagome-ice and the fully polarized state in Dy 2 Ti 2 O 7
Papers in Physics, vol. 7, art. 070009 (2015) www.papersinphysics.org Received: 17 May 2015, Accepted: 12 June 2015 Edited by: A. Vindigni Reviewed by: M. Perfetti, Dipartimento di Chimica, Universitá
More informationS j H o = gµ o H o. j=1
LECTURE 17 Ferromagnetism (Refs.: Sections 10.6-10.7 of Reif; Book by J. S. Smart, Effective Field Theories of Magnetism) Consider a solid consisting of N identical atoms arranged in a regular lattice.
More informationPCE STAMP. Physics & Astronomy UBC Vancouver. Pacific Institute for Theoretical Physics
PCE STAMP Physics & Astronomy UBC Vancouver Pacific Institute for Theoretical Physics Limitations of EFFECTIVE HAMILTONIANS- Dissipation and Decoherence P.C.E. Stamp Arrows of Time 2004 (Outing Lodge,
More informationThe Pennsylvania State University. The Graduate School. Eberly College of Science. FIELD DEPENDENT SPIN DYNAMICS IN Dy 2 Ti 2 O 7.
The Pennsylvania State University The Graduate School Eberly College of Science FIELD DEPENDENT SPIN DYNAMICS IN Dy 2 Ti 2 O 7 A Dissertation in Physics by Maria Jane Matthews 2012 Maria Jane Matthews
More informationTitleMagnetic anisotropy of the spin-ice. Citation PHYSICAL REVIEW B (2002), 65(5)
TitleMagnetic anisotropy of the spin-ice Author(s) Fukazawa, H; Melko, RG; Higashinaka MJP Citation PHYSICAL REVIEW B (2002), 65(5) Issue Date 2002-02-01 URL http://hdl.handle.net/2433/49928 RightCopyright
More informationMagnetism in low dimensions from first principles. Atomic magnetism. Gustav Bihlmayer. Gustav Bihlmayer
IFF 10 p. 1 Magnetism in low dimensions from first principles Atomic magnetism Gustav Bihlmayer Institut für Festkörperforschung, Quantum Theory of Materials Gustav Bihlmayer Institut für Festkörperforschung
More informationSpin ice behavior in Dy 2 Sn 2-x Sb x O 7+x/2 and Dy 2 NbScO 7
Spin ice behavior in Dy 2 Sn 2-x Sb x O 7+x/2 and Dy 2 NbScO 7 X. Ke 1*, B. G. Ueland 1*, D.V. West 2, M. L. Dahlberg 1, R. J. Cava 2, and P. Schiffer 1 1 Department of Physics and Materials Research Institute,
More informationDepartment of Physics, Princeton University. Graduate Preliminary Examination Part II. Friday, May 10, :00 am - 12:00 noon
Department of Physics, Princeton University Graduate Preliminary Examination Part II Friday, May 10, 2013 9:00 am - 12:00 noon Answer TWO out of the THREE questions in Section A (Quantum Mechanics) and
More informationProgress toward a Monte Carlo Simulation of the Ice VI-VII Phase Transition
Progress toward a Monte Carlo Simulation of the Ice VI-VII Phase Transition Christina Gower 2010 NSF/REU PROJECT Physics Department University of Notre Dame Advisor: Dr. Kathie E. Newman August 6, 2010
More informationFerromagnetism. Iron, nickel, and cobalt are ferromagnetic.
Ferromagnetism Technische Universität Graz Institute of Solid State Physics Ferromagnetism elow a critical temperature (called the Curie temperature) a magnetization spontaneously appears in a ferromagnet
More informationQuantum order-by-disorder in Kitaev model on a triangular lattice
Quantum order-by-disorder in Kitaev model on a triangular lattice George Jackeli Max-Planck Institute & University of Stuttgart, Germany Andronikashvili Institute of Physics, Tbilisi, Georgia GJ & Avella,
More informationNMR relaxation in spin ice due to diffusing emergent monopoles I
NMR relaxation in spin ice due to diffusing emergent monopoles I Christopher L. Henley Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York, 14853-2501 At low temperatures,
More informationarxiv:quant-ph/ v2 24 Dec 2003
Quantum Entanglement in Heisenberg Antiferromagnets V. Subrahmanyam Department of Physics, Indian Institute of Technology, Kanpur, India. arxiv:quant-ph/0309004 v2 24 Dec 2003 Entanglement sharing among
More informationMetropolis Monte Carlo simulation of the Ising Model
Metropolis Monte Carlo simulation of the Ising Model Krishna Shrinivas (CH10B026) Swaroop Ramaswamy (CH10B068) May 10, 2013 Modelling and Simulation of Particulate Processes (CH5012) Introduction The Ising
More informationHigh-Temperature Criticality in Strongly Constrained Quantum Systems
High-Temperature Criticality in Strongly Constrained Quantum Systems Claudio Chamon Collaborators: Claudio Castelnovo - BU Christopher Mudry - PSI, Switzerland Pierre Pujol - ENS Lyon, France PRB 2006
More informationPhase Transitions and Critical Behavior:
II Phase Transitions and Critical Behavior: A. Phenomenology (ibid., Chapter 10) B. mean field theory (ibid., Chapter 11) C. Failure of MFT D. Phenomenology Again (ibid., Chapter 12) // Windsor Lectures
More informationDimer model implementations of quantum loop gases. C. Herdman, J. DuBois, J. Korsbakken, K. B. Whaley UC Berkeley
Dimer model implementations of quantum loop gases C. Herdman, J. DuBois, J. Korsbakken, K. B. Whaley UC Berkeley Outline d-isotopic quantum loop gases and dimer model implementations generalized RK points
More informationSurface effects in frustrated magnetic materials: phase transition and spin resistivity
Surface effects in frustrated magnetic materials: phase transition and spin resistivity H T Diep (lptm, ucp) in collaboration with Yann Magnin, V. T. Ngo, K. Akabli Plan: I. Introduction II. Surface spin-waves,
More informationQuantum Phase Transitions
Quantum Phase Transitions Subir Sachdev Department of Physics Yale University P.O. Box 208120, New Haven, CT 06520-8120 USA E-mail: subir.sachdev@yale.edu May 19, 2004 To appear in Encyclopedia of Mathematical
More informationMagnetism in Condensed Matter
Magnetism in Condensed Matter STEPHEN BLUNDELL Department of Physics University of Oxford OXFORD 'UNIVERSITY PRESS Contents 1 Introduction 1.1 Magnetic moments 1 1 1.1.1 Magnetic moments and angular momentum
More informationNon-magnetic states. The Néel states are product states; φ N a. , E ij = 3J ij /4 2 The Néel states have higher energy (expectations; not eigenstates)
Non-magnetic states Two spins, i and j, in isolation, H ij = J ijsi S j = J ij [Si z Sj z + 1 2 (S+ i S j + S i S+ j )] For Jij>0 the ground state is the singlet; φ s ij = i j i j, E ij = 3J ij /4 2 The
More informationZ2 topological phase in quantum antiferromagnets. Masaki Oshikawa. ISSP, University of Tokyo
Z2 topological phase in quantum antiferromagnets Masaki Oshikawa ISSP, University of Tokyo RVB spin liquid 4 spins on a square: Groundstate is exactly + ) singlet pair a.k.a. valence bond So, the groundstate
More informationSpin liquid and quantum phase transition without symmetry breaking in a frustrated three-dimensional Ising model
Spin liquid and quantum phase transition without symmetry breaking in a frustrated three-dimensional Ising model Masterarbeit zur Erlangung des akademischen Grades Master of Science vorgelegt von Julia
More information3. General properties of phase transitions and the Landau theory
3. General properties of phase transitions and the Landau theory In this Section we review the general properties and the terminology used to characterise phase transitions, which you will have already
More informationSpin Superfluidity and Graphene in a Strong Magnetic Field
Spin Superfluidity and Graphene in a Strong Magnetic Field by B. I. Halperin Nano-QT 2016 Kyiv October 11, 2016 Based on work with So Takei (CUNY), Yaroslav Tserkovnyak (UCLA), and Amir Yacoby (Harvard)
More informationM02M.1 Particle in a Cone
Part I Mechanics M02M.1 Particle in a Cone M02M.1 Particle in a Cone A small particle of mass m is constrained to slide, without friction, on the inside of a circular cone whose vertex is at the origin
More informationSECOND PUBLIC EXAMINATION. Honour School of Physics Part C: 4 Year Course. Honour School of Physics and Philosophy Part C C3: CONDENSED MATTER PHYSICS
A11046W1 SECOND PUBLIC EXAMINATION Honour School of Physics Part C: 4 Year Course Honour School of Physics and Philosophy Part C C3: CONDENSED MATTER PHYSICS TRINITY TERM 2015 Wednesday, 17 June, 2.30
More informationMagnetic Materials. The inductor Φ B = LI (Q = CV) = L I = N Φ. Power = VI = LI. Energy = Power dt = LIdI = 1 LI 2 = 1 NΦ B capacitor CV 2
Magnetic Materials The inductor Φ B = LI (Q = CV) Φ B 1 B = L I E = (CGS) t t c t EdS = 1 ( BdS )= 1 Φ V EMF = N Φ B = L I t t c t B c t I V Φ B magnetic flux density V = L (recall I = C for the capacitor)
More informationInteraction of matter with magnetic fields
LN07-1 Interaction of matter with magnetic fields All substances have magnetic properties, which can be determined by examining their behaviour in the presence of an external magnetic field, H. N S When
More informationFrom Pyrochlore to the Tripod Kagome Lattice: Magnetism of New Compound Family A2RE3Sb3O14 (A = Mg, Zn; RE = Pr, Nd, Gd, Tb, Dy, Ho, Er, Yb)
University of Tennessee, Knoxville Trace: Tennessee Research and Creative Exchange Doctoral Dissertations Graduate School 12-2017 From Pyrochlore to the Tripod Kagome Lattice: Magnetism of New Compound
More informationAn introduction to magnetism in three parts
An introduction to magnetism in three parts Wulf Wulfhekel Physikalisches Institut, Karlsruhe Institute of Technology (KIT) Wolfgang Gaede Str. 1, D-76131 Karlsruhe 0. Overview Chapters of the three lectures
More informationTransition Elements. pranjoto utomo
Transition Elements pranjoto utomo Definition What is transition metal? One of which forms one or more stable ions which have incompletely filled d orbitals. 30Zn? Definition Zink is not transition elements
More informationThe Oxford Solid State Basics
The Oxford Solid State Basics Steven H. Simon University of Oxford OXFORD UNIVERSITY PRESS Contents 1 About Condensed Matter Physics 1 1.1 What Is Condensed Matter Physics 1 1.2 Why Do We Study Condensed
More informationLecture 2: Deconfined quantum criticality
Lecture 2: Deconfined quantum criticality T. Senthil (MIT) General theoretical questions Fate of Landau-Ginzburg-Wilson ideas at quantum phase transitions? (More precise) Could Landau order parameters
More informationElectromagnetism II. Instructor: Andrei Sirenko Spring 2013 Thursdays 1 pm 4 pm. Spring 2013, NJIT 1
Electromagnetism II Instructor: Andrei Sirenko sirenko@njit.edu Spring 013 Thursdays 1 pm 4 pm Spring 013, NJIT 1 PROBLEMS for CH. 6 http://web.njit.edu/~sirenko/phys433/phys433eandm013.htm Can obtain
More informationObservation of topological phenomena in a programmable lattice of 1800 superconducting qubits
Observation of topological phenomena in a programmable lattice of 18 superconducting qubits Andrew D. King Qubits North America 218 Nature 56 456 46, 218 Interdisciplinary teamwork Theory Simulation QA
More informationthrough a few examples Diffuse scattering Isabelle Mirebeau Laboratoire Léon Brillouin CE-Saclay Gif-sur Yvette, FRANCE
through a few examples Diffuse scattering Isabelle Mirebeau Laboratoire Léon Brillouin CE-Saclay 91191 Gif-sur Yvette, FRANCE Outline General features Nuclear diffuse scattering: local chemical order and/or
More informationFrustrated Magnets as Magnetic Refrigerants
Frustrated Magnets as Magnetic Refrigerants M. E. Zhitomirsky, A. I. Golov, I. B. Berkutov, O. A. Petrenko European Synchrotron Radiation Facility, BP-220, F-38043 Grenoble, France Dept. of Phys. and Astr.,
More informationarxiv: v2 [cond-mat.str-el] 14 Jun 2013
arxiv:106.11v [cond-mat.str-el] 1 Jun 01 Determination of the Entropy via Measurement of the Magnetization: Application to the Spin ice Dy Ti O 7 L. Bovo 1 and S. T. Bramwell 1 1. London Centre for Nanotechnology
More informationNeutron Scattering of Magnetic excitations
Neutron Scattering of Magnetic excitations Magnetic excitations, magnons, and spin chains by Ibrahima Diallo Technische Universität Muenchen Outline Properties of the Neutron Spin, spin waves, and magnons
More informationOut of equilibrium dynamics in the bidimensional spin-ice model
epl draft Out of equilibrium dynamics in the bidimensional spin-ice model Demian Levis and Leticia F. Cugliandolo Université Pierre et Marie Curie - Paris 6, Laboratoire de Physique Théorique et Hautes
More informationCHAPTER 6 CHEMICAL BONDING SHORT QUESTION WITH ANSWERS Q.1 Dipole moments of chlorobenzene is 1.70 D and of chlorobenzene is 2.5 D while that of paradichlorbenzene is zero; why? Benzene has zero dipole
More information