DOCSLIB.ORG

Bose-Einstein Condensation in Quantum Glasses

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Bose-Einstein Condensation in Quantum Glasses Motivations The quantum cavity method A lattice model for the superglass Discussion Conclusions Bose-Einstein condensation in Quantum Glasses Giuseppe Carleo, Marco Tarzia, and Francesco Zamponi∗ Phys. Rev. Lett. 103, 215302 (2009) Collaborators: Florent Krzakala, Laura Foini, Alberto Rosso, Guilhem Semerjian ∗Laboratoire de Physique Th´eorique, Ecole Normale Sup´erieure, 24 Rue Lhomond, 75231 Paris Cedex 05 March 29, 2010 Motivations The quantum cavity method A lattice model for the superglass Discussion Conclusions Outline 1 Motivations Supersolidity of He4 Helium 4: Monte Carlo results 2 The quantum cavity method Regular lattices, Bethe lattices and random graphs Recursion relations Bose-Hubbard models on the Bethe lattice 3 A lattice model for the superglass Extended Hubbard model on a random graph Results A variational argument 4 Discussion Disordered Bose-Hubbard model: the Bose glass 3D spin glass model with quenched disorder Quantum Biroli-M´ezard model: a lattice glass model 5 Conclusions Motivations The quantum cavity method A lattice model for the superglass Discussion Conclusions Outline 1 Motivations Supersolidity of He4 Helium 4: Monte Carlo results 2 The quantum cavity method Regular lattices, Bethe lattices and random graphs Recursion relations Bose-Hubbard models on the Bethe lattice 3 A lattice model for the superglass Extended Hubbard model on a random graph Results A variational argument 4 Discussion Disordered Bose-Hubbard model: the Bose glass 3D spin glass model with quenched disorder Quantum Biroli-M´ezard model: a lattice glass model 5 Conclusions Experimental Results Discovery by Kim & Chan in He4 (Nature & Science 2004). Motivations• The quantumExperimental cavity method A lattice modelResults for the superglass Discussion Conclusions Reproduced after by many4 other groups. Motivations:•• Discovery supersolidity by Kim & Chan of Hein He4 (Nature & Science 2004). Non-classicalReproduced rotational inertia after observed by many in other groups. •4 solid He (Kim and Chan) P=51 bars P=51 bars Possible interpretation: supersolidity 4 Supersolidity excluded in perfect He crystals (Boninsegni, Ceperley et al.) Supersolidity strongly enhanced by fast quenches (Rittner and Reppy) History dependent response and some evidence for aging (Davis et al.) Are BEC and superfluidity possible in disordered solids? Motivations The quantum cavity method A lattice model for the superglass Discussion Conclusions Helium 4: Monte Carlo results Quantum Monte Carlo simulation of He4 at high pressure P > 32 bar Quench from the liquid phase down in the solid phase 2 hcp 0 glass superglass 1 -2 o -3 0.0359 A 0 -4 g(r) hcp glass 10 -6 1 log (n(r)) o -3 hcp crystal 0.0292 A -8 0 0 2 4 6 8 10 12 14 o -10 0 5 10 r(A) o r (A) ODLRO observed in the one-particle Density-density correlations similar to the density matrix ! BEC, superfluidity liquid (large Lindemann ratio) At P = 32 bar, n0 = 0:5% and ρs /ρ = 0:6 Boninsegni et al., PRL 96, 105301 (2006) Motivations The quantum cavity method A lattice model for the superglass Discussion Conclusions Helium 4: Monte Carlo results 0 0 Amorphous condensate wavefunction: n(r − r ) ∼ n0φ(r)φ(r ) Plot of φ(x; y; z) on slices at fixed z Boninsegni et al., PRL 96, 105301 (2006) Motivations The quantum cavity method A lattice model for the superglass Discussion Conclusions Many open problems Difficulties of QMC Strong ergodicity problems in the glass phase No access to real time dynamics: is this phase really metastable? Difficulty in determining the phase boundary: what is the phase diagram? Open questions What are the physical ingredients (disorder, frustration)? What is the nature of the transition? Is it accompanied by slow dynamics in the liquid phase? Where does superfluidity come from? Strong interaction and disorder: need for a nonperturbative analysis Our result { G.Carleo, M.Tarzia, FZ, PRL 103, 215302 (2009) A solvable model displaying a thermodynamic superglass phase Disorder is self-induced by frustration in absence of external potentials Realistic mechanism for He4 Motivations The quantum cavity method A lattice model for the superglass Discussion Conclusions Outline 1 Motivations Supersolidity of He4 Helium 4: Monte Carlo results 2 The quantum cavity method Regular lattices, Bethe lattices and random graphs Recursion relations Bose-Hubbard models on the Bethe lattice 3 A lattice model for the superglass Extended Hubbard model on a random graph Results A variational argument 4 Discussion Disordered Bose-Hubbard model: the Bose glass 3D spin glass model with quenched disorder Quantum Biroli-M´ezard model: a lattice glass model 5 Conclusions Motivations The quantum cavity method A lattice model for the superglass Discussion Conclusions Regular lattices, Bethe lattices and random graphs Bethe approximation Discard the small loops of the lattice, graph becomes a tree: The tree allows for a simple recursive solution but the frustration is lost Motivations The quantum cavity method A lattice model for the superglass Discussion Conclusions Regular lattices, Bethe lattices and random graphs Cavity approximation Replace the lattice by a random graph of the same connectivity: The exact solution on the random graph can still be obtained (cavity method) Key property: loops have size log L, locally tree-like Motivations The quantum cavity method A lattice model for the superglass Discussion Conclusions Regular lattices, Bethe lattices and random graphs Cavity approximation Replace the lattice by a random graph of the same connectivity: The exact solution on the random graph can still be obtained (cavity method) Key property: loops have size log L, locally tree-like Unfrustrated phase (RS cavity method) Correlations decay fast enough Long loops can be neglected ! back to a tree Cavity approximation is equivalent to Bethe approximation Motivations The quantum cavity method A lattice model for the superglass Discussion Conclusions Regular lattices, Bethe lattices and random graphs Cavity approximation Replace the lattice by a random graph of the same connectivity: The exact solution on the random graph can still be obtained (cavity method) Key property: loops have size log L, locally tree-like Frustrated phase (1RSB cavity method) Correlations do not decay fast enough The recursion relation on a tree is initiated from a given boundary condition For each boundary condition, a different fixed point is obtained One has to sum over boundary conditions in a consistent way Cavity approximation describes the glassy phase Motivations The quantum cavity method A lattice model for the superglass Discussion Conclusions Classical ferromagnet on the Bethe lattice P H = −J hi;ji σi σj P βJσ(σ +···+σ ) Zg+1(σ) = Zg (σ1) ::: Zg (σz−1) e 1 z−1 σ1,...,σz−1 Zg (σ) eβhg σ Normalized probability : ηg (σ) = = Zg (+)+Zg (−) 2 cosh(βhg ) Recursion on the effective magnetic field : z−1 hg+1 = β atanh (tanh(βJ) tanh(βhg )) Fixed point when g ! 1 : (infinitesimal field to break the symmetry) h = 0 at high temperature h 6= 0 at low temperature True magnetic field can be recovered with z instead of z − 1 neighbors on the root Motivations The quantum cavity method A lattice model for the superglass Discussion Conclusions Quantum lattice models P y y H = −J hi;ji(ai aj + aj ai ) + V (n) = K + V (n) −βH P Z = Tr e jni = jn1;:::; nN i 11 = jnihnj n Quantum model , Classical model with one additional dimension (imaginary time) " M # M β D − β K E Z = lim P exp − P V (nα) Q nαje M jnα+1 M!1 M n1;:::;nM α=1 α=1 becomes a path integral : N R Q h R β i Z = Dni (τ) exp − 0 dτV (n(τ) W[n(τ)] i=1 where the ni (τ) are piecewise constant integer functions (periodic) For a hopping h at time τh, ni ! ni + 1, and one of the neighbors j has nj ! nj − 1 p p Wh = J ni (τh) + 1 nj (τh). Q W[n(τ)] = h Wh Motivations The quantum cavity method A lattice model for the superglass Discussion Conclusions Quantum lattice model on the Bethe lattice Path integral construction valid for any graph Classical degree of freedom = trajectories ni (τ) Recursive computation on trees, formally similar, but n(τ) (function) instead of σ 2 f+1; −1g P βJσ(σ +···+σ ) Zg+1(σ) = Zg (σ1) ::: Zg (σz−1) e 1 z−1 σ1,...,σz−1 becomes R Zg+1[n(τ)] = Dn1(τ)Zg [n1(τ)] ::: Dnz−1(τ)Zg [nz−1(τ)] w[n; n1;:::; nz−1] The quantum cavity method Functional recurrence equations for the local action Zg [n(τ)] = exp{−S[n(τ)]g A quadratic action gives back DMFT (correct for z ! 1) Laumann, Scardicchio, Sondhi (2008), Byczuk, Vollhardt (2008) Numerical resolution for bosons and spins { Krzakala, Rosso, Semerjian, FZ (2008) Represent Z[n(τ)] by a weighted sample of trajectories Use the iteration equation to construct a new sample Works only if Z[n(τ)] is a probability Numerical method similar to QMC or GFMC, but here L = 1 (no FSS) Motivations The quantum cavity method A lattice model for the superglass Discussion Conclusions Bose-Hubbard models on the Bethe lattice Test: study of the Mott transition in the Bose-Hubbard model G. Semerjian, M. Tarzia, FZ, PRB 80, 014524 (2009) P y y U P P H = −J hi;ji(ai aj + aj ai ) + 2 i ni (ni − 1) − i µni 3 3 Cavity B-DMFT 2.5 Mean Field 2.5 Monte Carlo Monte Carlo Mean Field Cavity 2 2 µ/U Z=4 µ/U Z=6 1.5 1.5 1 1 0.5 0.5 0 0 0 0.01 0.02 0.03 0.04 0.05 0.06 0 0.01 0.02 0.03 0.04 J/U J/U We can compute many observables Local density hni i and condensate wavefunction hai i D y E Local green function ai (τ)ai (0) and correlation hni (τ)ni (0)i D y E Spatial correlations ai aj Motivations The quantum cavity method A lattice model for the superglass Discussion Conclusions
Load more

Recommended publications
  • SPASER As a Complex System: Femtosecond Dynamics Traced by Ab-Initio Simulations
    SPASER as a complex system: femtosecond dynamics traced by ab-initio simulations Item Type Conference Paper Authors Gongora, J. S. Totero; Miroshnichenko, Andrey E.; Kivshar, Yuri S.; Fratalocchi, Andrea Citation Juan Sebastian Totero Gongora ; Andrey E. Miroshnichenko ; Yuri S. Kivshar and Andrea Fratalocchi " SPASER as a complex system: femtosecond dynamics traced by ab-initio simulations ", Proc. SPIE 9746, Ultrafast Phenomena and Nanophotonics XX, 974618 (March 14, 2016); doi:10.1117/12.2212967; http:// dx.doi.org/10.1117/12.2212967 Eprint version Publisher's Version/PDF DOI 10.1117/12.2212967 Publisher SPIE-Intl Soc Optical Eng Journal Ultrafast Phenomena and Nanophotonics XX Rights Copyright 2016 Society of Photo Optical Instrumentation Engineers. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited. Download date 27/09/2021 00:14:10 Link to Item http://hdl.handle.net/10754/619757 SPASER as a complex system: femtosecond dynamics traced by ab-initio simulations Juan Sebastian Totero Gongoraa, Andrey E. Miroshnichenkob, Yuri S. Kivsharb, and Andrea Fratalocchia aPRIMALIGHT, King Abdullah University of Science and Technology (KAUST),Thuwal 23955-6900, Saudi Arabia bNonlinear Physics Centre, Australian National University, Canberra ACT 2601, Australia. ABSTRACT Integrating coherent light sources at the nanoscale with spasers is one of the most promising applications of plasmonics. A spaser is a nano-plasmonic counterpart of a laser, with photons replaced by surface plasmon polaritons and the resonant cavity replaced by a nanoparticle supporting localized plasmonic modes.
    [Show full text]
  • Arxiv:0807.2458V2 [Cond-Mat.Dis-Nn] 29 Oct 2008 Se Oee,Tevr Eetwr Eotdi E.7)
    Theory of the superglass phase Giulio Biroli,1 Claudio Chamon,2 and Francesco Zamponi3 1Institut de Physique Th´eorique, CEA, IPhT, F-91191 Gif-sur-Yvette, France CNRS, URA 2306, F-91191 Gif-sur-Yvette, France 2Physics Department, Boston University, Boston, MA 02215, USA 3CNRS-UMR 8549, Laboratoire de Physique Th´eorique, Ecole´ Normale Sup´erieure, 24 Rue Lhomond, 75231 Paris Cedex 05, France (Dated: October 29, 2008) A superglass is a phase of matter which is characterized at the same time by superfluidity and a frozen amorphous structure. We introduce a model of interacting bosons in three dimensions that displays this phase unambiguously and that can be analyzed exactly or using controlled approxima- tions. Employing a mapping between quantum Hamiltonians and classical Fokker-Planck operators, we show that the ground state wavefunction of the quantum model is proportional to the Boltzmann measure of classical hard spheres. This connection allows us to obtain quantitative results on static and dynamic quantum correlation functions. In particular, by translating known results on the glassy dynamics of Brownian hard spheres we work out the properties of the superglass phase and of the quantum phase transition between the superfluid and the superglass phase. I. INTRODUCTION Solids do not flow. This apparently tautological statement can be wrong in two ways. First, solidity is in general a timescale-dependent phenomenon. Crystal or glasses, well known solids on most experimentally relevant timescales, do flow if one waits long enough (see Ref. 1 for example). Second, at very small temperatures, quantum solids may become superfluids as suggested theoretically in the early seventies2–4.
    [Show full text]
  • Phase Transitions in Spin Glasses
    Phase Transitions in Spin Glasses Peter Young Talk available at http://physics.ucsc.edu/˜peter/talks/columbia.pdf e-mail:[email protected] Supported by the Hierarchical Systems Research Foundation. Recent collaborators: H. G. Katzgraber, L. W. Lee, J. Pixley, D. Larson, V. Martin-Mayor, A. Tarancon, L. A. Fernandez, S. Gaviro, Colloquium at Columbia University, October 19, 2009. – p.1 Overview • Basic Introduction • What is a spin glass? Why are they important? • Why are Monte Carlo simulations for spin glasses hard? • Try to answer two important questions concerning phase transitions in spin glasses: • Is there a phase transition in an isotropic Heisenberg spin glass? • Is there a transition in an Ising spin glass in a magnetic field (Almeida-Thouless line)? – p.2 What is a spin glass? A system with disorder and frustration. or Most theory uses the simplest model with these ingredients: the Edwards-Anderson Model: H = − Jij Si · Sj − hi · Si . i,j i hXi X Interactions are quenched and are random (have either sign). 2 1/2 Take a Gaussian distribution: [Jij ]av = 0; [Jij ]av = J (= 1) Spins, Si, fluctuate and have m–components: m = 1 (Ising) m = 2 (XY) m = 3 (Heisenberg). – p.3 Spin Glass Systems • Metals: Diluted magnetic atoms, e.g. Mn, in non-magnetic metal, e.g. Cu. RKKY interaction: cos(2kF Rij ) Jij ∼ 3 Rij Random in magnitude and sign, which gives frustration. Note: Mn (S-state ion) has little anisotropy; → Heisenberg spin glass. • Important because relevant to other systems: • “Vortex glass” transition in superconductors • Optimization problems in computer science (including solving optimization problems on a quantum computer) • Protein folding • Error correcting codes – p.4 Slow Dynamics (free) energy Slow dynamics The dynamics is very slow barrier at low T .
    [Show full text]
  • Insulation Solutions Guide
    Creating Intelligent Environments Insulation Solutions Guide Has anyone ever put more thought into insulation? Our world has changed. The way we live is affecting our planet more than ever, and the buildings we construct need to address this – now. 2 Technical Department: 0808 1645 134 It’s time to think carefully about our future. All our futures. What we do today will have an immeasurable impact on tomorrow. And if we do the right thing, we’ll all benefit. As will the next generation. Superglass may be a brand with 40 years behind it, but our thinking is light years ahead. We create intelligent insulation solutions that enable comfortable living and working environments. And that protect our global environment by saving energy and using recycled glass. A global leader We may still be based in Scotland, but we’re part of global leader in roofing, waterproofing and insulation TECHNONICOL – a business with over 6500 people, 51 manufacturing plants and offices in 79 countries, dedicated to researching and investing in new energy saving solutions to improve the lives of millions of people worldwide. So while insulation is what we make, what we contribute makes an important difference to our planet. www.superglass.co.uk 3 The smartest way to use energy is to not use it at all. That’s the underlying principle behind Superglass thinking. It drives everything we do – from creating new ways of insulating to helping housebuilders make best use of resources. 4 Technical Department: 0808 1645 134 We’ve long been innovators – bringing new ideas, products and thinking to the construction industry.
    [Show full text]
  • Bose-Einstein Condensation in Quantum Glasses
    Bose-Einstein condensation in quantum glasses Giuseppe Carleo,1 Marco Tarzia,2 and Francesco Zamponi3, 4 1SISSA – Scuola Internazionale Superiore di Studi Avanzati and CNR-INFM DEMOCRITOS – National Simulation Center, via Beirut 2-4, I-34014 Trieste, Italy. 2Laboratoire de Physique Th´eorique de la Mati`ere Condens´ee, Universit´ePierre et Marie Curie-Paris 6, UMR CNRS 7600, 4 place Jussieu, 75252 Paris Cedex 05, France. 3Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA 4Laboratoire de Physique Th´eorique, Ecole Normale Sup´erieure, UMR CNRS 8549, 24 Rue Lhomond, 75231 Paris Cedex 05, France. The role of geometrical frustration in strongly interacting bosonic systems is studied with a com- bined numerical and analytical approach. We demonstrate the existence of a novel quantum phase featuring both Bose-Einstein condensation and spin-glass behaviour. The differences between such a phase and the otherwise insulating “Bose glasses” are elucidated. Introduction. Quantum particles moving in a disor- frustrated magnets [10], valence-bond glasses [11] and dered environment exhibit a plethora of non-trivial phe- the order-by-disorder mechanism inducing supersolidity nomena. The competition between disorder and quan- on frustrated lattices [12]. Another prominent manifes- tum fluctuations has been the subject of vast literature tation of frustration is the presence of a large number [1, 2] in past years, with a renewed interest following of metastable states that constitutes the fingerprint of from the exciting frontiers opened by the experimental spin-glasses. When quantum fluctuations and geomet- research with cold-atoms [3, 4]. One of the most striking rical frustration meet, their interplay raises nontrivial features resulting from the presence of a disordered ex- questions on the possible realisation of relevant phases ternal potential is the appearance of localized states [1].
    [Show full text]
  • Quantum Fluctuations Can Promote Or Inhibit Glass Formation
    LETTERS PUBLISHED ONLINE: 9 JANUARY 2011 | DOI: 10.1038/NPHYS1865 Quantum fluctuations can promote or inhibit glass formation Thomas E. Markland1, Joseph A. Morrone1, Bruce J. Berne1, Kunimasa Miyazaki2, Eran Rabani3* and David R. Reichman1* Glasses are dynamically arrested states of matter that do not 0.7 1–4 exhibit the long-range periodic structure of crystals . Here Glass 0.7 we develop new insights from theory and simulation into the 0.6 impact of quantum fluctuations on glass formation. As intuition may suggest, we observe that large quantum fluctuations serve 0.6 φ 0.5 to inhibit glass formation as tunnelling and zero-point energy 0.4 allow particles to traverse barriers facilitating movement. 0.3 However, as the classical limit is approached a regime is 10¬2 10¬1 100 φ 0.5 observed in which quantum effects slow down relaxation Λ∗ making the quantum system more glassy than the classical system. This dynamical ‘reentrance’ occurs in the absence of obvious structural changes and has no counterpart in the phenomenology of classical glass-forming systems. 0.4 Although a wide variety of glassy systems ranging from metallic to colloidal can be accurately described using classical theory, Liquid quantum systems ranging from molecular, to electronic and 5,6 0.3 magnetic form glassy states . Perhaps the most intriguing of these 10¬2 10¬1 100 is the coexistence of superfluidity and dynamical arrest, namely Λ∗ the `superglass' state suggested by recent numerical, theoretical and experimental work7–9. Although such intriguing examples exist, Figure 1 j Dynamic phase diagram calculated from the QMCT for a at present there is no unifying framework to treat the interplay hard-sphere fluid.
    [Show full text]
  • Arxiv:Cond-Mat/0503344 V1 15 Mar 2005 Local Vs. Global Variables For
    Local vs. Global Variables for Spin Glasses C. M. Newman∗ D. L. Stein† newman@ cims.nyu.edu dls @ physics.arizona.edu Courant Institute of Mathematical Sciences Depts. of Physics and Mathematics New York University University of Arizona New York, NY 10012, USA Tucson, AZ 85721, USA Abstract We discuss a framework for understanding why spin glasses differ so remarkably from ho- mogeneous systems like ferromagnets, in the context of the sharply divergent low temperature behavior of short- and infinite-range versions of the same model. Our analysis is grounded in understanding the distinction between two broad classes of thermodynamic variables – those that describe the global features of a macroscopic system, and those that describe, or are sen- sitive to, its local features. In homogeneous systems both variables generally behave similarly, but this is not at all so in spin glasses. In much of the literature these two different classes of variables were commingled and confused. By analyzing their quite different behaviors in finite- and infinite-range spin glass models, we see the fundamental reason why the two sys- tems possess very different types of low-temperature phases. In so doing, we also reconcile apparent discrepancies between the infinite-volume limit and the behavior of large, finite vol- umes, and provide tools for understanding inhomogeneous systems in a wide array of contexts. We further propose a set of ‘global variables’ that are definable and sensible for both short- range and infinite-range spin glasses, and allow a meaningful basis for comparison of their arXiv:cond-mat/0503344 v1 15 Mar 2005 low-temperature properties.
    [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]
  • Arxiv:1902.01645V1 [Cond-Mat.Mtrl-Sci] 5 Feb 2019 Magnetic Phases of Fe-Cr Alloys Are Fairly Complex
    The Dynamics of Magnetism in Fe-Cr Alloys with Cr Clustering Jacob B. J. Chapman,∗ Pui-Wai Ma, and S. L. Dudarev UK Atomic Energy Authority, Culham Science Centre, Oxfordshire, OX14 3DB, United Kingdom The dynamics of magnetic moments in iron-chromium alloys with different levels of Cr clustering show unusual features resulting from the fact that even in a perfect body-centred cubic structure, magnetic moments experience geometric magnetic frustration resembling that of a spin glass. Due to the long range exchange coupling and configuration randomness, magnetic moments of Cr solutes remain non-collinear at all temperatures. To characterise magnetic properties of Fe-Cr alloys, we explore the temperature dependence of magnetisation, susceptibility, Curie temperature and spin- spin correlations with spatial resolution. The static and dynamic magnetic properties are correlated with the microstructure of Fe-Cr, where magnetisation and susceptibility are determined by the size of Cr precipitates at nominal Cr concentrations. The Curie temperature is always maximised when the solute concentration of Cr in the α phase is close to 5 to 6 at.%, and the susceptibility of Fe atoms is always enhanced at the boundary between a precipitate and solid solution. Interaction between Cr and Fe stimulates magnetic disorder, lowering the effective Curie temperature. Dynamic simulation of evolution of magnetic correlations shows that the spin-spin relaxation time in Fe-Cr alloys is in the 20 to 40 ps range. I. INTRODUCTION and 84 at.% Cr, Fe magnetic moments prevent long range AFM-like correlations, causing the moments to freeze 15 Iron and chromium are the main components of steels.
    [Show full text]
  • Quantum Spin Glasses on the Bethe Lattice
    Introduction AKLT states on the Bethe lattice A lattice model with a superglass phase Conclusions Quantum Spin Glasses on the Bethe lattice Francesco Zamponi∗ with C.R.Laumann, S. A. Parameswaran, S.L.Sondhi, PRB 81, 174204 (2010) with G.Carleo and M.Tarzia, PRL 103, 215302 (2009) ∗Laboratoire de Physique Th´eorique, Ecole Normale Sup´erieure, 24 Rue Lhomond, 75231 Paris Cedex 05 June 2, 2010 Introduction AKLT states on the Bethe lattice A lattice model with a superglass phase Conclusions Outline 1 Introduction Classical spin glasses Random lattices and the cavity method Ising antiferromagnet on a random graph 2 AKLT states on the Bethe lattice AKLT states: mapping on a classical model AKLT models on the tree AKLT models on the random graph Phase diagram Spectrum of the quantum spin glass phase 3 A lattice model with a superglass phase Extended Hubbard model on a random graph Results A variational argument 4 Conclusions Introduction AKLT states on the Bethe lattice A lattice model with a superglass phase Conclusions Outline 1 Introduction Classical spin glasses Random lattices and the cavity method Ising antiferromagnet on a random graph 2 AKLT states on the Bethe lattice AKLT states: mapping on a classical model AKLT models on the tree AKLT models on the random graph Phase diagram Spectrum of the quantum spin glass phase 3 A lattice model with a superglass phase Extended Hubbard model on a random graph Results A variational argument 4 Conclusions Introduction AKLT states on the Bethe lattice A lattice model with a superglass phase Conclusions
    [Show full text]
  • Introduction to AC Susceptibility
    QuantumDesign Introduction to: AC Susceptibility AC Magnetic Measurements Dinesh Martien Introduction AC magnetic measurements, in which an AC field is applied to a sample and the resulting AC moment is measured, are an important tool for characterizing many materials. Because the induced sample moment is time-dependent, AC measurements yield information about magnetization dynamics which are not AC Magnetometry obtained in DC measurements, where the sample moment is constant during the measurement time. This application note In AC magnetic measurements, a small AC drive magnetic field will briefly describe how AC magnetic measurements are is superimposed on the DC field, causing a time-dependent performed, discuss the meaning of the data that come out of moment in the sample. The field of the time-dependent an AC measurement, and show some measurement examples. moment induces a current in the pickup coils, allowing meas- urement without sample motion. The detection circuitry is configured to detect only in a narrow frequency band, normally DC Magnetometry at the fundamental frequency (that of the AC drive field). DC magnetic measurements determine the equilibrium value In order to understand what is measured in AC magnetometry, of the magnetization in a sample. The sample is magnetized first consider very low frequencies, where the measurement is by a constant magnetic field and the magnetic moment of the most similar to DC magnetometry. In this case, the magnetic sample is measured, producing a DC magnetization curve moment of the sample follows the M(H) curve that would be M(H) . The moment is measured by force, torque or induc- measured in a DC experiment.
    [Show full text]
  • Aging, Rejuvenation and Memory : the Example of Spin Glasses
    Aging, rejuvenation and memory : the example of spin glasses Eric VINCENT Service de Physique de l’Etat Condensé (CNRS URA 2464), DSM/DRECAM/SPEC, CEA Saclay, 91191 Gif sur Yvette Cedex, France [email protected] This paper is written on the basis of a course given at the summer school “Ageing and the glass transition” in the University of Luxembourg. The results presented here are the joint work of the Saclay group: F. Bert, J.-P. Bouchaud, V. Dupuis, J. Hammann, D. Hérisson, F. Ladieu, M. Ocio, D. Parker, E.V., and others. 1. What is a spin glass ? 2. Slow dynamics and aging 2.1 DC experiments 2.2 AC susceptibility 2.3 Noise measurements 2.4 Rejuvenation by a stress 3. Aging, rejuvenation and memory 3.1 Cooling rate effects 3.2 Memory dip experiments 3.3 Rejuvenation and memory versus cumulative aging 4. Characteristic length scales for aging 4.1 Length scales from field variation experiments 4.2 Length scales from temperature variation experiments 4.3 The dynamical correlation length from both temperature and field variation experiments 4.4 Separation of time and length scales with temperature: how much ? 5. Conclusions Abstract - In this paper, we review the general features of the out-of-equilibrium dynamics of spin glasses. We use this example as a guideline for a brief description of glassy dynamics in other disordered systems like structural and polymer glasses, colloids, gels etc. Starting with the simplest experiments, we discuss the scaling laws used to describe the isothermal aging observed in spin glasses after a quench down to the low temperature phase (these scaling laws are the same as established for polymer glasses).
    [Show full text]