Geometrical frustration, phase transitions and dynamical order
|
|
|
- Austin Sims
- 5 years ago
- Views:
Transcription
1 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) September / 36
2 Outline 1 Introduction 2 The Tb 2 M 2 O 7 compounds (M = Ti, Sn) 3 Tb 2 Ti 2 O 7 : sample study 4 Crystal field levels 5 Conclusions ann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
3 Outline 1 Introduction geometrical frustration connectivity and degeneracy spin ice 2 The Tb 2 M 2 O 7 compounds (M = Ti, Sn) 3 Tb 2 Ti 2 O 7 : sample study 4 Crystal field levels 5 Conclusions ann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
4 Introduction geometrical frustration impossibility to satisfy simultaneously all the magnetic interactions frustration index : f = θ CW /T c ; frustration if f 5 θ CW : Curie-Weiss temperature T c : transition temperature example of 2D Ising antiferromagnets ann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
5 Introduction geometrical frustration triangular lattice Kagomé lattice garnet lattice pyrochlore lattice ann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
6 Introduction connectivity and degeneracy low connectivity = large degeneracy Yann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
7 Introduction spin ice water ice (on the left) and spin ice (on the right) : analogy between protons displacement vectors and magnetic moments water ice = each oxygen with two protons close and two protons away (Pauling) spin ice = two spins in, two spins out six equivalent configurations ann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
8 Introduction spin ice entropy of the spin ice compound Dy 2 Ti 2 O 7 source : Moessner and Ramirez, Physics Today 2006 non vanishing entropy for T 0 ann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
9 Outline 1 Introduction 2 The Tb 2 M 2 O 7 compounds (M = Ti, Sn) the pyrochlore structure general points and spin dynamics Tb environment energy levels 3 Tb 2 Ti 2 O 7 : sample study 4 Crystal field levels 5 Conclusions ann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
10 The Tb 2 M 2 O 7 compounds (M = Ti, Sn) the pyrochlore structure on the left : pyrochlore structure = three dimensional arrangement of corner-sharing tetrahedra on the right : projection of the pyrochlore structure on the (111) plane space group Fd 3m compounds Tb 2 Ti 2 O 7 Tb 2 Sn 2 O 7 lattice parameter Å Å Yann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
11 The Tb 2 M 2 O 7 compounds (M = Ti, Sn) general points : Tb 2Ti 2O 7 Christophe Marin (CEA-Grenoble/Inac/SPSMS) Curie-Weiss temperature θ CW = 18.4(5) K (AF interactions) no obvious magnetic transition frustration index f ann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
12 The Tb 2 M 2 O 7 compounds (M = Ti, Sn) general points : Tb 2Sn 2O 7 Curie-Weiss temperature θ CW = 12 K (AF interactions) Matsuhira et al., J. Phys. Soc. Jpn. 71 (2002) magnetic transition at T c = 0.88(1) K frustration index f 14 neutron diffraction : ordered spin ice magnetic moments with both ferro and antiferromagnetic components Mirebeau et al., Phys. Rev. Lett. 94 (2005) Dalmas de Réotier et al., Phys. Rev. Lett. 96 (2006) ann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
13 The Tb 2 M 2 O 7 compounds (M = Ti, Sn) general points : Tb 2Sn 2O 7 fluctuation times in the ordered phase + no relaxation in our neutron spin echo data (IN11 at ILL) : τ > 10 8 s complex spin dynamics mechanism characterized by different fluctuation times : static at low Q and dynamic at high Q? ann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
14 The Tb 2 M 2 O 7 compounds (M = Ti, Sn) Tb environment spin angular momentum : S = 3 orbital angular momentum : L = 3 total angular momentum : J = 6 Landé factor : g J = 3/2 d 8b (Å) d 48f (Å) Tb 2 Ti 2 O Tb 2 Sn 2 O with d the distance between the oxygen and the rare earth ann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
15 The Tb 2 M 2 O 7 compounds (M = Ti, Sn) energy levels trigonal symmetry with main axis to 111 (local symmetry 3m) H CF tri = B 0 2 O0 2 + B0 4 O0 4 + B3 4 O3 4 + B0 6 O0 6 + B3 6 O3 6 + B6 6 O6 6 Gingras et al., Phys. Rev. B 62 (2000) Mirebeau et al., Phys. Rev. B 76 (2007) two lowest energy levels doublets ann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
16 The Tb 2 M 2 O 7 compounds (M = Ti, Sn) energy levels Tb 2 Ti 2 O 7 φ ± 0 = ± 4 ± ± φ ± e = ± 5 ± ± ground state magnetic moment : µ CF = 5.1 µ B ann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
17 The Tb 2 M 2 O 7 compounds (M = Ti, Sn) energy levels Tb 2 Ti 2 O 7 φ ± 0 = ± 4 ± ± φ ± e = ± 5 ± ± ground state magnetic moment : µ CF = 5.1 µ B Tb 2 Sn 2 O 7 φ ± 0 = ± ± φ ± e = ±0.938 ± ± 1 ± ground state magnetic moment : µ CF = 6.0 µ B ann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
18 The Tb 2 M 2 O 7 compounds (M = Ti, Sn) energy levels Tb 2 Ti 2 O 7 φ ± 0 = ± 4 ± ± φ ± e = ± 5 ± ± ground state magnetic moment : µ CF = 5.1 µ B Tb 2 Sn 2 O 7 φ ± 0 = ± ± φ ± e = ±0.938 ± ± 1 ± ground state magnetic moment : µ CF = 6.0 µ B swap of m z state mainly contributing to φ ± 0 and φ± e, depending on the B 0 6 parameter ann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
19 Outline 1 Introduction 2 The Tb 2 M 2 O 7 compounds (M = Ti, Sn) 3 Tb 2 Ti 2 O 7 : sample study sample dependence of some properties characteristic temperatures 4 Crystal field levels 5 Conclusions ann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
20 Tb 2 Ti 2 O 7 : sample study sample dependence of some properties crystals initial powders growth rate, flow A, B TiO 2 + Tb 4 O 7 8 mm/h, argon C TiO 2 + Tb 2 O 3 7 mm/h, oxygen D TiO 2 + Tb 4 O 7 3 & 8 mm/h, argon crystal growth rate dependence of specific heat + possible well defined anomaly at 0.4 K Hamaguchi et al., Phys. Rev. B 69 (2004) ann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
21 Tb 2 Ti 2 O 7 : sample study sample dependence of some properties same sample as Hamaguchi et al. Yasui et al., J. Phys. Soc. Jpn. 71 (2002) some weak differences between samples ann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
22 Tb 2 Ti 2 O 7 : sample study sample dependence of some properties muon = magnetic local probe (µsr measurements from ISIS) counts rate : N(t) = N 0 exp( t/τ µ )[1 + a 0 P Z (t)] asymmetry : a 0 P z (t) = a s exp[ (λ Z t) β ] + a bg at 6 K : β = 1.00(3) ; and at 0.06 K : β = 1.30(2) ann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
23 Tb 2 Ti 2 O 7 : sample study sample dependence of some properties no sample dependence of the relaxation rate λ Z sample dependence of the exponent β needs to be checked ann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
24 Tb 2 Ti 2 O 7 : sample study characteristic temperatures inelastic neutron scattering measurements from IN12 at ILL [ I (Q, ω) = F (Q) 2 R }] L inel (ω, ω 0, δ, σ inel, A inel ) ω 1 exp( ω/k B T ) { L q (ω, ω 0, Γ, A L ) + + G inc (ω, ω 0, σ inc, A inc ) + C bg weakly inelastic contribution only for T 10 K and relative high Q ann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
25 Tb 2 Ti 2 O 7 : sample study characteristic temperatures λ Z T A(Q) χ(q) Γ(Q) d 3 Q from inelastic neutron scattering and muon spin relaxation : two characteristic temperatures = 2 and 50 K ann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
26 Tb 2 Ti 2 O 7 : sample study characteristic temperatures Luo et al., Phys. Lett. A 291 (2001) low temperature µsr spectra (from PSI) : no oscillation susceptibility : anomaly at around 0.1 K magnetic transition or not? nature of the lowest temperature phase? ann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
27 Outline 1 Introduction 2 The Tb 2 M 2 O 7 compounds (M = Ti, Sn) 3 Tb 2 Ti 2 O 7 : sample study 4 Crystal field levels inelastic neutron scattering entropy variation study 5 Conclusions ann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
28 Crystal field levels inelastic neutron scattering for Tb 2 Ti 2 O 7, our data are consistent with the ones of Mirebeau et al. and Yasui et al. Mirebeau et al., Phys. Rev. B 76 (2007) Yasui et al., J. Phys. Soc. Jpn. 71 (2002) weakly inelastic contribution : energy level at 2 K similar results for Tb 2 Sn 2 O 7 are obtained by Mirebeau et al. Yann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
29 Crystal field levels entropy variation study on the left, total specific heat, nuclear and phonons contributions nuclear contribution from Zeeman splitting ( N = 82(5) mk) µ SH = 4.5(7) µ B phonons from non magnetic and isostructural compound on the right, magnetic specific heat ann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
30 Crystal field levels entropy variation study 2 doublets E = exp( β ) exp( β ) = exp( β ) 1 + exp( β ) 2 singlets and 1 doublet E = 0 + δ exp( βδ) + 2 exp( β ) 1 + exp( βδ) + 2 exp( β ) C v = d E /dt S = C v T dt S calculated between 200 K down to 0.13 K Yann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
31 Crystal field levels entropy variation study for 0 K T 20 K, no influence of higher energy levels similar results for Tb 2 Ti 2 O 7 and Tb 2 Sn 2 O 7 ann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
32 Crystal field levels entropy variation study on the left, magnetic entropy variation : S m (0 20K) > R ln(2) ground state splitting on the right, at low temperature : S m (T = 0K) = R ln(4)? ann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
33 Crystal field levels entropy variation study S m reaches R ln(4) at 20 K splitting observed by Mirebeau et al. with inelastic neutron scattering ann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
34 Outline 1 Introduction 2 The Tb 2 M 2 O 7 compounds (M = Ti, Sn) 3 Tb 2 Ti 2 O 7 : sample study 4 Crystal field levels 5 Conclusions summary outlook ann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
35 Conclusions summary Tb 2 Ti 2 O 7 sample dependence of specific heat, magnetization and µsr (?) a detailed structural study is required but sample independence of inelastic neutron scattering results characteristic temperatures T 2 K and 50 K : µsr and inelastic neutron scattering are consistent from muon frequency shift and susceptibility, possible transition at 0.1 K : what is the nature of the lowest temperature phase? Yann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
36 Conclusions summary Tb 2 Ti 2 O 7 sample dependence of specific heat, magnetization and µsr (?) a detailed structural study is required but sample independence of inelastic neutron scattering results characteristic temperatures T 2 K and 50 K : µsr and inelastic neutron scattering are consistent from muon frequency shift and susceptibility, possible transition at 0.1 K : what is the nature of the lowest temperature phase? Tb 2 Sn 2 O 7 low temperature spin dynamics characterized by different fluctuation times order of magnitude depending on Q : s / 10 9 s and > 10 8 s ann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
37 Conclusions summary Tb 2 M 2 O 7 2 K splitting of the ground state : deduced from inelastic neutron scattering ; consistent with the tetragonal distortion along [001] and now, confirmed by entropy variation study ann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
38 Conclusions summary Tb 2 M 2 O 7 2 K splitting of the ground state : deduced from inelastic neutron scattering ; consistent with the tetragonal distortion along [001] and now, confirmed by entropy variation study new energy levels scheme ann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
39 Conclusions outlook Tb 2 Ti 2 O 7 µsr measurements on sample C to know the behaviour of the exponent β versus the temperature specific heat measurements in dilution on sample C to compare with other samples : S R ln(4)? understand X-Ray and neutron diffraction patterns Yann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
40 Conclusions outlook Tb 2 Ti 2 O 7 µsr measurements on sample C to know the behaviour of the exponent β versus the temperature specific heat measurements in dilution on sample C to compare with other samples : S R ln(4)? understand X-Ray and neutron diffraction patterns Tb 2 Sn 2 O 7 the magnetic moment has both ferromagnetic and antiferromagnetic components : what are consequences on the spin dynamics? static at low Q and dynamic at high Q? why no oscillations have been observed in µsr spectra at low temperature? ann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
41 Thanks the jury P. Holdsworth I. Mirebeau A. Amato my coworkers S. debrion A. Yaouanc P. Dalmas de Réotier C. Marin, G. Lapertot, S. Vanishri, A. Forget (samples) C. Vaju, V. Glazkov, S. Sosin, D. Braithwaite (specific heat) J. F. Jacquot (magnetization) S. Pouget, P. Fouquet, L.-P. Regnault, B. Fåk, A. Cervellino, E. Ressouche, B. Grenier (neutrons) C. Baines, A. Amato, P.J.C. King (µsr) S. H. Curnoe (theory) And thank you for your attention... ann Chapuis (CEA/Grenoble - Inac/SPSMS) September / 36
GEOMETRICALLY 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
SUPPLEMENTARY INFORMATION
Materials and Methods Single crystals of Pr 2 Ir 2 O 7 were grown by a flux method [S1]. Energy dispersive x-ray analysis found no impurity phases, no inhomogeneities and a ratio between Pr and Ir of 1:1.03(3).
Tb 2 Hf 2 O 7 R 2 B 2 7 R B R 3+ T N
Tb Hf O 7 7 χ ac(t ) χ(t ) M(H) C p(t ) µ χ ac(t ) µ 7 7 7 R B 7 R B R 3+ 111 7 7 7 7 111 θ p = 19 7 7 111 7 15 7 7 7 7 7 7 7 7 T N.55 3+ 7 µ µ B 7 7 7 3+ 4f 8 S = 3 L = 3 J = 6 J + 1 = 13 7 F 6 3+ 7 7
NaSrMn 2 F 7, NaCaFe 2 F 7, and NaSrFe 2 F 7 : novel single crystal pyrochlore antiferromagnets
NaSrMn 2 F 7, NaCaFe 2 F 7, and NaSrFe 2 F 7 : novel single crystal pyrochlore antiferromagnets M.B. Sanders*, J.W. Krizan*, K.W. Plumb, T.M. McQueen, and R.J. Cava Department of Chemistry, Princeton University,
Electronic Higher Multipoles in Solids
Electronic Higher Multipoles in Solids Yoshio Kuramoto Department of Physics, Tohoku University Outline Elementary examples of multiple moments Role of multipole moments in solids Case studies octupole
Magnetic monopoles in spin ice
Magnetic monopoles in spin ice Claudio Castelnovo Oxford University Roderich Moessner MPI-PKS Dresden Shivaji Sondhi Princeton University Nature 451, 42 (2008) The fundamental question astroparticle physics
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
arxiv: v2 [cond-mat.str-el] 14 Jun 2013
![arxiv: v2 [cond-mat.str-el] 14 Jun 2013](/thumbs/88/115450563.jpg "arxiv: 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
Spin 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,
Spin 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)
Geometry, 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
Magnetism and superconductivity of UPt by muon spin techniques
Physica B 289}290 (2000) 10}14 Magnetism and superconductivity of UPt by muon spin techniques P. Dalmas de ReH otier*, A. Yaouanc, P.C.M. Gubbens, C.T. Kaiser, A.M. Mulders, F.N. Gygax, A. Schenck, A.
Artificial 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
Spin 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
arxiv: v1 [cond-mat.str-el] 6 Nov 2008
![arxiv: v1 [cond-mat.str-el] 6 Nov 2008](/thumbs/92/107899150.jpg "arxiv: v1 [cond-mat.str-el] 6 Nov 2008")
Unconventional spin freezing and fluctuations in the frustrated antiferromagnet arxiv:811.157v1 [cond-mat.str-el] 6 Nov 28 D. E. MacLaughlin, 1 Y. Nambu, 2 S. Nakatsuji, 2 R. H. Heffner, 3, 4 Lei Shu,
Zero 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
Degeneracy 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
SECOND 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
TitleMagnetic 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
Neutron Powder Diffraction Theory and Instrumentation
NTC, Taiwen Aug. 31, 212 Neutron Powder Diffraction Theory and Instrumentation Qingzhen Huang (qing.huang@nist.gov) NIST Center for Neutron Research (www.ncnr.nist.gov) Definitions E: energy; k: wave vector;
D.H. Ryan. Centre for the Physics of Materials and Physics Department, McGill University, Montreal, Quebec CANADA
μsr D.H. Ryan Centre for the Physics of Materials and Physics Department, McGill University, Montreal, Quebec CANADA ISU Physics-590B 01 March 2019 1 What is μsr? μsr is one of a group of nuclear precession
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) 25 th International Conference on
Frustrated 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).
through 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
Degeneracy 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
Frustration 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
arxiv: v1 [physics.comp-ph] 27 Sep 2018
![arxiv: v1 [physics.comp-ph] 27 Sep 2018](/thumbs/93/113637396.jpg "arxiv: 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,
MAGNETIC MATERIALS. Fundamentals and device applications CAMBRIDGE UNIVERSITY PRESS NICOLA A. SPALDIN
MAGNETIC MATERIALS Fundamentals and device applications NICOLA A. SPALDIN CAMBRIDGE UNIVERSITY PRESS Acknowledgements 1 Review of basic magnetostatics 1.1 Magnetic field 1.1.1 Magnetic poles 1.1.2 Magnetic
Magnetoelastics 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
Supplemental materials for: Pressure-induced electronic phase separation of magnetism and superconductivity in CrAs
Supplemental materials for: Pressure-induced electronic phase separation of magnetism and superconductivity in CrAs Rustem Khasanov 1,*, Zurab Guguchia 1, Ilya Eremin 2,3, Hubertus Luetkens 1, Alex Amato
A 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
Lone 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
Muon-spin spectroscopy of the organometallic spin-1/2 kagome-lattice compound Cu(1,3-benzenedicarboxylate)
Muon-spin spectroscopy of the organometallic spin-1/2 kagome-lattice compound Cu(1,3-benzenedicarboxylate) The MIT Faculty has made this article openly available. Please share how this access benefits
Competing Ferroic Orders The magnetoelectric effect
Competing Ferroic Orders The magnetoelectric effect Cornell University I would found an institution where any person can find instruction in any study. Ezra Cornell, 1868 Craig J. Fennie School of Applied
Spin 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.
Complementarity: muons and neutrons
Complementarity: muons and neutrons Sue Kilcoyne Salford M5 4WT What can neutrons tell us? Neutrons: have wavelengths comparable to interatomic spacings (0.3-15 Å) have energies comparable to structural
Intermediate valence in Yb Intermetallic compounds
Intermediate valence in Yb Intermetallic compounds Jon Lawrence University of California, Irvine This talk concerns rare earth intermediate valence (IV) metals, with a primary focus on certain Yb-based
Dynamics as probed by muons
Dynamics as probed by muons P. Dalmas de Réotier and A. Yaouanc Institut Nanosciences et Cryogénie Université Grenoble Alpes & CEA Grenoble, France. 13th PSI Summer School on Condensed Matter Research
Edinburgh Research Explorer
Edinburgh Research Explorer Short-range magnetic order in the frustrated pyrochlore antiferromagnet CsNiCrF6 Citation for published version: Zinkin, MP, Harris, M & Zeiske, T 1997, 'Short-range magnetic
Field induced magnetic order in the frustrated magnet Gadolinium Gallium Garnet
Highly Frustrated Magnetism 28 (HFM 28) Journal of Physics: Conference Series 145 (29) 1226 doi:1.188/1742-6596/145/1/1226 Field induced magnetic order in the frustrated magnet Gadolinium Gallium Garnet
The 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
RICHARD 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
The electronic structure of materials 1
Quantum mechanics 2 - Lecture 9 December 18, 2013 1 An overview 2 Literature Contents 1 An overview 2 Literature Electronic ground state Ground state cohesive energy equilibrium crystal structure phase
Magnetic systems for refrigeration & thermometry
Magnetic systems for refrigeration & thermometry * Paramagnetic salts * * Hyperfine enhanced systems * * Nuclear spins * Magnetic moments can be aligned by external magnetic field Thermal disorder counteracts
Structure, crystal fields, magnetic interactions, and heavy-fermion behavior in Ce 1 x La x 3 Al
PHYSICAL REVIEW B VOLUME 55, NUMBER 9 1 MARCH 1997-I Structure, crystal fields, magnetic interactions, and heavy-fermion behavior in Ce 1 x La x 3 Al Y. Y. Chen and Y. D. Yao Institute of Physics, Academia
Slow Spin Dynamics in Non-Fermi-Liquid UCu 5 x Pd x, x = 1.0 and 1.5 arxiv:cond-mat/ v1 [cond-mat.str-el] 5 Sep 2001
![Slow Spin Dynamics in Non-Fermi-Liquid UCu 5 x Pd x, x = 1.0 and 1.5 arxiv:cond-mat/ v1 [cond-mat.str-el] 5 Sep 2001](/thumbs/85/92931996.jpg "Slow Spin Dynamics in Non-Fermi-Liquid UCu 5 x Pd x, x = 1.0 and 1.5 arxiv:cond-mat/ v1 [cond-mat.str-el] 5 Sep 2001")
Slow Spin Dynamics in Non-Fermi-Liquid UCu 5 x Pd x, x = 1. and 1.5 arxiv:cond-mat/197v1 [cond-mat.str-el] 5 Sep 21 D. E. MacLaughlin a, R. H. Heffner b O. O. Bernal c G. J. Nieuwenhuys d J. E. Sonier
Magnetic Transition in the Kondo Lattice System CeRhSn 2. Z. Hossain 1, L.C. Gupta 2 and C. Geibel 1. Germany.
Magnetic Transition in the Kondo Lattice System CeRhSn 2 Z. Hossain 1, L.C. Gupta 2 and C. Geibel 1 1 Max-Planck Institute for Chemical Physics of Solids, Nöthnitzer Str. 40, 01187 Dresden, Germany. 2
Schematic for resistivity measurement
Module 9 : Experimental probes of Superconductivity Lecture 1 : Experimental probes of Superconductivity - I Among the various experimental methods used to probe the properties of superconductors, there
Dynamics 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
Magnetic ordering of local moments
Magnetic ordering Types of magnetic structure Ground state of the Heisenberg ferromagnet and antiferromagnet Spin wave High temperature susceptibility Mean field theory Magnetic ordering of local moments
Topological 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
The 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
NMR: Formalism & Techniques
NMR: Formalism & Techniques Vesna Mitrović, Brown University Boulder Summer School, 2008 Why NMR? - Local microscopic & bulk probe - Can be performed on relatively small samples (~1 mg +) & no contacts
Quantum 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,
arxiv:cond-mat/ v1 [cond-mat.dis-nn] 21 Jan 2000
![arxiv:cond-mat/ v1 [cond-mat.dis-nn] 21 Jan 2000](/thumbs/79/79928382.jpg "arxiv:cond-mat/ v1 [cond-mat.dis-nn] 21 Jan 2000")
Magnetic and Thermodynamic Properties of the Collective Paramagnet Spin Liquid Pyrochlore Tb 2 Ti 2 O 7 arxiv:cond-mat/0001317v1 [cond-mat.dis-nn] 21 Jan 2000 M. J. P. Gingras 1,2, B. C. den Hertog 2,
Fe Co Si. Fe Co Si. Ref. p. 59] d elements and C, Si, Ge, Sn or Pb Alloys and compounds with Ge
![Fe Co Si. Fe Co Si. Ref. p. 59] d elements and C, Si, Ge, Sn or Pb Alloys and compounds with Ge](/thumbs/72/66917236.jpg "Fe Co Si. Fe Co Si. Ref. p. 59] d elements and C, Si, Ge, Sn or Pb Alloys and compounds with Ge")
Ref. p. 59] 1.5. 3d elements and C, Si, Ge, Sn or Pb 7 1.75 1.50 Co Si 0.8 0. 3.50 3.5 Co Si 0.8 0. H cr Magnetic field H [koe] 1.5 1.00 0.75 0.50 0.5 C C IF "A" P Frequency ωγ / e [koe] 3.00.75.50.5.00
arxiv: v1 [cond-mat.dis-nn] 12 Nov 2014
![arxiv: v1 [cond-mat.dis-nn] 12 Nov 2014](/thumbs/79/78895904.jpg "arxiv: 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
Magnetic 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
Roger Johnson Structure and Dynamics: Displacive phase transition Lecture 9
9.1. Summary In this Lecture we will consider structural phase transitions characterised by atomic displacements, which result in a low temperature structure that is distorted compared to a higher temperature,
XY Rare-Earth Pyrochlore Oxides an Order-by-Disorder Playground
SPICE-Workshop on "Computational Quantum Magnetism, Mainz May 2015 XY Rare-Earth Pyrochlore Oxides an Order-by-Disorder Playground Michel Gingras Department of Physics & Astronomy, University of Waterloo,
Tutorial 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
S 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.
Linear temperature dependence of electron spin resonance linewidths in La 0.7 Ca 0.3 MnO 3 and YBaMn 2 O 6
Linear temperature dependence of electron spin resonance linewidths in La 0.7 Ca 0.3 MnO 3 and YBaMn 2 O 6 Abstract D. L. Huber Department of Physics, University of Wisconsin-Madison, Madison, WI 53706
Summer School on Methods and Applications of Neutron Spectroscopy NIST Center for Neutron Research
The Magnetic Phase Transition and Spin Fluctuations in the Geometrically Frustrated Antiferromagnetic Spinel CdCr 2 O 4 : An Experiment Using the SPINS Triple-Axis Spectrometer Summer School on Methods
University of Groningen. Orbital ordering and multiferroics Nenert, Gwilherm
University of Groningen Orbital ordering and multiferroics Nenert, Gwilherm IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from it. Please check
Unusual magnetic excitations in a cuprate high-t c superconductor
Unusual magnetic excitations in a cuprate high-t c superconductor Yuan Li Max Planck Institute for Solid State Research Stuttgart, Germany Collaborators University of Minnesota / Stanford University, USA
Magnetic Order versus superconductivity in the Iron-based
Magnetic Order versus superconductivity in the Iron-based layered La(O 1-x F x )FeAs systems Clarina de la Cruz 1,2, Q. Huang 3, J. W. Lynn 3, Jiying Li 3,4, W. Ratcliff II 3, J. L. Zarestky 5, H. A. Mook
The 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
Synthesis, crystal structure, and magnetic properties of RE 3 Sb 3 Mg 2 O 14 (RE=La, Pr, Sm, Eu, Tb, Ho): new 2D Kagome materials
Synthesis, crystal structure, and magnetic properties of RE 3 Sb 3 Mg 2 O 14 (RE=La, Pr, Sm, Eu, Tb, Ho): new 2D Kagome materials M.B. Sanders*, K.M. Baroudi, J.W. Krizan, O.A. Mukadam, and R.J. Cava*
Magnetic properties of the natural mineral Boleite
Magnetic properties of the natural mineral Boleite Bachelor Rapport une 0, 04 Kenneth Lønbæk Niels Bohr Institute University of Copenhagen Supervisors: Prof. Dr. Kim Lefmann Sonja Lindahl Holm External
Lattice dynamics of ferromagnetic superconductor UGe 2
PRAMANA c Indian Academy of Sciences Vol. 71, No. 5 journal of November 2008 physics pp. 1147 1151 Lattice dynamics of ferromagnetic superconductor UGe 2 SATYAM SHINDE 1 and PRAFULLA K JHA 2, 1 Nirma University
Ground state of the geometrically frustrated system Y Sc Mn 2 studied by muon spin relaxation
PHYSICAL REVIEW B VOLUME 61, NUMBER 6 1 FEBRUARY 2000-II Ground state of the geometrically frustrated system Y Sc Mn 2 studied by muon spin relaxation M. Mekata and T. Asano Department of Applied Physics,
SUPPLEMENTARY INFORMATION
doi:10.1038/nature09910 Supplementary Online Material METHODS Single crystals were made at Kyoto University by the electrooxidation of BEDT-TTF in an 1,1,2- tetrachloroethylene solution of KCN, CuCN, and
Physics Qual - Statistical Mechanics ( Fall 2016) I. Describe what is meant by: (a) A quasi-static process (b) The second law of thermodynamics (c) A throttling process and the function that is conserved
Low-temperature spin freezing in the Dy 2 Ti 2 O 7 spin ice
PHYSICAL REVIEW B 69, 064414 2004 Low-temperature spin freezing in the Dy 2 Ti 2 O 7 spin ice J. Snyder, 1 B. G. Ueland, 1 J. S. Slusky, 2 H. Karunadasa, 2 R. J. Cava, 2 and P. Schiffer 1, * 1 Department
Phase Transitions in Strontium Titanate
Phase Transitions in Strontium Titanate Xinyue Fang Department of Physics, University of Illinois at Urbana-Champaign Abstract Strontium Titanate SrTiO 3 (STO) is known to undergo an antiferrodistortive
Quantum effects melt the spin ice: the spontaneous Hall effect and the time-reversal symmetry breaking without magnetic dipole order
2009/12/09 Quantum effects melt the spin ice: the spontaneous Hall effect and the time-reversal symmetry breaking without magnetic dipole order Our recent research in collaboration with University of Tokyo
Verwey transition in magnetite (Fe3O4), unveiled?
Verwey transition in magnetite (Fe3O4), unveiled? J.E. Lorenzo Keywords: Charge, orbital orderings; lattice distortion; spin reorientation; resonant X ray scattering S. Grenier N. Jaouen Y. Joly D. Mannix
Frustrated 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.,
Spin 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
STATISTICAL 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
Magnetic Structure of TbRu 2 Al 10
Magnetic Structure of TbRu 2 Al 10 R. White a, W.D. Hutchison a and T. Mizushima b a School of Physical, Environmental and Mathematical Sciences, The University of New South Wales, Canberra ACT 2600, Australia.
Quantum Magnetism. P. Mendels Lab. Physique des solides, UPSud From basics to recent developments: a flavor
Quantum Magnetism P. Mendels Lab. Physique des solides, UPSud philippe.mendels@u-psud.fr From basics to recent developments: a flavor Quantum phase transitions Model physics for fermions, bosons, problems
Solid State Spectroscopy Problem Set 7
Solid State Spectroscopy Problem Set 7 Due date: June 29th, 2015 Problem 5.1 EXAFS Study of Mn/Fe substitution in Y(Mn 1-x Fe x ) 2 O 5 From article «EXAFS, XANES, and DFT study of the mixed-valence compound
Soft Modes and Relaxor Ferroelectrics
Soft Modes and Relaxor Ferroelectrics R. A. Cowley 1, S. N. Gvasaliya 2,* and B. Roessli 2 1 Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU 2 Laboratory for Neutron Scattering ETH
Magnetic Correlations In Deuteronium Jarosite, A Model S = 5/2 Kagomé Antiferromagnet
Magnetic Correlations In Deuteronium Jarosite, A Model S = 5/2 Kagomé Antiferromagnet A. S. Wills and A. Harrison *, Department of Chemistry, University of Edinburgh, The King's Buildings, West Mains Rd.,
WORLD 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
Yusuke Tomita (Shibaura Inst. of Tech.) Yukitoshi Motome (Univ. Tokyo) PRL 107, (2011) arxiv: (proceedings of LT26)
Yusuke Tomita (Shibaura Inst. of Tech.) Yukitoshi Motome (Univ. Tokyo) PRL 107, 047204 (2011) arxiv:1107.4144 (proceedings of LT26) Spin glass (SG) in frustrated magnets SG is widely observed in geometrically
7.2 Dipolar Interactions and Single Ion Anisotropy in Metal Ions
7.2 Dipolar Interactions and Single Ion Anisotropy in Metal Ions Up to this point, we have been making two assumptions about the spin carriers in our molecules: 1. There is no coupling between the 2S+1
SECOND PUBLIC EXAMINATION. Honour School of Physics Part C: 4 Year Course. Honour School of Physics and Philosophy Part C C3: CONDENSED MATTER PHYSICS
2753 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 2011 Wednesday, 22 June, 9.30 am 12.30
High Field NMR Investigation of Yb 2 Pt 2 O 7
McMaster University Masters Thesis High Field NMR Investigation of Yb 2 Pt 2 O 7 Author: Sean Kentaro Sullivan Takahashi Supervisor: Dr. Takashi Imai A thesis submitted in fulfilment of the requirements
arxiv: v2 [cond-mat.str-el] 14 Mar 2017
![arxiv: v2 [cond-mat.str-el] 14 Mar 2017](/thumbs/83/88071900.jpg "arxiv: v2 [cond-mat.str-el] 14 Mar 2017")
Structural and magnetic properties of two branches of the Tripod Kagome Lattice family A RE 3 Sb 3 O (A = Mg, Zn; RE = Pr, Nd, Gd, Tb, Dy, Ho, Er, Yb) arxiv:6.8396v [cond-mat.str-el] Mar 7 Z. L. Dun, J.
Chapter 8 Magnetic Resonance
Chapter 8 Magnetic Resonance 9.1 Electron paramagnetic resonance 9.2 Ferromagnetic resonance 9.3 Nuclear magnetic resonance 9.4 Other resonance methods TCD March 2007 1 A resonance experiment involves
The Pennsylvania State University. The Graduate School. Department of Physics STUDY OF ARTIFICIAL FRUSTRATED ARRAYS OF SINGLE-DOMAIN FERROMAGNETS
The Pennsylvania State University The Graduate School Department of Physics STUDY OF ARTIFICIAL FRUSTRATED ARRAYS OF SINGLE-DOMAIN FERROMAGNETS A Dissertation in Physics by Jie Li 2011 Jie Li Submitted
APEX CARE INSTITUTE FOR PG - TRB, SLET AND NET IN PHYSICS
Page 1 1. Within the nucleus, the charge distribution A) Is constant, but falls to zero sharply at the nuclear radius B) Increases linearly from the centre, but falls off exponentially at the surface C)
Magnetism 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
Luigi Paolasini
Luigi Paolasini paolasini@esrf.fr LECTURE 5: MAGNETIC STRUCTURES - Mean field theory and magnetic order - Classification of magnetic structures - Collinear and non-collinear magnetic structures. - Magnetic
Spin dynamics of the pyrochlore magnets Gd 2 Ti 2 O 7 and Gd 2 Sn 2 O 7 in the paramagnetic state
Spin dynamics of the pyrochlore magnets Gd 2 Ti 2 O 7 and Gd 2 Sn 2 O 7 in the paramagnetic state S. S. Sosin, L. A. Prozorova, and A. I. Smirnov P. L. Kapitza Institute for Physical Problems RAS, 119334
14. Structure of Nuclei
14. Structure of Nuclei Particle and Nuclear Physics Dr. Tina Potter Dr. Tina Potter 14. Structure of Nuclei 1 In this section... Magic Numbers The Nuclear Shell Model Excited States Dr. Tina Potter 14.
Quantum kagome spin liquids
Quantum kagome spin liquids Philippe Mendels - Univ Paris-Sud Orsa The discovery of Herbertsmithite, ZnCu 3 (OH) 6 Cl 2, which features a perfect kagome geometry, has been coined as the "end to the drought