KIAS Emergence Workshop 2005 Manybody Physics Group SKKU Valence bond solid order through spin-lattice coupling Jung Hoon Han & Chenglong Jia Sung Kyun.

Slides:



Advertisements
Similar presentations
THE ISING PHASE IN THE J1-J2 MODEL Valeria Lante and Alberto Parola.
Advertisements

One-dimensional approach to frustrated magnets
Quantum effects in a pyrochlore antiferromagnet: ACr2O4
1 Spin Freezing in Geometrically Frustrated Antiferromagnets with Weak Bond Disorder Tim Saunders Supervisor: John Chalker.
Strong Correlations, Frustration, and why you should care Workshop on Future Directions  For some other perspectives, see
Inelastic Magnetic Neutron Scattering on the Spin-Singlet Spin- ½ FCC System Ba 2 YMoO 6 Jeremy P. Carlo Canadian Neutron Beam Centre, National Research.
SPIN STRUCTURE FACTOR OF THE FRUSTRATED QUANTUM MAGNET Cs 2 CuCl 4 March 9, 2006Duke University 1/30 Rastko Sknepnek Department of Physics and Astronomy.
Quantum critical phenomena Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu Quantum critical phenomena Talk online: sachdev.physics.harvard.edu.
Kagome Spin Liquid Assa Auerbach Ranny Budnik Erez Berg.
Junghoon Kim and Jung Hoon Han Department of Physics Sungkyunkwan University.
Lattice instability in frustrated systems Maxim Mostovoy MPI, Stuttgart Groningen, April 22, 2004 D. Khomskii, Cologne J. Knoester, Groningen R. Moessner,
Degeneracy Breaking in Some Frustrated Magnets Doron BergmanUCSB Physics Greg FieteKITP Ryuichi ShindouUCSB Physics Simon TrebstQ Station Itzykson meeting,
Degeneracy Breaking in Some Frustrated Magnets Doron BergmanUCSB Physics Greg FieteKITP Ryuichi ShindouUCSB Physics Simon TrebstQ Station HFM Osaka, August.
Anomalous excitation spectra of frustrated quantum antiferromagnets John Fjaerestad University of Queensland Work done in collaboration with: Weihong Zheng,
Frustration and fluctuations in various spinels Leon Balents Doron Bergman Ryuichi Shindou Jason Alicea Simon Trebst Emanuel Gull Lucile Savary.
Spin Liquid and Solid in Pyrochlore Antiferromagnets
Spin Liquid Phases ? Houches/06//2006.
Houches/06//2006 From Néel ordered AFMs to Quantum Spin Liquids C. Lhuillier Université Paris VI & IUF.
Crystal Lattice Vibrations: Phonons
Classical Antiferromagnets On The Pyrochlore Lattice S. L. Sondhi (Princeton) with R. Moessner, S. Isakov, K. Raman, K. Gregor [1] R. Moessner and S. L.
Neutron Scattering from Geometrically Frustrated Antiferromagnets Spins on corner-sharing tetrahedra Paramagnetic phase Long Range Ordered phase (ZnCr.
Impurities in Frustrated Magnets
ISSP TASSP workshop Jun 19, 2008 Multiferroic behavior in spin-chirality- and exchange-striction-driven compounds Jung Hoon Han (SungKyunKwan U, Korea)
Neutron Scattering of Frustrated Antiferromagnets Satisfaction without LRO Paramagnetic phase Low Temperature phase Spin glass phase Long range order Spin.
The 5th Korea-Japan-Taiwan Symposium on Strongly Correlated Electron System Manybody Lab, SKKU Spontaneous Hexagon Organization in Pyrochlore Lattice Jung.
Solving Impurity Structures Using Inelastic Neutron Scattering Quantum Magnetism - Pure systems - vacancies - bond impurities Conclusions Collin Broholm*
Correlated States in Optical Lattices Fei Zhou (PITP,UBC) Feb. 1, 2004 At Asian Center, UBC.
Frustrated Quantum Magnets in Strong Magnetic Fields F. Mila Institute of Theoretical Physics Ecole Polytechnique Fédérale de Lausanne Switzerland.
Neutron Scattering Studies of Tough Quantum Magnetism Problems
Vector Chiral States in Low- dimensional Quantum Spin Systems Raoul Dillenschneider Department of Physics, University of Augsburg, Germany Jung Hoon Kim.
Finite Temperature Spin Correlations in Quantum Magnets with a Spin Gap Collin Broholm* Johns Hopkins University and NIST Center for Neutron Research *supported.
Self-Organizations in Frustrated Spinels Seung-Hun Lee National Institute of Standards and Technology.
Magnets without Direction Collin Broholm Johns Hopkins University and NIST Center for Neutron Research  Introduction  Moment Free Magnetism in one dimension.
KIAS workshop Sept 1, 2008 A tale of two spin chiralities in frustrated spin systems Jung Hoon Han (SungKyunKwan U, Korea)
The Magnetic phase transition in the frustrated antiferromagnet ZnCr 2 O 4 using SPINS Group B Ilir Zoto Tao Hong Yanmei Lan Nikolaos Daniilidis Sonoko.
Magnets without Direction Collin Broholm Johns Hopkins University and NIST Center for Neutron Research  Introduction  Moment Free Magnetism in one dimension.
Collin Broholm Johns Hopkins University and NIST Center for Neutron Research Quantum Phase Transition in a Quasi-two-dimensional Frustrated Magnet M. A.
Quasi-1D antiferromagnets in a magnetic field a DMRG study Institute of Theoretical Physics University of Lausanne Switzerland G. Fath.
Magnetic Frustration at Triple-Axis  Magnetism, Neutron Scattering, Geometrical Frustration  ZnCr 2 O 4 : The Most Frustrated Magnet How are the fluctuating.
M. Ueda, T. Yamasaki, and S. Maegawa Kyoto University Magnetic resonance of Fe8 at low temperatures in the transverse field.
Vector spin chirality in classical & quantum spin systems
Recontres du Vietnam August 2006 Electric Polarization induced by Magnetic order Jung Hoon Han Sung Kyun Kwan U. (SKKU) Korea Collaboration Chenglong Jia.
Collin Broholm * Johns Hopkins University and NIST Center for Neutron Research Y. ChenJHU, Baltimore, USA M. EnderleILL, Grenoble, France Z. HondaRiken,
Magnon Another Carrier of Thermal Conductivity
O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY Electronically smectic-like phase in a nearly half-doped manganite J. A. Fernandez-Baca.
Hiroshima Nov 2006 Electric Polarization induced by Magnetic order Jung Hoon Han Sung Kyun Kwan U. (SKKU) Korea Collaboration Chenglong Jia (KIAS) Shigeki.
D=2 xy model n=2 planar (xy) model consists of spins of unit magnitude that can point in any direction in the x-y plane si,x= cos(i) si,y= sin(i)
Vector spin chirality in classical & quantum spin systems
Hidden topological order in one-dimensional Bose Insulators Ehud Altman Department of Condensed Matter Physics The Weizmann Institute of Science With:
KIAS Emergent Materials 2006 Bond Polarization induced by Magnetic order Jung Hoon Han Sung Kyun Kwan U. Reference: cond-mat/0607 Collaboration Chenglong.
Antiferromagnetic Resonances and Lattice & Electronic Anisotropy Effects in Detwinned La 2-x Sr x CuO 4 Crystals Crystals: Yoichi Ando & Seiki Komyia Adrian.
Collin Broholm Johns Hopkins University and NIST Center for Neutron Research Quantum Phase Transition in Quasi-two-dimensional Frustrated Magnet M. A.
Frustrated magnetism in 2D Collin Broholm Johns Hopkins University & NIST  Introduction Two types of antiferromagnets Experimental tools  Frustrated.
Neutron Scattering of Frustrated Antiferromagnets Satisfaction without LRO Paramagnetic phase Low Temperature phases Spin glass phase Long range order.
March Meeting 2007 Spin-polarization coupling in multiferroic transition-metal oxides Shigeki Onoda (U. Tokyo) Chenglong Jia (KIAS) Jung Hoon Han (SKKU)
One Dimensional Magnetic Systems Strong Fluctuations in Condensed Matter Magnetism in one dimension Pure systems Doped systems Magnetized states Conclusions.
Collin Broholm Johns Hopkins University and NIST Center for Neutron Research Quantum Phase Transition in Quasi-two-dimensional Frustrated Magnet M. A.
GNSF: KITP: PHY Krakow, June 2008 George Jackeli Max-Planck Institute for Solid State Research, Stuttgart In collaboration with:
Solving Impurity Structures Using Inelastic Neutron Scattering Quantum Magnetism - Pure systems - vacancies - bond impurities Conclusions Collin Broholm*
Spin-Peierls Effect on Frustrated Spin Systems
Spontaneous Hexagon Organization in Pyrochlore Lattice
Quantum effects in a pyrochlore antiferromagnet: ACr2O4
Phase Transitions in Quantum Triangular Ising antiferromagnets
Chiral Spin States in the (SungKyunKwan U, Korea)
Spin-lattice Interaction Effects in Frustrated Antiferromagnets
Chiral Spin States in the Pyrochlore Heisenberg Magnet
Phases of Mott-Hubbard Bilayers Ref: Ribeiro et al, cond-mat/
Bond Polarization induced by Magnetic order
Hiroyuki Nojiri, Department of Physics, Okayama University
Institute for Theoretical Physics,
Presentation transcript:

KIAS Emergence Workshop 2005 Manybody Physics Group SKKU Valence bond solid order through spin-lattice coupling Jung Hoon Han & Chenglong Jia Sung Kyun Kwan U. 成均館大 Ref: Jia(Kim) 2 Han, PRB (2005); Jia & Han, cond-mat/

KIAS Emergence Workshop 2005 Manybody Physics Group SKKU Lattice-Coupled Antiferromagnetic Spin Model Spin and lattice are coupled through magneto-striction effect (Pytte, PRB 1974) i j uiui ujuj R ij Lattice displacement related to local spin-spin correlation by

KIAS Emergence Workshop 2005 Manybody Physics Group SKKU Application to Frustrated Lattices – Triangular, Kagome NO LATTICE DEFORMATION!

KIAS Emergence Workshop 2005 Manybody Physics Group SKKU Triangular/Kagome lattices – meanfield theory Ground state of Heisenberg model gives 120 degrees for neighboring spins for triangular/Kagome According to linearized spin-lattice theory local displacement is zero. Classical degeneracy of Kagome is not lifted.

KIAS Emergence Workshop 2005 Manybody Physics Group SKKU 3D Frustrated Lattice - Pyrochlore Tetrahedron as a building block Ground state condition for each tetrahedron Macroscopic classical ground state degeneracy in pristine Heisenberg model

KIAS Emergence Workshop 2005 Manybody Physics Group SKKU Lifting of degeneracy through spin-lattice coupling For pyrochlore lattice, there are infinitely many ways to deform the lattice through linearized spin-lattice coupling Some clues to the deformation pattern must come from experiment

KIAS Emergence Workshop 2005 Manybody Physics Group SKKU Experiments on Pyrochlore – ZnCr2O4 Below Tc S.H.Lee et al. PRL, 2000 : Spins on Cr 3+ (S=3/2) order antiferromagnetically at as first-order transition, acccompanied by cubic-to-tetragonal distortion.

KIAS Emergence Workshop 2005 Manybody Physics Group SKKU Theory of spin-Peierls transition by Tschernyshyov, Moessner, and Sondhi TMS, PRL, 2002 TMS, PRB, 2002 Elongation (contraction) of a tetrahedron along an axis And collinear antiferromagnetic spins is the ground state

KIAS Emergence Workshop 2005 Manybody Physics Group SKKU Experiments on Pyrochlore – ZnCr2O4 Above Tc S.H.Lee et al. Nature, 2002 : Neutron scattering of paramagnetic state at T=15K Structure factor consistent with hexagon spin cluster (spin-loop director) Conclude: Neutrons scatter off a hexagon cluster of spins, rather individual, fluctuating spins (very unusual paramagnetic state!)

KIAS Emergence Workshop 2005 Manybody Physics Group SKKU Lifting of degeneracy through spin-lattice coupling Tetrahedron Unit (Tschernyshyov et al. PRL 2002) Hexagon Unit (Jia et al. PRB 2005)

KIAS Emergence Workshop 2005 Manybody Physics Group SKKU Interpreting Experiments as Spin-Lattice Coupling Invoking spin-lattice coupling, each independent hexagon shrinks, taking advantage of finite lattice stiffness and lowering exchange energy Directors of nearby hexagons interact via

KIAS Emergence Workshop 2005 Manybody Physics Group SKKU Spins within a hexagon are collinear Spins of nearby hexagons are orthogonal Director-Director Interaction

KIAS Emergence Workshop 2005 Manybody Physics Group SKKU Hexagon Organization of Spins in Pyrochlore Hexagons form a super-lattice with each color representing a director orientation All nearby directors are orthogonal (3-states Potts)

KIAS Emergence Workshop 2005 Manybody Physics Group SKKU Energy Comparison In comparing energies for both distortion modes, Tetrahedron-based distortion has a lower energy, but hexagon shrinkage is a viable, metastable state

KIAS Emergence Workshop 2005 Manybody Physics Group SKKU A picture of paramagnetic state in ZnCr 2 O 4 Spin-lattice interaction leads to enhanced singlet (collinear antiferromagnet) tendency within a hexagon Residual spin-lattice interaction leads to orthogonality of nearby directors (3-states Potts model) At finite temperature, thermal fluctuations smear out the inter-hexagon interaction, spin-spin correlation remains confined to a single hexagon Further lowering temperature might lead to condensation of spin-loop directors, but it appears that a tetragonal distortion pre-empts this possibility in ZnCr 2 O 4

KIAS Emergence Workshop 2005 Manybody Physics Group SKKU Spin-Lattice Coupling in YMnO 3 Mn 3+ (S=2) spins form triangular network in MnO 2 plane Katsufuji et al. PRB (2001)

KIAS Emergence Workshop 2005 Manybody Physics Group SKKU Experiments on triangular S=2 AFM – YMnO 3 Expansion of Mn triangles (red) at the onset of magnetic order But simple spin-lattice theory won’t work…. S Lee et al. PRB (2005)

KIAS Emergence Workshop 2005 Manybody Physics Group SKKU New order parameter ? Possible order parameters of spin: (1) spin density wave – magnetism (2) valence-bond – VBS or VBL(RVB)

KIAS Emergence Workshop 2005 Manybody Physics Group SKKU 1D Chain (S=1) 2D square (S=2) 2D hexagonal (S=3/2) Examples of VBS (AKLT states)

KIAS Emergence Workshop 2005 Manybody Physics Group SKKU IDEA: Spin-Lattice Coupling-induced VBS ? Magnetic order doesn’t work, but valence-bond order might. PARTIAL VBS ORDER At most 4 VB’s can form for coordination = 6 Without SLC, VB’s will resonante, but with SLC, VBS patterns can be formed.

KIAS Emergence Workshop 2005 Manybody Physics Group SKKU Calculations Take spin-lattice Hamiltonian and use Schwinger boson mean-field theory (Jia & Han, cond-mat/ ) Bond order Bose condensation Spin singlet LRO

KIAS Emergence Workshop 2005 Manybody Physics Group SKKU Results Energy corresponding to a particular VBS pattern below is lower than that of uniform state for sufficiently large spin-lattice coupling strength (Not spin Jahn-Teller type)

KIAS Emergence Workshop 2005 Manybody Physics Group SKKU Results This state is also Bose-condensed, so LRO co-exists with VBS Elementary excitations: (1) Spin waves for |LRO> (2) Triplet wave for |PVBS>

KIAS Emergence Workshop 2005 Manybody Physics Group SKKU A New Excitation We calculate excitation spectra for the VBS within SMA VBS Spin waveComparison

KIAS Emergence Workshop 2005 Manybody Physics Group SKKU Interpretation (1) A new spectrum is gapped, has a minimum at (4pi/3a,0), same as spin wave minimum (2) Dispersion is extremely flat! Reminiscent of the flat band in kagome AFM.

KIAS Emergence Workshop 2005 Manybody Physics Group SKKU Relation to Experiments? – YMnO 3 Tc=70K Quasi-elastic peak at high T, into Neel region (Takagi: fluctuating XY spins but 40K seems too far from Tc) Any sign of flat band? (must extract spin waves first) Park et al. PRB (2003)

KIAS Emergence Workshop 2005 Manybody Physics Group SKKU Summary A naïve inclusion of magneto-striction leads to a variety of interesting phenomena (1) Classical spin degeneracy of pyrochlore lattice can be lifted through magneto-striction in a number of interesting ways; tetrahedron-based or hexagon-based (2) Formation of valence-bond-solid is facilitated by the spin-lattice coupling and may lead to an interesting excitation spectrum