Novel Order and Dynamics in Frustrated and Random Magnets

Transcription

1 ISPF symposium, Osaka Nov. 17, 2015 Novel Order and Dynamics in Frustrated and Random Magnets Hikaru Kawamura Osaka University

2 What is frustration? Everyone is happy No frustration! Someone is unhappy Frustration!

3 Geometrical frustration (A) Ising spin Some spin is unhappy Spin direction is not uniquely determined Nontrivial degeneracy Enhanced fluctuations

4 Geometrical frustration (B) Vector spin Frustration partially resolved due to the spin canting New symmetry New degrees of freedom

5 Chirality right-handed chirality k + mirror reflection left-handed chirality k ー

6 Gemetrically frustrated lattices Triangular lattice Kagome lattice Pyrochlore lattice

7 Frustrated magnets Spins are located on the lattice interacting with each other, with certain frustration in it, often leading to exotic order.. Spin: Si Ising spin: S=Sz XY spin: S=(Sx,Sy) Heisenberg spin: S=(Sx,Sy,Sz)

8 Magneteic phase transition Energy gain Entropy gain Ferromagnet Ordered state Tc Transition point (paramagnetic state) Temperature T Disordered state Paramagnet Antiferromagnet (AF) Critical behaviors

9 Contents 0. Introduction I. Spins are ordered Novel topological excitations and textures Coupling to other degrees of freedom II. Spins are frozen Randomness Spin glass III. Spins remain disordered Quantum fluctuations Quantum spin liquid

10 I. Spins are ordered but often with some structures in the presence of frustration vector spin Nonollinear or chiral Appearance of chirality on macroscopic scale spin composite

11 Chirality-induced topogical excitations I in noncollinear magnets Vortex formed by vector chirality Z 2 vortex S i S j II Topologically nontrivial texture formed by scalar chirality skyrmion S i S j S k

12 Topological excitation in triangular Heisenberg AF * Novel type of vortex Z 2 vortex [H.Kawamura & S. Miyashita, 84] No topological distinction between R & L (no circulation in the usual sense) V = SO(3) P 1 (SO(3) ) = Z 2 [two-valued topological quantum number] k=si Sj k Vortex formed by chirality vectors

13 Novel topological transition and dynamics * Novel finite-temperature topological transition (or a crossover) occurring at T=Tv within the paramagnetic state driven by the Z 2 -vortex binding-unbinding. [H. Kawamura and S. Miyashita] T < Tv vortex binding-unbinding T > Tv * Novel dynamics borne by free Z 2 vortices, leading to curtain-like characteristic dispersion spectrum. Dispersion relation of the triangular AF (simulation) [T. Okubo and H. Kawamura] w T>T V ~ Spin wave Spin wave (To be examined experimentally) Z 2 vortex q

14 Skyrmion and skyrmion lattice skyrmion Topologically stable spin texture where scalar chiralities wrap the sphere helical [S. Mori et al.] skyrmion lattice Applying magnetic field Manganese oxide forms a lattice electron microscope

15 Frustration-induced skyrmions Skyrmions usually induced by antisymmetric Dzaloshinskii- Moriya interaction Skyrmions induced by frustrated symmetric exchange interaction ever possible? Yes! Anti-particle of Anti-skyrmions should also exist! the skyrmion world 200 nm skyrmion chirality + anti-skyrmion chirality -

16 Frustration induced skyrmion lattice J1-J3 (J1-J2) triangular lattice Heisenberg model in fields [T. Okubo, H. Kawamura et al 11] incommensurate spin order appears triple-q Z skyrmion Magnetic phase diagram Energy Energy minima minimum in q-space points antiskyrmion Skymion/anti-skyrmion domain state 1 st Brillouin zone

17 Coupled composite I: To lattice ー gigantic magnetostriction CdCr 2 O 4 (ZnCr 2 O 4, HgCr 2 O 4 ) Frustration resolved by lattice distortion Regular triangle triangle deformed Spinel compound:cdcr 2 O 4 Spins order due to frustration resolution Formation of spin-lattice coupled couposite magnetization Thermal expansivity gigantic magnetostriction [H. Ueda et.al., 05] H Magnetic field H

18 Coupled composite II: To conduction electrons - Scalar chirality and quantum Berry phase S 2 S 1 Φ S 3 Scalar chirality c = S 1 S 2 S 3 breaks time- reversal symmetry Phase of conduction electron Effective flux Φ = 1/2 scalar chirality c right-handed left-handed Coupling to current Chirality serves as a fictitious magnetic field Quantum Berry phase Chirality-driven anomalous Hall effect

19 Novel chiral order probed by the anomalous Hall effect Metallic pyrochlore Pr 2 Ir 2 O 7 [Y.Machida, S.Nakatsuji et al. 10] Hall conductivity susceptibility Hall measurements temperature Time-reversal symmetry breaking not accompanying the magnetic order Chiral spin liquid

20 Skyrmion exhibits chirality-driven anomalous Hall effect Skyrmion exhibits chirality-driven anomalous Hall effect skyrmion anti-skyrmion chirality + - Rich electromagnetic response exhibited by skyrmions and antiskyrmions

21 II. Spins are frozen Randomness and spin glass (SG) Canonical SG CuMn, AuFe, etc. Antiferromagnetic (AF) Ferromagnetic (F) * Competition between F and AF arising from RKKY interaction * Alloying randomness dilute magnetic alloy Frustration + Randomness

22 What is the fate of the spin in SG? No periodicity in the system AuFe Does not order? Slow down gradually toward T=0? A sharp thermodynamic transition! Experimental finding of the SG transition ac susceptibility [Canella and Mydosh, 1972] dc susceptibility T CuMn T [Nagata, Keesom, Harrison 1979]

23 In SG, spins are frozen in time, but in a spatially random manner breaks ergodicity Exhibits various intriguing phenomena Typical test case of complex systems

24 Canonical SG CuMn, AuFe, etc. Heisenberg system with weak random magnetic anisotropy The true nature of experimental SG transition and SG ordered state is still at issue Standard scenario assumes: Weak magnetic anisotropy induces the crossover from the isotropic Heisenberg to the anisotropic Ising behaiovr. tedns to fail in several respects e.g., critical properties, phase diagram, absence of crossover etc.

25 Chirality scenario of SG transiton [H. Kawamura, 92~] Chirality is a hidden order parameter of real SG transitions. Experimental SG transition is a disguized chiral-glass transition [Part I] Isotropic Heisenberg SG in 3D exhibits spin-chirality decoupling, with the chiral-glass ordered phase not accompanying accompanying the standard SG order. [Part II] The spin is recoupled to the chirality, i.e., mixed into the chirality via the random magnetic anisotropy. [chiral-glass state]

26 Spin-chirality decoupling in the 3D isotropic Heisenberg SG How the spin and chiral correlations grow? T CG > T SG chiral glass spin glass 0 T SG T CG T Spin-chirality decoupling

27 Large-scale Monte Carlo simulations on the SG model chirality correlation length ratios x/l spin spin Chiral critical properties b~1 g~2 n~1.4 h~0.6 [Viet and Kawamura, 09]

28 Chirality hypothsis [H.Kawamura 92] Isotropic (ideal) system spin-chirality decoupling Real system is weakly anisotropic! Spin is recoupled to the chirality due to the weak random magnetic anisotropy D. Z 2 [chiral] SO(3) [spin-rotation] Z 2 SO(3) chirality spin rotation The chiral-glass transition now appears as the SG transition. spin-chirality recoupling T CG SG experimental SG exponents = CG exponents para phase SG(CG) phase D

29 Critical properties of canonical SG Canonical SG Exp. 3D Ising Chiral (Heisenberg) b~1 g~2 n~1.4 h~0.6 Close to exp.!

30 Direct test of the chirality scenario Chirality directly measured with anomalous Hall effect as a probe! Hall coefficient Hall coefficient d c =3.3 [T.Taniguchi et al ( 04)] Chirality exhibits an eminent singularity! d c =1.7 [T.Taniguchi et al ( 06)]

31 III. Spins remain disordered Novel liquid-like quantum spin state without magnetic long-range order? Quantum spin liquid (QSL)

32 Quantum fluctuations antiferromagnetically coupled two spins * classical spin * S =1/2 quantum spin spin antiparallel spin singlet (valence bond) (1/ 2)( > - >) S=0 non-magnetic state (energy gap to triplet) RVB state [P.W. Anderson ( 73)] Realizable in frustrated systems? Long quest

33 Ground state of the simplest nearest- neighbor bilinear Heisenberg model Theory suggests Triangular lattice AF magnetic LRO at T=0 even for S=1/2 + + Kagome lattice [ 120 degree structure ] Liquid-like ground state without magnetic long-range order nor the spin freezing

34 Experimental discovery of the quantum spin liquid state Quantum spin liquid states observed in certain S=1/2 frustrated AFs Triangular lattice k-(et) 2 Cu 2 (CN) 3 EtMe 3 Sb[Pd(dmit) 2 ] 2 Kagome lattice S=1/2 organic salts Mott insulator [K. Kanoda, Y.Shimizu, R.Kato, M.Tamura et al] [D.G. Nocera et al] herbersmithite: ZnCu 3 (OH) 6 Cl 2 What is its nature? still remains controvertial

35 S=1/2 organic triangular AF k-(et) 2 Cu 2 (CN) 3 slightly distorted triangular lattice NMR spectrum [Y. Shimizu, K. Kanoda et al 03] Specific heat EtMe 3 Sb[Pd(dmit) 2 ] 2 NMR spectrum Gapless spin liquid behavior!

36 Role of possible randomness? Randomness in the interaction might induce Anderson-localization of singlets. RVB state Randomness random singlet state SG magnet Specific heat T In spin and molecular glasses, the T linear low-t specific heat prevails, reflecting its local low-energy collective excitations.

37 Randomness really exists? Likely! Charge inhomogeneity in triangular organic salts QSL in the vicinity of charge (ferroelectric) order [K. Itoh et al., 13] Domain growth associated with the CO QCP hindered CO (dipole-glass) state? Critical slowing down associated with a CO QCP? Randomness in the anion layer plays a role of seed?

38 Strong coupling between the spin and the charge (polarization) κ-(bedt-ttf) 2 Cu 2 (CN) 3 Intradimer charge imbalance? AC dielectric constant Random freezing of electric polarization at low T [ M. A. Jawad, et al. Phys.Rev.B (2010) ] Effective randomness in the exchange interaction between spins

39 Bond-random S=1/2 AF Heisenberg model on the triangular lattice Δ : randomness parameter (0 Δ 1 ) uniform distribution no randomness maximal randomness 0 Exact numerical calculations on finite spin clusters of N<32 [K.Watanabe, H.Kawamura et al., 14] Transition from the AF state to the nonmagnetic (random-singlet) state at ~0.6.

40 Computed physical quantities Specific heat [Exp.] T - Linear T [K.Watanabe, H.Kawamura et al., 14] NMR relaxation rate [Exp.] γ-term: calc. ~ 20 mjk -2 exp. κ-et ~ 12; dmit ~ 20 mjk -2 [T.Itou et al 08, 10]

41 What about kagome? Randomness due to Zn 2+ replacement by Cu 2+ S=1/2 kagome AF Herbersmithite ZnCu 3 (OH) 6 Cl 2 Jahn-Teller distortion A phase transition at ~0.4 between the randomness-irrelevant non-magnetic state and the randomness-relevant random-singlet state.

42 [H.Kawamura et al., 14] Computed physical quantities Magnetization curve M [Exp.] M [T. -H. Han, et al., 14] H [T. Shimokawa et al., 15] [T] H [T] Dynamical structure factor Δ=1 [Exp.] Neutron inelastic [T. -H. Han, et al., 12]

43 Frustration + Quantum fluctuations + Randomness = Random singlet state QSL-like gapless non-magnetic state

44 Summary Frustration, together with randomness and quantum fluctuations, gives rise to a variety of novel order, new dynamics and exotic thermodynamic states, developing new states of matter, new concepts, and potential new applications.