Quantum Phase Transitions in XXZ Spin-1/2 Chain Materials Cs2CoCl4 and Cu(C4H4N2)(NO3)2

Transkript

1 Quantum Phase Transitions in XXZ Spin-1/2 Chain Materials Cs2CoCl4 and Cu(C4H4N2)(NO3)2 University of Cologne, Germany

2 Quantum Phase Transitions in XXZ Spin-1/2 Chain Materials Cs2CoCl4 and Cu(C4H4N2)(NO3)2 Motivation Outline Cu(C4H4N2)(NO3)2 or CuPzN - quantum criticality in Heisenberg spin-1/2 chains Cs2CoCl4-1d XY spin-1/2 chain in transverse field - complex 3D ordered phases summary

3 Acknowledgement Oliver Breunig, J. Rohrkamp measurements & analysis University of Cologne P. Becker, L. Bohaty, R. Müller single crystals Cs 2 CoCl 4 University of Cologne M.D. Phillips, M.M. Turnbull single crystals CuPzN Clark University, USA B. Buldmann, M. Garst, A. Rosch theory University of Cologne E. Sela theory Tel-Aviv University, Israel A. Klümper theory Wuppertal University, Germany

4 XXZ Spin-1/2 Chain Materials Model systems for field-induced quantum phase transitions: Heisenberg, XY: H z gapless gapped Ising spin chain transverse field quantum fluctuations Luttinger liquid 0 H C field polarized H h c h Sachdev, Quantum Phase Transitions

5 XXZ Spin-1/2 Chain Materials Model systems for field-induced quantum phase transitions: Real materials: interchain couplings => 3D magnetic order magnetoelastic coupling => dimerization (Spin Peierls) magnetic field scales => H sat too large how to vary

6 XXZ Spin-1/2 Chain Materials XY 0 Heisenberg 1 Ising

7 Cu(C4H4N2)(NO3)2 copper pyrazine dinitrate Cu 2+ (3d 9 ) S=1/2 Cu C H N O J/kB 10 K, J /J 10-3, TN = 107 mk T. Lancaster, et al., Phys. Rev. B 73, (2006) AF spin-1/2 Heisenberg chain magnetic field quantum phase transition structure data: A. Santoro, et al., Acta Crystallographica Section B 26, 979 (1970) H c ~ 14 T

8 LITERATURE Losee, J. Chem. Phys. 59 (1973) Kono, Physical Review Letters 114 (2015) Mennenga, JMMM 44 (1984) P. Hammar, et al., Phys Rev. B 59, 1008 (1999) D. B. Losee, J. Chem. Phys. 59, 3600 (1973) Y. Kono et al., Phys. Rev. Lett. 114, (2015) G. Mennenga et al. J. Mag. Mag. Mat. 44, 89 (1984) A.V. Sologubenko, TL et al., Phys. Rev. Lett. 98, (2007) M. Stone et al., Phys. Rev. Lett. 91, (2003) M. Mourigal et al., Nat. Phys. 9, 435 (2013) T. Lancaster et al., Phys. Rev. B 73, (2006) 0.25 K - 30 K 0 T - 17 T Stone, PRL 91 (2003)

9 Magnetization

10 magneto- striction thermal expansion L/L 0 (10-6 ) (a) (c) L/L 0 (10-6 ) (10-6 K -1 ) (b) exp. theory 0 T 5 T 10 T 12 T 13 T 14 T 15 T (d) exp. theory 0.25 K 0.43 K 0.72 K 1.05 K 2.06 K 4.15 K 8.30 K (10-6 T -1 ) T (K) H b (T) 0

11 Specific heat

12 Specific heat

13 Magnetocaloric Effect magnetic Grüneisen parameter

14 Magnetocaloric Effect of CuPzN is expected to diverge close to QCP Zhu, Garst, Rosch & Si, Phys. Rev. Lett. 91, (2003)

15 Universal divergencies & scaling behavior close to QCP Zhu, Garst, Rosch & Si, Phys. Rev. Lett. 91, (2003)

16 Quantum criticality in CuPzN almost perfectly fits to S=1/2 Heisenberg chain model

17 Specific heat there is only one single parameter J = K (M: K, L: K) deviations up to about 10 % between theory & experiment

18 Cs2CoCl4 isostructural to Cs2Cu(Cl/Br)4 Cs2CuCl4 J ~ 4.3 K J bc ~ J/3 => 1d chains & frustrated interchain coupling Cs2CuBr4 J ~ 12 K J bc ~ ( ) J => 2d frustrated triangular magnet Cs2CuBr4 Fortune et al., Phys. Rev. Lett. 102, (2009) Starykh et al., Phys. Rev. B 82, (2010)

19 Cs2CoCl4 CoCl4 tetrahedra exchange J b J < 0.1J crystal field D - magnetisation anisotropy - z aixs alternates from (1,3) to (2,4) Co 2+ S=3/2 Sz=±3/2 Sz=±1/2 ~2D Algra et al. Physica B+C 82 (1976) McElearney et al., J. Chem. Phys. 66 (1977) Kenzelmann et al. Phys. Rev. B 65 (2002) structure data: Porai-Koshits, Kristallografiya (1956)

20 Cs2CoCl4 4 CoCl4 tetrahedra exchange J b J < 0.1J crystal field D - magnetisation anisotropy - z axis alternates from (1,3) to (2,4) 1 3 Co 2+ S=3/2 Sz=±3/2 Sz=±1/2 ~2D 2 Pnma a=9.71 Å b=7.27 Å c=12.73 Å - effective easy-plane spin 1/2 structure data: Porai-Koshits, Kristallografiya (1956)

21 LITERATURE McElearney et al., J. Chem. Phys. 66 (1977) Algra et al., Physica B+C 82 (1976)

22 SPECIFIC HEAT Phonons Co 2+ S=3/2 Sz=±3/2 Sz=±1/2 ~2D 3D (magnetic order) 1D Schottky 1D XXZ model In literature: XY-like anisotropy as expected for Algra H., Physica B+C. (1976)

23 Magnetic field influence longitudinal field H z : 1d chain J, T, H << D: Jordan-Wigner fermions field varies of band filling QCP = metal-insulator transition Zeeman splitting +3/2-3/2 +1/2-1/2 cannot be realized in Cs 2 CoCl 4 transverse field H in XY plane : breaks rotational symmetry 1d chain J, T, H << D: spin-1/2 chain in transverse field

24 XXZ chain in transverse field 4 Siahatgar & Langari Phys. Rev. B. 77 (2008) breaking rotational symmetry quantum phase transition realized in Cs2CoCl4 for H b 1 2 3

25 XXZ chain in transverse field Exact Diagonalization based on ALPS (B. Bauer et al., J. Stat. Mech. (2011) P05001) Heat Capacity Thermal Expansion

26 Specific Heat T(K) phonons S = ½ XXZ spin chain

27 Thermal Expansion fit yields:

28 Effective Spin-1/2 Cs2CoCl4: Co 2+ 3d 7 S=3/2 isotropic JH spin 3/2 spin 1/2 0 th order 1 st order

29 significant if change of p Jz XXZ anisotropy determined by JH and D JH = 0.74 K D = 7 K not independent Cs2CoCl Δ = Jz/Jxy

30 XXZ ANISOTROPY D< 0 Sz=±1/2 Sz=±3/2 Co 2+ S=3/2 Sz=±3/2 Sz=±1/2 D> 0 Cs2CoCl4

31 applicability of the XXZ model B > 3 T entanglement of Sz=±3/2 and Sz=±1/2 T > 2 K thermal population of Sz=±3/2 quantum phase transition Hc ~ 2.0 T sign change of α, linear field dependences in /T, c/t (including 1 st order)

32 MAGNETIC ORDER M. Kenzelmann et al. Physical Review B 65 (2002) H.A. Algra et al. Physica B+C 82 (1976) 3D T < TN ~ 220 mk magnetic order in bc plane B a specific heat thermal expansion T > 50 mk, H a,b,c < 3T

33 H c

34 phase II probably not a spin-liquid phase Kenzelmann et al., Phys. Rev. B. 65 (2002)

35 Magnetic Field a, c b

36 Magnetic Field interchain Dzyaloshinskii-Moriya dominant J b

37 Magnetic Field interchain Dzyaloshinskii-Moriya dominant J b 2-stage spin-flop transition

38 Magnetic Field interchain Dzyaloshinskii-Moriya dominant J b 2-stage spin-flop transition

39 Phase II a) incommensurate order a c b not seen in experiment competes with alternating orientation of easy planes b) nematic phase two sub-systems M 1,2 & M 4,3 with frustrated coupling J bc nematic order lifts frustration due to correlated fluctuations: Kenzelmann et al. Phys. Rev. B. 65 (2002) Fernandes et al., Nat. Phys. 10 (2014)

40 SUMMARY Cu(C4H4N2)(NO3)2 quantitative agreement with the Heisenberg model J/kB = 10.59(2) K quantum phase transition Hc = 13.9 T Cs2CoCl4 1D magnetism spin-1/2 XXZ model corrections: =0.12 magnetic order phase II (probably a nematic phase) H b complex phase diagram (including 1 st order) Breunig et al., PRL 111, (2013) Breunig et al., PRB 91, (2015)