Magnetic Surprises on a Triangular Lattice Collin Broholm Johns Hopkins University & NIST

1. Magnetic Surprises on a Triangular Lattice Collin BroholmJohns Hopkins University & NIST Introduction Frustration Neutron Scattering Triangular Lattice AFM Theoretical Status Experimental Status Triangular lattice systems Neel (RbFe(MoO4)2) Glassy (NiGa2S4) Conclusions

2. Collaborators NiGa2S4 S. Nakatsuji Y. Nambu H. Tonomura O. Sakai C. Stock S. Jonas Y. Qiu Y. Maeno J. Chung RbFe(MoO4)2 G. Gasparovic M. Kenzelmann S. Park A. Smirnov L. N. Demianets A. Ya. Shapiro G. Lawes A. P. Ramirez La4Cu3MoO12 Y. Qiu S. Ishiwata M. Azuma M. Takano R. Bewley W. J. L. Buyers Rutgers Seminar

3. Frustrated Condensed Matter Lattice symmetry established by chemical bonding (large energy scales) can “frustrate” weaker magnetic interactions “Satisfied” “Frustrated” Frustration produces classically degenerate states of matter with a potential for “emergent” quantum properties Rutgers Seminar

4. MACS spectrometer under construction at NIST pi pf ħQ MACS spectrometer under construction at NIST Rutgers Seminar

5. z=3/4 CuMoO plane La4Cu3MoO12: A lattice of spin-1/2 trimers Magnetic susceptibility Crystal Structure (Azuma et. al., PRB 62 R3588) Rutgers Seminar

6. J2 J1 J J J3 J Frustrated quantum spin triangles Rutgers Seminar Yiming Qiu et al. PRB 2005

7. 0.2 10 K Transition to quartet 0.1 0.0 70 K 0.1 0.0 Spectroscopy of spin trimers Phonons Rutgers Seminar Yiming Qiu et al. PRB 2005

8. Magnetic Ordering of Composite spin-1/2 Rutgers Seminar

9. Strongly fluctuating spin trimer AFM Yiming Qiu et al. PRB 2005 Rutgers Seminar

10. Neutron Scattering Stone et al. (2003). Exact two-spinon cross-section Karbach et al. 2000 Rutgers Seminar

11. Kagome lattice Frustrated Linkage of Triangles Triangular lattice Rutgers Seminar

12. A brief status of Triangular lattice research • Theory • RVB state proposed (Anderson 1973) • Classical Heisenberg model has 120o LRO at T=0 (Huse, Rutenberg) • S=1/2 model has LRO for T=0 (Huse, Singh) • Finite temperature KT transition (Kawamura & Miyashita) • RVB state in Ising model (Moessner and Sondhi) • Experiments • Spin-1/2 insulators generally have some form of dimerization and no LRO • Spin-1/2 κ(ET)2Cu2(CN)3close to MIT shows no spin order. It superconducts under pressure • Spin-1/2 anisotropic system has de-confined excitations in a field (Cs2CuCl4) Rutgers Seminar

13. RbFe(MoO4)2:spin-5/2 triangular AFM J1’ J’ J J2’ Kenzelmann, Gasparovic et al. (2005) Rutgers Seminar

14. Field Dependent Long Range Order Kenzelmann, Gasparovic et al. (2005) • 120o structure • Field dependent Incommensurate stacking • Spins in triangular plane • Moment reduced to 75(1)% • Incommensurate state is ferroelectric! Rutgers Seminar

15. NiGa2S4 : Spin-1 Triangular Lattice AFM Nakatsuji et al. Science (2005) J1 1 x 97o 2 x 2.42 Å J2 2 x 100o 2 x 2.42 Å 1 x 3.21 Å J3 2 x 138.5o 2 x 2.42Å 1 x 3.63 Rutgers Seminar

16. No phase transition as T/QCW → 0 • QCW=80 K so AFM • Cusp in c for T≈7 K • No conventional phase transition • Two maxima in C/T • Finite T entropy plateau Nakatsuji et al. (2005) Rutgers Seminar

17. Single crystal Spin freezing without C(T) anomaly Nakatsuji et al. (2005) Rutgers Seminar

18. Short range magnetic correlations Nakatsuji et al. (2005) Surprises: Å Rutgers Seminar

19. Single crystals confirm 2D Incom. SRO C. Stock et al. (2005) FM inter-plane correlations Planar spin structure Å Rutgers Seminar

20. Excitations from low T state “Early” dispersion relation What is clear so far: • Spin wave like modes at low T • A “slow” low E mode throughout zone • + A highly dispersive mode Rutgers Seminar

21. Classical Short range fluctuations at high T Correlations at entropy plateau: • Relaxation rate ħG<kBT • Correlation length ~ a Rutgers Seminar

22. The weak response to H//a* With increasing field: • Intra plane correlations unchanged • Reduce Inter-plane correlations • Moments more to plane Rutgers Seminar

23. Frozen spin structure • ≈120o structure on 2a super-lattice (colors) • Incommensurate modulation • Spins in triangular plane • Moment reduced to 75(8)% • Weak ferromagnetic inter-plane correlations Nakatsuji et al. (2005) Rutgers Seminar

24. J1-J3 model on triangular lattice? • Accounts for • no peak • incommensurability • Plausible given likely exchange paths • Further confirmation needed J1=0 J1=-0.2J3 Rutgers Seminar

25. Thought on quantum glassy phase • Not conventional disordered glass: • Coherent wave propagation • No forward scattering • Impurities involved but unlikely to define short length scale • Puddles of AFM around impurities in isolated singlet ground state system • Gapped triplet sector gapless singlet sector pinned by impurities Rutgers Seminar

26. Conclusions • Glassy phases endemic to real spin systems near quantum critical point • Distinguishing characteristics of glassy phase • Coherent modes despite short range spin-correlations • Absence of forward scattering • Gapless triplet spectrum • RbFe(MoO4)2 • 120o structure for sufficient inter-plane coupling • Competing interplane interactions yield incommensurate ferroelectric phase • NiGa2S4 • spin-1 system with potential for J1-J3 model • Glassy incommensurate phase at low T suggest weak interlayer coupling and weak or absent 2D Neel order • Double peak structure in C(T) indicates a gapped phase may be present in this problem Rutgers Seminar

27. Future plans • RbFe(MoO4)2 • Explore multiferroic properties in particular electric field induced handedness of magnetic state • Establish exchange constants through spin wave measurements • NiGa2S4 • Carrier doping may be possible. • Effects of uni-axial stress and pressure • Spin wave measurements to determine hamiltonian • Increase disorder (Zn, S) • Theoretical issues: • Spin-1 triangular lattice AFM: spin liquid? • J1-J3 triangular lattice model: entropy plateau? • Phenomenology of glassy quantum magnetism Rutgers Seminar