1. Quantum Spin Glasses & Spin Liquids

2.  QUANTUM RELAXATION Ising Magnet in a Transverse Magnetic Field (1) Aging in the Spin Glass (2) Erasing Memories  HOLE-BURNING in a SPIN LIQUID Dilute “AntiGlass”: Intrinsic Quantum Mechanics (1) Non-Linear Dynamics (2) Coherent Spin Oscillations (3) Quantum Magnet in a Spin Bath -------------------------------------------------------- S. Ghosh et al., Science 296, 2195 (2002) and Nature 425, 48 (2003). H. Ronnow et al., Science 308, 389 (2005). C. Ancona-Torres et al., unpublished.

3. LiHo x Y 1-x F 4 Ho 3+ magnetic, Y 3+ inert Ising (g // = 14) Dipolar coupled (long ranged) x = 1 Ferromagnet T C = 1.53 K x ~ 0.5 Glassy FM T C = xT C (x=1) x ~ 0.2 Spin Glass Frozen short-range order x ~ 0.05 Spin Liquid Short-range correlations 5.175 Å 10.75 Å

4. Effect of a Transverse Field with [ H,  z ] ≠ 0

5. Experimental Setup  ~ H t 2 h ac, Ising axis

6. T (mK)  (K) Paramagnet Net Moment Glass LiHo 0.20 Y 0.80 F 4 Aging & Memory in the Quantum Spin Glass

7. Aging in  ac Time Temperature  Cool at constant rate  decreases at fixed temperature Aging reinitialized when cooling resumes

8. Thermal vs. Quantum Aging Quantum aging More pronounced & crosses hysteresis Quantum rejuvenation Increases to meet the reference curve  ’ (emu/cm 3 ) Temperature (K) Aging Cooling Reference Warming Reference  ’ (emu/cm 3 ) H t (kOe) Aging Decreasing Reference Increasing Reference

9. Erasing the Memory (1)Quench system into the spin glass and age (2) Small step to a lower H t rejuvenates (3) On warming, system should remember the original state Negative effective aging time 2.5kG2kG2.5kG t1t1 t2t2 t3t3 Time (s)  ’ (emu/cm 3 ) Time (s)  ’ (emu/cm 3 ) Time (s)  ’ (emu/cm 3.)

10. Time (s)  ’ (emu/cm 3.) Time (s) Grandfather states Greater Erasure with Greater Excursions

11. The Spin Liquid Examples: CuHpCl, Gd 3 Ga 5 O 12 (3D geometric frustration) Tb 2 Ti 2 O 7, LiHo 0.045 Y 0.955 F 4 (quantum fluctuations) SrCu 2 (BO 3 ) 2, Cs 2 CuCl 4 (2D triangular lattice) —Geometric frustration —Quantum fluctuations —Reduced dimensionality No long range order as T  0 Not a spin glass – spins not frozen, fluctuations persist Not a paramagnet – develops short-range correlations Collective behavior What prevents freezing ?

12. LiHo 0.045 Y 0.955 F 4 Addressing Bits in the Spin Liquid Encode Information Excite collective excitations with long coherence times (seconds): Rabi Oscillations Separate competing ground states Use non-linear dynamics to…

13. Signatures of spin liquid no peak in   no LRO sub-Curie T dependence  correlations T -0.76 T -1 dc susceptibility

14. Quantum fluctuations Ising axis HH H  E E -E H  ≠ 0 ––  +  + a  +   +  + b  +  –– E -E H  = 0    

15. Quantum spin liquid H t = 0H t ≠ 0

16.  ac narrows with decreasing T  “Antiglass” Dynamic magnetic susceptibility

17. Scaled susceptibility Relaxation spectral widths : Debye width (1.14 decades in f) single relaxation time if broader… multiple relaxation times e.g. glasses if narrower… not relaxation spectrum FWHM ≤ 0.8 decades in f

18. Hole Burning * 10 17 cm -3 spins missing ~ 1% available * Excitations labeled by f pump probe

19. Simultaneous Encoding Square pump at 3 Hz 9 Hz hole 3 Hz hole

20. Coherent Oscillations 5Hz Q ~ 50

21. Brillouin Fit Magnetization Phase ac Excitation Spins per Cluster

22. Gd 3 Ga 5 O 12 GGG : Geometrically frustrated, Heisenberg AFM exchange coupling Phase diagram P.Schiffer, A. Ramirez, D. A. Huse and A. J. Valentino PRL 73 1994 2500-2503

23. Encryption in GGG… …in the liquidbut not in the glass

24. Decoherence from the (nuclear) Spin Bath

25. Conclusions Li(Ho,Y)F 4 a model solid state system to test quantum annealing – quantum fluctuations and ground state complexity can be regulated independently Quantum annealing allows search of different minima, speedier optimization and memory erasure in glasses Coherent excitations in spin liquids of hundreds of spins labeled by frequency can encode information: cf. NMR computing Self-assembly common to “hard” quantum systems

26. S. Ghosh, J. Brooke, R. Parthasarathy, C. Ancona-Torres, T. F. Rosenbaum University of Chicago G. Aeppli University College, London S. N. Coppersmith University of Wisconsin, Madison