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Quantum Spin Glasses & Spin Liquids

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Quantum Spin Glasses & Spin Liquids.  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

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slide2
QUANTUM RELAXATION

Ising Magnet in a Transverse Magnetic Field

(1) Aging in the Spin Glass

(2) Erasing Memories

 HOLE-BURNING in aSPIN LIQUID

Dilute “AntiGlass”: Intrinsic Quantum Mechanics

(1) Non-Linear Dynamics

(2) Coherent Spin Oscillations

(3) Quantum Magnet in a Spin Bath

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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C. Ancona-Torres et al., unpublished.

liho x y 1 x f 4

10.75 Å

5.175 Å

LiHoxY1-xF4
  • Ho3+ magnetic, Y3+ inert
  • Ising (g// = 14)
  • Dipolar coupled (long ranged)
  • x = 1Ferromagnet

TC = 1.53 K

  • x ~ 0.5Glassy FM

TC = xTC(x=1)

  • x ~ 0.2 Spin Glass

Frozen short-range order

  • x ~ 0.05 Spin Liquid

Short-range correlations

experimental setup
Experimental Setup

G ~ Ht2

hac, Ising axis

aging in ac

Temperature

Time

Temperature

Aging in ac
  • Cool at constant rate
  • decreases at fixed temperature
  • Aging reinitialized when cooling resumes
thermal vs quantum aging

’ (emu/cm3)

Aging

Cooling Reference

Warming Reference

Temperature (K)

’ (emu/cm3)

Aging

Decreasing Reference

Increasing Reference

Ht (kOe)

Thermal vs. Quantum Aging
  • Quantum aging
  • More pronounced
    • & crosses hysteresis
  • Quantum rejuvenation
  • Increases to meet
  • the reference curve
slide9

t3

t2

t1

’ (emu/cm3)

2.5kG

2kG

2.5kG

Time (s)

’ (emu/cm3.)

’ (emu/cm3)

Time (s)

Erasing the Memory

Quench system into

the spin glass and age

(2) Small step to a lower Ht rejuvenates

(3) On warming, system should remember the original state

Negative effective

aging time

Time (s)

the spin liquid
The Spin Liquid
  • No long range order as T  0
  • Not a spin glass – spins not frozen, fluctuations persist
  • Not a paramagnet– develops short-range correlations
  • Collectivebehavior

Examples: CuHpCl, Gd3Ga5O12 (3D geometric frustration)

Tb2Ti2O7, LiHo0.045Y0.955F4(quantum fluctuations)

SrCu2(BO3)2, Cs2CuCl4(2D triangular lattice)

  • Geometric frustration
  • Quantum fluctuations
  • Reduced dimensionality

What prevents freezing ?

liho 0 045 y 0 955 f 4 addressing bits in the spin liquid
LiHo0.045Y0.955F4Addressing Bits in the Spin Liquid

Use non-linear dynamics to…

  • Encode Information
  • Excite collective excitations with long coherence times (seconds): Rabi Oscillations
  • Separate competing ground states
signatures of spin liquid
Signatures of spin liquid

dc susceptibility

T-1

  • no peak in 
  •  no LRO
  • sub-Curie T dependence
  •  correlations

T-0.76

quantum fluctuations

H

H

Ising axis

E

++ a+

E



E

–

H= 0

H≠ 0

–

-E



-E

+ + b+

-E

Quantum fluctuations
quantum spin liquid
Quantum spin liquid

Ht = 0

Ht≠ 0

slide16

Dynamic magnetic susceptibility

ac narrows with decreasing T

 “Antiglass”

scaled susceptibility
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

hole burning

pump

probe

Hole Burning

* 1017 cm-3 spins missing

~ 1% available

* Excitations

labeled by f

simultaneous encoding
Simultaneous Encoding

9 Hz hole

3 Hz hole

Square pump at 3 Hz

brillouin fit
Brillouin Fit

Magnetization

Spins per

Cluster

Phase

ac Excitation

slide22

Gd3Ga5O12

Phase diagram

GGG : Geometrically frustrated, Heisenberg

AFM exchange coupling

P.Schiffer, A. Ramirez, D. A. Huse and A. J. Valentino PRL 73 1994 2500-2503

conclusions
Conclusions
  • Li(Ho,Y)F4 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

slide26

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

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