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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 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C. Ancona-Torres et al., unpublished.

10.75 Å

5.175 Å

- 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

with [ H,sz] ≠ 0

G ~ Ht2

hac, Ising axis

Paramagnet

(K)

Glass

Net Moment

T (mK)

Temperature

Time

Temperature

- Cool at constant rate
- decreases at fixed temperature
- Aging reinitialized when cooling resumes

’ (emu/cm3)

Aging

Cooling Reference

Warming Reference

Temperature (K)

’ (emu/cm3)

Aging

Decreasing Reference

Increasing Reference

Ht (kOe)

- Quantum aging
- More pronounced
- & crosses hysteresis

- Quantum rejuvenation
- Increases to meet
- the reference curve

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)

’ (emu/cm3.)

Time (s)

Time (s)

Grandfather states

- 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 ?

Use non-linear dynamics to…

- Encode Information
- Excite collective excitations with long coherence times (seconds): Rabi Oscillations
- Separate competing ground states

dc susceptibility

T-1

- no peak in
- no LRO
- sub-Curie T dependence
- correlations

T-0.76

H

H

Ising axis

E

++ a+

E

E

–

H= 0

H≠ 0

–

-E

-E

+ + b+

-E

Ht = 0

Ht≠ 0

Dynamic magnetic susceptibility

ac narrows with decreasing T

“Antiglass”

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

pump

probe

* 1017 cm-3 spins missing

~ 1% available

* Excitations

labeled by f

9 Hz hole

3 Hz hole

Square pump at 3 Hz

Coherent Oscillations

5Hz

Q ~ 50

Magnetization

Spins per

Cluster

Phase

ac Excitation

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

…in the liquid

but not in the glass

Decoherence from the (nuclear) Spin Bath

- 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

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