Quantum Spin Glasses & Spin Liquids

QUANTUM RELAXATIONIsing Magnet in a Transverse Magnetic Field

(1) Aging in the Spin Glass(2) Erasing Memories

HOLE-BURNING in a SPIN LIQUIDDilute “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Science 296, 2195 (2002) and Nature 425, 48 (2003).H. Ronnow et al., Science 308, 389 (2005).C. Ancona-Torres et al., unpublished.

LiHoxY1-xF4

• Ho3+ magnetic, Y3+ inert• Ising (g// = 14)• Dipolar coupled (long ranged)

• x = 1 Ferromagnet TC = 1.53 K

• x ~ 0.5 Glassy FM TC = xTC(x=1)

• x ~ 0.2 Spin GlassFrozen short-range order

• x ~ 0.05 Spin Liquid Short-range correlations

5.175 Å

10.75 Å

Effect of a Transverse Field

H Jij iz j

z

i, j

N

ix

i

N

with [ H, z ] ≠ 0

Experimental Setup

~ Ht2

hac, Ising axis

T (mK)

(

K)

0

0.1

0.2

0 50 100 150 200 250

Paramagnet

Net MomentGlass

LiHo0.20Y0.80F4

Aging & Memory in the Quantum Spin Glass

Aging in ac

Time

Tem

pera

ture

Temperature

• Cool at constant rate

• decreases at fixed

temperature

• Aging reinitialized

when cooling resumes

Thermal vs. Quantum Aging

• Quantum aging More pronounced

& crosses hysteresis

• Quantum rejuvenation Increases to meet the reference curve

’ (

emu/

cm3 )

Temperature (K)

0.06

0.09

0.12

0.15

0.18

0.11 0.12 0.13 0.14

AgingCooling ReferenceWarming Reference

0.05

0.1

0.15

0.2

0 3 6 9

’ (

emu/

cm3 )

Ht (kOe)

AgingDecreasing ReferenceIncreasing Reference

Erasing the Memory(1) 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

2.5kG 2kG 2.5kG

t1t2 t3

Time (s)

0.05

0.1

0.15

0.2

0 2 104 4 104 6 104

’ (

emu/

cm3 )

Time (s)

0.05

0.1

0.15

0.2

0 2 104 4 104 6 104

t1

t3

’ (

emu/

cm3 )

Time (s)

’ (

emu/

cm3 .)

0.05

0.1

0.15

0.2

0 2 104 4 104

t1

t3

0.05

0.1

0.15

0.2

0 2 104 4 104 6 104

t1

t2

t3

2.5 kOe 1 kOe 2.5 kOe

Time (s)

’ (

emu/

cm3 .)

0.05

0.1

0.15

0.2

0 1 104 2 104 3 104 4 104

t1

t3

Time (s)

Grandfather states

Greater Erasure with Greater Excursions

The Spin Liquid

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

• 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 ?

LiHo0.045Y0.955F4

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…

Signatures of spin liquid

• no peak in

no LRO

• sub-Curie T dependence

correlations

T-0.76

T-1

dc susceptibility

Quantum fluctuations

Ising axis

H

H

E

E

-E

-E

H≠ 0

– + + a+

+ + b+ –

E

-E

H= 0

Quantum spin liquid

Ht = 0 Ht ≠ 0

ac narrows with decreasing T “Antiglass”

Dynamic magnetic 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

* 1017 cm-3 spins missing

~ 1% available * Excitations labeled by f

pump

probe

Simultaneous Encoding

Square pump at 3 Hz

9 Hz hole

3 Hz hole

Coherent Oscillations

5Hz

Q ~ 50

Brillouin Fit

Magnetization

Phase

ac Excitation

Spins per Cluster

Gd3Ga5O12

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

Encryption in GGG…

…in the liquid but not in the glass

Decoherence from the (nuclear) Spin Bath

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

S. Ghosh, J. Brooke, R. Parthasarathy, C. Ancona-Torres, T. F. Rosenbaum

University of Chicago G. Aeppli University College, LondonS. N. Coppersmith University of Wisconsin, Madison