Quantum phase transitions in anisotropic dipolar magnets

1
Quantum phase transitions in anisotropic dipolar
magnets
Moshe Schechter
University of British Columbia
In collaboration with Philip Stamp, Nicolas
laflorencie
2
LiHoY F
x
1-x
4
1. Transverse field Ising model
3
LiHoY F
x
1-x
4
1. Transverse field Ising model
2. Dilution!
Reich et al, PRB 42, 4631 (1990)
4
QPT in dipolar magnets
Thermal and quantum transitions
MF of TFIM
MF with hyperfine
Bitko, Rosenbaum, Aeppli PRL 77, 940 (1996)
5
Various dilutions
Ghosh, Parthasarathy, Rosenbaum, Aeppli Science
296, 2195 (2002)
Brooke, Bitko, Rosenbaum, Aeppli Science 284, 779
(1999)
Ronnow et. Al. Science 308, 389 (2005)
Giraud et. Al. PRL 87, 057203 (2001)
6
LiHoF - a model quantum magnet
4
S. Sachdev, Physics World 12, 33 (1999)
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Dilution quantum spin-glass

• -Thermal vs. Quantum disorder
• -Cusp diminishes as T lowered
• Wu, Bitko, Rosenbaum, Aeppli, PRL 71, 1919 (1993)

8
Fall and rise of QPT in dilute dipolar magnets

• Hyperfine interactions and off-diagonal dipolar
  terms
• No QPT in spin-glass regime
• In FM regime can study classical and quantum
  phase transitions with controlled disorder and
  with coupling to spin bath

9
Anisotropic dipolar magnets
Large spin, strong lattice anisotropy
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Anisotropic dipolar magnets
Large spin, strong lattice anisotropy
Single molecular magnets
Magnetic insulators
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Anisotropic dipolar magnets - TFIM
Large spin, strong lattice anisotropy
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Hyperfine interaction electro-nuclear Ising
states
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Hyperfine interaction electro-nuclear Ising
states
Hyperfine spacing 200 mK
- M.S. and P. Stamp, PRL 95, 267208 (2005)
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Phase diagram transverse hyperfine and dipolar
interactions
Splitting
PM
SG
Experiment
No off. dip.
With off. dip.
- M.S. and P. Stamp, PRL 95, 267208 (2005)
15
Anisotropic dipolar systems offdiagonal terms
symmetry
symmetry
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Anisotropic dipolar systems offdiagonal terms
symmetry
symmetry
M. S. and N. Laflorencie, PRL 97, 137204 (2006)
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Imry-Ma argument
Ground state
(all spins up)
Domain
(spins down)
Energy cost
Energy gain
Spontaneous formation of domains
Critical dimension 2 (for Heisenberg
interaction 4)
Y. Imry and S. K. Ma, PRL 35, 1399 (1975)
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Spin glass correlation length
Energy gain
Y. Imry and S. K. Ma, PRL 35, 1399 (1975)
M.S. and N. Laflorencie, PRL 97, 137204 (2006)
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Spin glass correlation length
Energy gain
Energy cost
Y. Imry and S. K. Ma, PRL 35, 1399 (1975)
M.S. and N. Laflorencie, PRL 97, 137204 (2006)
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Spin glass correlation length
Energy gain
Energy cost
Only extra sqrt of surface bonds are satisfied,
can optimize boundary.
Fisher, Huse PRL 56, 1601 (86) PRB 38, 386 (88)
M.S. and N. Laflorencie, PRL 97, 137204 (2006)
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Spin glass correlation length
Energy gain
Energy cost
Only extra sqrt of surface bonds are satisfied,
can optimize boundary.
Flip a droplet gain vs. cost
Fisher, Huse PRL 56, 1601 (86) PRB 38, 386 (88)
M.S. and N. Laflorencie, PRL 97, 137204 (2006)
22
Spin glass correlation length
Energy gain
Energy cost
Only extra sqrt of surface bonds are satisfied,
can optimize boundary.
Flip a droplet gain vs. cost
Droplet size Correlation length
Fisher, Huse PRL 56, 1601 (86) PRB 38, 386 (88)
M.S. and N. Laflorencie, PRL 97, 137204 (2006)
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SG unstable to transverse field!
Finite, transverse field dependent correlation
length
M. S. and N. Laflorencie, PRL 97, 137204 (2006)
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Enhanced transverse field phase diagram
Quantum disordering harder than thermal
disordering
Main reason hyperfine interactions
Off-diagonal dipolar terms in transverse field
also enhanced effective transverse field
M.S. and P. Stamp, PRL 95, 267208 (2005)
25
Random fields not particular to SG!
Reich et al, PRB 42, 4631 (1990)
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Interest in FM RFIM
Diluted anti-ferromagnets
- Equivalence only near transition
- No constant field in the staggered magnetization
- Not FM - applications
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Interest in FM RFIM

• Verifying interesting results on DAFM
• Experimental techniques
• Novel fundamental research (away from transition,
  conjugate field, quantum term)
• Applications in ferromagnets, e.g. domain wall
  dynamics in random fields

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Are the fields random?
Square of energy gain vs. N, different dilutions
Inset Slope as Function of dilution
M. S., cond-mat/0611063
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Random field and quantum term are independently
tunable!
M. S., cond-mat/0611063
M. S. and P. Stamp, PRL 95, 267208 (2005)
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Ferromagnetic RFIM
M. S., cond-mat/0611063
M. S. and P. Stamp, PRL 95, 267208 (2005)
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Ferromagnetic RFIM
- Independently tunable random and transverse
fields!
M. S., cond-mat/0611063
- Classical RFIM despite applied transverse field
M. S. and P. Stamp, PRL 95, 267208 (2005)
32
Realization of FM RFIM
Sharp transition at high T, Rounding at low T
(high transverse fields)
Silevitch et al., Nature 448, 567 (2007)
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Conclusions

• Strong hyperfine interactions in LiHo result in
  electro-nuclear Ising states. Dictates quantum
  dynamics and phase diagram in various dilutions
• Ising model with tunable quantum and random
  effective fields can be realized in anisotropic
  dipolar systems
• SG unstable to transverse field, no SG-PM QPT
• First FM RFIM implications to fundamental
  research and applications