1. Order and disorder in dilute dipolar magnets
Moshe Schechter (BGU)
Juan Carlos Andresen (KTH, Sweden)
Creighton Thomas (Google)
Helmut Katzgraber (Texas A&M)
Vadim Oganesyan (CUNY)
Nicolas Laflorencie (Toulouse)
Philip Stamp (UBC)

2. Introduction Dilute dipolar Ising model
1. Moderate dilutions: Competing interactions with FM mean – disordering by random fields different from
simple mechanism, different from Imry-Ma
2. Extreme dilution in dipolar Ising – is there SG phase?
Relation to experiments in LiHoxY1-xF4
J. C. Andresen, C. Thomas, H. Katzgraber, M. S., PRL 111, (2013)
J. C. Andresen, H. Katzgraber, V. Oganesyan, M. S., PRX 4, (2014)

3. Outline Competing interactions: Dipolar glass in dilute regime:
Standard Imry-Ma
LiHo - competing interactions and random fields
Experimental results
Disordering of FM with competing interactions
Dipolar glass in dilute regime:
Overview
Results

4. RFIM and Imry Ma Flip a droplet Energy cost: Energy gain:
Large droplets flip – FM phase disordered!
Lower critical dimension - two
d≤2 : infinitesimal random field, large FM domains
d>2 : disordering at h≈J, single spins reorient
Imry and Ma, PRL 35, 1399 (1975)

5. Competing interactions
σ – standard deviation. Mean=1

6. Competing interactions
σ – standard deviation. Mean=1

7. Competing interactions
C.I. d=3
FM d≤2
FM d>2 ? J≈ hc
FM domains
Single spins
mechanism
σ – standard deviation. Mean=1

8. Competing interactions
C.I. d=3
FM d≤2
FM d>2 ? J≈ hc
FM domains
Single spins
mechanism
σ – standard deviation. Mean=1

9. LiHoF4 - Dipolar Ising model

10. LiHoF4 with hyperfine interactions
Hyperfine spacing: 200 mK S -S

11. LiHoxY1-xF4 - Continuous dilution
σ – standard deviation. Mean=1
LiHoxY1-xF4

12. LiHoF4 - Transverse field Ising model

13. QPT in dipolar magnets Thermal and quantum transitions MF of TFIM
MF with hyperfine
Bitko, Rosenbaum, Aeppli PRL 77, 940 (1996)

14. Ferromagnetic RFIM S -S
M. S. and N. Laflorencie, PRL 97, (2006)
M. S., PRB 77, (R) (2008)

15. Ferromagnetic RFIM S -S

16. Ferromagnetic RFIM - Independently tunableS -S
- Independently tunable
random and transverse fields!
- Classical RFIM despite
applied transverse field

17. Imry Ma for SG – correlation length
Flip a droplet –
gain vs. cost:
Lower critical dimension – infinity!
Droplet size –
Correlation length
Imry and Ma, PRL 35, 1399 (1975)
Fisher and Huse PRL 56, 1601 (1986); PRB 38, 386 (1988)

18. Dilution: quantum spin-glass
-Thermal vs. Quantum disorder
-Cusp diminishes as T lowered
Wu, Bitko, Rosenbaum, Aeppli, PRL 71, 1919 (1993)

19. SG unstable to transverse field!
Finite, transverse field dependent correlation length SG
quasi
M. S. and N. Laflorencie, PRL 97, (2006)
Young, Katzgraber, PRL 93, (2004)

20. Disordering of FM at x=0.44 Sharp transition at high T,
Rounding at low T
(high transverse fields)
Decrease of critical
Temperature with random
Field (roughly) linear
Silevitch et al., Nature 448, 567 (2007)

21. FM and SG phases in random field

22. FM and SG phases in random field
Disordering of the FM phase in 3D by finite, yet SMALL random field
Disordered phase: SG domains of size

23. Finite temperature Decrease of critical Sharp transition at high T,
Temperature with random
Field (roughly) linear
Sharp transition at high T,
Rounding at low T
(high transverse fields)
Andresen et. al., PRL 111, (2013)
Silevitch et al., Nature 448, 567 (2007)

24. Finite temperature

25. Finite temperature T>0.3K : FM to PM transition
T<0.3K : Intermediate frozen QSG phase
Andresen et. al., PRL 111, (2013)
Silevitch et al., Nature 448, 567 (2007)

26. Finite temperature
“Standard” PM
Glassy
domains

27. Conclusions 1
Generalized Imry-Ma: 3D FM with competing interactions – disordering at small random field
Disordered phase: spin glass domains with typical size depending on random field
At low temperatures disordered phase is frozen, explains rounding off of the susceptibility cusp
Critical temperature linear with field down to small fields

28. Dilute Dipolar Glass
Reich et al, PRB 42, 4631 (1990)

29. Dilute Dipolar Glass
Ghosh, Parthasarathy, Rosenbaum, Aeppli Science 296, 2195 (2002)
Quilliam, Meng, Kycia,
PRB 85, (2012)

30. Dilute Dipolar Glass Experiment: Anti-glass? Spin liquid? Analytics
Mean field theory (Stephen and Aharony): Tc linear in x
Fluctuations are large, could dominate
RG ineffective
Numerical
Fluctuations increase with dilution
Snider and Yu, Biltmo and Henelius – no glass phase
Tam and Gingras – Glass phase down to 6.25%

31. Finite size scaling Parallel tempering Monte Carlo
Parallel tempering Monte Carlo
Combine single spin flip with cluster renormalization algorithm
J. C. Andresen, H. Katzgraber, V. Oganesyan, M. S., PRX 4, (2014)

32. Strong fluctuations
Can not use one method for strongly interacting and typical spins.
Cluster strongly interacting spins, standard MC for resulting entities
Algorithm: 1. cluster all spins with .
2. Repeat for
for all n until left only with pairs.
3. Sweep spins, flip: single spin - 75%, random cluster – 25%
Algorithm efficiency concentration independent!!
Size limited by Ewald sums
Strong fluctuations coming from nearby spins
do not effect thermodynamic transition, nor efficiency of algorithm

33. Tc linear in dipole concentration
Tc=ax; a=0.59(1)

34. LiHoxY1-xF4 - phase diagram
1. FM-SG boundary at x=0.3. No significant reentrant SG regime
2. SG phase down to x=0, with linear Tc

35. Dilute dipolar glass - broad distribution of random fields
Assume:
- Random field dictated by rare events of nearest neighbor impurities.
- Interactions are dictated by typical strength.
Typical random field:
M.S. and P. Stamp, EPL 88, (2009)

36. Conclusions 2
Dilute dipolar Ising spins order at any small concentration with Tc linear in concentration
Induced random field – non trivial dependence of domain size on concentration

37. Dipolar glasses – scaling with dilution
Interaction allows diliution – expect scaling