Dilute anisotropic dipolar systems as random field Ising ferromagnets In collaboration with: Philip Stamp, Nicolas Laflorencie Moshe Schechter University of British Columbia

Random field Ising model DAFM - Constant field is random in staggered magnetization - FM - Field conjugate to order parameter - Quantum fluctuations - Verification of results near transition “trompe l’oeil critical behavior” Experiments, crackling noise Away from criticality, applications Quantum dynamics, QPT S. Fishman and A. Aharony, J. Phys. C 12, L729 (1979) No FM realization

Outline RF in anisotropic dipolar magnets RF in anisotropic dipolar magnets Consequences in FM and SG regimes Consequences in FM and SG regimes LiHo system – hyperfine interactions LiHo system – hyperfine interactions – transverse dipolar int. – transverse dipolar int.

Anisotropic dipolar systems Magnetic insulators, large spin, strong lattice anisotropy, dominant dipolar interaction S-S Rare-earth magnetic insulators Single molecular magnets

Anisotropic dipolar systems - TFIM S-S Single molecular magnets Magnetic insulators, large spin, strong lattice anisotropy, dominant dipolar interaction Rare-earth magnetic insulators

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

LiHoY F x1-x 4 Reich et al, PRB 42, 4631 (1990)

Dilution, transverse field – effective random longitudinal field S-S M. S. and N. Laflorencie, PRL 97, (2006) M. S., PRB 77, (R) (2008)

Offdiagonal dipolar terms S-S M. S. and N. Laflorencie, PRL 97, (2006) M. S., PRB 77, (R) (2008)

Offdiagonal dipolar terms S-S symmetry M. S. and N. Laflorencie, PRL 97, (2006) M. S., PRB 77, (R) (2008)

Offdiagonal dipolar terms S-S symmetry M. S. and N. Laflorencie, PRL 97, (2006) M. S., PRB 77, (R) (2008)

Are the fields random? Square of energy gain vs. N, different dilutions Inset: Slope as Function of dilution M. S., PRB 77, (R), (2008)

Ferromagnetic RFIM S-S M. S., PRB 77, (R) (2008)

Ferromagnetic RFIM S-S M. S., PRB 77, (R) (2008)

Ferromagnetic RFIM S-S M. S. and P. Stamp, PRL 95, (2005) M. S., PRB 77, (R) (2008) - Independently tunable random and transverse fields! - Classical RFIM despite applied transverse field

RF in disordered systems Transverse field, still, but no T. Transverse field, still, but no T. Disordered systems: no pure Ising without T symmetry. No pure TFIM in field. Disordered systems: no pure Ising without T symmetry. No pure TFIM in field. Anisotropic dipolar magnets: Anisotropic dipolar magnets: M. S. and P. Stamp, in preparation

Experimental realization Silevitch et al., Nature 448, 567 (2007) Sharp transition at high T, Rounding at low T (high transverse fields)

Random fields not specific to FM! Reich et al, PRB 42, 4631 (1990)

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

Spin glass – correlation length Flip a droplet – gain vs. cost: M.S. and N. Laflorencie, PRL 97, (2006) Fisher and Huse PRL 56, 1601 (1986); PRB 38, 386 (1988) Lower critical dimension – infinity! Droplet size – Correlation length Imry and Ma, PRL 35, 1399 (1975)

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

Correlation length - experiment Jonsson, Mathieu, Wernsdorfer, Tkachuk, Barbara, PRL 98, (2007) Domains of >10^3 spins

Remarks Validity of droplet picture Validity of droplet picture Reduction of susceptibility in mean field Reduction of susceptibility in mean field - Tabei, Gingras, Kao, Stasiak, Fortin, PRL 97, (2006) - Young, Katzgraber, PRL 93, (2004) - Jonnson, Takayama, Katori, Ito, PRB 71, (R) (2005) - Pirc, Tadic, Blinc, PRB 36, 8607 (1987)

Hyperfine interaction: electro- nuclear Ising states

Hyperfine spacing: 200 mK - M.S. and P. Stamp, PRL 95, (2005) - N. Prokof’ev and P. Stamp, Rep. Prog. Phys. 63, 669 (2000)

Hyperfine interaction: electro- nuclear Ising states Hyperfine spacing: 200 mK - M.S. and P. Stamp, PRL 95, (2005) - N. Prokof’ev and P. Stamp, Rep. Prog. Phys. 63, 669 (2000)

Enhanced transverse field – phase diagram SG PM No off. dip. With off. dip. Experiment M.S. and P. Stamp, PRL 95, (2005) Quantum disordering harder than thermal disordering Main reason – hyperfine interactions Off-diagonal dipolar terms in transverse field – also enhanced effective transverse field

Re-entrance of crossover field SG PM No off. dip. With off. dip. Experiment Larger x – stronger reduction of c-o field by offdiagonal dipolar terms! - M.S. and P. Stamp, PRB 78, (2008) - Ancona-Torres, Silevitch, Aeppli, Rosenbaum, PRL 101, (2008) X=0.167 X=0.045

Conclusions Ising model with tunable quantum and random effective fields can be realized in anisotropic dipolar systems Ising model with tunable quantum and random effective fields can be realized in anisotropic dipolar systems FM RFIM – implications to fundamental research and applications FM RFIM – implications to fundamental research and applications Quasi-SG, no SG-PM QPT in Ising magnets Quasi-SG, no SG-PM QPT in Ising magnets Disordered systems: Ising model is only realizable with time-reversal symmetry Disordered systems: Ising model is only realizable with time-reversal symmetry LiHo – hyperfine, offdiagonal dipolar interactions dictate low-T physics LiHo – hyperfine, offdiagonal dipolar interactions dictate low-T physics