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)

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, 177202 (2013) J. C. Andresen, H. Katzgraber, V. Oganesyan, M. S., PRX 4, 041016 (2014)

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

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)

Competing interactions σ – standard deviation. Mean=1

Competing interactions σ – standard deviation. Mean=1

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

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

LiHoF4 - Dipolar Ising model

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

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

LiHoF4 - Transverse field Ising model

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

Ferromagnetic RFIM S -S M. S. and N. Laflorencie, PRL 97, 137204 (2006) M. S., PRB 77, 020401(R) (2008)

Ferromagnetic RFIM S -S

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

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)

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

SG unstable to transverse field! Finite, transverse field dependent correlation length SG quasi M. S. and N. Laflorencie, PRL 97, 137204 (2006) Young, Katzgraber, PRL 93, 207203 (2004)

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)

FM and SG phases in random field

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

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, 177202 (2013) Silevitch et al., Nature 448, 567 (2007)

Finite temperature

Finite temperature T>0.3K : FM to PM transition T<0.3K : Intermediate frozen QSG phase Andresen et. al., PRL 111, 177202 (2013) Silevitch et al., Nature 448, 567 (2007)

Finite temperature “Standard” PM Glassy domains  

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

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

Dilute Dipolar Glass Ghosh, Parthasarathy, Rosenbaum, Aeppli Science 296, 2195 (2002) Quilliam, Meng, Kycia, PRB 85, 184415 (2012)

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%

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, 041016 (2014)

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

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

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

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, 66002 (2009)

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

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