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Quantum phase transitions in anisotropic dipolar magnets In collaboration with: Philip Stamp, Nicolas laflorencie Moshe Schechter University of British Columbia

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LiHoY F x1-x 4 1. Transverse field Ising model:

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LiHoY F x1-x 4 Reich et al, PRB 42, 4631 (1990) 1. Transverse field Ising model: 2. Dilution!

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

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Ronnow et. Al. Science 308, 389 (2005) Ghosh, Parthasarathy, Rosenbaum, Aeppli Science 296, 2195 (2002) Brooke, Bitko, Rosenbaum, Aeppli Science 284, 779 (1999) Giraud et. Al. PRL 87, 057203 (2001) Various dilutions

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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)

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

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Anisotropic dipolar magnets Large spin, strong lattice anisotropy S-S

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Anisotropic dipolar magnets Large spin, strong lattice anisotropy S-S Magnetic insulators Single molecular magnets

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Anisotropic dipolar magnets - TFIM Large spin, strong lattice anisotropy S-S

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Hyperfine interaction: electro- nuclear Ising states

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Hyperfine spacing: 200 mK - M.S. and P. Stamp, PRL 95, 267208 (2005)

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Phase diagram – transverse hyperfine and dipolar interactions SG PM No off. dip. With off. dip. Experiment Splitting Splitting - M.S. and P. Stamp, PRL 95, 267208 (2005)

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Anisotropic dipolar systems – offdiagonal terms S-S symmetry

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Anisotropic dipolar systems – offdiagonal terms S-S symmetry M. S. and N. Laflorencie, PRL 97, 137204 (2006)

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Imry-Ma argument Ground state: Domain: Energy costEnergy gain (spins down) (all spins up) 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 M.S. and N. Laflorencie, PRL 97, 137204 (2006) Energy gain: Y. Imry and S. K. Ma, PRL 35, 1399 (1975)

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Spin glass – correlation length M.S. and N. Laflorencie, PRL 97, 137204 (2006) Energy cost: Energy gain: Y. Imry and S. K. Ma, PRL 35, 1399 (1975)

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Spin glass – correlation length M.S. and N. Laflorencie, PRL 97, 137204 (2006) Fisher, Huse PRL 56, 1601 (86); PRB 38, 386 (88) Energy cost: Energy gain: Only extra sqrt of surface bonds are satisfied, can optimize boundary.

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Spin glass – correlation length Flip a droplet – gain vs. cost: M.S. and N. Laflorencie, PRL 97, 137204 (2006) Fisher, Huse PRL 56, 1601 (86); PRB 38, 386 (88) Energy cost: Energy gain: Only extra sqrt of surface bonds are satisfied, can optimize boundary.

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Spin glass – correlation length Flip a droplet – gain vs. cost: M.S. and N. Laflorencie, PRL 97, 137204 (2006) Fisher, Huse PRL 56, 1601 (86); PRB 38, 386 (88) Energy cost: Energy gain: Only extra sqrt of surface bonds are satisfied, can optimize boundary. Droplet size – Correlation length

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

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Enhanced transverse field – phase diagram SG PM No off. dip. With off. dip. Experiment M.S. and P. Stamp, PRL 95, 267208 (2005) Quantum disordering harder than thermal disordering Main reason – hyperfine interactions Off-diagonal dipolar terms in transverse field – also enhanced effective transverse field

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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 Verifying interesting results on DAFM Experimental techniques Experimental techniques Novel fundamental research (away from transition, conjugate field, quantum term) Novel fundamental research (away from transition, conjugate field, quantum term) Applications in ferromagnets, e.g. domain wall dynamics in random fields 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! S-S M. S. and P. Stamp, PRL 95, 267208 (2005) M. S., cond-mat/0611063

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Ferromagnetic RFIM S-S M. S. and P. Stamp, PRL 95, 267208 (2005) M. S., cond-mat/0611063

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Ferromagnetic RFIM S-S M. S. and P. Stamp, PRL 95, 267208 (2005) M. S., cond-mat/0611063 - Independently tunable random and transverse fields! - Classical RFIM despite applied transverse field

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Realization of FM RFIM Silevitch et al., Nature 448, 567 (2007) Sharp transition at high T, Rounding at low T (high transverse fields)

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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 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 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 SG unstable to transverse field, no SG-PM QPT First FM RFIM – implications to fundamental research and applications First FM RFIM – implications to fundamental research and applications

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