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Vortex Glass, Dislocation Glass, Stripe Glass: Long Range Interactions at Work 1. Vortex Glass: Long vs. Short Range Interactions 2. Dislocation Structures in 2D Vortex Matter 3. Stripe Glasses in Magnetic Films & 2DEG M. Chandran, C. Pike, R. Scalettar M. Winklhofer & G.T. Zimanyi U.C. Davis B. Bako, G. Gyorgyi & I. Groma Budapest

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Long Range Interactions Form Slow Structures in Cuprates Competing Energies: Kinetic energy Short range magnetic Long range Coulomb - Phase separation (Emery, Kivelson) - Stripe formation (Littlewood, Zaanen Emery, Kivelson, …) Experiment (Davis, Yazdani, …) J.C. Davis, Physics Today, September 2004

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1. Vortex Glass: The Original Proposition

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Vortex Glass with Long Range Interactions: the Gauge Glass No Screening: Glass Transition (Young 91)

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Expt.: No Extended Defects - No Vortex Glass Yeh (1997) Lopez, Kwok (1997) Lobb (2001) Foglietti, Koch (1989)

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Screening: Short Range Interactions: No Gauge Glass Young (95)

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Vortex Glass Transition Arrested by Screening: Vortex Molasses Jc does not vanish as a power law: levels off around Langevin dynamics for vortices: 1. Interacting elastic lines 2. In random potential 3. Overdamped dynamics

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Resistivity in Vortex Molasses Resistivity finite below “J sc ”: Vortex Molasses Resistivity can be fitted by a - power law; or the - Vogel-Fulcher law

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Finite Size Scaling Long Range Interaction Short Range Interaction

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log (T-T G ) Vortex Glass Vortex Molasses Interaction Crossover from Long Range to Short Range Causes Criticality Crossover from Scaling to Structural Glasses Vortex Molasses short range interactions long range interactions

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2. Dislocation Glass In 2D Disordered Vortex Matter dislocations were supposed to: Distributed homogeneously Characterized by single length scale D Giamarchi-Le Doussal ’00 Inspired by KT-Halperin- Nelson-Young theory of 2D melting

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Magnetic Field Sweep B/B c2 = 0.1 (a) 0.4 (b) 0.5 (c) 0.6 (d) 0.8 (e) 0.9 (f) v Blue & Red dots: 5 & 7 coordinated vortices: disclinations Come in pairs: dislocations Dislocations form domain walls at intermediate fields

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What is the physics? Dislocations are dipoles of disclinations, with anisotropic logarithmic interaction. Theory averages anisotropy and applies pair unbinding picture ~ KTHNY melting. However: - The dipole-dipole interaction is strongly anisotropic: - parallel dipoles attract when aligned; - energy is minimized by wall formation; - energetics different from KTHNY. Dislocation structures formed by anisotropic interactions

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“Absence of Amorphous Vortex Matter” Fasano, Menghini, de La Cruz, Paltiel, Myasoedov, Zeldov, Higgins, Bhattacharya, PRB, 66, 020512 (2002) NbSe 2 T= 3-7K H= 36-72 Oe Simulations NbSe 2

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Low Disorder Medium Disorder NbSe 2 Simulation Domain Configurations We accessed lowest dislocation densities

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Dislocation Domain Structures in Crystals Pattern formation is typical Rudolph (2005)

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Dislocation Simulations 1. Overdamped dynamics 2. is the glide/climb component of the stress-related Peach-Kohler force 3. Dislocation interaction is in-plane dipole-dipole type 4. No disorder Novelty: 1. Dislocations move in 2D: B g - glide mobility, B c - climb mobility; 2. Dislocations rotate: through antisymmetric part of the displacement tensor 3. Advanced acceleration technique Glide Climb

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Computational Details Kleinert formalism 1. Separate elastic and inelastic displacement 2. Isolate the antisymmetric component of displacement tensor 3. Rotate Burgers vector

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Observation I: Separation of Time Scales Fast fluctuations: from near dislocations Slow fluctuations: large scale dynamics from far dislocations

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Observation II: Stress Distribution Modeling

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Stochastic Coarse Graining 1. Divide simulation space into boxes 2. Calculate mean (coarse grained) dislocation density for each box 3. Slow interactions (AX): Approximate stress from box A in box X by using coarse grained density. 4. Fast interactions (BX): Generate random stress t from distribution P(t) with average stress t ave. 5. Move dislocations by eq. of motion. 6. Repeat from 2. 1-10 million dislocations simulated in 128x128 boxes X A B

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Stochastic Coarse Graining: No Climb, No Rotation, Shearing Full simulations: -1 million dislocations -(~20 million vortices) -Profound structure formation -Sensitive to boundary, history -Work/current hardening

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Stochastic Coarse Graining: No Climb, No Rotation, Shearing Box counting: - Domains have fractal dimension -D=1.86 - No single characteristic length scale Number of domains N(L) of size L with no dislocations

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Stochastic Coarse Graining: Climb, No Rotation, No Shearing Climb promotes structure formation, even without shearing

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Stochastic Coarse Graining: Climb, Rotation, No Shearing log(time) B c /B g =1.0 B c /B g =0.1 1. Domain structure formation without shear 2. Climb makes domain structures possible 3. Domain distribution: not fractal 4. Effective diffusion const goes to zero: Domain structure freezes: Dislocation Glass

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Andrei group PRL 81, 2354 (1998) Expt.: Shearing Increases Ic

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Rudolph et al Expt.: GaAs: Increasing Climb Induces Domain Structure Formation Climb

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3. Stripe Glass Co/Pt magnetic easy axis: out of plane Potential perpendicular recording media [Co(4Å)/Pt(7Å)] N : Hellwig, Denbeaux, Kortright, Fullerton, Physica B 336, 136 (2003). Co Pt H app N=50

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Transmission X-ray Microscopy 3m3m Stage 1: Sudden propagation of reversal domains. Stage 2:Expansion/contraction of domains, domain topology preserved. Stage 3:Annihilation of reversal domains.

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Modeling Magnetic Films Classical spins, pointing out of the plane Spins correspond to total spin of individual domains: spin length is continuous variable Competing interactions: –Exchange interaction: nearest neighbor ferromagnetic –Dipolar interaction: long range antiferromagnetic (perpendicular media) Finite temperature Metropolis algorithm (length updated) Spivak-Kivelson: Hamiltonian same as 2DEG & Coulomb systems Tom Rosenbaum: Glassy phases in dipolar LiHoYF

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T C(T) Equilibrium Phases

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Expt.: Two Phases Observed in FeSiBCuNb Films Henninger

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Non-equilibrium Anneal: Supercooled Stripe Liquid Stripe Glass Protocol: 1.Cool at a finite rate to T 2.Study relaxation at T Typically configuration is far from equilibrium: Supercooled Stripe Liquid Stripe Glass ~ Schmalian-Wolynes

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T 1/T ~ Fragile Glass ~ Strong Glass Relaxation of Persistence

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Aging P(t, t w ) t w =10 4 t w =10 5 t w =10 6 t w =10 7 Good fit: P(t, t w ) = P[(t-tw)/tw] t Blue regions: frozen

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Summary 1. Vortex Glass: - Crossover of range of interaction from long to short changes Glass transition from Scaling to Molasses transition 2. Dislocation Glass: - In 2D in-plane dipoles form frozen domain structures: Dislocations, Vortex matter - Climb, rotation, shearing, disorder - Stochastic Coarse Gaining, ~ 10 million vortices 3. Stripe Glass: - In 2D out-of plane dipoles form Stripe Glass: Magnetic films, 2DEG, Coulomb systems - Persistence, aging - Strong and Fragile Glass aspects observed How to see your glass? Low frequency spectrum of noise is large (Popovic), slow dynamics, imaging

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