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Vortex Glass, Dislocation Glass, Stripe Glass: Long Range Interactions at Work

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

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Vortex Glass, Dislocation Glass, Stripe Glass: Long Range Interactions at Work

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  1. 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

  2. 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

  3. 1. Vortex Glass: The Original Proposition

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

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

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

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

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

  9. Finite Size Scaling Short Range Interaction Long Range Interaction

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

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

  12. Magnetic Field Sweep • B/Bc2 = 0.1 (a) • 0.4 (b) • 0.5 (c) • 0.6 (d) • 0.8 (e) • 0.9 (f) • D = 0.02 N(v) = 4096 • Blue & Red dots: 5 & 7 coordinated vortices: disclinations • Come in pairs: dislocations Dislocations form domain walls at intermediate fields

  13. 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

  14. “Absence of Amorphous Vortex Matter” • NbSe2 • T= 3-7K • H= 36-72 Oe Fasano, Menghini, de La Cruz, Paltiel, Myasoedov, Zeldov, Higgins, Bhattacharya, PRB, 66, 020512 (2002) NbSe2 Simulations

  15. Domain Configurations Medium Disorder Low Disorder NbSe2 Simulation We accessed lowest dislocation densities

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

  17. Dislocation Simulations Climb Glide 1. Overdamped dynamics 2. t 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: Bg- glide mobility, Bc - climb mobility; 2. Dislocations rotate: through antisymmetric part of the displacement tensor 3. Advanced acceleration technique

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

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

  20. Observation II: Stress Distribution Modeling

  21. 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 tave. • 5. Move dislocations by eq. of motion. • 6. Repeat from 2. • 1-10 million dislocations simulated in 128x128 boxes A B X

  22. 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

  23. 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

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

  25. Stochastic Coarse Graining:Climb, Rotation, No Shearing 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 log(time) Bc/Bg=0.1 Bc/Bg=1.0

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

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

  28. Happ Co Pt 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). N=50

  29. 3mm Transmission X-ray Microscopy Stage 1: Sudden propagation of reversal domains. Stage 2: Expansion/contraction of domains, domain topology preserved. Stage 3: Annihilation of reversal domains.

  30. 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

  31. Equilibrium Phases C(T) T

  32. Expt.: Two Phases Observed in FeSiBCuNb Films Henninger

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

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

  35. Aging P(t, tw) tw=107 tw=106 tw=105 tw=104 t Blue regions: frozen Good fit: P(t, tw) = P[(t-tw)/tw]

  36. 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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