Vortex Glass, Dislocation Glass, Stripe Glass: Long Range Interactions at Work ortex Glass: Long vs. Short Range Interactio islocation Structures in 2D Vortex Matter tripe Glasses in Magnetic Films & 2DEG ndran, C. Pike, R. Scalettar M. Winklhofer & G.T. Zimanyi U.C o, G. Gyorgyi & I. Groma Budapest
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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 - PowerPoint PPT Presentation
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Vortex Glass, Dislocation Glass, Stripe Glass: Long Range Interactions at Work
1. Vortex Glass: Long vs. Short Range Interactions2. Dislocation Structures in 2D Vortex Matter3. Stripe Glasses in Magnetic Films & 2DEG
M. Chandran, C. Pike, R. Scalettar M. Winklhofer & G.T. Zimanyi U.C. DavisB. Bako, G. Gyorgyi & I. Groma Budapest
Long Range Interactions Form Slow Structures in Cuprates
Competing Energies:Kinetic energyShort range magnetic
Experiment (Davis, Yazdani, …)J.C. Davis,Physics Today, September 2004
1. Vortex Glass: The Original Proposition
2~ scJ
Vortex Glass with Long Range Interactions: the Gauge Glass
No Screening: Glass Transition(Young 91)
Expt.: No Extended Defects - No Vortex Glass
Yeh (1997)Lopez, Kwok (1997)Lobb (2001)
Foglietti, Koch (1989)
Screening: Short Range Interactions: No Gauge Glass
Young (95)
Vortex Glass Transition Arrested by Screening: Vortex Molasses
Jc does not vanish as a power law:levels off around
Langevin dynamics for vortices:
1~/ renBCS
ren
1. Interacting elastic lines 2. In random potential3. Overdamped dynamics
Resistivity in Vortex Molasses
Resistivity finite below “Jsc”:Vortex Molasses
Resistivity can be fitted by a - power law; or the- Vogel-Fulcher law
Finite Size Scaling
Long Range Interaction Short Range Interaction
log (T-TG)
)/log(
)log(
)log(
Vortex GlassVortex Molasses
Interaction Crossover from Long Range to Short Range Causes Criticality Crossover from Scaling to Structural Glasses
Vortex Molasses
~
short rangeinteractions
long rangeinteractions
2. Dislocation Glass
In 2D Disordered Vortex Matterdislocations were supposed to:
• Distributed homogeneously• Characterized by single
length scaleD
Giamarchi-Le Doussal ’00Inspired by KT-Halperin-Nelson-Young theory of 2D melting
Magnetic Field SweepB/Bc2 = 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: dislocationsDislocations form domain walls at intermediate fields
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
“Absence of Amorphous Vortex Matter”Fasano, Menghini, de La Cruz, Paltiel, Myasoedov, Zeldov, Higgins, Bhattacharya, PRB, 66, 020512 (2002)
• NbSe2
• T= 3-7K • H= 36-72 Oe
Sim
ulat
ions
NbS
e 2
Low DisorderMedium DisorderN
bSe 2
Sim
ulat
ion
Domain Configurations
We
acce
ssed
low
est
disl
ocat
ion
dens
ities
Dislocation Domain Structures in Crystals
Pattern formation is typical
Rudolph (2005)
Dislocation Simulations
)()(g rnBrnBv PKccc
PKgg
1. Overdamped dynamics2.is the glide/climb component of the stress-related Peach-Kohler force3. Dislocation interaction is in-plane dipole-dipole type4. No disorder
Novelty:
1. Dislocations move in 2D: Bg- glide mobility, Bc - climb mobility; 2. Dislocations rotate: through antisymmetric part of the displacement tensor3. Advanced acceleration technique
Glide
Climb
Computational Details
Kleinert formalism
1. Separate elastic and inelastic displacement
2. Isolate the antisymmetric component of displacement tensor
3. Rotate Burgers vector
Observation I: Separation of Time Scales
Fast fluctuations: from near dislocationsSlow fluctuations: large scale dynamics from far dislocations
Observation II: Stress Distribution Modeling
2/32 )]()[()()(rC
rCPave
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
X
A
B
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
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
Stochastic Coarse Graining:Climb, No Rotation, No Shearing
Climb promotes structure formation, even without shearing
Stochastic Coarse Graining:Climb, Rotation, No Shearing
log(
time)
Bc/Bg=1.0 Bc/Bg=0.1
1. Domain structure formation without shear
2. Climb makes domain structures possible
3. Domain distribution:not fractal
4. Effective diffusion constgoes to zero:Domain structure freezes:Dislocation Glass