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

Long range Coulomb

- Phase separation (Emery, Kivelson)

- Stripe formation (Littlewood, ZaanenEmery, Kivelson, …)

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 potential

3. 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 Sweep

B/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: dislocations

Dislocations 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

ula

tion

sN

bS

e 2

Low DisorderMedium DisorderN

bS

e 2S

imu

lati

on

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 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: Bg- glide mobility, Bc - climb mobility;

2. Dislocations rotate: through antisymmetric part of the displacement tensor

3. 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

rCP

ave

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

Andrei group PRL 81, 2354 (1998)

Expt.: Shearing Increases Ic

Rudolph et al

Expt.: GaAs: Increasing Climb Induces Domain Structure Formation

Climb

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

Happ

N=50

Transmission X-ray Microscopy

3m

Stage 1: Sudden propagation of reversal domains.

Stage 2: Expansion/contraction of domains, domain

topology preserved.

Stage 3: Annihilation of reversaldomains.

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

T

C(T)

Equilibrium Phases

Expt.: Two Phases Observed in FeSiBCuNb Films

Henninger

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 LiquidStripe Glass

~ Schmalian-Wolynes

T 1/T

~ Fragile Glass ~ Strong Glass

Relaxation of Persistence

)(T )](log[ T

])/(exp[~)( 0tPtP

)/exp()( 0 TT

Aging

P(t, tw)

tw=104

tw=105

tw=106

tw=107

Good fit: P(t, tw) = P[(t-tw)/tw]

t

Blue regions: frozen

Summary1. 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