Peak effect in Superconductors - Experimental aspects

G. Ravikumar

Technical Physics & Prototype Engineering Division,

Bhabha Atomic Research Centre, Mumbai

Type II superconductivity – Mixed state

AbrikosovVortex solid

Hc2

0 2.01 × 10-7 G. cm2

B = n 0

a0 (0 /B)1/2

Hc1 100 OeHc1

Meissner State B = 0Uel (0 /4) 2 ln (a0/ ) (a0 < )

(0 /4) 2 exp( a0/ ) (a0 > )

- M

H

• Lorentz Force

F = J × B

• Causes vortex motion

Electric field

E = v X B

Can not carry any bulk current

Current transport through Abrikosov Vortex lattice

Ic

V

I

Vortex pinning by lattice defects and impurities

Upin = 0Hc23

V = 0 below I = Ic (critical current)

Ic

H / T

Usually Ic is a monotonically decreasing function of H / T

vortex lattice imaged by bitter decoration

Conventional view:

Unique solid vortex phase – disordered solid with various kinds of vortex lattice defects. Increase in material disorder leads to more defective vortex solid.

Current view:

Two distinct solid phases in weakly pinned superconductors

• Bragg Glass: Quasi-ordered (or weakly disordered) solid without lattice defects. Lattice correlations decay with distance as a power law.

• Vortex Glass: Highly disordered solid

Peak effect in NbSe2

Hc2

Measurement at different T

Autler et al, PRL 1962.

0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.40

2

4

6

8

10

12I c

(mA

)

H (T)

T = 5 KE = 1V/cm

0.0 0.5 1.0 1.5 2.00

2

4

6

8

10

12

7.0K

6.8K

6.6K6.3K

6K5.7K

5.4K

5K

Ic (

mA

)

H ( T )

H

T

Peak effect Low Tc materials

0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.40

2

4

6

8

10

12

I c (m

A)

H (T)

T = 5 KE = 1V/cm

Neutron beam

H

X. S. Ling et al, PRL

Small Angle Neutron Scattering (SANS) gives structure of the vortex lattice

Below peak – Long range order exists

Correlation volumeVc is large

Above peak – No long range order

Vc is small

Peak effect is seen only for weak pinning

• In V3Si defects introduced by fast neutron irradiation.

• At low dose pinning weak – peak is sharp

• Peak broadens with increasing dose (increase in pinning)

• For strong pinning Jc – H is monotonic

Küpfer et al

Jc from Magnetization hysteresis measurements – Critical State Model

• Resistivity = 0 For J < Jc,

0 For J

> Jc

• Persistent currents of density Jc induced in response to field variation

• Direction of currents depends on the direction of field scan

• M (H) = – 0JcR

• M (H) = 0JcR

• Jc(H) = { M (H) – M (H) } / 2 0R

M + Jc R

HH

M - Jc R

Peak effect in magnetization measurements

peak

onset

Critical current vs Field/Temp

Hc2

Jc

H

M

H

Jc(H) ~ M (H)/0R

M

1400 1600 1800 2000 2200 2400 2600

-0.0020

-0.0015

-0.0010

-0.0005

0.0000

0.0005

0.0010

m (

emu)

H (Oe)

NbSe2T = 6.8K

Hc2

z

SQUID Pick-up loopFig. 1Ravikumar et al

S

QU

IDR

esp

onse

Z

2R

sample

SQ

UID

Pick-up coil in a SQUID magnetometer

Peak effect in LaSrCaCuO (Tc 38 K)

– Peak is broad – Anisotropic

Peak effect in YBCO (Tc 90 K)

Nishizaki et al PRB 58, 11169

Vortex lattice melting at high Temperatures in YBCO

A sharp kink in vs T

A sharp jump in reversible Magnetization

It is established that vortex lattice melts through a first order transition

Phase diagram in YBCO (Tc 90 K)

kT is important in the peak effect regime in addition to Uel and Upin

kTUpin

Uel

Bragg Glass

Bragg Glass – Vortex LiquidTransition is aFirst order transition

Onset

peak

Plastically deformed vortex lattice

Peak effect in Bi2Sr2CaCu2O8 (Highly anisotropic)

Melting

– Peak occurs at very low fields

– Peak field is almost constant

– Peak effect line and melting line meet at a critical point

Khaykovich et al, PRL 76 (1996) 2555

• Over-doped : Weakest pinning

• Optimally doped : Strongest pinning

Surprisingly Melting line follows the peak effect line

Not the Final Summary

H

T

Peak effect inLow Tc

0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.40

2

4

6

8

10

12

I c (m

A)

H (T)

T = 5 KE = 1V/cm

Sharp & Just below Hc2

BSCCO YBCO

Nomenclature

Peak effect (low Tc)Second Magnetization Peak (SMP) or just second peak (high Tc)Fishtail Effect

Bragg Glass Phase (Dislocation free)Quasi-Ordered Vortex SolidOrdered Solid Phase

Bragg Glass – Vortex Glass TransitionBragg Glass – Disordered Solid TransitionSolid – Solid TransitionOrder – Disorder transition

History dependence in the peak region

Jc depends on how a particular point (H,T) in the phase diagram is approached

ZFC

FC

Hp

Henderson et al PRL (1996)

NbSe2

Strong history dependence observed below Hp

Above Hp , Jc is unique

T

H

FC

ZFC

HpJc

FC (H,T) > JcZFC (H,T)

0.4 0.6 0.8 1.0 1.2 1.4

-0.4

-0.2

0.0

0.2

0.4

0.6

Ravikumar et al - fig.2a

Hpl

-

M calculated with 5mmX4mmX0.5mm

2H-NbSe2

T = 6.95K

Envelope loop Minor curves

M (

emu/

cc)

H (kOe)

0.4 0.6 0.8 1.0 1.2 1.4

-0.4

-0.2

0.0

0.2

0.4

0.6

Ravikumar et al - fig.2b

2H-NbSe2

T = 6.95 K

Envelope loop Minor curves

M (

emu/

cc)

H (kOe)

200 400 600 800 1000 1200

0.0

0.2

0.4

0.6

0.8NbSe2H // c6.95 K

Jc

RevJc

For

Jc

FC Hp

Hpl

+Hpl

-

FC-REV Reverse Forward

J c

4

M (

Gau

ss)

H (Oe)

History dependence in magnetization

History dependence due to metastability

Metastability

820 840 860-0.002

-0.001

0.000

0.001

2

1

2

1

C G K O S W

m(e

mu)

H (Oe)

• Repeated field cycling drives a metastable state towards equilibrium

Minor Hysteresis Loops

• A large number of metastable states are possible

• Each metastable state can be macroscopically characterized by a Jc

1000 1020

-0.002

0.000

0.002

0.004

1030 1040 1050

JAG07A

C C G K O S W

m (

em

u)

H(Oe)

H > HpH < H

p

JA

G07B

(N-O

)JA

G07B

(J-K

)

C K O

H(Oe)

Just below Just above

No Metastability

No History effect

( ii )( i )

fig.1 - Ravikumar et al

dc

b

Jc = J

c

st

Jc

B

a

C (Jc < J

c

st)

A (Jc > J

c

st)

Model to describe History dependent Jc

• Each Jc corresponds to a metastable vortex configuration

• Transformation from one configuration to another is governed by

Jc(B+B) = Jc(B) + |B | (Jcst – Jc)/Br

G. Ravikumar et al, Phys. Rev. B, 61, 6479 (2000)

80 12080 120-0.04

0.00

0.04

-0.1

0.0

0.1

Expt.( d )

Expt.

H (mT)

( c )

NbSe2

Model( b )

Model( a )M

(m

T )

G. Ravikumar et al, Phys. Rev. B, 61, 6479 (2000)

History dependence of the vortex state

80 120

-0.04

0.00

0.04

40 80 120

-0.1

0.0

0.1

6.95KH//c

Expt.(b)

MFC

(H)

NbSe2

MFC

(H)

(a) Model

M (m

T )

H (mT)

91 92

-0.02

0.00

0.02

82 84

-0.02

0.00

40 80 120 160-0.04

0.00

0.04

-0.02

0.00

-0.02

0.00

0.02

(e)

D

(d)

Forward

Reverse

0H (mT)

(c)

B

A

Fig. 4 - Ravikumar et al

(b)

2

1

2

1

PE region

reverse

forwardH

p

Hpl

+

D

CA

B

(a)NbSe2

6.95 KH // c

M (

mT

)

A

C

G. Ravikumar et al, Phys. Rev. B 63, 24505 (2001)

Equilibrium state by Repeated field cycling

Jc < Jceq

Jc > Jceq

0

20

40

60

80 90 100-0.01

0.00

0.01

40 60 80 100 1200

20

40

60

Hp

2H-NbSe2

6.95K

(a)10-4 X

Jcst

(A

/m2 )

Hpl

+

Meq

(b)

Fig. 6 - Ravikumar et al

Meq

(m

T)

0H (mT)

G. Ravikumar et al, Phys. Rev. B 63, 24505 (2001)

Meq shows “melting - like” change across the order-disorder transition

Avraham et al Nature 411 (2001) 451

Equilibration by transverse AC magnetic field

H

Hac

Peak effect – First order transition

Fig. 1 : Küpfer et al

A

sample

B(t)

Intermediate dB/dt

Small dB/dt

Large dB/dt

Bef

f(t)

t

Magnetization measurements of spherical V3Si crystal

Sample experiences

B(t) = Const time

+Oscillatory field due to sample vibration in non-uniform field

Order/disorder transition

step in the reversible region of the BG

Summary

• History dependence and metastability near order-disorder transition.

• “Repeated field cycling” to access the equilibrium state

• Order-disorder transition is a first order transition.

• History dependence Near Peak effect

• Many metastable states

(multiple Jc’s)

• Disorder and low kT - difficult to access equilibrium state 0 2 4 6 8 10 12

-0.04

-0.02

0.00

0.02

0.04

m (

emu)

H (T)

Meq(H) = [ M (H) + M(H) ]/2

Assuming Jc (microscopic vortex state) is same in the increasing and decreasing field branches

V3Si / 9.5 K