Size effect in the Size effect in the vortex-matter phase vortex-matter phase

transition transition in Biin Bi22SrSr22CaCuOCaCuO8+8+ ??

B. Kalisky, A. Shaulov

and Y. Yeshurun

Bar-Ilan University Israel

T. Tamegai University of Tokyo

Vortex Matter Workshop, Mombay, India

February 2005

Khaykovich et al., PRL 76 (1996), 2555

Disordered Solid

high j

Ordered Solid(Abrikosov) low j

Liquid

0 200 400 600 800 1000

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

22 K

M [

emu/

cm3 ]

H [G]

Vortex Phase Diagram - Vortex Phase Diagram - BiBi22SrSr22CaCuCaCu22OO8+8+

SMPM

elting lineOrdered Solid(Abrikosov) low j

Disordered Solid

high j

Liquid

SMPM

elting lineOrdered Solid(Abrikosov) low j

Disordered Solid high j

Liquid

SMPM

elting lineLarge sampleSmall sample

Th

?

gap

T

?

termination

Termination (low T)

Y. Yeshurun et al., PRB (1994)

B. K Khaykovich et al., PRL (1996)

S.L. Li and H. H. Wen, PRB (2002)

B. Kalisky et al., PRB (2003).

Gap (high T) and effect of size

Y. Kopelevich, P. Esquinazi et al., J. Low Temp. (1998, 1999)

M. Wang, A.Zettl, T.Tamegai et al., PRL (2001)

Large (70 microns)

sample

Small (30 microns)

sample

Goals of this talkGoals of this talk

1. Explain the origin of :

• Gap - high T

• Termination - low T

2. Understand the role of sample size

BSCCO samplesBSCCO samples

1225 m 700m

500m

~200 m

~400 m

SD

D = 1225 m

Sd

D = 200 m

2D image of induction distribution2D image of induction distributionin a BSCCO samplein a BSCCO sample

Magneto-optical techniqueMagneto-optical technique

B

1D induction profile1D induction profile

x

mlocal = B(x) - Hext

B

M M vs.vs. B at different T B at different T

The SMP decreases with temperature

Th

Peak height Peak height vs.vs. T at 4 G/s T at 4 G/s

Peak height = m from onset to peak

Large sample still demonstrates SMP at 27 K

SD

Sd

200 300 400 500

-150

-100

-50

0

50

100

4 G/s

Sd 27 K

m

[G]

B [G]200 300 400 500

-150

-100

-50

0

50

100

4 G/s

Sd 27 K

m

[G]

B [G]

20 G/s

200 300 400 500

-150

-100

-50

0

50

100

4 G/s

Sd 27 K

m

[G]

B [G]

20 G/s80 G/s

200 300 400 500

-150

-100

-50

0

50

100

4 G/s

Sd 27 K

m

[G]

B [G]

230 G/s

20 G/s80 G/s

200 300 400 500

-150

-100

-50

0

50

100

4 G/s

Sd 27 K

m

[G]

B [G]

230 G/s400 G/s

20 G/s80 G/s

200 300 400 500

-150

-100

-50

0

50

100

4 G/s

800 G/s

Sd 27 K

m

[G]

B [G]

230 G/s400 G/s

20 G/s80 G/s

200 300 400 500

-150

-100

-50

0

50

100

4 G/s

800 G/s1600 G/s

Sd 27 K

m

[G]

B [G]

230 G/s400 G/s

20 G/s80 G/s

m m vs.vs. B, different field sweep B, different field sweep ratesrates

SMP increases with SR

Peak height Peak height vs.vs. field sweep rate, field sweep rate, 27 K27 K

Increase of peak height with sweep rate is a result of increase in the persistent current due to shorter time window of the experiment

Persistent current density Persistent current density vs.vs. sweep sweep raterate

Persistent current density is larger in larger sample

j obtained by fit to Biot-Savart law

Why j is larger in larger samples?

relaxation of j by a certain amount requires the entry of more fluxons in the larger sample and, consequently, longer time

Why j is larger in larger samples?

A certain amount of vortices entering the samples causes stronger reduction of j in the small sample

Time is scaled by t0 d

Calculation of the size Calculation of the size dependence of j in SR dependence of j in SR

experimentsexperiments

B Et x

n

0c

jE=E

j

4 Bj

c x

nB B

=At x x

n

0c

cA=E

4 j

x 0

B0

x

t 0

B 0

x d

B SR t

SR and d appear only in the integration constant and boundary conditions

Numerically calculated j/jNumerically calculated j/jcc vs.vs. SR SR

• j increases with SR • j increases with the sample size• Results are qualitatively similar to experimental results

Hext = 1000 Gn=3jc=106 A/cm2

Summary of behavior at high Summary of behavior at high temperaturestemperaturesDecay of persistent currents

Disappearance of SMP above Th

Small samples: Faster relaxation

Disappearance of SMP at lower Th

In comparing samples of different size, one should compensate for the reduction in the persistent current in the smaller samples by, e.g., adjusting the field SR

10 100 1000

0

10

20

30

40

50

60

27 K

Sd

peak

hei

ght

[G]

field sweep rate [G/s]

27 K – peak height increases with SR

10 100 1000

0

10

20

30

40

50

60

21 K27 K

Sd

peak

hei

ght

[G]

field sweep rate [G/s]27 K – peak height increases with SR21 K – peak height decreases with SR

10 100 1000

0

10

20

30

40

50

60

21 K

23 K

25 K

27 K

Sd

peak

hei

ght

[G]

field sweep rate [G/s]27 K – peak height increases with SR21 K – peak height decreases with SR

maximum in the peak height at intermediate SR

Effect of field sweep rate on the Effect of field sweep rate on the peak height at different Tpeak height at different T

TDVS are injected through the sample edges

Paltiel, Zeldov et al., Nature 403, 398 (2000).“Edge contamination”

Disorder is induced by inhomogeneous surface barriersHext

Bod low-j

hig

h-j

Appearance of TVS

Short

As sweep rate increases, TVS with shorter lifetime play a role

Transient Disordered Vortex States (TDVS)

For high sweep rates the SMP is masked by TDVS

T=23 K

EffectEffect of TDVS on magnetization of TDVS on magnetization curvescurves

10 100 1000

0

10

20

30

40

50

60

21 K

23 K

25 K

27 K

Sd

peak

hei

ght

[G]

field sweep rate [G/s]27 K – peak height increases with SR21 K – peak height decreases with SR

maximum in the peak height at intermediate SR

Effect of SR on the peak height at Effect of SR on the peak height at different Tdifferent T

(B)

small big

Transient disordered statesQuasi-ordered phase

Bod

B

Bodtime

Effects of metastable states are more severe in the smaller sample Effects vortex state of states

Summary and conclusionsSummary and conclusions

• Two mechanisms for the disappearance of the SMP:

1. High temperatures

Decay of persistent currents

SMP “disappears” with time

2. High temperatures

Involvement of transient states

Large M below SMP mask the peak

0 200 400 600 800 1000

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

22 K

M [

emu/

cm3 ]

H [G]

0 200 400 600 800 1000

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

22 K

M [

emu/

cm3 ]

H [G]

• Sample size plays an important role:

1. Relaxation rate

2. Relative contribution of TDVS

are enhanced in smaller samples

Summary and conclusions Summary and conclusions (cont.)(cont.)

T and Th depend on sample size

Summary and conclusions (cont.)Summary and conclusions (cont.)

Our results question previous reports on size effect in the vortex matter phase

transition

• Compensate experimentally for these effects :

1.Increasing SR - high T

2.Decreasing SR - low T

Peak height Peak height vs.vs. SR at 25 K SR at 25 K

The maximum widens for the larger sample

The SMP in the larger sample is less affected by relaxation of j and by the engagement of

metastable states, for low and high field sweep rates

BSCCO samplesBSCCO samples

1225 m 670750m

520460m

~200 m

~400 m

SD

D = 1225 m

Sd

D = 200 m

BSCCO samplesBSCCO samples

1225 m 700m

500m

~200 m

~400 m

SD

D = 1225 m

Sd

D = 200 m

The sample size plays important role in superconductors, since the basic quantity, the magnetization, depends on sample size.

Unlike in ferromagnetic materials, where the basic quantity is an intrinsic or uniform volume property.

IntroductionIntroduction

=> The order-disorder phase => The order-disorder phase transition depends on sample transition depends on sample

sizesize

• Tc ??? [ ??? ]

• Irreversibility line [ ??? ]

• Critical current density [Qin 2004]

• Magnetic properties like relaxation rates rates [Weir 1991, ??? 0000 , Yafit 2004]

• What else ???

• The SMP disappears in samples with reduced size

[Esquinazi 1998, Wang 2001]

Effect of size in Effect of size in superconductorssuperconductors

=> “size effect” in SC=> “size effect” in SC

We start with the lower termination– below Tl.

קישור לשקף הבאקישור לשקף הבא

Injection through the sample edges

Paltiel, Zeldov et al., Nature 403, 398 (2000).“Edge contamination”

Disorder is induced by inhomogeneous surface barriersHext

Bod low-j

hig

h-j

Appearance of TVS

Short

As sweep rate increases, TVS with shorter lifetime play a role

MO imaging of generation of TVS

Effect of sweep rateMagnetization curves

For high sweep rates the SMP is masked by TDVS

T=23 K

Effect of temperatureMagnetization curves

For low temperatures the SMP is masked by TDVS

30 K

21 K

160 G/s

20 22 24 26 28 30100

200

300

400

500

B [G

]

T [K]

Bod 16 G/s 160 G/s 1600 G/s

?

Ordered Solid

DisorderedSolid

Liquid

- artifact caused by long living TDVS

Transition masked by TDVS

“Termination” of the transition line at low temperatures

Khaykovich et al., PRL 76, 2555 (1996).

(B2)

(B1)

(B1) < (B2)

small big

Transient disordered states

Bod

B

Bod

time=0

(B)

small big

Transient disordered statesQuasi-ordered phase

Bod

B

Bodtime

Effects of metastable states are more severe in the smaller sample Effects vortex state of states

small big

Transient disordered statesQuasi-ordered phase

Bod

(B)

Bod

B

time

small big

Transient disordered statesQuasi-ordered phase

Bod

(B)

Bod

B

time

Quasi-ordered phase

small big

BodBod

B

(B)

time

Bod

time1

H3

H2

H1

time2 time3

Bod

B

big

HH1 H2 H3

stat

e wit

h ti

me

3

2

1

H1 H2 H3

stat

e wit

h ti

me

H

small3

2

1

Ferromagnets: Magnetization, M, is a uniform volume property M is independent of sample size SIZE EFFECT ONLY IN NANO-SCALE REGIME

Introduction:Introduction:

Size effects in Size effects in ferromagnets ferromagnets

and and superconductorssuperconductors

Bean model m d2

M d

In this talk: Special effects of size near vortex phase transition

d0

Hext

B

X

Superconductors:inhomogeneous distribution of the induction M depends on sample size (e.g. Bean model: Md) PRONOUNCED EFFECT OF SIZE IN ALL SCALES

Summary and conclusionsSummary and conclusions

• Two mechanisms for the absence of the SMP:

1. Decay of persistent currents - high T

2. Involvement of metastable states - low T• Sample size plays an important role:

1. Relaxation rate

2. Relative contribution of TDVS

are enhanced in smaller samples