Types of measurements in superconductivity

Adrian CrisanSchool of Metallurgy and Materials, University of Birmingham, UK

andNational Institute of Materials Physics, Bucharest, Romania

CONTENTS

• I. Transport measurements

• II. DC magnetization

• III. AC susceptibility

I. Transport measurements• Contacts: rather easy for wires/tapes

(soldering with low temperature soldering alloys based on Indium), quite easy for bulk and melt-textured (Silver paste), and quite difficult for films

• Need to use photolitography (photoresist S1818, UV400 Exposure Optics, Karl Suss MJB3 Mask Aligner, Microsposit MF-319 developer ) and etching (Diluted Nitric acid 0.1% ) to produce micron-sized bridges

Karl Suss MJB3 Mask Aligner system An overview of 4 bridges after etching

Patterned sample with 4 wires connection on sample broad

Rotator part of the PPMS with transport option

Quantum Design SQUID MPMSQ.D. PPMS looks rather similar

Scheme of rotation measurement of YBCO bridge

Resistivity vs. temperature: Tc(H), magnetoresistance

Resistivity transition of 1μm BZO-doped YBCO film in magnetic fields of 0, 0.5, 1, 2, 3, 4, 5 and 6 T with H//c

Resistivity transition of 1μm BZO-doped YBCO film in magnetic fields of 0, 0.5, 1, 2, 3, 4, 5 and 6 T with H//ab

Phase diagram of High-Tc superconductors

The vortex lattice undergoes a first-order melting transition transforming the vortex solid into a vortex liquid [Fisher et al, PRB 43,130, 1991]. At low magnetic fields (approx 1 Oe in BSCCO [A.C. et al, SuST 24, 115001, 2011), there is a reentrance of the melting line [Blatter et al, PRB 54, 72, 1996].The flux lines in the vortex -liquid are entangled resulting in an ohmic longitudinal response, hence the vortex liquid and normal metallic phases are separated by a crossover at Hc2.

Low enough currents

- VL- linear dissipation: E ≈ J- VS (VGlass)- strongly nonlinear dissipation: E ≈ exp[-(JT/J)m]

Vortex melting from transport measurements

YBCO single-grain

I-V curves of [(BaCuO2)2/(CaCuO2)2]×35 artificial superlattices in three magnetic fields. The dashed lines represent power-law fits at the chosen melting temperatures: a) B=0.55 kG, T between 57 and 79.8 K, Tm=72.8 K; b) B=4.4 kG, T between 55.85 and 78.1 K, Tm=70.9 K; and c) B=10.8 kG, T between 49.75 and 75.4 K, Tm=68.1 K.

[A. C. et al, Physica C 313, 70, 1999][A. C. et al, Physica C 355, 231, 2001]

Above Tm(B), the I–V curves crossover from an Ohmic behaviour at low currents to a power-law relation at high currents and every I–V curve displays an upward curvature.

Below Tm(B), the I–V curves show an exponential relation at low currents and a power-law behaviour at high currents, with a downward curvature, suggestingthat the system approaches to a truly superconducting phase VG for J exponentially small.

At Tm(B), where the crossover between downward and upward curvatures occurs, the whole I–V curve displays a power-law relation, which takes the

form: V (I, T=Tm) ≈ I(z+1)/(d-1) , where z is the critical dynamical exponent of VG, and d dimensionality of the system (3 in this case).

Above Tm(B) and for low currents, the Ohmic region in the I–V curves, the linear

resistance Rl(T) can be scaled as: Rl ≈ (T/Tm-1)n(z+2-d) , where n is the static critical exponent.

nn 2)1( /1/1 m

zm TTT

IFTTIV

Fisher, Fisher, Huse scaling(PRB 43, 130, 1991)

Angle dependence of critical current

0 90 180 270 360

104

105

J c(A/c

m2 )

(Degree)

77.3K

H//cH//ab H//ab 2T

2.5

3

3.5

4

4.5

5

6

0 90 180 270 360

104

105

J c(A/c

m2 )

(Degree)

82K

H//cH//ab H//ab

0.02T0.050.10.2

0.5

1

2

(15Ag/1mm BZO-doped YBCO)x2

Dependence of Ic on the field orientation for (Ag/(YBCO+BZO))x3, showing a small anisotropy for intermediate fields.

II. DC magnetization

Jc=Ct.DM

Depends strongly on sample geometry

thin films; m=DM/2; d-thickness; a,b-rectangle dimension:

.)

31(

42

babda

mJ c

Field dependence of the critical current at 77 K for some quasi-multilayers grown in Birmingham in comparison with some results of other EU groups (green and black symbols)

Bulk pinning force• Fp=BxJc

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

F p/Fpm

ax

irr

77.3 K

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

FFp PinningEquation3 (User) Fit of Book4_FFp

FFp

Birr

Equation F=((A*h p̂1)*(1-h)̂ q1)+((B*h p̂2)*(1-h)̂ q2)+((C*h p̂3)*(1-h)̂ q3)

Adj. R-Square 0.98955Value Standard Error

Book4_FFp A 2.33248 0.17315Book4_FFp p1 0.5 0Book4_FFp q1 2 0Book4_FFp B 1.49827 0.59304Book4_FFp p2 1 0Book4_FFp q2 2 0Book4_FFp C 0.63981 0.20869Book4_FFp p3 1 0Book4_FFp q3 1 0

3.15h1/2(1-h)2+0.57h(1-h)2+0.19h3/2(1-h)Surface normal (90%), point normal (8%), surface Dk (2%)

2.33h1/2(1-h)2+1.5h(1-h)2+0.63h(1-h)Surface normal (65%), point normal (22%), volume Dk (13%)

III. AC susceptibility measurements• fundamental and 3rd harmonic

• Quantum Design PPMS

- (T) at various HDC, hac ( 15 Oe), f ( 10 kHz): Tc(H)

- ”(hac), 3(hac) at various fixed T and HDC and varying f: Jc(T,HDC,

f), Ueff(T,HDC)

Tm is the on-set of third harmonic susceptibility 3(T)

[A. C. et al., 2003 Appl. Phys. Lett. 83 506]

Critical current density as function of temperature, field, and frequency, using

AC susceptibility measurements

JC = h*/da (in A/cm2)

h* - position of maximum (in Oe)d – film thickness (in cm)a coefficient slightly dependent

on geometry (approx. 0.9)

E.H. Brandt, Physical Review B 49/13 (1994) 9024.

4 5 6 7 8 9 10

104

105

exp. fit Zeldov fit A-K fit col. pin.

J c (A

/cm

2 )

ln (f0/f)

(20Pr/565nmY)x2 = 1.13 mm

T = 77.3 K

m0H

Dc = 4 T

col. pin.

ZeldovA-K

)ln(ln0

tJc

nn

Anderson-Kim

Collective pinning

mm

nn

/1

0

0

/1

00

lnln)(

UkTJ

tt

UkTJtJ cc

Zeldov

JJUU eff

*

0 ln

kTU

V effexp

kTU

kTU

JJCt

JJCt

JJ

kTUCtV

00***

0 .lnexp.lnexp.

ffbaJc 0lnln

00 lnlnln

ttbJJ

b

ttJJ

00

EXPERIMENTAL:

)1(

0

100

b

tttbJ

dtdJV

TkUb

TkUb

BB

tt

JJCt

tttbJ

00

00

*)1(

0

100 .

bTkU B

110

A.C. et al, SuST 22, 045014, 2009

5 6 7 8 9 10

103

104

105

3 T

4 T

LNO10/YBCO(1.6mm) YBCO(0.96mm)

J c (A/c

m2 )

ln(f0/f)

5 T

T = 77.3 K

4 5 6 7 8 9 10

102

103

104

105

5T

(15Pr/885nmY)x6=5.31mm(20Pr/565nmY)x2=1.13mm(15Pr/843nmY)x3=2.53mm

5T

4T

3T

J c (A/c

m2 )

ln (f0/f)

5T5T

ref. sampleYBCO 0.96 mm

T = 77.3 K

Sample U0(77.3 K, 3 T)

U0(77.3 K, 4 T)

U0(77.3 K, 5 T)

(20Pr/565nmY)x2 370.1 K 254.6 K 151.63 K

(15Pr/885nmY)x6 NA 295.05 K 181.06 K

(15Pr/843nmY)x3 433.5 K 310.1 K 215.8 K

YBCO 363.6 K 247.2 K 150.9 K

” is a measure of total dissipation: -linear: Thermal Activated Flux Flow (TAFF) and Flux Flow (FF)-nonlinear:Flux Creep3 is a measure on nonlinear dissipation (flux-creep) only[P. Fabricatore et al, PRB 50, 3189, 1994]

30 40 50 60 70

0.000

0.001

VGVL

T2 T1

3

"

",

3 (em

u/O

e)

Temperature (K)

Vortex melting line from ac susceptibility

2/122242

50

42

)sin(cos)()(

aa

abB

Lm Tk

cCTB

-two-fluid: ab(T)= ab(0)[1–(T/Tc)4]-1/2

-3D XY : ab(T)= ab(0)[1–T/Tc]-1/3

-mean-field: ab(T)= ab(0)[1–T/Tc]-1/2

C 1/42 , cL = 0.15, a=90

Examples

10 20 30 40 50 60 70 80 90 100 1100

5

10

Hg:1245, Tc = 107 K Hg:1245, T

c = 100 K

fit, = 48.3 fit, = 41.0

Bm (T

)T (K)

Two-fluid3D XY

[A. C. et al., 2003 Appl. Phys. Lett. 83 506] [A. C. et al., 2007 PRB 76 21258]

YBCO = 5.4Tl:1223=12.6

HgBa2Can-1CunOy (with n ≥ 6 )

n=9

HgBa2O2

913

14

986

89

10a

c -D(z)

Nh

O(1)2-

O(2)2-

Z

OP (SC)

IP (AF)(n-2)

OP (SC)

[A. C. et al., 2008 PRB 77 144518]

Magnetically-coupled pancake vortex moleculescomposed of two pancakes separated by thethin CRL, strongly coupled by Josephson coupling

Two-fluid (1245 and 1234)

Ba2Ca3Cu4O8(O1−yFy)2 [ F(2y)-0234]

• Ba2Can-1CunO2n+2 (n=3-5), F=0, samples are

optimally doped with Tc larger than 105 K, but

they are very unstable

• The system becomes stable after substitution of F

at the apical O site; underdoped states

• F(2.0)-0234 is not a Mott insulator, but a SC with

Tc=58 K

• Thin CRL (0.74 nm) as compared with other

multilayered cuprates

• Allow the investigation of underdoped region by

varying the F doping

• 2y = 1.3, 1.6, 2.0 (105, 86, 58 K)

[D. D. Shivagan,.., A.C., et al., SuST 24, 095002]

• Penetration depth: 3D XY critical fluctuations model

• F(1.3)-0234 near-optimally-doped, enough carriers in both OP

and IPs, 3D SC, strong Josephson coupling

• Penetration depth: mean-field model• F(1.6)-0234 under-doped; out of the region of critical

fluctuations; rearrangement of Fermi surfaces through hybridization between OP and IP bands; OP Fermi surface has a 2D character, IP Fermi surface has a 3D character

• Penetration depth: two-fluid model

• F(2.0)-0234 heavily under-doped; formal Cu valence is 2+, should be half-filled Mott insulator; evidence of self-doped thick IPs block, as compared with thin IP block of F(2.0)-0212 that shows 3D-2D cross-over

• Absence of 3D-2D cross-over is a manifestation of cooperative coupling in CRL and IPs