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![Page 1: Types of measurements in superconductivity Adrian Crisan School of Metallurgy and Materials, University of Birmingham, UK and National Institute of Materials.](https://reader035.fdocuments.us/reader035/viewer/2022062515/56649c745503460f94927384/html5/thumbnails/1.jpg)
Types of measurements in superconductivity
Adrian CrisanSchool of Metallurgy and Materials, University of Birmingham, UK
and
National Institute of Materials Physics, Bucharest, Romania
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CONTENTS
• I. Transport measurements
• II. DC magnetization
• III. AC susceptibility
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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
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Karl Suss MJB3 Mask Aligner system An overview of 4 bridges after etching
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Patterned sample with 4 wires connection on sample broad
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Rotator part of the PPMS with transport option
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Quantum Design SQUID MPMSQ.D. PPMS looks rather similar
Scheme of rotation measurement of YBCO bridge
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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
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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]
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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]
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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.
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2)1(
/1/1 m
z
m TTT
IF
TTI
V
Fisher, Fisher, Huse scaling(PRB 43, 130, 1991)
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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
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Dependence of Ic on the field orientation for (Ag/(YBCO+BZO))x3, showing a small anisotropy for intermediate fields.
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II. DC magnetization
Jc=Ct.DM
Depends strongly on sample geometry
thin films; m=DM/2; d-thickness; a,b-rectangle dimension:
.)
31(
4
2
b
abda
mJ c
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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)
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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
Fp/F
pmax
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 0.98955
Value Standard Error
Book4_FFp A 2.33248 0.17315
Book4_FFp p1 0.5 0
Book4_FFp q1 2 0
Book4_FFp B 1.49827 0.59304
Book4_FFp p2 1 0
Book4_FFp q2 2 0
Book4_FFp C 0.63981 0.20869
Book4_FFp p3 1 0
Book4_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%)
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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]
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Critical current density as function of temperature, field, and frequency, using
AC susceptibility measurements
JC = h*/d a (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.
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4 5 6 7 8 9 10
104
105
exp. fit Zeldov fit A-K fit col. pin.
J c (
A/c
m2 )
ln (f0/f)
(20Pr/565nmY)x2 = 1.13 m
T = 77.3 K
0H
Dc = 4 T
col. pin.
Zeldov
A-K
)ln(ln0
tJ c
Anderson-Kim
Collective pinning
/1
0
0
/1
00
lnln)(
U
kTJ
t
t
U
kTJtJ cc
Zeldov
J
JUU eff
*
0 ln
kT
UV effexp
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kT
U
kT
U
J
JCt
J
JCt
J
J
kT
UCtV
00***
0 .lnexp.lnexp.
f
fbaJc
0lnln
00 lnlnln
t
tbJJ
b
t
tJJ
00
EXPERIMENTAL:
)1(
0
100
b
t
ttbJ
dt
dJV
Tk
Ub
Tk
Ub
BB
t
t
J
JCt
t
ttbJ
00
00
*)1(
0
100 .
bTkU B
110
A.C. et al, SuST 22, 045014, 2009
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5 6 7 8 9 10
103
104
105
3 T
4 T
LNO10/YBCO(1.6m) YBCO(0.96m)
J c (A
/cm
2 )
ln(f0/f)
5 T
T = 77.3 K
4 5 6 7 8 9 10
102
103
104
105
5T
(15Pr/885nmY)x6=5.31m(20Pr/565nmY)x2=1.13m(15Pr/843nmY)x3=2.53m
5T
4T
3T
J c (A
/cm
2 )
ln (f0/f)
5T5T
ref. sampleYBCO 0.96 m
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
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” 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
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2/122242
50
42
)sin(cos)()(
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, =90
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Examples
10 20 30 40 50 60 70 80 90 100 1100
5
10
Hg:1245, Tc = 107 K
Hg:1245, Tc = 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]
gYBCO = 5.4gTl:1223=12.6
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HgBa2Can-1CunOy (with n ≥ 6 )
n=9
HgBa2O2
9
13
14
986
89
10a
c -(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]
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Magnetically-coupled pancake vortex moleculescomposed of two pancakes separated by thethin CRL, strongly coupled by Josephson coupling
Two-fluid (1245 and 1234)
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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]
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• 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
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• 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
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• 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