1. Transport Measurements in Superconductivity and DC Magnetization
Adrian Crisan
National Institute of Materials Physics, Bucharest, Romania

2. CONTENTS I. Transport measurements II. DC magnetization
III. DC magnetization relaxation

3. 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

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

5. Patterned sample with 4 wires connection on sample broad

6. Rotator part of the PPMS with transport option

7. Scheme of rotation measurement of YBCO bridge
Quantum Design SQUID MPMS
Q.D. PPMS looks rather similar

8. 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

9. 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, , 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]

10. Vortex melting from transport measurements
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 and 78.1 K, Tm=70.9 K; and
c) B=10.8 kG, T between and 75.4 K, Tm=68.1 K.
YBCO single-grain
[A. C. et al, Physica C 313, 70, 1999]
[A. C. et al, Physica C 355, 231, 2001]

11. 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, suggesting
that 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.

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

13. Angle dependence of critical current
(15Ag/1mm BZO-doped YBCO)x2

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

15. II. DC magnetization Jc=Ct.DM Depends strongly on sample geometry
thin films; m=DM/2;
d-thickness; a,b-rectangle dimension:

16. 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)

17. Fp=BxJc Bulk pinning force 2.33h1/2(1-h)2+1.5h(1-h)2+0.63h(1-h)
Surface normal (65%), point normal (22%), volume Dk (13%)
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%)

18. III. DC Magnetic relaxation
U(J, B,T) = (Uc/p)[(Jc/J)p  1] = Tln(t/t0)
Uc – characteristic pinning energy, J(t) m(t)
Jc is the creep-free critical current density
Vortex creep exponent, p
m(t) = m(t0)[1 + pTln(t/t0)/Uc]1/p
Elastic (collective) creep, EC, p = 1.5  2.5
Plastic creep, p < 0
Single creep, p = 1

19. Columnar tracks, heavy ion irradiation
0H ≤ B, the matching field
J-dependent vortex excitations in the presence of columnar defects (T < Tdp): half-loops (HL), double vortex kinks (DK), variable range vortex hopping (VRH) vortex-creep exponent p
HL  p = 1
VRH, p = 1/3
DK  p < 0
J(t, T)/Jc = [1 + pTln(t/t0)/Uc]1/p

20. YBCO films with nonsuperconducting nanorods
J. L. MacManus-Driscoll et al. Nature Mat.3, 439 (2004)
B. Maiorov et al., Nature Mat. 8, 398 (2009)
“thin”, below ~400 nm, small nanorod splay
P. Mele et al., SUST 21, (2008)
YBCO on STO or STO buffered MgO
4 wt% BZO (left) or BSO (right) nanorods
YBZ0.3
YBZNPYO0.4
P. Mele et al., SUST 21, (2008)
YBCO + 3 wt% BZO nanorods + 2 at% Y2O3 NP
YBZND1
P. Mikheenko et al., IEEE Trans. Appl. Supercond. 21,
3184 (2011), ~1100 nm YBCO with 4 wt% BZO
on Ag-nanodot decorated STO

21. Normalized magnetization relaxation rate and the normalized vortex-creep activation energy
(Uc/p){[m(t0)/m(t)]p  1} = Tln(t/t0)
Normalized magnetic relaxation rate S
S = dln(m)/dln(t)
S ~ T/[Uc + pTln(tw/t0)]
tw – relaxation time window
’Effective vortex-creep activation energy’
U* = T/S
U*(T) ~ Uc + pTln(tw/t0)
U*(J) = Uc(Jc/J)p
S = ln(m)/ln(t)

22. Standard DC magnetization relaxation results in the low-T range
S = T/[Uc + pTln(tw/t0)]
HL  VRH  EC
p = 1  1/3  1.5  2 1)
S(T) maximum at low T
Tdp ~ 0.5Tc 2)   3)
S(T) maximum around 30 K is generated
by thermomagnetic instabilities, TMI

23. DC magnetization relaxation results over an extended T range: Ta >Tdp is located at high T
BZ, BZ + Y2O3 NP, thick with BS, DK inhibition T. Haugan et al., Nature 430, 867 (2004)
U* = T/S, U*(J) = Uc(Jc/J)p
YBZ0.3, B ~ 2 T
30 K ÷ 45 K, HL, p ~ 1
45 K ÷ 62 K, DK, p ~ 0.07
62 K ÷ 77 K, VRH, p ~ 1/3
T > 77 K, SVC, p ~ 1
YBZNPYO0.4
S = T/[Uc + pTln(tw/t0)]
L. Miu, PRB (2012)

24. Inhibition of DK formation in thick YBCO films with
nonsuperconducting nanorods
U*(T)  Uc + pTln(tw/t0)]
U*(Tcr) = Uc
Uc ~ 2.5103 K
L. Miu et al., PRB 78,
(2008)
D. Miu et al., SUST 26,
(2013)
thin, YBZ0.3
thick + ND, YBZND1