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Types of measurements in superconductivity Adrian Crisan School 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 MPMS Q.D. PPMS looks rather similar Scheme of rotation measurement of YBCO bridge

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Resistivity vs. temperature: T c (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 H c2. Low enough currents -VL- linear dissipation: E ≈ J -VS (VGlass)- strongly nonlinear dissipation: E ≈ exp[-(J T /J) ]

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Vortex melting from transport measurements YBCO single-grain I-V curves of [(BaCuO 2 ) 2 /(CaCuO 2 ) 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, T m =72.8 K; b) B=4.4 kG, T between 55.85 and 78.1 K, T m =70.9 K; and c) B=10.8 kG, T between 49.75 and 75.4 K, T m =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 T m (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 T m (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 T m (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=T m ) ≈ 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 T m (B) and for low currents, the Ohmic region in the I–V curves, the linear resistance R l (T) can be scaled as: R l ≈ (T/T m -1) (z+2-d), where is the static critical exponent.

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

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Angle dependence of critical current (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 J c =Ct. M Depends strongly on sample geometry thin films; m= M/2; d-thickness; a,b- rectangle dimension:

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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 F p =BxJ c 3.15h 1/2 (1-h) 2 +0.57h(1-h) 2 +0.19h 3/2 (1-h) Surface normal (90%), point normal (8%), surface k (2%) 2.33h 1/2 (1-h) 2 +1.5h(1-h) 2 +0.63h(1-h) Surface normal (65%), point normal (22%), volume k (13%)

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III. AC susceptibility measurements fundamental and 3 rd harmonic Quantum Design PPMS - (T) at various H DC, h ac ( 15 Oe), f ( 10 kHz): T c (H) - ”(h ac ), 3 (h ac ) at various fixed T and H DC and varying f: J c (T,H DC, f), U eff (T,H DC ) T m 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 J C = h*/d (in A/cm 2 ) h * - position of maximum (in Oe) d – film thickness (in cm) coefficient slightly dependent on geometry (approx. 0.9) E.H. Brandt, Physical Review B 49/13 (1994) 9024.

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Anderson-Kim Collective pinning Zeldov

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

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SampleU 0 (77.3 K, 3 T) U 0 (77.3 K, 4 T) U 0 (77.3 K, 5 T) (20Pr/565nmY)x2370.1 K254.6 K151.63 K (15Pr/885nmY)x6NA295.05 K181.06 K (15Pr/843nmY)x3433.5 K310.1 K215.8 K YBCO363.6 K247.2 K150.9 K

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” is a measure of total dissipation: -linear: Thermal Activated Flux Flow (TAFF) and Flux Flow (FF) -nonlinear:Flux Creep 3 is a measure on nonlinear dissipation (flux-creep) only [P. Fabricatore et al, PRB 50, 3189, 1994] Vortex melting line from ac susceptibility

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- two-fluid: ab (T)= ab (0)[1–(T/T c ) 4 ] -1/2 -3D XY : ab (T)= ab (0)[1–T/T c ] -1/3 -mean-field: ab (T)= ab (0)[1–T/T c ] -1/2 C 1/4 2, c L = 0.15, =90

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Examples Two-fluid3D XY [A. C. et al., 2003 Appl. Phys. Lett. 83 506] [A. C. et al., 2007 PRB 76 21258] YBCO = 5.4 Tl:1223 =12.6

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HgBa 2 Ca n-1 Cu n O y (with n ≥ 6 ) n=9 HgBa 2 O 2 9 13 14 9 8 6 8 9 10 a c - (z) NhNh 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 molecules composed of two pancakes separated by the thin CRL, strongly coupled by Josephson coupling Two-fluid (1245 and 1234)

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Ba 2 Ca 3 Cu 4 O 8 (O 1−y F y ) 2 [ F(2y)-0234] Ba 2 Ca n-1 Cu n O 2n+2 (n=3-5), F=0, samples are optimally doped with T c 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 T c =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

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