Penetration of a magnetic field into the YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7−δ</Subscript> high-temperature superconductor: Magnetoresistance in weak magnetic fields

The penetration of a magnetic field into superconducting grains and weak links of YBa₂Cu₃O_7?δ ceramic high-temperature superconductors is investigated using measurements of the transverse and longitudinal magnetoresistances at T=77.3 K and 0≤H≤～500 Oe as a function of the transport current in the range ～0.01≤I/I _c ≤～0.99. The effects associated with the complete penetration of Josephson vortices into weak links of the high-temperature superconductor in magnetic fields H_c2J, the onset of penetration of Abrikosov vortices into superconducting grains in magnetic fields H_c1A, and the first-order transition from the Bragg glass phase to the vortex glass phase in fields H_BG-VG are revealed and interpreted. The I-H phase diagrams YBa₂Cu₃O_7?δ high-temperature superconductors are constructed for I ⊥ H and I ‖ H.     

Magnetoresistance hysteresis in granular HTSCs as a manifestation of the magnetic flux trapped by superconducting grains in YBCO + CuO composites

Hysterestic behavior of the magnetoresistance of granular HTSCs and its interaction with the magnetic hysteresis are studied by measuring magnetoresistance R(H) and critical current I _c(H) of composites formed by HTSC Y_0.75Lu_0.25Ba₂Cu₃O₇ and CuO. A network of Josephson junctions is formed in such composites, in which the nonsuperconducting component plays the role of barriers between HTSC grains. Hysteretic dependences R(H) of magnetoresistance are studied in a wide range of transport current density j and are analyzed in the framework of the two-level model of a granular superconductor, in which dissipation takes place in the Josephson medium and the magnetic flux can be pinned both in grains and in the Josephson medium. The interrelation between the hysteresis of critical current I _c(H) and the evolution of the hysterestic dependence R(H) of the magnetoresistance upon transport current variation is demonstrated experimentally. The effect of the magnetic past history on the hysteretic behavior of R(H) and the emergence of a segment with a negative magnetoresistance are analyzed. It is shown for the first time that the R(H) dependences are characterized by a parameter that is independent of the transport current, viz., the width of the R(H) hysteresis loop.     

Pinning of vortices and penetration of the magnetic field into a periodically modulated long Josephson contact

The upper field of the Meissner regime, H _up, and overheat field H′_c1, above which vortices start penetrating into a Josephson contact, are calculated throughout the range of pinning parameter I. The stability of likely configurations is investigated. It is shown that H _up = H′_c1 at any I. The existence of a single vortex centered at the extreme cell in the contact is demonstrated to be a possibility. At I > 3.69, such a vortex may exist even in a zero magnetic field. At 1.48 < I < 3.69, this vortex can exist in an external field in the range from some H _v to H _up. At I < 1.48, the vortex cannot exist under any conditions. From the equality of H _up and H′_c1 at any I, the conclusion is drawn that penetration of vortices into any Josephson medium is conditioned by the need to satisfy flux quantization conditions. Here, not the forces of vortex pinning at defects in the medium but quantization requirements are of major importance, which are satisfied in specific quantum ways rather than by meeting equilibrium conditions for vortices, forces, etc.     

Magnetic field penetration into the weak-link system of the YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7−<Emphasis Type="Italic">x</Emphasis></Subscript> granular superconductor

The differential magnetic susceptibility χ_d(H) of YBa₂Cu₃O_7?x polycrystalline samples is studied experimentally in fields H<150 Oe. The empirical χ_d(H) dependence is determined. The results are explained on the basis of the critical-state model of a Josephson medium with hypervortices.     

Phase transitions and vortex structure evolution in two-level high-temperature granular superconductor YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7 – δ</Subscript> under temperature and magnetic field

Temperature dependences of the resistivity ρ(T) of samples of granular high-temperature superconductor YBa₂Cu₃O_{7 – δ} are measured at various transverse external magnetic fields at 0 < H _ext < 1900 Оe in the temperature range from the upper Josephson critical temperature of “weak bonds” T _c2J to temperatures slightly exceeding the superconducting transition temperature T _c . Based on the data obtained, the behavior of the field dependences of the critical temperatures of superconducting grains and “weak bonds,” and temperature and field dependences of the magnetic contribution to the resistivity \(\left[ {\Delta \rho \left( {T,H} \right) = \rho {{\left( T \right)}_{{H_{ext}} = const}} - \rho {{\left( T \right)}_{{H_{ext}} = 0}}} \right]\). It is shown that the behavior of the magnetic contribution to the resistivity Δρ along the line of the phase transition related to the onset of the magnetic field penetration in the form of Abrikosov vortices into the subsystem of superconducting grains T _c1g (H _ext) is anomalous. The concepts on the magnetic flux redistribution between both subsystems of two-level HTSC near in the vicinity of T _c1g : the Josephson vortex decreases, and the Abrikosov vortex density increases.     

Relaxation of the remanent resistance of granular HTSC Y-Ba-Cu-O + CuO composites after magnetic field treatment

The hysteresis of magnetoresistance R(H) and relaxation of the remanent resistance R _rem with time after magnetic field treatment of HTSC (Y-Ba-Cu-O) + CuO composites are studied. Such a composite constitutes a network of Josephson junctions wherein the nonsuperconducting component (CuO) forms Josephson barriers between HTSC grains. By comparing the experimental R _rem(t) and R(H) dependences, it is shown that the relaxation of the remanent resistance is caused by the decreased magnetic field in the intergrain medium due to relaxation of magnetization. The reason is uncovered for the differences between the published values of pinning potentials determined by measuring the relaxation of magnetization or resistance and fitting them by the Anderson law.     

Magnetoresistance of granular YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7 − δ</Subscript> HTSC in weak magnetic field: Angular dependence

The magnetoresistance of ceramic YBa₂Cu₃O_～6.5 HTSC samples is studied as a function of the mutual orientation of the current I and external magnetic field H _ext at T = 77.3 K in magnetic fields of up to ～500 Oe. It is found that, if the demagnetization factor D is taken into account, the effective critical field of complete penetration of Josephson vortices into weak links H _c2J ^eff does not depend on the mutual orientation of I and H _ext. The lower critical field H _c1A ^eff associated with the beginning of penetration of Abrikosov vortices into superconducting grains increases substantially with the angle between I and H _ext. The strongest variation with the mutual orientation of I and H _ext is exhibited by the critical field of the Bragg glass-vortex glass first-order phase transition H _BG-VG ^eff and by the magnetoresistance jump at this phase transition.     

Commensurability effects in a Josephson tunnel junction in the field of an array of magnetic particles

Commensurability effects have been theoretically studied in a hybrid system consisting of a Josephson junction located in a nonuniform field induced by an array of magnetic particles. A periodic phase-difference distribution in the junction that is caused by the formation of a regular lattice of Abrikosov vortices generated by the magnetic field of the particles in superconducting electrodes is calculated. The dependence of the critical current through the junction I _c on the applied magnetic field H is shown to differ strongly from the conventional Fraunhofer diffraction pattern because of the periodic modulation of the Josephson phase difference created by the vortices. More specifically, the I _c(H) pattern contains additional resonance peaks, whose positions and heights depend on the parameters and magnetic state of the particles in the array. These specific features of the I _c(H) dependence are observed when the period of the Josephson current modulation by the field of the magnetic particles and the characteristic scale of the change in the phase difference by the applied magnetic field are commensurable. The conditions that determine the positions of the commensurability peaks are obtained, and they are found to agree well with experimental results.     

Effect of magnetostriction on the transport current in granulated type-II superconductors

The effect of magnetostriction on the dependence of the critical current density on the magnetic field applied normally to the current in granulated superconductors is investigated. In sufficiently high magnetic fields (H ? H _c1), magnetostriction suppresses the current-carrying capacity of the material. It is shown that the effect of magnetostriction on the transport current is sensitive to variation of the effective parameters of the Josephson medium, specifically, the grain bond strength and ratio between the sizes of grains constituting the junction.     

Local approximation oscillatory differential method for the analysis of physical processes at the interface between vortex and Meissner regions in superconductors

A “differential” method for local diagnostics of superconductors has been developed. Regular steps with identical heights through certain intervals of an external field have been revealed on the magnetic-field dependences of the trapped magnetic flux density B _tr(H ₀) and the effective demagnetizing factor n _eff (H ₀) of bulk and film YBCO samples. It has been shown that the sample in high magnetic fields “decays” stepwise into subcrystallites and nanocrystallites whose size is much smaller than the depth of penetration of the magnetic field λ.     

Hysteresis of the magnetoresistance of granular HTSC YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7 − δ</Subscript> in weak fields

Hysteresis of the magnetoresistance of ceramic YBa₂Cu₃O_～6.95 HTSC samples is studied at T = 77.3 K in an external magnetic field H _ext changing in 0 → H _max → 0 cycles, where H _max is the maximum magnitude of H _ext. Information is obtained about the dependences of the critical fields of Josephson weak links H _c2J , the lower critical fields of superconducting grains H _c1A , and the critical fields H _BG-VG of the Bragg glass-vortex glass phase transition in the vortex matter on transport current I, magnetic field, and the mutual orientation of I and H _ext. It is found that the magnetoresistance δρ⁺/ρ_{273 K} measured with increasing H _ext is significantly higher than Δρ^?/ρ_{273 K} and that H _c2J ⁺ < H _c2J ^? , H _c1A ⁺ < H _c1A ^? , and H _BG-VG ⁺ < H _BG-VG ^? .     

Maximal supercurrent of a Josephson junction in a field of magnetic particles

The maximal supercurrent I_m of a short Josephson junction formed by an edge contact of two superconducting films is calculated for the case where the junction is placed in a periodic field produced by a chain of magnetic nanoparticles. The commensurability effects occurring when the magnetic flux of a homogeneous external field H₀ through an elementary cell is equal to an integral number of magnetic flux quanta Φ₀ are considered. The effects give rise to additional maxima in the I_m(H₀) dependence.     

Critical current of a textured granular superconductor in high magnetic fields

The critical current density J _c is studied theoretically using the cluster model of a granular superconducting structure for the case where Abrikosov vortices are present in the grains. It is found that the dependence of J _c on the effective ratio of the sizes of grains forming an intergrain Josephson junction is Gaussian. The dependence of J _c on the anisotropy of the penetration of a magnetic field into the grains is shown to reduce to the dependence on the coupling strength between the crystallites.     

Nonperturbative phenomena in QCD at finite temperature in a magnetic field

The norperturbative QCD vacuum at finite temperature in a external magnetic field is studied. Equations that relate nonperturbative QCD condensates at finite temperature to the thermodynamic pressure at T ≠ 0 and H ≠ 0 are obtained, and low-energy theorems are derived. The free energy of the QCD vacuum in the hadronic phase at H ≠ 0 is calculated, and expressions for the quark and gluon condensates are obtained. Various limiting cases for the behavior of the condensates at low and high temperatures and in weak and strong magnetic fields are investigated. A new interesting phenomenon that consists in the freezing of the quark condensate by a magnetic field is found. The character of spontaneous chiral-symmetry breaking in finite-temperature QCD in a magnetic field is studied. For this purpose, the Gell-Mann-Oakes-Renner formula relating the pion mass M _π and the axial-vector coupling constant F _π to the quark condensate is derived at T ≠ 0 and H ≠ 0. It is shown that this formula preserves its form at finite temperature after taking into account a magnetic field—that is, no additional terms independent of T and H appear. Thus, the scheme of soft chiral-symmetry breaking remains unchanged. The quark-hadron phase transition in QCD in a magnetic field is studied. It is shown that the phase-transition temperature becomes lower than that in the case of zero magnetic field.     

Anomalous transport properties of a paramagnetic NiTiO<Subscript>3</Subscript> + HTSC two-phase system representing a random Josephson junction network

Composites representing a network of random Josephson junctions and characterized by the compositions 92.5 at. % Y_3/4Lu_1/4Ba₂Cu₃O₇+7.5 at. % NiTiO₃ and 92.5 at. % Y_3/4Lu_1/4Ba₂Cu₃O₇+7.5 at.% MgTiO₃ are synthesized, and their magnetoresistance properties are studied. The temperature dependence of the resistance R(T) measured for the composite that contains the paramagnetic NiTiO₃ compound exhibits a characteristic feature below the superconducting transition temperature T_c of the high-T_c superconductor, namely, a region where R is independent of the current j and weakly depends on the magnetic field H. Below a certain temperature T_m, a strong dependence of R on j and H is observed, which is peculiar to a network of Josephson junctions. The dependences R(T, j, H) obtained for the “reference” samples with the nonmagnetic MgTiO3 compound exhibit no such features. The anomalous behavior of the HTSC + NiTiO3 composite is explained by the effect produced by the magnetic moments of Ni atoms in the insulating barriers on the transport current.     

Enhancement of superconductivity in disordered films by parallel magnetic field

We show that the superconducting transition temperature T _c (H) of a very thin highly disordered film with strong spin-orbital scattering can be increased by a parallel magnetic field H. This effect is due to the polarization of magnetic impurity spins, which reduces the full exchange scattering rate of electrons; the largest effect is predicted for spin-1/2 impurities. Moreover, for some range of magnetic impurity concentrations, the phenomenon of superconductivity induced by magnetic field is predicted: the superconducting transition temperature T _c (H) is found to be nonzero in the range of magnetic fields 0 < H* ≤ H ≤ H _c .     

Field dependence of the superconducting properties induced by proximity effects: Breakdown fields

It has been shown that the proximity-effect induced superconductivity in the normal partN of a superconductor-normal metal binary layer (such asIn Bi/Zn) can screen a magnetic field up to a critical fieldH _b. AtH _b, a sharp penetration of flux intoN occurs. However, the breakdown fieldH _b can only be observed for certain values of the thickness ofN and of temperature. We study here the domain of existence ofH _b as a function of these two parameters. We also show that studies onH _b yield some information on the properties of the pair potential inN. Thus measurements onH _b performed at the critical temperature ofN confirm the theoretical predictions concerning the remarkable behavior of the order parameter inN at this temperature.     

The possibility of the “giant” isotope effect for ultrasound absorption in crystals

The Zeeman effect, magnetization M(H), and differential magnetic susceptibility dM/dH of ErVO₄ crystals in a pulsed magnetic field have been experimentally and theoretically studied. In magnetic fields H ∥ [001] and H ∥ [100], the energy levels of Er³⁺ ions exhibit mutual approach and crossing (the crossover effect), which results in the peaks in dM/dH and the jumps in M(H) curves at low temperatures. The anomalies in the magnetic properties related to the crossover in ErVO₄ for H ∥ [001] are highly sensitive to the electronic structure of Er³⁺ ion, which allows this effect to be used for refining the crystal field parameters. The influence of the temperature, field misorientation from the symmetry axis, parameters of pair interactions, and other factors on the magnitude and character of magnetic anomalies in ErVO₄ crystals is considered.     

Critical magnetic field of the vortex-free state in NbC thin films and prospects for its observation in MgB<Subscript>2</Subscript>

The critical magnetic fields H _c‖ and H _c2 are measured for thin films of the isotropic superconductor NbC. It is revealed that the critical fields exhibit strong anisotropy due to the vortex-free state of the film in a magnetic field aligned parallel to its surface. The H _c‖/H _c2 ratio at 2 K exceeds 6 and increases with increasing temperature. The dependence H _c‖(T) agrees quantitatively with the concepts of microscopic theory on the vortex-free state of a thin film of a clean superconductor in the temperature range below T _c . As the electron mean free path decreases under irradiation of the film with a low dose of He⁺ ions, the critical field H _c‖ remains unchanged near T _c but increases significantly at lower temperatures. The well-known theoretical models are used to estimate the electronic parameters and thicknesses of MgB₂ films for which the specific features associated with the vortex-free state of the two-gap superconductor can manifest themselves in the temperature dependence of the critical magnetic field H _c‖(T).     

Current-phase relation of double-barrier Josephson junctions with a two-gap superconductor as intermediate electrode

The current-phase (I-?) relation of a double-barrier Josephson junction with a two-gap superconductor as intermediate electrode is derived by means of a simplified version of Ohta’s model. As in conventional double-barrier Josephson junctions, a marked skewness in the I-? curves is present. Moreover, as in heterotic Josephson devices, a reduction of the maximum Josephson current is predicted. An appropriate experiment to verify the rich behavior of this type of Josephson device is suggested.