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.     

Mechanism of the hysteretic behavior of the magnetoresistance of granular HTSCs: The universal nature of the width of the magnetoresistance hysteresis loop

The hysteretic behavior of the magnetoresistance R(H) of granular high-temperature superconductors (HTSCs) of the Y-Ba-Cu-O, Bi-Ca-Sr-Cu-O, and La-Sr-Cu-O classical systems is investigated for transport current densities lower and higher than the critical density (at H = 0). All systems exhibit universal behavior of the width of the magnetoresistance hysteresis loop: independence of transport current under identical external conditions. This means that flux trapping in HTSC grains is the main mechanism controlling the hysteretic behavior of the magnetoresistance of granular HTSCs, while pinning of Josephson vortices in the intragranular medium makes no appreciable contribution to the formation of magnetoresistance hysteresis (when transport current flows through the sample). Experimental data on relaxation of residual resistance after the action of a magnetic field also confirm this conclusion.     

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.     

The Langevin formula for describing the magnetization curve of a magnetic liquid

It has been shown that, at the initial stage of the magnetization curve, the magnetic susceptibility of magnetic liquid determined as χ = Mμ₀/B (M is the magnetization, B is the magnetic induction in a sample) obeys the Curie law, and the magnetic susceptibility determined as χ = M/H (H is the magnetic field intensity in a sample) obeys the Curie–Weiss law. Since the Curie law is a particular case of the Langevin dependence, it is assumed that an experimental magnetization curve is described by the Langevin formula with a Langevin parameter ξ = PB/kT, where P is the magnetic moment of a particle and T is the temperature. Experimental verification has shown that, at parameter ξ, the mean relative deviation between the values of M measured and calculated by the Langevin formula is 5%. This deviation can be accounted for by the influence of dispersion of the magnetic moments of nanoparticles.     

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.     

The effects of the composition,temperature and geometry on the hysteretic properties of the Ising-type barcode nanowire

In the present study, a theoretical approach to investigate the magnetic hysteresisproperties in barcode nanowire are used and applied to study Ising system on hexagonalstructure. The hysteresis behaviors of Ising-type barcode nanowire (IBN) are studiedwithin the effective-field theory with correlations. The effects of the composition(p),temperature (T) and geometry (interlayer length (d), shell length(s), andwire length (r)) on the hysteresis behaviors are examined indetail. The phase diagrams are presented in the five different planes, namely(p,T),(d,r),(d, T), (r, T) and (s, T) as function of coercive field (H _C ) and remanence(M _r ), and investigatedsoft/hard the magnetic characteristics of the system. We find that the hysteresis loopsareas decrease case as the temperature, wire and lengths increase. Moreover, whenp increasesthe hysteresis loop areas increase. Moreover, H _C exhibits an increasein around d =1 value, then H _C does not change withthe increasing d values. Theoretical results have qualitativelycompatible with some experimental works of multilayer nanowire.     

The Features of the Structural and Magnetic Characteristics of Low-Dimensional Thin-Film Systems Based on Cobalt and Copper

The results of investigation of the structural and magnetic characteristics of Co/Cu/Co thin-film systems obtained by magnetron sputtering on glass substrates are presented. The thickness of the cobalt layer in all samples was 5 nm and the thickness of the copper layer was varied from 0.5 to 4 nm. The saturation field H _S of the studied samples was found to oscillate in magnitude with changes in the copper-layer thickness with a period on the order of 1 nm. The maximum values of H _S are observed for the thin-film systems with t_Cu = 1.4, 2.2, and 3.2 nm. The hysteresis loops measured for these systems in a magnetic field applied along the easy magnetization axis of the samples have a two-stage shape, while for the samples with other values of tCu the hysteresis loops are rectangular. These data are explained by the presence of exchange coupling between the ferromagnetic layers through a copper spacer and its oscillating behavior with changing t_Cu.     

Magnetic properties of arrays of cobalt nanoparticles on the CaF<Subscript>2</Subscript>(110)/Si(001) surface

The Co/CaF₂/Si(001) heterostructures with the corrugated (110) surface of the CaF₂ buffer layer have been grown by molecular beam epitaxy. The structures are nanoparticle arrays of single-crystal Co, mostly of the cubic fcc modification. The behavior of the magnetic hysteresis loops as a function of the density of coverage of the substrate by cobalt islands, the island size, and the temperature is studied using the magnetooptical technique. At low coverage densities, where the effective cobalt film thickness d _eff is less than the critical value d _eff ^c , the magnetic structure of the films at T = 294 K can be visualized as an ensemble of superparamagnetic, weakly interacting nanoparticles and is characterized by small values of the coercive field H _c and the remanent magnetization M _rem. A decrease in the temperature leads to a strong increase in H _c and M _rem, which is associated with the transition of the islands to the blocked state. The blocking temperature of the structures is T _b ～ 280 K. The magnetic anisotropy parameter K and the saturation magnetization M _s of the islands depend on the growth temperature of cobalt T _Co. An increase in the coverage density above the critical thickness d _iff ^c at T = 294 K brings about a strong increase in H _c and M _rem and the appearance of a hysteresis loop anisotropy originating from the corrugated structure of the CaF₂ buffer layer. The experimental results are compared with the model of an ensemble of noninteracting superparamagnetic particles.     

On the possibility of determining the diffusion length of excitons in semiconductors from photomagnetic measurement data

The effect of a magnetic field on the photocurrent I_ph in Si and GaAs solar cells is investigated. It is shown that the observed change in the photocurrent I_ph of the solar cells in response to a magnetic field can be caused by a decrease in the diffusion length of excitons L_exc. A simplified model of the photomagnetic experiment is proposed to estimate the diffusion length of excitons L_exc and the contribution made by excitons to the photocurrent of the solar cells.     

Dependence of the coercive force on the magnetic field sweep rate in (PrDy)(FeCo)B alloys

The dependence between the coercive force and the average hysteresis loop record time was revealed in sintered (Pr_{1 – x} Dy _x )₁₃(Fe_{1 – y} Co _y )₇₉B₈ magnets. The coercive force was established to grow by 22% with an increase in the average hysteresis loop sweep rate within a range of 1.1 × 10²–3 × 10⁵ Oe/min, obeying a logarithmic dependence on the loop passage velocity with saturation at low rates. Some domain structure transformations produced by a magnetic field in the process of magnetization were established by magnetic force microscopy.     

Dependence of the magnitude and direction of the persistent current on the magnetic flux in superconducting rings

The obtained periodic magnetic-field dependences I _c+(Φ/Φ₀) and I _c?(Φ/Φ₀) of the critical current measured in opposite directions on asymmetric superconducting aluminum rings has made it possible to explain previously observed quantum oscillations of dc voltage as a result of alternating current rectification. It was found that a higher rectification efficiency of both single rings and ring systems is caused by hysteresis of the current-voltage characteristics. The asymmetry of current-voltage characteristics providing the rectification effect is due to the relative shifts of the magnetic dependences I _c?(Φ/Φ₀) = I _c+(Φ/Φ₀ + Δ?) of the critical current measured in opposite directions. This shift means that the position of I _c+(Φ/Φ₀) and I _c?(Φ/Φ₀) minima does not correspond to n + 0.5 magnetic flux Φ quanta, which is in direct contradiction to measured Little-Parks resistance oscillations. Despite this contradiction, the amplitude I _{c, an}(Φ/Φ₀) = I _c+(Φ/Φ₀) ? I _c?(Φ/Φ₀) of critical current anisotropy oscillations and its variations with temperature correspond to the expected amplitude of persistent current oscillations and its variations with temperature.     

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.     

Switching of spontaneous electric polarization in the DyMnO<Subscript>3</Subscript> multiferroic

For the DyMnO₃ multiferroic with a modulated magnetic structure, switching of its spontaneous electric polarization (P ‖ c axis) near the ferroelectric transition (T < T _FE ～ 20 K) is revealed by measuring the dielectric hysteresis loops. It is found that the coercive field strongly increases as the temperature decreases (up to 2.6 kV/mm at 17.6 K). The values obtained for the spontaneous polarization are found to agree well with the data obtained from pyroelectric measurements. In addition, anomalies are observed in the temperature dependences of the spontaneous polarization P _c , dielectric constant ? _c , and magnetic susceptibility x _b at T ～ 6 K; these anomalies are attributed to the antiferromagnetic ordering of the Dy³⁺ ions.     

Effect of nonuniform mechanical stresses on the domain structure of iron borate

A magnetooptic method is used to study the effect of nonuniform radial mechanical stresses on the domain structure, magnetic susceptibility, and magnetic hysteresis loops of a FeBO₃ single crystal. When a magnetic field is applied in the basal plane of FeBO₃ along the stress vector, a system of tapered domains appears in the crystal during magnetization. These domains exist in a certain temperature-dependent field range H₀ ≤ H ≤ H _c . The appearance of a system of tapered domains is found to substantially affect the technical magnetization of a stressed crystal. The results obtained are discussed within the thermodynamic theory of a domain structure. A theoretical model used is shown to adequately describe the experimental temperature and field dependences of the ratio \({D \mathord{\left/ {\vphantom {D {\sqrt L }}} \right. \kern-\nulldelimiterspace} {\sqrt L }}\) (where D and L are the average width and length of a tapered domain, respectively). The calculated value of D is approximately 1.3 times smaller than the experimentally observed domain width.     

Nonlinear Hall effect in a quasi-two-dimensional electron system

The nonlinear electron transport in GaAs double quantum wells with two occupied size-quantization levels has been studied at a temperature of 4.2 K in the magnetic fields B < 1 T. It has been found that a sinusoidal electric current I _ac induces the generation of higher harmonics of both longitudinal V _xx (B) and Hall V _xy (B) voltages in the quasi-two-dimensional electron system under consideration. The Hall voltage oscillating in the magnetic field has been shown to appear in the electron system with two occupied size-quantization levels in the presence of microwave radiation and dc electric current I _dc. The experimental data indicate the independent contributions of the diagonal and off-diagonal components of the conductivity tensor to the nonlinear magnetotransport at high filling factors.     

Various Quantum Correlations in Two-Qubit Two-Axis Spin Squeezing Model in Thermal Equilibrium under an External Magnetic Field

This paper investigates the influence of the spin squeezing parameter γ, the external magnetic field B and the temperature T on the concurrence (C), the quantum discord (QD), and the geometric quantum discord (GQD) in the two-qubit two-axis spin squeezing model in thermal equilibrium under an external magnetic field. The results show that the spin squeezing parameter γ has a positive effect on all three correlations. When the system is in the ground state, the external magnetic field B has a weakening effect on the three types of quantum correlations. Particularly, the spin squeezing parameter can be used to alleviate the destructive effect of the magnetic field on the geometric quantum discord. At a relatively high temperature, the externally applied magnetic field B helps enhance the quantum discord (QD). Further, the quantum discord is more robust than concurrence, and thus is more suitable for use as a quantum resource in information processing.     

Finite size and surface effects on the magnetic properties of cobalt ferrite nanoparticles

Cobalt ferrite, CoFe₂O₄, nanoparticles in the size range 2–15 nm have been prepared using a non-aqueous solvothermal method. The magnetic studies indicate a superparamagnetic behavior, showing an increase in the blocking temperatures (ranging from 215 to more than 340 K) with the particle size, D _TEM. Fitting M versus H isotherms to the saturation approach law, the anisotropy constant, K, and the saturation magnetization, M _S, are obtained. For all the samples, it is observed that decreasing the temperature gives rise to an increase in both magnetic properties. These increases are enhanced at low temperatures (below ~160 K) and they are related to surface effects (disordered magnetic moments at the surface). The fit of the saturation magnetization to the T ² law gives larger values of the Bloch constant than expected for the bulk, increasing with decreasing the particle size (larger specific surface area). The saturation magnetization shows a linear dependence with the reciprocal particle size, 1/D _TEM, and a thickness of 3.7 to 5.1 Å was obtained for the non-magnetic or disordered layer at the surface using the dead layer theory. The hysteresis loops show a complex behavior at low temperatures (T ≤ 160 K), observing a large hysteresis at magnetic fields H > ~1000 Oe compared to smaller ones (H ≤ ~1000 Oe). From the temperature dependence of the ac magnetic susceptibility, it can be concluded that the nanoparticles are in magnetic interaction with large values of the interaction parameter T ₀, as deduced by assuming a Vogel–Fulcher dependence of the superparamagnetic relaxation time. Another evidence of the presence of magnetic interactions is the almost nearly constant value below certain temperatures, lower than the blocking temperature T _b, observed in the FC magnetization curves.     

Nonlinear magnetotransport in a high-mobility quasi-two-dimensional electron system

The influence of a dc electric current I _dc on the low-temperature magnetotransport of high-mobility electrons in a GaAs double quantum well with two occupied size-quantization levels has been studied. The oscillations of the resistance ρ _xx , which are periodic in the inverse magnetic field, have been shown to appear in the quasitwo-dimensional system under consideration at a temperature of T = 4.2 K in magnetic fields B > 0.1 T; the oscillations are caused by isoenergetic resonance transitions of the electrons between the Landau levels of different subbands. The inversion of the oscillations with an increase in I _dc has been discovered. It has been found that the observed effect is due to the electron transport in a nonlinear regime.     

Self-similar distribution in “giant” magnetic flux creep

The problem of magnetic field penetration into the half-space is considered in parallel geometry in an external magnetic field increasing with time in accordance with the law B(0, t, τ₀ = B _{c 1} (1 + t/τ₀) ^m , m ≥ 0, t ≥ 0 (τ ₀ is the time of magnetic flux redistribution and B _{c 1} is the lower critical field). It is assumed that the flow of vortices is thermally activated in the “giant” creep mode (i.e., for weak pinning creep and high temperatures). A model equation is derived for describing the magnetic flux evolution. Analytic formulas are obtained for the depth and velocity of magnetic field penetration. It is shown that the giant creep regime is stable for 0 ≤ m ≤ 1/2.     

Enhancement of the intrinsic pinning by a magnetic field in a single crystal of high-temperature superconductor TmBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript><Emphasis Type="Italic">y</Emphasis></Subscript>

This paper presents a comparative study of the complex permeability μ* of single crystals of hightemperature superconductors RBa₂Cu₃Oy (R = Y, Tm) as a function of the magnetic field applied along the crystallographic ab-plane. Contributions to μ* from the oscillatory motion of vortices perpendicular to layers of the crystal lattice, μ_v, and realization of the critical state along the layers are obtained. It is found that, as the temperature approaches T _c, the behavior of the field dependences of μ_v and the critical current is substantially different for the given samples. This effect is related to the manifestation of an additional unusual mechanism of intrinsic pinning, which arises when Y₃₊ is replaced with the Tm³⁺ magnetic ion. The revealed specificities of the interaction of vortices with the magnetic ion layer suggest that, most probably, they have a magnetic nature and are not related to the variation in the condensation energy in the core of the vortex.