Anisotropy of the superconducting properties of YBa2Cu3O7−x single crystals with reduced oxygen content

In an investigation of the resistivity anisotropy of YBa₂Cu₃O_7−x single crystals with suboptimal oxygen content it is observed that the superconducting transition for the component ρc of the resistivity tensor is shifted to lower temperatures with respect to the transition for the component ρab. A similar shift is also observed for the transition in the temperature dependence of the dynamic magnetic susceptibility. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 4, 309–313 (25 August 1998)     

Upper critical field <Emphasis Type="Italic">H</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis>2</Subscript> in anisotropic superconductors with varying charge carrier density: Application of the theory to doped MgB<Subscript>2</Subscript>

A theory describing the magnetic properties of a two-band superconductor with a varying charge carrier density is constructed. The upper critical field H _c2^(ab) parallel to the ab plane and field H _c2^(c) parallel to the c axis are determined in the entire temperature range 0 < T < T _c . A considerable increase in upper critical field H _c2^(ab) as compared to H _c2^(c) because of strong anisotropy of the system is detected. Anisotropy of coefficient γ _H = H _c2^(ab) / H _c2^(c) is obtained as a function of temperature for pure MgB₂ and as a function of the chemical potential in the case when Mg and B atoms are replaced with other chemical elements. A correlation between the variation in the superconducting transition temperature upon an increase in the chemical potential and critical magnetic fields H _c2^(ab) and H _c2^(c) is observed. The effect of doping on magnetic anisotropy is also determined.     

Dynamic magnetic permeability of a thin, high-T c superconducting wafer

The field dependence of the vibrational contribution to the dynamic magnetic permeability μ _V(H) is calculated for a thin (of thickness d∼λ) high-T _c superconducting wafer in a magnetic field parallel to the surface. The resulting curves are plotted on the basis of an exact numerical analysis of the vortex structures both for the thermodynamic-equilibrium vortex lattice and in the presence of pinning forces and the Bean-Livingston surface barrier. It is shown that the μ _V(H) curves are highly sensitive to the size factor (d/λ) and exhibit abrupt changes corresponding to a change in the number of vortex rows. The equilibrium μ _V(H) curve is found to be similar in its general behavior and absolute value (obtained with allowance for the distribution of grain sizes and with appropriate values of λ and ϰ) to the experimental μ _V(H) curve plotted at nitrogen temperature for fine-grained YBa₂Cu₃O_x with grain diameters 〈D〉∼λ in an increasing magnetic field. It is established that the main cause of the experimentally observed irreversible behavior of the μ _V(H) curves during cyclic variation of the applied magnetic field is the existence of a surface barrier to the exit of vortices from the superconductor. The lower limit H _min(B) of stability of the mixed state in the presence of an ideal surface barrier in a thin, high-T _c superconducting wafer (d∼λ) is determined, along with the range of the vortex state (H _max-H _min) for a fixed number of vortices in micrometer-size grains of the investigated YBaCuO samples. Fiz. Tverd. Tela (St. Petersburg) 39, 1943–1947 (November 1997)     

Colossal magnetodielectric effect in SmFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> multiferroic

The colossal (more than threefold) decrease in the dielectric constant ɛ in the easy-plane SmFe₃(BO₃)₄ ferroborate in a magnetic field of ∼5 kOe applied in the basal ab plane of the crystal has been found. A close relation of this effect to anomalies in the field dependence of the electric polarization has been established. It has been shown that this magnetodielectric effect is due to the contribution to ɛ from the electric susceptibility, which is related to the rotation of spins in the ab plane, arises in the region of the antiferromagnetic ordering T < T _N = 33 K, and is suppressed by the magnetic field. A theoretical model describing the main features of the behavior of ɛ and electric polarization in the magnetic field has been proposed, taking into account the additional anisotropy in the basal plane induced by the magnetoelastic stresses.     

Upper critical magnetic field in Ba0.68K0.32Fe2As2 and Ba(Fe0.93Co0.07)2As2

We report measurements of the temperature dependence of the radio frequency magnetic penetration depth in Ba_0.68K_0.32Fe₂As₂ and Ba(Fe_0.93Co_0.07)₂As₂ single crystals in pulsed magnetic fields up to 60 T. From our data, we construct an H-T-phase diagram for the inter-plane (H ‖ c) and in-plane (H ‖ ab) directions for both compounds. For both field orientations in Ba_0.68K_0.32Fe₂As₂ we find a concave curvature of the H _c2(T) lines with decreasing anisotropy and saturation towards lower temperature. Taking into account Pauli spin paramagnetism we can describe H _c2(T) and its anisotropy. In contrast, we find that Pauli paramagnetic pair breaking is not essential for Ba(Fe_0.93Co_0.07)₂As₂. For this electron-doped compound, the data support a H _c2(T) dependence that can be described by the Werthamer-Helfand-Hohenberg model for H ‖ ab and a two-gap behavior for H ‖ c.     

Magnetic anisotropy of an extended double exchange model for layered manganites: A Monte Carlo study

The magnetic ground state properties of layered manganites are investigated on the basis of an anisotropic double exchange model using a Monte Carlo technique. The temperature dependence of magnetization and spin-spin correlations are calculated in a highly anisotropic hopping integral t _c/t _ab regime. The ferromagnetic ordering temperature (T_c) is suppressed by introducing t _c/t _ab, and eventually a layered ferromagnetic structure appears along the c-axis, but there are block-walls. The significant change of magnetic anisotropy is also observed for the antiferromagnetic superexchange integral J _c/t _ab. We discuss the connection of these results to the magnetic anisotropy observed in the La_1.4Sr_1.6Mn₂O₇.     

Low-temperature resistivity of YBa2Cu3O6+x single crystals in the normal state

A scan of the superconductor-nonsuperconductor transformation in single crystals of YBa₂Cu₃O_6+x (x≈0.37) is done in two alternative ways, namely, by applying a magnetic field and by reducing the hole concentration through oxygen rearrangement. The in-plane normal-state resistivity ρ_ab obtained in the two cases is quite similar; its temperature dependence can be fitted by a logarithmic law in a temperature range of almost two decades. However, an alternative representation of the temperature dependence of σ_ab=1/ ρ _ab by a power law, typical for a 3D material near a metal-insulator transition, is also plausible. The vertical conductivity σ_c=1/ρ_c followed a power law, and neither σ_c(T), nor ρ_c(T) could be fitted by log T. It follows from the ρ_c measurements that the transformation at T=0 is split into two transitions: superconductor-normal-metal and normal-metal-insulator. In our samples, they are separated in oxygen content by Δx≈0.025. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 11, 834–839 (10 June 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Muonic study of type II superconductors

A theory of μSR method is developed for uniaxial anisotropic high-T _c superconductors. In two extreme cases ofH _ext‖c andH _ext⊥c analytical formulas are obtained which makes it possible to determine from the position of van Hove singularities in the Fourier-spectrum of muonium polarization, the type and parameters of the vortex lattice, such as λ _ab (λ _c ). In caseH _ext≲H _c2 we obtained the shape of the Fourier-spectrum in analytical form and the simple method of determining the Ginsburg-Landau parameter κ. Convenient expressions for numerical calculations are obtained for the arbitrary orientation of the external field, and an algorithm is provided to compute the mean fieldB, the vortex lattice parameters and the bulk field distribution in anisotropic superconductor. The Fourier spectrum of polarization based on these calculations can be used to independently check the validity of the high-T _c parameters determination for “appropriate” orientations.     

Anisotropy inc-axis oriented YBa2Cu3O7−δ

Muon spin relaxation (μSR) data taken at LAMPF on ac-axis oriented fine powder sample of YBa₂Cu₃O_7−δ (YBCO) embedded in epoxy are analyzed for relaxation rate anisotropy. Clear differences beyond simple magnetic field penetration depth anisotropy are observed forB‖c andB c. The low-temperature anisotropy ratio is consistent with oriented ceramic data. Small crystallite size and anisotropic flux pinning characteristics are suggested as the fundamental cause of the additional effects.     

Influence of magnetic field on the superconducting transition in a Nd1.82Ce0.18CuO4−δ film

The temperature and magnetic-field dependences of the resistivity ρ and Hall effect R(j‖ab, B‖c) in a Nd_1.82Ce_0.18CuO_4−δ single crystal film (T _c =6 K) is investigated at temperatures 1.4≤T≤20 K and magnetic fields 0≤B≤5.5 T. At the lowest temperature T=1.4 K the resistive state (exhibiting resistivity and the Hall effect) arises in a magnetic field B=0.5 T. A transition to the normal state is completed at B _c 2≃3 T, where the Hall coefficient becomes nearly constant. The negative magnetoresistance due to the weak-localization effect in the normal state is observed for B>3 T. The nonmonotonic behavior and the inversion of the sign of R(B) in the mixed state are explained in a reasonable way by the flux-flow model with the effect of pinning taken into account. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 6, 407–411 (25 September 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Temperature dependences of thermal expansion and exchange magnetostriction of holmium and dysprosium single crystals

Information on the character of the temperature relationships of linear expansion coefficients (α_a, α_c) and exchange magnetostrictions (λ_a, λ_a) of single crystal Ho and Dy, based on temperature dependence of thec- anda-axis lattice constants, were accurately determined by X-ray diffraction from 4,2 to 300 K. In the helical phases we observed a large anisotropy of expansion coefficients (α_a>0, α_c<0) and their variations at 24,5, 45 and 96 in Ho and 156 K in Dy. These anomalies were caused by the commensurate transitions. The Curie transition in Ho is found to be of the 1-st order.     

Resistive transition and upper critical field in underdoped YBa2Cu3O6+x single crystals

A superconducting transition in the temperature dependence of the ab-plane resistivity of underdoped YBa₂Cu₃O_6+x crystals in the range T _c≲30 K has been investigated. Unlike the case of samples with the optimal level of doping, the transition width increased insignificantly with magnetic field, and in the range T≲13 K it decreased with increasing magnetic field. The transition point T _c(B) was determined by analyzing the fluctuation conductivity. The curves of B _c2(T) measured in the region T/T _c≳0.1 did not show a tendency to saturation and had a positive second derivative everywhere, including the immediate neighborhood of T _c. The only difference among the curves of B _c2(T) for different crystal states is the scales of Tand B, so they can be described in terms of a universal function, which fairly closely follows Alexandrov’s model of boson superconductivity. Zh. éksp. Teor. Fiz. 115, 268–284 (January 1999)     

Magnetostriction and magnetization of the intermetallic compounds R Fe2 ? x Co x ( R = Tb, Dy, Er) with compensated magnetic anisotropy

The compounds Tb_0.35Dy_0.45Er_0.2Fe_{2 − x} Co _x (0 ≤ x ≤ 2) are synthesized in both polycrystalline and single-crystal states. The composition of the new multicomponent alloys with compensated magnetic anisotropy is calculated in the framework of the single-ion magnetic anisotropy model with allowance for the data on the temperature dependences of the magnetic anisotropy constants for RFe₂ single crystals. The synthesized compounds are characterized using metallographic, chemical, X-ray diffraction, and thermomagnetic methods. A combined analysis of the magnetic and magnetoelastic properties is also carried out. It is established that the high magnetostriction characteristics of the rare-earth intermetallic compounds Tb_0.35Dy_0.45Er_0.2Fe_{2 − x} Co _x with a structure of Laves phases are observed in the region of the spin-reorientational phase transition whose temperature can be varied by properly choosing the Co content. It is found that, in the room-temperature region, the magnetic susceptibility (dλ/dH) of the composition with x = 1.3 reaches levels in excess of the value of dλ/dH for terphenol D due to the compensation of magnetic anisotropy. Original Russian Text ? I.S. Tereshina, S.A. Nikitin, G.A. Politova, A.A. Opalenko, E.A. Tereshina, I.V. Telegina, 2009, published in Fizika Tverdogo Tela, 2009, Vol. 51, No. 1, pp. 85–90.     

Vortex dynamics in single crystal Hg-1201

Anisotropic superconducting materials often show an enhanced pinning along their crystallographic ab-planes. To obtain information about such a behavior of the high-T_c system Hg-1201 (HgBa₂CuO₄) magnetic investigations on a single crystal are performed for the two field orientations, parallel to the c-axis and parallel to the ab-planes. The dependence of the ac magnetization on temperature, magnetic field and frequency is determined. Compared to former results on powder samples of this system no indication of a second peak in the imaginary part of the susceptibility χ′′ is found. It seems to be shifted to higher temperatures overlapping now with the first peak. The corresponding irreversibility lines for both orientations, parallel to c and parallel to ab, are determined and discussed within the framework of a “diffusion” model.     

Magnetostriction of the spin-Peierls compound CuGeO3

The longitudinal and transverse magnetostriction λ of the spin-Peierls compound CuGeO₃ in the b-c plane is measured in magnetic fields up to 20 T both above and below the transition temperature T _sp=14.3K. It is found that for a given crystallographic direction the value of magnetostriction is weakly dependent on the magnetic field direction. In the uniform U phase at T⩾T _sp, λ is negative and approximately equal in the b and c directions, while in the dimerized D phase at T<T _sp, λ is positive and λ _b >λ _c . At low temperatures, λ increases sharply at the magnetic-field-induced transition from the dimerized to the magnetic M phase. The experimental data allow estimation of the stress derivatives of the antiferromagnetic intrachain exchange interaction parameter and of the stress dependence of the critical field of the D-Mphase transition. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 3, 156–159 (10 August 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Electron transport and anisotropy of the upper critical magnetic field in Ba<Subscript>0.68</Subscript>K<Subscript>0.32</Subscript>Fe<Subscript>2</Subscript>As<Subscript>2</Subscript> single crystals

Early work on the iron-arsenide compounds supported the view, that a reduced dimensionality might be a necessary prerequisite for high-T _c superconductivity. Later, however, it was found that the zero-temperature upper critical magnetic field, H _c2(0), for the 122 iron pnictides is in fact rather isotropic. Here, we report measurements of the temperature dependence of the electrical resistivity, ρ(T), in Ba_0.5K_0.5Fe₂As₂ and Ba_0.68K_0.32Fe₂As₂ single crystals in zero magnetic field and in Ba_0.68K_0.32Fe₂As₂ in static and pulsed magnetic fields up to 60 T. We find that the resistivity of both compounds in zero field is well described by an exponential term due to inter-sheet umklapp electron-phonon scattering between light electrons around the M point to heavy hole sheets at the Γ point in reciprocal space. From our data, we construct an H-T phase diagram for the inter-plane (H | c) and in-plane (H | ab) directions for Ba_0.68K_0.32Fe₂As₂. Contrary to published data for 122 underdoped FeAs compounds, we find that H _c2(T) is in fact anisotropic in optimally doped samples down to low temperatures. The anisotropy parameter, γ = H _c2 ^ab /H _c2 ^c , is about 2.2 at T _c . For both field orientations we find a concave curvature of the H _c2 lines with decreasing anisotropy and saturation towards lower temperature. Taking into account Pauli spin paramagnetism, we perfectly can describe H _c2 and its anisotropy.     

Magnetic and crystalline properties of GdxLa1−x FeSi compounds

The magnetic and crystalline properties of the polycrystalline compounds Gd_xLa_1−x FeSi (x=0, 0.1, 0.3, 0.45, 0.55, 0.65, 0.8, 1) and single crystal GdFeSi are studied. All the compounds have the CeFeSi tetragonal structure. The temperature dependences of the magnetization and initial susceptibility show that ferromagnetic behavior is characteristic of these compounds; the exception is the Pauli paramagnetic LaFeSi. Substitution of gadolinium by the nonmagnetic lanthanum leads to a sharp drop in the Curie temperature T _c, and to a reduction in the saturation magnetic moment μ ₀, effective magnetic moment μ _eff, and paramagnetic Curie temperature Θ_p. Measurements on single crystal GdFeSi imply that the easy magnetization axis of this compound is the c axis and the anisotropy field is H _a∼4 kOe. No magnetic moment was observed on the iron ion in any of these compounds. Fiz. Tverd. Tela (St. Petersburg) 39, 325–329 (February 1997)     

The magnetic field and energy of an Abrikosov vortex in an anisotropic London superconductor

The behavior of a straight Abrikosov vortex in an anisotropic uniaxial London superconductor is studied. Analytical expressions are derived that approximately describe the magnetic field in three regions: the asymptotic region, where the distance r from the vortex line is greater than λΓ (λ is the London length and Γ is the anisotropy constant), the intermediate region λ<r<λΓ, and the region r<λ. It is found that in the intermediate region with high anisotropy the component of the magnetic field along the vortex line changes sign for a certain interval of angles between the vortex line and the anisotropy axis. Because of this the interaction of parallel vortices whose plane is parallel to the anisotropy axis has a minimum and a maximum. This means that numerous metastable vortex lattices can exist. Additional terms in the vortex self-energy are obtained, and although they are smaller than the leading logarithmic term, they display a different dependence on the angle between the vortex line and the anisotropy axis. Zh. éksp. Teor. Fiz. 111, 954–963 (March 1997)     

Quantum Monte Carlo investigation of the 2D Heisenberg model with S=1/2

The two-dimensional (2D) Heisenberg model with anisotropic exchange (Δ = 1−J _x /J _z ) and S=1/2 is investigated by the quantum Monte Carlo method. The energy, susceptibility, specific heat, spin-spin correlation functions, and correlation radius are calculated. The sublattice magnetization (σ) and the Néel temperature of the anisotropic antiferromagnet are logarithmic functions of the exchange anisotropy: 1/σ+1+0.13(1)ln(1/Δ). Crossover of the static magnetic structural factor as a function of temperature from power-law to exponential occurs for T _c /J≈0.4. The correlation radius can be approximated by 1/ξ=2.05T ^1.0(6)/exp(1.0(4)/T). For La₂CuO₄ the sublattice magnetization is calculated as σ=0.45, the exchange is J=(1125–1305) K; for Er₂CuO₄ J∼625 K and the exchange anisotropy Δ∼0.003. The temperature dependence of the static structural magnetic factor and the correlation radius above the Néel temperature in these compounds can be explained by the formation of topological excitations (spinons). Fiz. Tverd. Tela (St. Petersburg) 41, 116–121 (January 1999)     

Pinning by twin boundaries and peak effect in YBaCuO high-T c superconductors

Measurements of the imaginary part of the ac magnetic susceptibility of single crystals and melt-textured samples of YBa₂Cu₃O_x (YBCO) at T=77 K in a magnetic field ranging between 1 and 20 kOe are reported. If the dc magnetic field H _dc is rotated in the ab plane of the sample, the magnetic susceptibility and critical current density j _c have peaks corresponding to the magnetic field aligned with twin boundaries. Peaks in the curve of j _c versus magnetic field are observed at angles corresponding to these peaks, where AH _dc in a wide range of magnetic fields. The results have been interpreted in terms of the theory describing twin boundaries as a system of quasi-planar pinning sites. The pinning is strong if the elastic displacements of flux lines are of the order of the vortex lattice constant d _f. These displacements decrease with the magnetic field because of the decrease in d _f, and the contribution of the elastic energy to the Gibbs potential is reduced accordingly, which is the cause of the peak effect. Zh. éksp. Teor. Fiz. 111, 2158–2174 (June 1997)