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.     

Non-analytical angular dependence of the upper critical magnetic field in a quasi-one-dimensional superconductor

We have derived the so-called gap equation, which determines the upper critical magnetic field, perpendicular to conducting chains of a quasi-one-dimensional superconductor. By analyzing this equation at low temperatures, we have found that the calculated angular dependence of the upper critical magnetic field is qualitatively different than that in the so-called effective mass model. In particular, our theory predicts a non-analytical angular dependence of the upper critical magnetic field, H _c2(0) − H _c2(α) ∼ α^3/2, when magnetic field is close to some special crystallographic axis and makes an angle α with it. We discuss possible experiments on the superconductor (DMET)₂I₃ to discover this non-analytical dependence.     

Ginzburg-landau slopes of the anisotropic upper critical magnetic field and band parameters in the superconductor (TMTSF)<Subscript>2</Subscript>ClO<Subscript>4</Subscript>

We theoretically determine the Ginzburg-Landau slopes of the anisotropic upper critical magnetic field in a quasi-one-dimensional superconductor and correct the previous works on this issue. By using the experimentally measured values of the Ginzburg-Landau slopes in the superconductor (TMTSF)ClO₄, we determine band parameters of its electron spectrum. Our main result is that the so-called quantum dimensional crossover has to happen in this material in magnetic fields, H = 3–8 T, which are much lower than the previously assumed. We discuss how this fact influences metallic and superconducting properties of the (TMTSF)₂ClO₄.     

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.     

Dynamics of the magnetic flux component normal to the layers of Bi<Subscript>2</Subscript>Sr<Subscript>2</Subscript>CaCu<Subscript>2</Subscript>O<Subscript>8</Subscript> in a tilted field

High-frequency losses in the strongly anisotropic layered superconductor Bi₂Sr₂CaCu₂O₈ are measured at 600 MHz under a magnetic field rocking about the ab plane. Anomalies in losses and hysteretic phenomena are found while performing periodic rocking, i.e., cycling the magnetic field component normal to the sample surface. Based on these observations, conclusions are drawn about the nature of magnetic-flux penetration into the superconductor. It is found that, in the range between 60 K and T _c , the dynamics of magnetic-flux vortex lines normal to the ab plane in the presence of a constant magnetic field applied parallel to this plane is governed by the critical penetration field H _c ^⊥* and the surface barrier in the presence of thermally activated vortex motion (giant flux creep). The dependences of H _c1 ^⊥* and the characteristic field of the surface barrier on the magnitude of the parallel magnetic field are measured.     

Helical magnetic structure in a quasi-one-dimensional LiCu<Subscript>2</Subscript>O<Subscript>2</Subscript> multiferroic crystal according to <Superscript>63,65</Superscript>Cu NMR studies

The NMR spectra of ⁶³Cu and ⁶⁵Cu natural copper isotopes in a LiCu₂O₂ multiferroic single crystal compound have been measured above and below the temperature of magnetic phase transition (T _c = 23 K) in zero magnetic field and in applied magnetic field H ₀ = 94 kOe parallel to the c axis of the crystal. In LiCu₂O₂ below T _c, a complicated helical magnetic structure with the magnetic moment of copper ions Cu²⁺ varying along the chain according to the harmonic law with the wave vector being incommensurate to the crystal lattice constants has been revealed. The experimental results have been successfully interpreted using the model based on the planar helical magnetic structure. It has been found that the plane of rotation for Cu²⁺ magnetic moments in LiCu₂O₂ does not coincide at H ₀ = 0 with the ab plane. The high magnetic field (H ₀ = 94 kOe) applied along the c axis of the single crystal does not affect the spatial orientation of the plane of rotation.     

Surface critical magnetic field H<Subscript>c3</Subscript>(T) of a bulk superconductor MgB<Subscript>2</Subscript> using two-band Ginzburg-Landau theory

Two-band Ginzburg-Landau (TB G–L) equations for a bulk MgB₂ were solved analytically to determine the temperature dependence of surface critical magnetic fieldH _c3 (T). It is shown thatH _c3 (T) has the same temperature dependence with H_c2 (T), similar to the case of a single-band superconductor,H _c3 (T) = 166H _c2 (T). We use an elimination procedure for the decoupling of G–L equations of two-band superconductivity, which eases the calculations. It is expected that the temperature dependence forH _c3 (T) gives positive curvature nearT _c .     

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).     

Observation of multiple superconducting gaps in the infrared reflectivity spectra of Ba(Fe<Subscript>0.9</Subscript>Co<Subscript>0.1</Subscript>)<Subscript>2</Subscript>As<Subscript>2</Subscript>

The results of infrared reflectivity measurements for the iron-based high-temperature superconductor Ba(Fe_0.9Co_0.1)₂As₂ are reported. The reflectivity is found to be close to unity at frequencies ω lower than 2Δ/h (2Δ is the superconducting gap and h is Planck’s constant). This is evidence for the s ^+/− or s ^+/+ symmetry of the superconducting order parameter in the studied compound. The infrared reflectivity spectra of Ba(Fe_0.9Co_0.1)₂As₂ manifest opening of several superconducting gaps at temperatures lower than critical T _c .     

Anisotropy of the vortex structure and resistivity in the basal plane of YBa<Subscript>2</Subscript>Cu<Subscript>4</Subscript>O<Subscript>8</Subscript> single crystals

The vortex lattice of the YBa₂Cu₄O₈ high-temperature superconductor is studied in the basal plane of monocrystalline samples using the decoration technique in a field interval of 40–600 Oe. Vortex lattice anisotropy (field-independent “compression” of a regular hexagonal vortex cell in the poorly conducting direction by a factor of about 1.3) is detected. Resistivity anisotropy ρ _a /ρ _b measured at temperatures from T _c to room temperature is 16–9. Possible reasons for the discrepancy between our results and the available data are discussed.     

Physical properties,crystal and magnetic structure of layered Fe<Subscript>1.11</Subscript>Te<Subscript>1-</Subscript><Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Se<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> superconductors

The physical and structural properties of Fe_1.11Te and Fe_1.11Te_0.5Se_0.5 have been investigated by means of X-ray and neutron diffraction as well as physical property measurements. For the Fe_1.11Te compound, the structure distortion from a tetragonal to monoclinic phase takes place at 64 K accompanied with the onset of antiferromagnetic order upon cooling. The magnetic structure of the monoclinic phase was confirmed to be of antiferromagnetic configuration with a propagation vector k = (1/2, 0, 1/2) based on Rietveld refinement of neutron powder diffraction data. The structural/magnetic transitions are also clearly visible in magnetic, electronic and thermodynamic measurements. For superconducting Fe_1.11Te_0.5Se_0.5 compound, the superconducting transition with T _c = 13.4 K is observed in the resistivity and ac susceptibility measurements. The upper critical field H _c2 is obtained by measuring the resistivity under different magnetic fields. The Kim’s critical state model is adopted to analyze the temperature dependence of the ac susceptibility and the intergranular critical current density is calculated as a function of both field amplitude and temperature. Neutron diffraction results show that Fe_1.11Te_0.5Se_0.5 crystalizes in tetragonal structure at 300 K as in the parent compound Fe_1.11Te and no structural distortion is detected upon cooling to 2 K. However an anisotropic thermal expansion anomaly is observed around 100 K.     

Quantum oscillations of the resistivity and hall coefficient and the quantum limit in Bi<Subscript>0.93</Subscript>Sb<Subscript>0.07</Subscript> alloys in a magnetic field along the trigonal axis

The dependences of the electrical resistivity ρ and the Hall coefficient R on the magnetic field have been measured for single-crystal samples of the n-Bi_0.93Sb_0.07 semiconductor alloys with electron concentrations in the range 1 × 10¹⁶ cm⁻³ < n < 2 × 10¹⁸ cm⁻³. It has been found that the measured dependences exhibit Shubnikov-de Haas quantum oscillations. The magnetic fields corresponding to the maxima of the quantum oscillations of the electrical resistivity are in good agreement with the calculated values of the magnetic fields in which the Landau quantum level with the number N intersects the Fermi level. The quantum oscillations of the Hall coefficient with small numbers are characterized by a significant spin splitting. In a magnetic field directed along the trigonal axis, the quantum oscillations of the resistivity ρ and the Hall coefficient R are associated with electrons of the three-valley semiconductor and are in phase with the magnetic field. In the case of a magnetic field directed parallel to the binary axis, the quantum oscillations associated both with electrons of the secondary ellipsoids in weaker magnetic fields and with electrons of the main ellipsoid in strong magnetic fields (after the overflow of electrons from the secondary ellipsoids to the main ellipsoid) are also in phase. In magnetic fields of the quantum limit ħω _c /2 ≥ E _F, the electrical conductivity increases with an increase in the magnetic field: σ₂₂(H) ∼ H ^k . A theoretical evaluation of the exponent in this expression for a nonparabolic semiconductor leads to values of k close to the experimental values in the range 4 ≤ k ≤ 4.6, which were obtained for samples of the semiconductor alloys with different electron concentrations. A further increase in the magnetic field results in a decrease of the exponent k and in the transition to the inequality σ₂₂(H) ≤ σ₂₁(H).     

Normal-state electrical resistivity and superconducting magnetic penetration depth in Eu<Subscript>0.5</Subscript>K<Subscript>0.5</Subscript>Fe<Subscript>2</Subscript>As<Subscript>2</Subscript> polycrystals

We report measurements of the temperature dependence of the electrical resistivity, ρ(T), and magnetic pen-etration depth, λ(T), for polycrystalline samples of Eu_0.5K_0.5Fe₂As₂ with T _c = 31 K. ρ(T) follows a linear temperature dependence above T _c and bends over to a weaker temperature dependence around 150 K. The magnetic penetration depth, determined by radio frequency technique displays an unusual minimum around 4 K which is associated with short-range ordering of localized Eu³⁺ moments. The article is published in the original.     

Magnetic properties of ordered nanowires of the quasi-two-dimensional antiferromagnet SpFeMn(C<Subscript>2</Subscript>O<Subscript>4</Subscript>)<Subscript>3</Subscript>

Ordered arrays of nanowires of the photochromic antiferromagnet SpFeMn(C₂O₄)₃ (where Sp is 1-{(1′,3′,3′-trimethyl-6-nitro-5′-chlorospiro[2H-1-benzopyran-2,2′-indolin]-8-yl)methyl}pyridinium) have been fabricated in anodized aluminum oxide pores with diameters of 20 and 200 nm. It has been revealed that the growth of the spin-glass phase with noncollinear ordering of spins in nanowires is suppressed in favor of the uniaxial antiferromagnetic phase. A decrease in the nanowire diameter leads to an increase in the anisotropy of the magnetic resonance spectra. This is associated with the magnetocrystalline anisotropy that considerably exceeds the anisotropy of the nanowire shape.     

Dependence of the upper critical field on the defect concentration in MgB<Subscript>2</Subscript> and the electronic structure parameters

The upper critical field H _c 2 (H ‖ c) of the two-band superconductor MgB₂ is studied as a function of the residual resistivity ρ_n. It is found that the superconductor follows the standard trend: the slope-dH_c2/dT of the temperature dependence of H_c2(T) increases with the number of defects. The upper critical field in the clean limit is found, and direct estimations of the parameters of carriers in the 2D σ band (including the Fermi velocity and the coherence length) are made. The contribution of the electron scattering to the magnitude of H_c2 is determined, and the mean free path of electrons in samples with various defect concentrations is estimated. The density of states of σ electrons at the Fermi level is calculated using the dependence of the slope-dH_c2/dT on ρ_n and a band structure model. It is impossible to estimate this density of states directly, because the upper critical field is determined by the carriers of one band, whereas the resistivity depends on the carriers in both bands.     

Reluctance of the YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>x</Subscript> oxygen-deficient ceramics

Influence of an external magnetic field on the reluctance of the YBa ₂ Cu ₃ O _x ceramics is investigated. A significant reluctance of the oxygen-deficient ceramics (with critical temperature T_c < 77 K) is established for a sample in the normal state at T < 160 K. It is demonstrated that after ceramics annealing that restores the oxygen content to a nearly optimum value, the magnetic field has essentially no effect on the sample reluctance at temperatures exceeding T_c. To explain the revealed mechanisms, a model involving ferromagnetic clusters effectively decreasing the free carrier density is used. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 68–71, April, 2007.     

Physical property characterization of bulk MgB<Subscript>2</Subscript> superconductor

We report synthesis, structure/micro-structure, resistivity under magnetic field [ρ(T)H], Raman spectra, thermoelectric power S(T), thermal conductivity κ(T), and magnetization of ambient pressure argon annealed polycrystalline bulk samples of MgB₂, processed under identical conditions. The compound crystallizes in hexagonal structure with space group P6/mmm. Transmission electron microscopy (TEM) reveals electron micrographs showing various types of defect features along with the presence of 3–4 nm thick amorphous layers forming the grain boundaries of otherwise crystalline MgB₂. Raman spectra of the compound at room temperature exhibited characteristic phonon peak at 600 cm^-1. Superconductivity is observed at 37.2 K by magnetic susceptibility χ(T), resistivity ρ(T), thermoelectric power S(T), and thermal conductivity κ(T) measurements. The power law fitting of ρ(T) give rise to Debye temperature (Θ_D) at 1400 K which is found consistent with the theoretical fitting of S(T), exhibiting Θ _D of 1410 K and carrier density of 3.81 × 10²⁸/m³. Thermal conductivity κ(T) shows a jump at 38 K, i.e., at T_c, which was missing in some earlier reports. Critical current density (J_c) of up to 10⁵ A/cm² in 1–2 T (Tesla) fields at temperatures (T) of up to 10 K is seen from magnetization measurements. The irreversibility field, defined as the field related to merging of M(H) loops is found to be 78, 68 and 42 kOe at 4, 10 and 20 K respectively. The superconducting performance parameters viz. irreversibility field (H_irr) and critical current density J_c(H) of the studied MgB₂ are improved profoundly with addition of nano-SiC and nano-diamond. The physical property parameters measured for polycrystalline MgB₂ are compared with earlier reports and a consolidated insight of various physical properties is presented.     

Detection of vortex excitations in a Bi<Subscript>2</Subscript>Sr<Subscript>2</Subscript>Ca<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>10</Subscript> crystal at temperatures above the critical temperature by EPR of the surface layer

Vortex excitations have been detected at temperatures both below and above the critical temperature when investigating local magnetic fields on the surface of a Bi₂Sr₂Ca₂Cu₃O₁₀ single crystal by means of an electron paramagnetic resonance (EPR) probe. A thin layer of a diphenyl picrylhydrazyl organic radical deposited on the crystal surface is used as the EPR probe. A narrow EPR signal makes it possible to detect weak distortions of the magnetic field appearing at T ≿ T _c. The analysis of the temperature dependences of the resonance field and the EPR linewidth is thebasis of the assumption of the vortex nature of magnetic excitations in this temperature range.     

Magnetic state of the structural separated anion-deficient La<Subscript>0.70</Subscript>Sr<Subscript>0.30</Subscript>MnO<Subscript>2.85</Subscript> manganite

The results of neutron diffraction studies of the La_0.70Sr_0.30MnO_2.85 compound and its behavior in an external magnetic field are stated. It is established that in the 4–300 K temperature range, two structural perovskite phases coexist in the sample, which differ in symmetry (groups R[`3]cR\bar 3c and I4/mcm). The reason for the phase separation is the clustering of oxygen vacancies. The temperature (4–300 K) and field (0–140 kOe) dependences of the specific magnetic moment are measured. It is found that in zero external field, the magnetic state of La_0.70Sr_0.30MnO_2.85 is a cluster spin glass, which is the result of frustration of Mn³⁺-O-Mn³⁺ exchange interactions. An increase in external magnetic field up to 10 kOe leads to fragmentation of ferromagnetic clusters and then to an increase in the degree of polarization of local spins of manganese and the emergence of long-range ferromagnetic order. With increasing magnetic field up to 140 kOe, the magnetic ordering temperature reaches 160 K. The causes of the structural and magnetic phase separation of this composition and formation mechanism of its spin-glass magnetic state are analyzed.