Theoretical Study of Specific Heat, Density of States and Free Energy of Itinerant Ferromagnetic Superconductor URhGe

Following the equation of motion method and Green’s function technique, the coexistence of itinerant ferromagnetism (FM) and superconductivity (SC) is investigated in a single band homogeneous system. Self-consistent equations for superconducting order parameter (Δ) and magnetic order parameter (Δ_FM) are derived. It is shown that there generally exists a coexistent (Δ≠0 and Δ_FM≠0) solutions to the coupled equations of the order parameter in the temperature range 0<T<min (T _C,T _FM) where T _C and T _FM are respectively the superconducting and ferromagnetic transition temperatures. Expressions for the specific heat, density of states and free energy are derived. The specific heat has a linear temperature dependence at low temperatures as opposed to the exponential decrease in the BCS theory. The density of states for a finite Δ_FM increases as opposed to that of a standard ferromagnetic metal. The free energy shows that the superconducting ferromagnetic state has lower energy than the normal ferromagnetic state and therefore is realized at low enough temperature. The theory is applied to explain the observations of URhGe. The agreement between theory and experimental results is quite satisfactory.      

Point-Contact Spectroscopy of the Borocarbide Superconductor YNi2B2C in the Normal and Superconducting State

Point-contact (PC) spectroscopy measurements of YNi₂B₂C single crystals in the normal and superconducting (SC) state (T _c ≃ 15.4 K) for the main crystallographic directions are reported. The PC study reveals the electron–phonon interaction (EPI) spectral function with dominant phonon maximum around 12 meV and further weak structures (hump or kink) at higher energy at about 50 meV. No “soft” modes below 12 meV are resolved in the normal state. The PC EPI spectra are qualitatively similar for the different directions. Contrary, directional study of the SC gap results in Δ_{[100] ≈ 1.5 meV for the a direction and Δ_{[001] ≈ 2.3 meV along the c axis; however the critical temperature T _c in PC in all cases is near to that in the bulk sample. The value 2Δ_[001]/k _B T _c ≈ 3.6 is close to the BCS value of 3.52, and the temperature dependence Δ_[001](T) is BCS-like, while the for small gap Δ_[100](T) is below BCS behavior at T > T _c /2 similarly as in the two-gap superconductor MgB₂. It is supposed that the directional variation Δ can be attributed to a multiband nature of the SC state in YNi₂B₂C.     

Quench-condensed indium-hydrogen films. II. Changes in electric and superconducting characteristics near the metal-insulator transition

Electrical and superconducting properties of indium films condensed in a H₂ atmosphere (pressurep _{H 2}=6×10⁻⁶ to 1.4×10⁻⁴ Torr) onto a substrate cooled with liquid helium are investigated. As hydrogen content is increased, a continuous increase in residual resistivity ρ* is observed, permitting systematic study of the resistance vs. temperature dependenceR(T) and the superconducting transition temperatureT _c on approaching the metal-insulator transition (MIT). With regard to ρ*, four regimes of conductivity can be observed: (1) conductivity with a positive temperature resistance coefficient (TRC), (2) conductivity with a small, constant, negative TRC, (3) conductivity under weak localization with ΔR (T) ∼ln T or type corrections, (4) hopping conductivity.T _c rises continuously with ρ* and reaches its peak (∼5.2K) in the second regime. A further increase of ρ* leads to a decrease ofT _c and complete suppression of superconductivity. The experimental dependenceR(T) is compared with theory. TheT _c variation on approaching the MIT and the relation between Mooij's rule and the superconducting properties are discussed.     

Role of Coexistence of Superconductivity and Paramagnetism in Magnetostriction of High-T c Superconductors

Total magnetostriction in the superconducting state for high T _c superconductors has been separated into critical state and paramagnetic components in terms of a H(x) dependent magnetic flux density. We show that the paramagnetic part is χ(2+χ)〈H(x)²〉, where χ is paramagnetic susceptibility. We have reproduced successfully ΔL/L−H _a curves measured by de la Fuente et al. (Phys. C 244:214, [1995]), in which they clearly observed coexistence of superconductivity and paramagnetism, employing the concepts presented in this work.      

Thermal and magnetic measurements on YBa2Cu3O7−y

Specific heat measurements in zero and7T magnetic fields from 0·4 to 100 K, and magnetic susceptibility measurements aboveT _c on a series of polycrystalline samples of YBa₂Cu₃O_7−y (YBCO) reveal a number of regularities. The size of ΔC(T _c )/T _c for the samples [ΔC(T _c ) is the jump in the specific heat atT _c ] appears to vary linearly with the low-temperature value of the Debye Θ, with the entropy change between ≈ 85 K andT _c induced by the application of a 7 ^Г magnetic field, and with the variation of the observed low temperatureγ with magnetic field, dγ/dH. On the other hand the temperature-independent part of the magnetic susceptibility aboveT _c appears to be essentially independent of ΔC(T _c )/T _c . These results are consistent with the idea that samples of YBCO belowT _c are a mixture of superconducting and normal phases. Supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Materials Sciences Division of the U.S. Dept. of Energy under Contract DE-AC03-76SF00098, and by an EXXON Education Grant from the Research Corporation.     

The Upper Critical Field <Emphasis Type="Italic">H</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis>2</Subscript> in Advanced Superconductors with Anisotropic Energy Spectrum

A brief review of works on the microscopic theory of determining the upper critical field in two-band isotropic and anisotropic superconductors is given. The research is based on a set of the Ginzburg–Landau equations for the order parameters in a magnetic field that are studied in terms of the classical approach to a superconducting system in a magnetic field. Two inequivalent energy bands with different topology of Fermi surface cavities overlapping on the Fermi surface are discussed. The cases of the direction of the external magnetic field [(H)\vec]//\vec{H}// the (ab) plane and [(H)\vec]//\vec{H}// the crystallographic c axis are studied. The equations for determining H _c2(ab) and H _c2(c) for a pure superconductor and a superconductor doped with electrons and holes are derived. The analytical solutions to these equations in the vicinity of the superconducting transition temperature (T _c −T≪T _c ) and in the vicinity of zero (T≪T _c ) are found. The temperature and impurity dependences of the upper critical fields H _c2(ab) and H _c2(c), as well as the anisotropy coefficient γ _H, are studied. The resulting theory is applied to determine the dependences of the above magnetic characteristics of intermetallic compound MgB₂. The theory agrees qualitatively with experimental data.     

The Transport Properties of Li(1+x)Ti2O4 in High Magnetic Field

The spinel oxide superconductor LiTi₂O₄ shows intricate transport properties in both normal state and superconducting state. The Hall effect measurements exhibit an abrupt change in carrier density near T=170 K where the temperature derivative of resistivity changes sign from negative to positive on cooling. In addition, the sample shows significant positive magnetoresistance below 40 K, e.g., R(H)/R(H=0)3% at T=14 K and H=16 T. A most interesting feature is the magnetic field effect on the resistivity near the superconducting state. In addition to the field-induced broadening of R(T), there exhibits an anomalous upturn in R(T) near the superconducting regime when magnetic field is above 3T. The temperature T ₁ at which R(T) shows upturn linearly correlates with magnetic field H and can be expressed as T ₁/T _C(H=0)=1–0.04H for 3T<H<12T. The superconductivity is completely suppressed at field above 14T and the low temperature resistance behaves semiconductor-like.     

Thermodynamic properties of NaZr2(PO4)3

The heat capacity of crystalline NaZr₂(PO₄)₃ was measured between 7 and 340 K by adiabatic calorimetry. The results were used to calculate the thermodynamic functionsC _p ⁰ ,H ⁰(T) -H ⁰(0),S ⁰(T), andG ⁰(T) -H ⁰(0) in the range 0-340 K. The absolute entropy was found to be S⁰NaZr₂(PO₄)₃, cr, 298.15 K) = 327.1 ±1.0 J/(mol K), and the standard entropy of formation Δ_fS⁰(NaZr₂(PO₄)₃, cr, 298.15 K) = -1101±1 J/(mol K). Solution calorimetry was used to determine the standard enthalpy of formation, Δ_f H ⁰(NaZr₂(PO₄)₃, cr, 298.15 K) = -5236 ±5 kJ/mol. By combining the data obtained by the two techniques, the standard Gibbs energy of formation was determined to be Δ_fG⁰(NaZr₂(PO₄)₃, cr, 298.15 K) = -4908 ±5 kJ/mol.     

Interplay of Superconductivity and Ferromagnetism in UGe<Subscript>2</Subscript>

The emergence of pressure induced superconductivity (SC) under the background of ferromagnetic state in 5f-electron based itinerant ferromagnetic superconductor UGe₂ is studied in the single band model by using a mean-field approximation. The solutions to the coupled equations of superconducting gap (Δ) and magnetization (m) are obtained using Green’s function technique and equation of motion method. It is shown that there generally exists a coexistent (Δ≠0, m≠0) solution to the coupled equations of the order parameters in the temperature range 0<T<min (T _C,T _FM), where T _C and T _FM are respectively the superconducting and ferromagnetic transition temperatures. The study of electronic specific heat (C/T), density of states, free energy, etc. are also presented. The specific heat capacity at low temperature shows linear temperature dependence as opposed to the activated behavior. Density of states increases as opposed to the case of a standard ferromagnetic metal. Free energy study reveals that the superconducting ferromagnetic state has lower energy than the normal ferromagnetic state and, therefore, realized at low enough temperature. The agreement between theory and experimental results for UGe₂ is quite satisfactory.      

Occurrence of Superconductivity and Magnetism in Nominally Undoped LaOFeAs

Superconductivity in a LaOFeAs system is known to get introduced by F-doping (LaO_1−x F _x FeAs) even under ambient conditions and oxygen deficiency (LaO_1−x FeAs) under high pressure conditions. Hitherto unreported, superconductivity in F-free undoped LaOFeAs samples is observed and confirmed for the first time by various characterization tools–resistive ρ(T,B), magnetic M(T,B) and modulated microwave absorption (MMA) measurements. The ρ(T) at B=0 shows a clear superconducting transition with an onset at T _con∼17 K and a tail-like behavior when R goes to zero at T _c0∼8 K. In the presence of B, the superconducting transition shifts to lower T with a rate ∼−5.5 and −1.65 T/K, depending on whether the ρ(T) has dropped to 90% or 5% of its normal state value, respectively. M(T) in zero field cooling at B=10 mT shows diamagnetic downturn below at ∼12 K. At T<T _c0 the change in MMA with B shows a low field (B∼1 mT) peak, which vanishes at T>T _c0, indicating the presence of weak link superconducting networks in the sample. The sample shows a complex electrical and magnetic behavior in the normal state. For instance, ρ(T) reveals a weak SDW-like anomaly at T∼132 K along with a resistivity minimum at T _min∼78 K. M(T) also shows the presence of a magnetic anomaly at T∼130 K. Both below and above T _con, presence of an additional ferromagnetic component is observed in the isothermal M(B) loop measurements. The superconducting and normal state features of our sample are compared with other undoped and doped LaOFeAs systems reported in the literature.     

Thermodynamic properties of NaZr<Subscript>2</Subscript>(AsO<Subscript>4</Subscript>)<Subscript>3</Subscript>

The heat capacity C _p ⁰ of crystalline NaZr₂(AsO₄)₃ has been measured in the range 7–650 K using precision adiabatic calorimetry and differential scanning calorimetry. The experimental data have been used to calculate the standard thermodynamic functions of the arsenate: C _p ⁰, enthalpy H ⁰(T) − H ⁰(0), entropy S ⁰(T), and Gibbs function G ⁰(T) − H ⁰(0) from T → 0 to 650 K. The standard entropy of its formation from elements is Δ_f S ⁰(NaZr₂(AsO₄)₃, cr, 298.15 K) = −1087 ± 1 J/(mol K).     

Scaling of the Temperature Dependent Resistivity and Hall Effect in Ba(Fe<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Co<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>)As<Subscript>2</Subscript>

We show that the temperature-dependent resistivity ρ(T), Hall number n _H(T) and the cotangent of the Hall angle cot θ _H(T) of Ba(Fe_1−x Co _x )As₂ (x=0.0–0.2) can be scaled using a recently proposed model-independent scaling method (Luo et al. in Phys. Rev. B 77:014529, 2008). The zero field normal-state resistivity above T _c can be reproduced by the expresion r(T) = r₀ +cTexp(- \frac2\varDelta T )\rho(T) = \rho_{0} +cT\exp(- \frac{2\varDelta }{T} ) and scaled using the energy scale Δ, c and the residual resistivity ρ ₀ as scaling parameters. The scaling parameters have been calculated and the compositional variation of 2Δ and ρ ₀ has been determined. The 2Δ(x) dependence show almost linear decreasing in underdoped regime, minimum corresponding to the T _c maximum and increasing in overdoped regime. The latter is different from that reported for cuprates. The existence of a universal metallic ρ(T) curve which, however, is restricted for the underdoped compounds to temperatures above a structural and antiferromagnetic transition is interpreted as an indication of a single mechanism which dominates the scattering of the charge carriers in Ba(Fe_1−x Co _x )As₂ (x=0.0–0.2).     

Revised heat capacity and thermodynamic functions of GdVO<Subscript>4</Subscript>

The heat capacity of GdVO₄ has been determined by adiabatic calorimetry in the range 5–345 K. The present experimental data and earlier results have been used to evaluate the thermodynamic functions of gadolinium orthovanadate (C _p ⁰(T), S ⁰(T), H ⁰(T) − H ⁰(0), and Φ⁰(T)) as functions of temperature (5–350 K). Its Gibbs energy of formation is determined to be Δ_f G ⁰(GdVO₄, 298.15 K) = −1684.5 ± 1.6 kJ/mol.     

Thermodynamics of the Superconducting State in Calcium at 200 GPa

The thermodynamic parameters of the superconducting state in Calcium under the pressure at 200 GPa were calculated. The Coulomb pseudopotential values (μ ^⋆) from 0.1 to 0.3 were taken into consideration. It has been shown that the specific heat’s jump at the critical temperature and the thermodynamic critical field near zero Kelvin strongly decrease with μ ^⋆. The dimensionless ratios r ₁≡ΔC(T _C)/C ^N (T _C) and r₂ o T_CC^N(T_C)/H²_C(0)r_{2}\equiv T_{\mathrm{C}}C^{N}(T_{\mathrm{C}})/H^{2}_{\mathrm{C}}(0) significantly differ from the predictions based on the BCS model. In particular, r ₁ decreases from 2.64 to 1.97 with the Coulomb pseudopotential; whereas r ₂ increases from 0.140 to 0.157. The numerical results have been supplemented by the analytical approach.     

Effect of magnetic iron impurity on the superconducting properties of an amorphous Nb50Zr35Si15 alloy

The effect of magnetic iron impurity on the superconducting properties of amorphous Nb₅₀Zr_35−x Si₁₅Fe _x (x⩽4 at %) alloys was examined. Doping with an iron impurity resulted in a linear depression ofT _c andH _c2(T) and a decrease in andρ _n after reaching a maximum value at 0.5 to 1.0 at % iron. The observed decrease was about 35% forT _c, 85% forH _c2 at 2.0 K, 16% for and 21% forρ _n. Although the decrease in occurs through the decrease inρ _n as expected from the GLAG theory, the depression inT _c caused by magnetic impurity could not be explained in terms of the GLAG theory which is applicable to Nb-Zr-Si amorphous alloys without magnetic impurity, but was interpreted as arising from the pair-breaking effect in the superconducting nature due to magnetic scattering. However, the pair-breaking effect was found to be smaller by about one-tenth for the present amorphous superconductors than for crystalline superconductors, indicating the high stability of the superconductivity of the Nb-Zr-Si-Fe alloys against the magnetic scattering arising from the magnetic impurity. The reduced magnetic field at which the reduced fluxoid pinning force exhibits a maximum value increased with iron concentration, indicative of an enhancement of fluxoid pinning force. The enhancement in fluxoid pinning force was interpreted as arising from the increase in compositional, electronic and/or magnetic fluctuations by the dope of iron impurity.     

Complex borides with a ferromagnetic component: Development of the problem of magnetic superconductors

Superconductors with a ferromagnet as one of the principal components are considered. A group of new stable superconductors (of the Y-Ni-B system) containing a ferromagnetic component up to 50% at. is found out as well. The YNi_1.9 B_1.2 phase is revealed to have the highest critical parameters among the known superconductors with a ferromagnetic component (T_c∼13,5 K , ΔT_c∼ 0,6 K, J_c∼ 5 ^.10⁴ A/cm², H_c2(0) up to 30 kOe) . The model of its crystal structure is proposed. The YNi_1.9B_1.2 superconductor is characterized by an anomalous position of the H_c2(T) curve (the positive convexity within 9.5−13.5 K). In a normal state, it is characterised by an anomalous dependence of magnetic susceptibility on the temperature and magnetic field, i.e. magnetic susceptibilityχ shows no changes with increasing temperature (within 15–273 K) in a fixed magnetic field and decreases with increasing magnetic field from 0.214 to 4.28 kOe at a fixed temperature. The anomalous position of the curve can be described within the WHH theory in the Fulde and Maki approximation, the positive convexity of the H_c2(T) curve being attributed to anomalous magnetic properties of the YNi_1.9B_1.2 compound in a normal state. The coexistence of superconductivity with antiferromagnetism is assumed in the analyzed compound. Received: 9 November 2000 / Reviewed: 23 January 2001 / Accepted: 23 January 2001     

Extraction of Critical Current Density and Flux Creep Exponent in the Magnetic Superconductor Ru-1212 Using the ac Magnetic Susceptibility Measurements

The ac susceptibility data was employed to extract the temperature dependence of the critical current density, J _c(T), as well as the variation of flux-creep exponent n(T,H _ac) with temperature and ac field amplitude in bulk samples of polycrystalline magnetic superconductor RuSr₂GdCu₂O₈ (Ru-1212). The critical state models and the collective flux-creep approximation model were successfully accounted to describe such behavior below the transition temperature. The calculated values of n(T,H) are well fitted to a power law of the following form: n(T,H)=n ₀(H)T ^−s(H), where s is field dependent exponent whose values varied from −2.4, −1.01 for field amplitudes ranging from 0.5 G and 3.8 G. The power law describing the frequency dependence of χ′ is found to be consistent with the results of the current-dependent effective activation energy of the form U(J)=U ₀ln (J _c/J). Additionally, the dependence of the current density is found to scale according as: J _c(T)=J _c0(1−T/T _c) ⁿ , where the exponent n values varied from 1.05 to 1.25. Such dependence is an indication of intergrain coupling that could be ascribed in terms of superconductor–insulator–superconductor junctions. The derived temperature dependence of J _c(T) is in good agreement with the data obtained from the measurements using the traditional “loss-maximum” approach. Furthermore, the flux-creep effect increased with increasing both ac fields and temperatures except at about 15–25 K below the onset of T _c, where a slowing down of the flux creep was observed.     

Comment on ‘Resistivity Minimum Behavior and Weak Magnetic Disorder Characteristics in La<Subscript>2/3</Subscript>Ca<Subscript>1/3</Subscript>MnO<Subscript>3</Subscript> Manganites’

In a recent paper (Chen et al. in J. Supercond. Nov. Magn. 22:465, 2009) Zhenping Chen et al. reported measurements of the electrical resistivity (ρ) and magnetization versus temperature (T) and magnetic field (H) on polycrystalline manganite compound La_2/3Ca_1/3MnO₃. In particular, the ρ(T) dependence shows a shallow minimum at T _min∼20 K. Application of the external H up to 8 T leads to marked flattening of such minimum and to notable lowering of the T _min on ρ(T,H) curves. The authors attributed this low-temperature anomaly to competitive quantum Kondo effect and three-dimensional electron–electron interaction, using the results of numerical fittings of ρ versus T and H dependences in the interval of about 5–30 K. It is suggested in the comment that such a claim seems to be doubtful due to the fundamental inapplicability of this approach for analysis of low-temperature conductivity in polycrystalline manganites. It is noted that a natural cause for both the low-temperature minimum on ρ(T) curve and its evolution upon magnetic field application, is the well-known grain boundary effect. The numerous uncertainties and obscurities are also characteristic for the paper being commented upon.     

Kinetics of Thermal Transformation of Mg<Subscript>3</Subscript>(PO<Subscript>4</Subscript>)<Subscript>2</Subscript> · 8H<Subscript>2</Subscript>O to Mg<Subscript>3</Subscript>(PO<Subscript>4</Subscript>)<Subscript>2</Subscript>

The kinetics of thermal dehydration of Mg₃(PO₄)₂ · 8H₂O was investigated using thermogravimetry at four different heating rates. The activation energies of the dehydration step of Mg₃(PO₄)₂ · 8H₂O were calculated through the isoconversional Ozawa and Kissinger-Akahira-Sunose (KAS) methods and iterative methods, which were found to be consistent and indicate a single mechanism. The possible conversion function of the dehydration reaction for Mg₃(PO₄)₂ · 8H₂O has been estimated through the Coats and Redfern integral equation, and a better kinetic model such as random nucleation of the “Avrami–Erofeev equation (A _3/2 model)” was found. The thermodynamic functions (ΔH*, ΔG*, and ΔS*) of the dehydration reaction are calculated by the activated complex theory and indicate that it is a non-spontaneous process when the introduction of heat is not connected.     

Contributions from Inter-grain Boundaries to the Magneto-resistive Effect in Polycrystalline High-<Emphasis Type="Italic">T</Emphasis><Subscript>C</Subscript> Superconductors. The Underlying Reason of Different Behavior for YBCO and BSCCO Systems

In order to clarify the mechanisms in charge of broadening of resistive transition R(T) in magnetic fields of bismuth-based polycrystalline high-T _C superconductor (HTSC), a comparative study of Bi_1.8Pb_0.3Sr_1.9Ca₂Cu₃O _x (BSCCO) and YBa₂Cu₃O_7−δ (YBCO) have been performed. Magnetoresistive effects and irreversibility line obtained from magnetic measurements have been studied. It was established that (1) for YBCO, the smooth part of R(T) dependence unambiguously corresponds to dissipation in the intergrain boundaries for arbitrary magnetic fields; (2) for polycrystalline BSCCO, the smooth part of R(T) dependences correspond to dissipation within intergrain boundary subsystem in the field range H<10² Oe only, while standard measurements of R(T) dependences in magnetic field range H>10² Oe reflect the dissipation processes occurring both in intergrain boundary and HTSC grain subsystems; (3) for the high-field range, the contribution from intergrain boundaries of BSCCO can be distinguished from magnetoresistance R(H) dependences obtained at high enough current density on textured samples. It is proposed that various magneto-resistive properties of these classical HTSC systems are due comparatively weak pinning in BSCCO.