Effect of gap anisotropy in superconductors containing paramagnetic impurities with local states within the gap

The Shiba model for the paramagnetic impurities in a superconductor has been generalized to include the effect of gap anisotropy. The calculated properties are the transition temperatureT _c and the specific heat jump atT _c. The changes brought in these properties by anisotropy are significant.Work supported in part by the Natural Sciences and Engineering Research Council of Canada.     

Effect of a magnetic field on the specific heat jump of a superconducting alloy containing paramagnetic impurities with local states within the gap

The effect of a uniform magnetic field on the specific heat jump \({\Delta C}\) of a superconductor containing paramagnetic impurities has been investigated. The impurities are described by the Shiba-Rusinov model. Taking the normalized position of the bound state within the BCS gap ε₀=0.8 and 0.0 and the parameter α(=〈S _z ² 〉/S²)=1.0 and 1/3 as typical values, we find the detailed dependence of \({\Delta C}\) on the impurity concentration \(\bar c\) and the transition temperature T_c. In some cases \({\Delta C}\) diverges at certain values of \(\bar c\) or T_c, signaling a change of the normal-superconductor phase transition from second order to first order.     

Superconducting and normal state properties of dilute alloys of LaSn3 containing Nd impurities

The results of an investigation of the superconducting and normal state physical properties of (LaNd)Sn₃ alloys are reported. Superconducting state data are presented describing the depression of the superconducting transition temperature T _cwith Nd impurity concentration, the reduction of the reduced jump in heat capacity C/C ₀ with decreasing reduced superconducting transition temperature T _c/T_c0, and the pressure dependence of T _c. Normal state data for the temperature dependences of the magnetic susceptibility and heat capacity demonstrate the importance of crystalline electric field effects in the physical behavior of (LaNd)Sn₃ alloys and indicate that Nd interimpurity magnetic interactions and possibly a small amount of Nd-Sn antisite disorder are manifested in the experimental results. Theories based on an isotropic exchange depairing model are unable to give a satisfactory account of all of the experimental data, suggesting that the physical properties of(LaNd)Sn₃ alloys may be modified by processes involving the orbital exchange scattering of host conduction electrons by the Nd impurities.Supported by the U.S. Department of Energy under Contract No. Ey-76-S-03-0034-PA227-3.Fellow of the Consejo Nacional de Investigaciones, Cientificas y Tecnicas, de la Republica Argentina; leave from Centro Atomico Bariloche, Bariloche, Argentina.     

On the theory of superconductors containing magnetic impurities: Crystalline field effects

We extend to finite concentrations a previous calculation of crystalline field effects in superconductors containing rare-earth impurities. The computations, which have to be done numerically, apply to non-Kramers ions as well as Kramers ions. A comparison between theory and available experimental data is made.The computer time used was supported in part by the Computer Science Center of the University of Maryland.     

Superconducting gap function and upper critical field in the presence of inhomogeneous magnetic order

Rare earth ternary superconductors are known to exhibit oscillatory magnetic orders below their superconducting transition temperatures. The study of behaviour of superconducting electrons in an inhomogeneous magnetic field is therefore important for such systems. We report here the results of our theoretical study of superconducting gap function Δ(T) and upper critical fieldH _c2 (T). The results are applied to analyse and explain the variation of Δ(T) andH _c2 (T) in case of NdRh₄B₄.     

On the problem of superconductors containing polarized magnetic impurities

We investigate theoretically the influence of impurity polarization on the superconducting transition temperature of superconductors containing magnetic impurities. From previous theoretical work it is known that the pair-breaking effect of magnetic impurities is reduced when the impurity spins are fixed by an internal field. This spin-dynamic effect is studied in detail on two models of the magnetic state of the system based on a mean field theory. In some cases the critical concentration of magnetic impurities that destroys superconductivity atT=0 is increased, but we find that the polarization energy of the magnetic impurities must be very large compared to the gap energy of the pure superconductor in order to increase the critical impurity concentration by the factor (S+1)/S reported in the literature. We conclude that the anomalous dependence of the superconducting transition temperature on the concentration of magnetic impurities observed on some dilute alloys with rare-earth impurities can only be attributed to spin-dynamic effects if extraordinary strong polarizing forces between the magnetic impurities exist.Supported in part by Deutsche Forschungsgemeinschaft.     

On the critical temperature of two-band superconductors with paramagnetic impurities

The influence of unpolarized and uncorrelated magnetic impurities on the critical temperature T _c of a two-band superconductor which has recently been discussed by Will and Brusberg and by Entel et al. is reinvestigated. It is found that all effects of unequal cutoff frequencies _ij (i, j = 1,2) for the pairing interactions _ij can be absorbed into weakly impurity-dependent effective interaction parameters _ij , and that, in contrast to Will and Brusberg, in the dilute limit T _c(c) always decreases with increasing impurity concentration c. Consequently there is no critical concentration at which the phase transition may change from second to first order.Work performed within the research program of the Sonderforchungsberich 125—Achen/ Jülich/Köln, Germany.     

真空磁场热处理对Fe-Ga-Al合金磁致伸缩的影响

采用电弧炉熔炼方法得到Fe82Ga18-xAlx(x=3,9,12)合金的多晶样品。利用X射线衍射(XRD)和金相观察对合金的相组成进行分析,并对其磁致伸缩系数进行测量。经过真空磁场热处理后,对Fe-Ga-Al合金的结构和磁致伸缩性能进行研究。结果表明,真空磁场热处理后Fe-Ga-Al合金磁致伸缩系数均有提高,其中Fe82Ga9Al9合金经磁场热处理后,磁致伸缩达到114×10-6;Fe82Ga15Al3合金经磁场热处理后,其磁致伸缩增幅最大,比处理前增加165%。     

On the theory of low-temperature magnetoresistance of metals with paramagnetic impurities

The low temperature magnetoresistance of a metal with paramagnetic impurities is studied in the case of large-phase shift for the potential scattering. It is shown that when cos 2<0 the impurity magnetoresistance may become positive for sufficiently strong fields and low temperatures.     

On the critical temperature of strong coupling superconductors with paramagnetic impurities

We calculate the effects of paramagnetic impurities on the critical temperature of several intermediate and strong coupling superconductors by numerically solving the Eliashberg equations, and compare the results with the results of Abrikosov-Gorkov theory. For all the superconductors considered, the values of critical impurity concentration obtained from this exact numerical calculation are found to be considerably larger than the values given by Abrikosov-Gorkov theory. By generalizing a previous work of Leavens and Carbotte, we derive simple analytical expressions for the critical temperature and the critical concentration that give results much closer to the exact values than the corresponding BCS values.     

Effect of interstitial impurities on the crack resistance of ductile titanium alloys. 2

We have investigated the failure ductility of a 2V-type ductile titanium alloy with a nitrogen and oxygen impurity content ranging from 0.05 to 0.35%. Here we have employed approaches that are based on utilization of the J integral. We have established the optimum values for nitrogen and oxygen impurity concentrations to ensure an adequate level of crack resistance and stress. We have proposed relationships for the calculation of microspall resistance, based on the geometric parameters of the structure when the a phase is laminar in form. The analytical determination of microspall resistance made it possible to estimate the crack resistance of the alloy to a high degree of accuracy over the entire range of variations in impurities, based on empirical relationships.Translated from Problemy Prochnosti, No. 8, pp. 30–36, August, 1991.     

Theory of paramagnetic spin waves in simple metals in a direct-current magnetic field

The transverse dynamic spin susceptibility of a normal, charged Fermi liquid is found. The formula depends on the first three antisymmetric Landau parametersB ₀,B ₁,B ₂ and is exact to orderk ² in the expressions both for the energy of spin waves and their oscillator strengths. It contains spin-wave poles with1=0 and 1 and easily reproduces all the results obtained previously by perturbation theory.On leave of absence from: Institute of Physics, University of Lattakia, Syria.     

Nucleation kinetics of paramagnetic and diamagnetic metal melts under a high magnetic field

The influence of a high magnetic field (HMF) on the nucleation kinetics of paramagnetic aluminum and diamagnetic zinc melts has been investigated by differential thermal analysis (DTA).It is found that the application of an HMF increases the undercooling of pure aluminum and pure zinc at the same heatingcooling rates.Moreover,the quantitative analysis of activation energy calculated from the DTA results using the Kissinger method manifests that the HMF reduces the activation energy of pure aluminum and pure zinc.Regardless of magnetism,the nucleation frequency under an HMF is higher than that without an HMF.Furthermore,the increase in undercooling under the HMF is mainly attributed to the increase of the contact angle,calculated by the functional relationship between the cooling rate and undercooling.This result is consistent with the increase of the calculated nucleation work for pure aluminum and pure zinc.Additionally,the increase in undercooling caused by the HMF is partly ascribed to the magnetic field-induced suppression of thermal convection in the undercooled melt.     

Effect of normal impurities on anisotropic superconductors with variable density of states

We develop a generalized BCS theory of impure superconductors with an anisotropic electron-electron interaction represented by the factorizable model introduced by Markowitz and Kadanoff, and a variable electronic density of statesN(), assumed to peak at the Fermi energy, which is modeled by a Lorentzian superimposed on a uniform background. As the impurity scattering is increased, the enhancement ofT _c by both the anisotropy and the peak inN() is washed out. The reduction is investigated for different values of the anisotropy and different peak heights and widths. It is concluded that the effects of anisotropy and the peak are reduced together in such a way that any effect due to anisotropy is not easily distinguishable from that due to the peak.Research supported by the Natural Sciences and Engineering Research Council of Canada and the McMaster University Science and Engineering Research Board.     

大间隙磁力传动系统驱动磁场的产生方法研究

针对永磁轴流式血泵大间隙磁力传动系统,提出了单磁极切换和双磁极切换两种产生驱动磁场的方法;基于ANSYS有限元分析软件仿真分析了磁场的耦合机理,计算比较了2种磁场驱动下系统的驱动力矩;通过轴流式血泵负载实验,利用大间隙磁力传动系统能量传递效率及电磁体损耗的数学模型,计算并比较了2种磁场驱动下系统磁力传动部分的能量传递效...     

Anisotropy effects on the specific heat jump of a superconductor with normal and paramagnetic impurities

We present analytical calculations of the specific heat jump of an anisotropic superconductor with normal and paramagnetic impurities. We solve the imaginary-axis Eliashberg equations with a square-well model for the electron-phonon interaction and obtain additional terms not present in BCS theory. For low concentrations of paramagnetic impurities, anisotropy decreases the specific heat jump normalized to the normal state specific heat, while this quantity is larger in the anisotropic superconductor than in the isotropic one for large enough concentrations of paramagnetic impurities.     

Penetration of a magnetic field into superconducting lead and lead-indium alloys

The temperature dependence of the magnetic field penetration depth of superconducting lead and lead-indium alloys has been studied over the temperature range between about 2 K andT _c. Data are analyzed in terms of the microscopic theory. The difficulties of a unique analysis of the penetration data are pointed out and a strategy for the best analysis is discussed. The penetration depth atT=0 K for pure lead is determined as 525 Å. This value, though higher than the previously accepted value for lead, is nevertheless consistent with the strong coupling character of lead.