Problem of the Coexistence of Superconductivity and Ferromagnetism

Abstract

vicinity of which the coexistence of superconductivity and ferromagnetism would be expected. The first experimental study of the coexistence problem had been carried out by Matthias et al. [S, 91 in the rare-earth superconductive systems with paramagnetic Gd impurities, namely in the alloys Y1-xGdxOs, and Lal -,Gdx. Fig. 2 shows the phase diagram in the temperature-concentration plane forY1-xGdxOs,. The region bordered by the curve T,, the dotted continuation of the curve T,, as well as by the abscissa is the region of coexistence of superconductivity and ferromagnetism. The phase diagram, shown in Fig. 2, is the typical one for quite a few systems in which the coexistence had been investigated (cf.[ll] to [IS]). Thus, in the papers [lo] to [12] the coexistence was confirmed in the system Gdx,in [15] it was confirmed in the system ,and in [18] in the system Cel-,Tb,Ru,.As to the compound Cel-,GdxRu,, the coexistence had been supposed to occur in it, but later on this supposition was not confirmed because it was shown in [18] that in the compound sample an inhomogeneous distribution of Gd over the volume existed resulting in an exfoliation into superconductive and ferromagnetic phases instead of coexistence.Up to present the nature of magnetic ordering in the superconductive phase has not been cleared up due to the perturbation of magnetic measurements by the Meissner effect, while direct neutronographic measurements on dilute magnetic systems had not been carried out yet. Nevertheless the coexistence of superconductivity and ferromagnetism in such systems is an established fact. A summary of experimental data on this question can be found in the review by Bennemann and Garland [19].The theory of superconductivity in metals with paramagnetic impurities which are ferromagnetically ordered had been formulated by Gorkov and Rusinov [20] who had managed to find out the limits of the coexistence region in the tempera-, y, , j 7 /' /' Pig. 2. The phase diagram for Y1 -xGdxOs, obtained by Suhl et al. [9] 0 2 4 6 8 1 0 1 2 7 4 nl%l---12 Yu. A. lzyuniov and Yu. N. SKRYABINture-concentration phase diagram. A qualitative agreement of theoretical results with the experimental ones (i.e. the phase diagram of Pig. 2) was achieved when the spin-orbital scattering of electrons a t impurities had been taken into account. Hence, in Gorkov-Rusinov's model, the behaviour of superconductivity in ferromagnetic dilute alloys is determined by the action of three physical mechanisms :1. The exchange field of the spin of the magnetically ordered localized impurity creates the polarization of itinerant electrons giving rise to the relative shift of the Permi surfaces for electrons with opposite spins and thus to the destruction of the superconductive state.2. The localized impurity spins are in a magnetic exchange field. Therefore, the scattering of electrons with spin flip leading to a destruction of the Cooper pairs is not so effective as in the paramagnetic case.3. The spin-orbital scatterers, whose role may be played by the heavy com...

Superconducting alloys containing paramagnetic impurities with local states within the gap. Effect of a magnetic field

“…Equations (17)- (20) are our generalized equations for o3• and A• Our equations reduce to earlier known results in appropriate limits.…”

“…Equations (17)- (20) are our generalized equations for o3• and /~:. Knowing these quantities, we can obtain the generalized Green function from Eqs.…”

“…Then Eqs. (17)- (20) reduce to the ones given by Gor'kov and Rusinov. TM In the absence of magnetic field, I = 0, (S2x)/S 2 = (SZz)/S 2 = 1/3, o3• = o3, 7~• = 7~, and U• = U.…”

“…(17)- (20) reduce to those derived by Shiba. 2 Knowing the Green function, we can obtain several thermodynamic and frequency-dependent properties of the superconducting alloy.…”

Superconductivity in Non-adiabatic Ferromagnetic Alloys

“…As a result we can apply the method of calculation used for the usual superconducting ferromagnetic alloys in BCS model, 9,12 to the system of equations (22), generalizing it to the case of electron-phonon interaction (see Appendix B). In this way we derive:…”