Theory of the electron-spin susceptibility in antiferromagnetic superconductors

Abstract

A theory of the longitudinal electron spin susceptibility χs for an antiferromagnetic superconductor (AFS) has been given. For the AFS, we have assumed a homogeneous superconducting order parameter and a one-dimensional electron band that satisfies the nesting condition ɛk=-ɛk+Q, where Q is the wave vector characterizing the antiferromagnetic (AF) order. First we have studied the dependence of χs on the scattering rates for the scattering of conduction electrons from the nonmagnetic, spin-orbit, and magnetic impurities by regarding HQ as a parameter and neglecting the spin-fluctuation effects (HQ is the AF field). The effect of impurities is found to be significant. Then we have investigated the temperature dependence of χs by taking TN<Tc and by including the spin-fluctuation effects and the temperature dependence of the AF field (TN is the AF ordering temperature and Tc is the superconducting transition temperature). The aim has been to see if χs is enhanced or depressed by the AF ordering occurring below TN. We find that (1) χs increases with the increase in scattering rate from spin-orbit impurities both above and below TN; (2) keeping other parameters fixed, the enhancement or depression of χs below TN depends on HQ(0)—there is enhancement (depression) when HQ(0) is larger (smaller) [HQ(0) is the zero-temperature value of HQ]; (3) nonmagnetic impurities have a dramatic effect on χs in the AF phase. For cleaner (dirtier) superconductors, χs is enhanced (depressed) below TN; (4) in SmRh4B4, one expects a depression in χs by the AF ordering.

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