Theory of the electron-spin susceptibility in antiferromagnetic superconductors

Abstract

A theory of the longitudinal electron spin susceptibility ${\ensuremath{\chi}}_{s}$ 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 ${\ensuremath{\varepsilon}}_{\mathrm{k}}$=-${\ensuremath{\varepsilon}}_{\mathrm{k}+\mathrm{Q}}$, where Q is the wave vector characterizing the antiferromagnetic (AF) order. First we have studied the dependence of ${\ensuremath{\chi}}_{s}$ on the scattering rates for the scattering of conduction electrons from the nonmagnetic, spin-orbit, and magnetic impurities by regarding ${H}_{Q}$ as a parameter and neglecting the spin-fluctuation effects (${H}_{Q}$ is the AF field). The effect of impurities is found to be significant. Then we have investigated the temperature dependence of ${\ensuremath{\chi}}_{s}$ by taking ${T}_{N}$${T}_{c}$ and by including the spin-fluctuation effects and the temperature dependence of the AF field (${T}_{N}$ is the AF ordering temperature and ${T}_{c}$ is the superconducting transition temperature). The aim has been to see if ${\ensuremath{\chi}}_{s}$ is enhanced or depressed by the AF ordering occurring below ${T}_{N}$. We find that (1) ${\ensuremath{\chi}}_{s}$ increases with the increase in scattering rate from spin-orbit impurities both above and below ${T}_{N}$; (2) keeping other parameters fixed, the enhancement or depression of ${\ensuremath{\chi}}_{s}$ below ${T}_{N}$ depends on ${H}_{Q}$(0)---there is enhancement (depression) when ${H}_{Q}$(0) is larger (smaller) [${H}_{Q}$(0) is the zero-temperature value of ${H}_{Q}$]; (3) nonmagnetic impurities have a dramatic effect on ${\ensuremath{\chi}}_{s}$ in the AF phase. For cleaner (dirtier) superconductors, ${\ensuremath{\chi}}_{s}$ is enhanced (depressed) below ${T}_{N}$; (4) in ${\mathrm{SmRh}}_{4}$${\mathrm{B}}_{4}$, one expects a depression in ${\ensuremath{\chi}}_{s}$ by the AF ordering.