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We first exploit the spin symmetry relation $f^{\rm xc}_{s\bar s}(\zeta)=f^{\rm xc}_{\bar s s}(-\zeta)$ for the exact exchange correlationkernel $f^{\rm xc}_{s\bar s}(\zeta)$ in an inhomogeneous many electron systemwith arbitrary spin polarization $\zeta$. The physical condition required tosatisfy the specific symmetry relation $f^{\rm xc}_{s\bar s}(\zeta) = f^{\rmxc}_{\bar s s}(\zeta)$ is derived and examined for simpleferromagnetic-nonmagnetic structure by taking the electrochemical potentialinto account. The condition is then applied to several composite systems usefulin spintronics applications such as the magnetic system with net spinpolarization.Comment: 5 pages, 1 figur

Physical condition for the spin-resolved exchange correlation kernel for an inhomogeneous many-electron system