Dynamic susceptibilities of a system with broken spin symmetry

We consider a spin-polarized electron gas (SPEG) consisting of n(sigma) ele ctrons of spin sigma(up arrow) and n(<(sigma)over bar>) electrons of spin < (sigma)over bar>(down arrow) and investigate the charge and spin density re sponses of the SPEG by employing spin-dependent local fields G(sigma). In t his work, we generalize the G(sigma)-dependent expressions of the charge an d spin susceptibilities, chi(ij), by extending the theory of Vashishita and Singwi to a system with broken spin symmetry. Here, we define the spin pol arization by zeta=(n(sigma)-n(<(sigma)over bar>))/n where n=n(sigma)+n(<(si gma)over bar>). In a system with vanishing spin polarization (zeta=0), the mixed susceptibilities chi(em) and chi(me) vanish. However, in a SPEG with chi not equal 0, the two mixed susceptibilities become finite and are as im portant as the usual susceptibilities chi(ee) and chi(L)(mm). We show expli citly that, unlike the unpolarized case, chi(em) and chi(me) are not identi cal, in general, in a system with finite spin polarization.