Density of states and spin susceptibility of a finite metal: Normal and giant surface effects

The size effect on the electronic density of states and spin susceptibility $\ensuremath{\chi}$ of small metal particles and thin films is evaluated to order (area/volume) within the spin-density functional formalism. Conditions are given under which the size effect arises only in the surface region. Size-effect parameters and magnetization profiles, as well as surface energies and work functions, are calculated self-consistently for the jellium surface using the random-phase approximation and the local spin-density approximation (LSDA) for exchange and correlation. The jellium surface is also used to test two approximations for $\ensuremath{\chi}$ which require only spin-unpolarized calculations. One of them, the Vosko-Perdew (VP) approximation, is found to agree closely with the full spin-polarized calculation within the LSDA. The VP theory, which gives lower bounds for the bulk and surface susceptibilities and does not necessarily require the LSDA, is used to discuss the possibility of a giant surface effect, i.e., a giant enhancement of the surface susceptibility, in any metal that is nearly ferromagnetic. The giant surface effect is illustrated by an LSDA calculation for a low-density jellium, and by two other instructive models.