Ferromagnetism in the strongly correlated Hubbard model.

Abstract

We use a self-consistent ``spectral-density approach'' for the strongly correlated Hubbard model in order to find out under what circumstances spontaneous band ferromagnetism may appear. The magnetic polarization m=${n}_{\ensuremath{\uparrow}}$-${n}_{\ensuremath{\downarrow}}$ is examined for a bcc lattice in terms of the temperature T and the band occupation n=${n}_{\ensuremath{\uparrow}}$+${n}_{\ensuremath{\downarrow}}$ (0\ensuremath{\le}n\ensuremath{\le}2). For T=0 and less than half-filled bands (n<1), ferromagnetism becomes possible as soon as n exceeds the critical value ${n}_{\mathrm{I}=0.54}$ and becomes saturated (m=n) above ${n}_{s}^{\mathrm{*}}$=0.74. A further, less polarized ferromagnetic solution appears for n\ensuremath{\ge}${n}_{\mathrm{II}=0.79}$. It turns out that a spin-dependent band shift, which consists of ``higher'' correlation functions, decisively determines the possibility of spontaneous moment ordering. This is demonstrated by a set of self-consistently calculated quasiparticle densities of states. The Curie temperature ${T}_{c}$ appears as strongly n dependent. Starting at ${0}^{+}$ for n=0.54, ${T}_{c}$ increases with n, reaching a maximum of about 710 K near n=0.75, and decreases again for n>0.8 down to ${0}^{+}$ for n=1. According to the free energy F, in cases of more than one solution, that solution with the highest polarization is always stable.