Ferromagnetism in the strongly correlated Hubbard model

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=$n_{\uparrow }$-$n_{\downarrow }$ is examined for a bcc lattice in terms of the temperature T and the band occupation n=$n_{\uparrow }$+$n_{\downarrow }$ (0≤n≤2). For T=0 and less than half-filled bands (n<1), ferromagnetism becomes possible as soon as n exceeds the critical value $n_{\mathrm{I}=0.54\mathrm{}}$ and becomes saturated (m=n) above $n_s^{\mathrm{*}}$=0.74. A further, less polarized ferromagnetic solution appears for n≥$n_{\mathrm{II}=0.79\mathrm{}}$. 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.