Low-temperature ferromagnetism in a weakly doped Hubbard magnet

In the framework of the diagrammatic method with self-consistent field, the maximum on the temperature dependence of the susceptibility of a weakly doped narrow-band Hubbard magnet below the Curie temperature $T_{\rm C}$ is predicted. By numerical calculations, it is proved that it appears at small hole concentrations $n_{h}$. In this case, the temperature dependence of the magnetization $M$($T$) has a typical Fermi-like shape with the point of inflection at a temperature $T_{\rm inf}$. The approximate solution of the system of equations for the mean spin and the chemical potential gives the Schottky susceptibility typical of a two-level system with a gap of order of $n_{h}(1-n_{h})W$, where W is the bandwidth. This behavior reflects the existence of two subbands with up- and down-spins. It may be observed experimentally in the surface layers of oxide metal nanoparticles with narrow bands and a weak oxygen nonstoichiometry.