Theory of Magnetic Properties of Narrow-Band Solids

Magnetic properties of narrow-band solids are considered by calculating the spontaneous magnetization and susceptibility as a function of temperature of the Hubbard Hamiltonian, which should be applicable to them, in the limit as the ratio of interaction to hopping energy approaches infinity. Results are found for those lattices shown rigorously by Nagaoka to have a ferromagnetic ground state. The calculation is performed by a diagrammatic expansion of the partition function in which the choice of diagrams to be summed dominates the expansion in the limit of temperatures much less than the hopping energy. The model is expected to be applicable to the transition-metal disulfides ${\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{\mathrm{S}}_2$ and ${\mathrm{Co}}_{1-x}{\mathrm{Ni}}_x{\mathrm{S}}_2 \mathrm{}(0<x<\mathrm{}1\mathrm{})\mathrm{}$, and the results of this paper are compared with experiments done on these compounds.