A Unified Theory of Magnetism in Narrow Band Electron Systems

A unified description is given for magnetism of narrow band electron systems on the basis of a functional integral formalism within the static approximation. A method is developed to calculate the free energy functional from a given band structure and its closed form expression is given for arbitrary amplitudes of the spin and charge density fluctuations, correponding to arbitrary strength of the electron-electron interaction. This expression is shown to lead to essentially correct results in both the weak and strong coupling limits. The metal-insulator (Mott) transition and related magnetic properties for the case of half-filled band and the magnetism of metals in the case of non-integral occupation number per atom are discussed with a numerical example for a tight-binding band in a simple cubic lattice.