A MEAN-FIELD TYPE APPROXIMATION FOR THE (T-J) MODEL

The equations for a mean-field-type approximation in the (t-J) model are formulated in terms of a diagrammatic technique with Hubbard X-operators. With their help, equations for the order parameter are derived derived in ferromagnetic and antiferromagnetic phases of a metal. In both cases, two coupled order parameters exist: a magnetization m and a gap DELTA in the electron spectrum. They reflect a dual behaviour of a strongly correlated system: it is simultaneously an itinerant and a localized magnet. Formulae for Curie temperature T(C) and Neel temperature T(N) are derived, from which the different nature of ferromagnetic and antiferromagnetic ordering is explicitly seen. For a simple cubic lattice the electron concentration n dependences of T(C) and T(N) are numerically calculated. It is shown that T(N) rapidly falls with deviation from half-filling, when n = 1. Magnetic correlation length l(c) varies at low temperature as approximately (1 - n)-1/2. Such behaviour corresponds to that observed in experiments in copper oxide high-T(C) superconductors. The magnetic phase diagram is constructed on the (t/U, n) plane. The equations for the coupled order parameters wr solved for T = 0 and the dependences of the order parameters m and DELTA on n are presented in a wide interval of electron concentrations. They indicate the growing degree of itinerancy with deviation from half-filling. It is shown that the critical concentration n(c) for a crossover from itinerant magnetism to magnetism with localized magnetic moments should be a peculiar point where perturbation theory breaks down.