A mean-field-type approximation for the (t-J) model

Abstract

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 parameters are 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 TC and Neel temperature TN 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 TC and TN are numerically calculated. It is shown that TN rapidly falls with deviation from half-filling, when n=1. Magnetic correlation length lc varies at low temperature as approximately (1-n)- 12 /. Such behaviour corresponds to that observed in experiments in copper oxide high-Tc superconductors. The magnetic phase diagram is constructed on the (t/U, n) plane. The equations for the coupled order parameters are 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 nc for a crossover from itinerant magnetism to magnetism with localized magnetic moments should be a peculiar point where perturbation theory breaks down.