A simplified model of double exchange in the dynamic mean-field theory approximation

The Vonsovskii s-f exchange model is considered in the limit of tight bindi ng, when the s-f exchange integral I is much greater than the width of the band of collective electrons. A simplification is introduced into this limi ting case, namely, fluctuations of transverse components of localized spins are neglected. The limit of the infinite dimensionality of space correspon ds to the dynamic mean-field approximation. It is shown that on the Bethe l attice (with an infinite number of nearest neighbors) the electron Green's function can be found analytically; for the order parameters (of the ferrom agnetic and antiferromagnetic phases) and chemical potential, exact self-co nsistent equations are derived, whose solution does not require laborious n umerical computations. The whole body of magnetic properties of such a mode l is investigated. In particular, it is shown that the static uniform param agnetic susceptibility obeys the Curie law (similar to 1/T, but as the Curi e temperature T-C is approached, a deviation appears in the opposite direct ion than that observed in the Heisenberg model. The temperature dependence of magnetization at 1 - n much less than 1 (n is the concentration of colle ctive electrons) is similar to the behavior of the magnetization in a Heise nberg ferromagnet with paramagnetic impurities. A magnetic phase diagram on the (T, n) plane was constructed with allowance for the paramagnetic, ferr omagnetic, and antiferromagnetic phases and the phase separation between th e ferromagnetic and antiferromagnetic states with reduced and enhanced elec tron concentrations. The observed picture of magnetic properties qualitativ ely corresponds to the experimental results for lanthanum manganites with h igh T-C.