Magnetization of Manganese Perovskites

Temperature dependence of spontaneous magnetization at a separate site in the compounds La_1-xCa_xMnO₃ (0 ⩽ x ⩽ 1) is investigated in the molecular field approximation using a homogeneous model for the magnetic sub-lattice with allowance for the Heisenberg superexchange and double exchange between nearest neighbors. Unlike with the usual magnets having one type of magnetic ions, in this case there appears a system of equations with two unknowns, mean spins of ions Mn³⁺ and Mn⁴⁺. In the vicinity of the ordering temperature, this system can be solved analytically and the expression for the ordering temperature can be obtained as well. To find the temperature dependence of magnetization in the whole temperature range, we used the exact expression for the double exchange operator containing spin operators under the square root. The numerical solutions were found in this case.