Magnetic structure and double exchange in hypothetical compound   La1-xCaxMnO3
  Question about the appearance of different magnetic structures in the family of compounds La1-xCaxMnO3,is investigated theoretically. It is supposed that the whole series has GdFeO3 structure type. The problem is considered at absolute zero temperature in the nearest neighbor approximation. Superexchange, double exchange and anisotropy energy are taken into account-all together 10 interaction parameters. The spin operator of double exchange interaction in crystal between ions with different valence Mn3+ and Mn4+ is the straight generalization of two-spin operator in the known problem of Anderson and Hasegawa molecule. Minimization of the ground state energy with respect to direction angles of magnetic sub-lattices leads to a system of transcendental equations whose solutions give 11 types of magnetic configurations: two ferromagnetic, three collinear antiferromagnetic and six non-collinear. When the concentration of Ca ions x changes one spin configuration replaces another as the ground state. As a whole the sequence of configurations when x changes from 0 till 1 can be brought in correspondence to those observed on the experiment. The comparison with experiment was made by means of mixed procedure: part of numerical values of interaction parameters and transition concentrations x from one configuration to another were taken from experiment while the missing values of these parameters were calculated with the help of the corresponding theoretical relations representing the conditions of equality of different phases energies at the concentration crossing. 
B.V.Karpenko, L.D.Falkovskaya, and A.V.Kuznetsov