  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.
