  The conventional paradigm of charge order for La_{1-x}Ca_xMnO_3 for x=0.5 has
been challenged recently by a Zener polaron picture emerging from experiments
and theoretical calculations. The effective low energy Hamiltonian for the
magnetic degrees of freedom has been found to be a cubic Heisenberg model, with
ferromagnetic nearest neighbor and frustrating antiferromagnetic next nearest
neighbor interactions in the planes, and antiferromagnetic interaction between
planes. With linear spin wave theory and diagonalization of small clusters up
to 27 sites we find that the behavior of the model interpolates between the A
and CE-type magnetic structures when a frustrating intraplanar interaction is
tuned. The values of the interactions calculated by ab initio methods indicate
a possible non-bipartite picture of polaron ordering differing from the
conventional one.
