Magnetic phase diagram of doped CMR manganites

The magnetic phase diagram of the colossal magnetoresistance (CMR) manganites is determined based on the Hamiltonian incorporating the double-exchange (DE) interaction between degenerate Mn $e_g$ orbitals and the antiferromagnetic (AF) superexchange interaction between Mn $t_{2g}$ spins. We have employed the rigorous quantum mechanical formalism and obtained the finite temperature phase diagram which describes well the commonly observed features in CMR manganites. We have also shown that the CE-type AF structure cannot be stabilized at $x$=0.5 in this model.