Magnetic superexchange in YIG and Ca2+:YIG

Starting with the Anderson periodic Hamiltonian for a system of the narrow- and wide-band electrons, an explicit expression for the superexchange coupling between spins of localized electrons is derived and analyzed. The superexchange coupling is based on the fourth-order p-d hybridization. One special aspect of the problem is systematically discussed at T=0 K. It is shown that the presence of compensating holes produced in Ca2+:YIG by the valence-uncompensated doping, can result in a decrease in the strength of the superexchange coupling and, depending on the concentration of the doping Ca2+ ions, a change of the sign of the coupling constant is obtained. Numerical results are calculated both for the charge-transfer and Mott–Hubbard models for insulators