Superexchange mechanisms in an ideal 3d1 cubic system of the perovskite type

In this article we extend the expression obtained by Kugel and Khomskii for cubic perovskites, where the transition metal ion has a 3d(1) electronic configuration with threefold (3dt(2g)) orbital degeneracy. We derive an effective spin-orbital Hamiltonian by taking into account both the role of the oxygen on the bond between the transition metal ions and the role of the 3de(g) levels in superexchange processes, while no simplifications are done concerning the electron-electron interactions. A simple mean-field treatment yields a competition between an antiferromagnetic (AFM) and a ferromagnetic phase. The stability of these phases is driven by several parameters including the following: the ratio t(pi)/t(sigma) = vertical bar(pd pi)/(pd sigma)vertical bar between pi-type and sigma-type electron hoppings, the charge transfer gap Delta(CT), the exchange (Hund's) coupling, the crystal field Delta(0) between the t(2g) and e(g) 3d orbitals, and the "pseudo" crystal field gap Delta(oxy)(zx) between the oxygen 2p orbitals. The addition of the spin-orbit coupling is shown to be able to lead to a sensible reduction of the ordered magnetic moment in the AFM phase as well as the appearance of a weak ferromagnetic moment.