Kinetic superexchange in a pair of pseudo-Jahn-Teller magnetic ions: Ferro- vs antiferromagnetic coupling

The main focus of this paper is to reveal the influence of the pseudo-Jahn-Teller effect (PJTE) on the exchange interaction in a pair of magnetic ions having a degenerate or pseudo-degenerate ground state. We consider the combined effect of the Anderson's type kinetic exchange (that is called superexchange) between the two one-electron centers each having two nearly-degenerate low-lying magnetic orbitals mixed by the vibration of a suitable symmetry. The superexchange is assumed to be comparable with the energy gap between the two orbitals. Under such condition the electronic energy spectrum of the dimer is shown to consist of three superimposed pairs of S = 1 and S = 0 levels, with the order of the levels inside each group obeying Goodenough-Kanamori rules. The overall effect of superexchange is antiferromagnetic if the energy gap between the two orbitals is large as compared with the superexchange and it is ferromagnetic otherwise. The PJT effect proves to be spin-dependent that drastically modifies the energy pattern arising from the superexchange. The most spectacular effect of the vibronic coupling is the predicted possibility of changing spin of the dimer. In all cases strong PJT coupling stabilizes an antiferromagnetic ground state. We demonstrate that depending on the electronic parameters involved, one of the two types of minima proves to be the global one. One of these types describes ferrodistortive antiferromagnetic state, while for other one the system proves to be ferromagnetic and antiferrodistortive. In a broader context, these results show that a dimeric PJT cluster can serve as a molecular model for interconnected cooperative phenomena in PJT crystals such as magnetic, structural and orbital types of ordering.