MAGNETIC EXCHANGE BETWEEN ORBITALLY DEGENERATE IONS - A NEW DEVELOPMENT FOR THE EFFECTIVE HAMILTONIAN

A new approach to the problem of the kinetic exchange for orbitally de generate ions is developed. The constituent multielectron metal ions a re assumed to be octahedrally coordinated, and strong crystal field sc heme is employed, making it possible to take full advantage from the s ymmetry properties of the fermionic operators and collective electroni c states. In the framework of the microscopic approach, the highly ani sotropic effective Hamiltonian of the kinetic exchange is constructed in terms of spin operators and standard orbital operators (matrices of the unit cubic irreducible tensors). As distinguished from previous c onsiderations, the effective Hamiltonian is derived for a most general case of the multielectron transition metal ions possessing orbitally degenerate ground states and for arbitrary topology of the system. The overall symmetry of the system is introduced through the restricted s et of the one-electron transfer integrals implied by the symmetry cond itions. All parameters of the effective Hamiltonian are expressed in t erms of the relevant transfer integrals and fundamental parameters of the two moieties, namely crystal field and Racah parameters for the me tal ions in their normal, reduced, and oxidized states. The developed approach is applied to two kinds of systems: edge-shared (D-2h) and co rner-shared (D-4h) bioctahedral clusters. In the particular case of d( 1) ions (T-2(2)-T-2(2) problem) the energy pattern in both cases consi sts of several multiplets splitted by the isotropic part of exchange. In both cases we have found a weak ferromagnetic splitting for several multiplets of the system. This splitting is due to the competition of ferro-and antiferromagetic contributions arising from the high-and lo w-spin reduced states in line with Anderson's considerations, Goodenou gh-Kanamori rules, and McConnell mechanism of ferromagnetic interactio n. On the contrary, these weak ferromagnetic interaction are found to coexist with strong ferro-and antiferromagnetic contributions in which only high-spin and low-spin excited states are respectively involved. In addition to these unexpected results in both topologies the ferro- and antiferromagnenic contributions vanish separately for one of the l evel, the last being thus paramagnetic. These results are in a strike contradiction with the generally accepted point of view on the ferroma gnetic role of orbital degeneracy in the magnetic exchange. They also show that the simple qualitative models have a restricted area of appl ications and that the peculiarities of the exchange problem in the cas e of orbital degeneracy are much more complicated. The energy pattern of the exchange levels is closely related to the topology of the syste m and to the network of the one-electron transfer intercenter connecti ons forming effective parameters of the kinetic exchange in the case o f orbital degeneracy.