Exchange interactions in rare earth chalcogenides

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Abstract
The author obtains explicit formulae for the admixtures of the J=1 level of Sm2+ (4f)6 7F into the J=0 level by exchange coupling to an adjacent Eu2+ (4f)7 8S ion. The problem is formulated using states which are antisymmetric with respect to interchanges of electrons. An unperturbed Hamiltonian is defined which is symmetric with respect to interchanges, and the difference between it and the full Hamiltonian is treated by perturbation theory, taken to second order. It is found that the dominant processes are those in which, in the intermediate states, either two electrons, one from each 4f shell, have been excited into unoccupied orbitals, or two electrons from closed shells have been excited into the 4f shells, one electron to each rare earth ion. By the use of equivalent operator techniques, it is shown that the admixtures can be derived from an equivalent anisotropic exchange interaction, with the important feature that the spin operators which appear are defined in second quantized forms and are not identical with the commonly used spin operators. It is suggested that in phenomenological exchange spin Hamiltonians these new definitions should be used.