An effective ion Hamiltonian for a magnetic 3d impurity in a metal

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Abstract
A derivation of an effective ion Hamiltonian is presented from an exact starting Hamiltonian describing a substitutional magnetic 3d impurity in an otherwise nonmagnetic metal. The impurity is assumed to have a well defined spin and orbital angular momentum in its groundstate throughout. The starting Hamiltonian contains spin-orbit coupling, the kinetic energy of electrons and nuclei, and the electron-electron and electron-nuclei potential energies. Zeeman energies have been omitted. It is found that the absolute magnitude of the effective spin-orbit coupling is increased over the free-ion value and 'crystal field' energies become considerably modified by the large exchange and Coulomb couplings between localised magnetic 3d and itinerant electrons, in agreement with recent experiments on Au:Co and Zn:Cr. The exchange interaction also gives rise to new zero-field contributions and in axial symmetries, evidence for which has been found in Zn:Cr and Zn:Mn.