Anisotropic spin-orbit interaction in paramagnetic resonance

Abstract

The part of the spin-orbit interaction due directly to crystalline electric fields or applied fields contributes to the g-tensor of a paramagnetic center a shift which, as Kneubühl has noted, may have a skew-symmetric part. We show (1) that in an applied electric field g-shifts from this source for centers lacking inversion symmetry are typically Δg ⪷ 10 −11 cm/kV , and thus negligible; (2) that these shifts are usually very much smaller (in cases where such shifts have been studied experimentally, by a factor of at least 10 5) than those produced by the applied field via an electron's electrostatic potential energy in the field, coupled with the unperturbed spin-orbit interaction due to the ion. We infer that crystalline fields (neglecting covalent effects) contribute to a skew-symmetric part of the g-tensor primarily through changes in the wave functions induced by the electrostatic potential energy, rather than through the field's contribution to the spin-orbit interaction. A skew-symmetric †g arising from applied fields or crystalline fields is probably not larger than a few per cent of the corresponding symmetric change in g. A proposal due to Ludwig for distinguishing the skew-symmetric part of a g-tensor in an applied field is described.