Effective Hamiltonians for EPR Spectroscopy of Exchange-Coupled Pairs

Abstract

The paper refers to the second-order spin-hamiltonian formalism, recently proposed by the author, describing the EPR properties of an exchange-coupled pair of orbitally not degenerate ions in the limit of strong isotropic exchange (higher-order effects such as biquadratic exchange or exchange striction are considered neglectable). Tables of numerical values for the relevant coefficients involved are given. This allows to write immediately the effective spin operators spanning each total spin multiplet which arises from the coupling between the ions. Explicit formulas for the recurrently encountered cases of pairs where 5, = S 2 = 3/2 or 5, = 5/2 and S 2 = 1/2 or 5, = 1 and S 2 = 1/2 are deduced. Some salient features of these, concerning the second-order contributions to the zero-field splitting, are discussed in the light of available experimental data. The conclusions drawn seems to encourage a more extensive use of the model.Recently we have proposed a spin-hamiltonian formalism in order to describe a system of two paramagnetic ions in singlet orbital ground-states and strongly interacting by isotropic exchange [1] (a brief summary is given in the Appendix). It consists of effective spin-hamiltonian operators which span the single multiplets of the total spin arising from the coupling between the ions and therefore appears to be particularly useful in the analysis of the electron paramagnetic resonance (EPR) spectra of coupled system where, due to the energy values involved (strong exchange limit) and to the magnetic dipole selection rules, microwave transitions can only occur between levels belonging to the same total spin multiplet. This formalism has sensibly larger applicability than previous well known similar models [2][3][4], In fact, it assumes contemporaneously arbitrary spin values 5, and S 2 for the two ions, a general tensorial form for all contributions to the pair energy, and second-order perturbative approximation of the zero-field terms with respect to J5, • S 2 . Owing to the generality, however, the resulting expression is somewhat cumbersome [5], The second-order corrections, in particular, depend on a lot of coefficients of which general implicit expressions were * Work partially supported by the Ministero della Publica Istruzione (MPI) of Italy.Reprint requests to E.