Exchange-coupled pairs of Cr³⁺ions in emerald (in EPR spectra)

Effective Hamiltonians for EPR Spectroscopy of Exchange-Coupled Pairs

“…and Ni 2+ -Cu 2+ , the magnetic properties of which have in the last years been considered with increasing interest [4,7,10,11]. In the first case one has four total spin states corresponding to 5=0, 1, 2, 3.…”

“…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.…”

“…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 given.…”

“…They are given in form of rational numbers as usual in earlier tables about the same topic [4,6], Values in brackets correspond to contributions which become null in the limit cases 5=1/2 and 3/2.…”

“…This fact has not a particular meaning in itself, but it may represent a fortunate circumstance. Thus, for a coupled pair where 5] = 5 2 = 3/2 we can estimate first-order values for the anisotropic interaction (dipolar or pseudopolar in origin) directly from the EPR spectra relative to only the 5=2 multiplet [7], To this fact we can also ascribe that the observed spectral resolution normally is better for 5 = 2 than for 5 = 3 [8,9], In the past, second-order formulas and coefficients have been given for the special case of two identical ions interacting by purely isotropic exchange [4] (5i = 5 2 , Z), = Z) 2 , Q = 0, A = 0, in our notation). In that case use was made of a zero-field spin-hamiltonian form in terms of the so-called equivalent operators O^, O^, O4, O4.…”