Mn²⁺centre in corundum

Operators for calculating the intensities of the allowed and forbidden hyperfine lines in electron paramagnetic resonance spectra

“…It is seen that the present results differ from theirs significantly. In the case of the allowed HF transitions ( A M = 1, Am = 0), it is noticed that the expression (equation ( 13)) obtained by Mialhe and Erbeia (1973a) does not simplify to that given by Bir (1964) for the case where the minteraction is absent, wheras the present result (equation ( 31)) does. The result derived in the present paper (equation ( 31)) is also in agreement with that of Subramanian and Misra (1989).…”

“…The derivation of the intensity operator J is illustrated below with the help of one specific example. To facilitate comparison with previously published results (Mialhe and Erbeia 1973a, b, Golding et a1 1972), it will be assumed that Q, D and A have axial symmetry and that the principal axes of D and A coincide with the x , y , z axes. One of the terms appearing in the intensity expression (21) for the where The admixture coefficient of the state IM -1, m) with the state IM + 1, m), c t ; i;;, is given in the second-order perturbation approximation as (Golding 1969)…”

“…The remaining constants in equation ( 11) are defined in equation ( 19). The non-parallelism of the axes of quantization of the electron and nuclear spins is most significant for M = + f (Mialhe and Erbeia 1972) Having determined the orientation of Beff relative to the laboratory coordinate system ( x , y , z ) , the HF interaction can be written as ( 11) In equation ( 12), the unit vector t2 is defined by…”

“…The electronic wavefunctions are obtained by applying the perturbation theory to the electronic part of the Hamiltonian and, for each of the electronic states thus obtained, the nuclear states are defined. If the crystal field and HF interactions are of comparable magnitude, the axis of quantization for the nuclear spin must still be taken along the direction of the effective magnetic field, but the separation of the eigenstates into electronic and nuclear parts cannot then be justified and therefore the complete SH of the paramagnetic ion must be considered in calculating the EPR line intensities (Mialhe and Erbeia 1972). Mialhe (1979) has given a detailed discussion of the various approximate methods used in obtaining analytical expressions for the EPR line intensities as well as a comparison of these expressions with the experimental results on the Mn2+ ion in some crystal fields.…”