Eigenvalue correlation diagrams for effective hamiltonians: The ESR spectrum of axial Gd(III)

Abstract

Correlation diagrams depicting the behavior of effective Hamiltonian eigenvalues over the ranges of its variables may reveal important properties of the models. The case in which a Hamiltonian is a sum of two terms, one going to zero in one limit and the other effectively zero in the other limit, is considered here. The electron spin resonance spectrum calculated from the spin Hamiltonian of axial gadolinium In is used here as an example. The zerofield splitting term of the spin Hamiltonian is expanded in terms of normalized irreducible tensorial matrices in order to take advantage of their transformation properties under rotations. Its eigenvalues are plotted in a correlation diagram from the zero-field to the high-field limit. A similar correlation diagram for the principal transitions is used to predict a resonance spectrum.