The Phonon‐Induced Temperature Dependences of Spin‐Hamiltonian Parameters for S‐State Ions

The temperature dependence of the spin‐Hamiltonian parameters including the hyperfine coefficient for S‐state ions is examined. The starting point in the theory is the dynamical spin‐Hamiltonian with experimentally determined values for the parameters. Using this Hamiltonian the contributions to the static spin‐Hamiltonian from spin‐phonon interactions are calculated. It is shown that the most important contributions to the crystal‐field parameters arise from lattice anharmonicity. Such mechanism cannot explain the temperature dependence of the hyperfine coupling parameters and it is suggested instead, that two‐phonon processes give the dominant contributions.