Magnon-phonon coupling in metamagnetic systems

The coupling between the phonons corresponding to rigid vibrations of the waters of hydration and magnons (which is due primarily to the modulation of the crystal field at the transition-metal ion site) is treated in detail for the linear-chain metamagnetic systems ${\mathrm{FeCl}}_{2}$ \ifmmode\cdot\else\textperiodcentered\fi{} ${2\mathrm{H}}_{2}$O, ${\mathrm{CoCl}}_{2}$ \ifmmode\cdot\else\textperiodcentered\fi{} ${2\mathrm{H}}_{2}$O, and ${\mathrm{CoBr}}_{2}$ \ifmmode\cdot\else\textperiodcentered\fi{} ${2\mathrm{H}}_{2}$O. A microscopic magnon-phonon interaction Hamiltonian is derived by treating the waters of hydration as point dipoles, and the resulting coupling constants are given in terms of the splittings of the low-lying electronic states of the transition-metal ions and the spin-orbit coupling parameter for all interactions involving up to two magnons and two phonons. The forms of the coupling for the three phonons of different polarization and the magnons is found to be fundamentally different for the cases of the ${\mathrm{Co}}^{++}$ and ${\mathrm{Fe}}^{++}$ transition-metal ion. The magnon-phonon Hamiltonian is used to calculate the Raman-scattering and infrared-absorption cross sections from the coupled magnon-phonon modes in these materials, and a consistent interpretation of all available experimental results on these coupled modes (magnon-phonon hybridizations, magnon-phonon bound states) is given. In addition, new experiments are proposed for the observation of several magnon-phonon hybridizations not yet reported. Among the effects treated in detail here is the magnon-phonon bound state observed in ${\mathrm{CoBr}}_{2}$ \ifmmode\cdot\else\textperiodcentered\fi{} ${2\mathrm{H}}_{2}$O; its excitation mechanism is given, the phonon is correctly identified, and its binding energy and infrared absorption are calculated.