Optical Exciton-Magnon Absorption in Mn<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">F</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

We present the results of a detailed theoretical and experimental investigation of the $^{6}A_{1g}$ to $^{4}T_{1g}$ optical absorption in Mn${\mathrm{F}}_{2}$. This transition is one in which a spin-wave sideband was identified in an earlier communication. A collective-mode theory of the excitations associated with the ${\mathrm{Mn}}^{2+}$ ions is developed. Excitations within the orbital ground-electronic state correspond to the familiar spin waves, while excitations involving the excited electronic states correspond to Frenkel excitons. The symmetry of these excitations is determined and is employed to develop the selection rules for optical absorption. It is shown that the two magnetic dipole absorptions in $\ensuremath{\sigma}$ polarization (denoted $E1$ and $E2$) correspond to the excitation of k = 0 excitons. It is also shown that the three sideband absorptions (denoted $\ensuremath{\pi}1$, $\ensuremath{\sigma}1$, and $\ensuremath{\sigma}2$) correspond to processes in which an exciton with a wave vector in the vicinity of the Brillouin zone is generated simultaneously with a spin wave of opposite wave vector. The theoretical position, shape, temperature dependence, and magnetic field dependence of these sidebands is shown to agree well with observation. The application of the theory to other transitions in Mn${\mathrm{F}}_{2}$ and to other magnetic materials is briefly discussed.

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