Absorption lines corresponding to the simultaneous creation of two excitons have been investigated in Mn${\mathrm{F}}_2$ and RbMn${\mathrm{F}}_3$. The particular zero-phonon transitions observed are those from the ground states of a Mn ion pair to the ${}_{}{}^4{}_{}{}^{}T_1^{}{}_{}{}^{}\mathrm{}\left(G\right)+{}_{}{}^4{}_{}{}^{}T_1^{}{}_{}{}^{}\mathrm{}\left(G\right)\mathrm{}$, ${}_{}{}^4{}_{}{}^{}T_1^{}{}_{}{}^{}\mathrm{}\left(G\right)+{}_{}{}^4{}_{}{}^{}A_1^{}{}_{}{}^{}$, ${}_{}{}^4{}_{}{}^{}E$, and ${}_{}{}^4{}_{}{}^{}T_1^{}{}_{}{}^{}\mathrm{}\left(G\right)+{}_{}{}^4{}_{}{}^{}T_2^{}{}_{}{}^{}\mathrm{}\left(D\right)\mathrm{}$ excited states in Mn${\mathrm{F}}_2$ and to the ${}_{}{}^4{}_{}{}^{}T_1^{}{}_{}{}^{}\mathrm{}\left(G\right)+{}_{}{}^4{}_{}{}^{}T_1^{}{}_{}{}^{}\mathrm{}\left(G\right)\mathrm{}$, ${}_{}{}^4{}_{}{}^{}T_1^{}{}_{}{}^{}\mathrm{}\left(G\right)+{}_{}{}^4{}_{}{}^{}A_1^{}{}_{}{}^{}$, ${}_{}{}^4{}_{}{}^{}E$, and ${}_{}{}^4{}_{}{}^{}A_1^{}{}_{}{}^{}$, ${}_{}{}^4{}_{}{}^{}E+{}_{}{}^4{}_{}{}^{}A_1^{}{}_{}{}^{}$, ${}_{}{}^4{}_{}{}^{}E$ states in RbMn${\mathrm{F}}_3$. An attempt is made to identify the particular excitons created in these transitions through their polarizations and uniaxial stress behavior. Selection rules are derived using the space-group representations along with the additional assumption that the transition mechaanism is an off-diagonal exchange interaction between pairs of Mn ions on opposite magnetic sublattices. The interaction between excitons is discussed; it is found experimentally that for those excitons which couple strongly to the lattice, the phonon coupling provides the major part of the interaction. The exciton-exciton interaction energy is positive or negative and varies from 10 to 400 ${\mathrm{cm}}^{-1\mathrm{}}$ in magnitude. A measurement of the $L$-point magnon energy in RbMn${\mathrm{F}}_3$ has been made from an analysis of the ${}_{}{}^6{}_{}{}^{}A_1^{}{}_{}{}^{}\to {}_{}{}^4{}_{}{}^{}T_1^{}{}_{}{}^{}\mathrm{}\left(G\right)\mathrm{}$ magnon sidebands; it is found to be 73±0.5 ${\mathrm{cm}}^{-1\mathrm{}}$.

• Received 9 June 1971

DOI:https://doi.org/10.1103/PhysRevB.4.3141