Exciton-Exciton Transitions in MnF2

Transitions involving the simultaneous creation of two excitons in Mn${\mathrm{F}}_2$ are reported. These double excitons are combinations of the $E1\mathrm{}$ (18 419.6 ${\mathrm{cm}}^{-1\mathrm{}}$) and $E2\mathrm{}$ (18 436.6 ${\mathrm{cm}}^{-1\mathrm{}}$) single excitons. Line transition identified as $E2+E2\mathrm{}$ (36 789 ${\mathrm{cm}}^{-1\mathrm{}}$) and $E1+E2\mathrm{}$ (36 917 ${\mathrm{cm}}^{-1\mathrm{}}$) were seen; however, the transition to the $E1+E1\mathrm{}$ state was not observed. The identification was made with the aid of uniaxial stress measurements; the energy shifts of the double excitons under stress are simply related to those of the $E1\mathrm{}$ and $E2\mathrm{}$ excitons. It is shown on the basis of one-electron molecular orbitals that for the $E1+E1\mathrm{}$ state the exchange interaction, and thus the transition probability, is small. The observed polarization of the double exciton lines is explained in terms of the Mn pair symmetry. It has also been confirmed that the $E1\mathrm{}$ exciton transforms as the $B_3$ representation of the group $D_{2h}$.