Magnetic order tuning of excitons in the magnetic semiconductor CrCl$_3$ through strain

Magnon-exciton coupling provides an unprecedented opportunity for the optical tunability of spin information and, viceversa, for the magnetic control of the optical response. Few-layered magnets are an ideal platform for the experimental study of this coupling, in part due to the strong excitonic character of the optical response in (quasi-)two dimensions. Here, we demonstrate a strong dependence of the excitonic oscillator strength on the magnetic order in a monolayer of chromium trichloride CrCl$_3$. Solving an effective Bethe-Salpeter equation, we evaluate the changes in the excitonic response as the magnetic order switches from the ferromagnetic state to the antiferromagnetic state when strain is applied. Our results reveal an abrupt change in the spatial localization of the excitons across the transition, which translates into a strong shift and a change of the oscillator strength of the excitonic peaks. This suggests the possibility of using strain as a binary switch of the optical response in this material.