Dichroic cavity mode splitting and lifetimes from interactions with a ferromagnetic metal

We study the effect of ferromagnetic metals (FM) on the circularly polarized modes of an electromagnetic cavity and show that broken time-reversal symmetry leads to a dichroic response of the cavity modes. With one spin-split band, the Zeeman coupling between the FM electrons and cavity modes leads to an anticrossing for mode frequencies comparable to the spin splitting. However, this is only the case for one of the circularly polarized modes, while the other is unaffected by the FM, allowing for the determination of the spin-splitting of the FM using polarization-dependent transmission experiments. Moreover, we show that for two spin-split bands, also the lifetimes of the cavity modes display a polarization-dependent response. The change in photon lifetimes can be understood as a suppression due to level attraction with a continuum of Stoner modes with the same wavevector. The reduced lifetime of modes of only one polarization could potentially be used to engineer and control circularly polarized cavities.