Topological Kerr Effect.

We study the magneto-optical Kerr effect in SrRuO$_3$ thin films, at different laser wavelengths and incidence angles, uncovering regimes of temperature and magnetic field where the Kerr rotation displays two-component behavior. One component of the Kerr signal tracks the magnetization, while the second component bears a strong similarity to the topological Hall effect seen in transport experiments and is thus attributable to the presence of skyrmions. A comparison of different substrates suggests that strain plays a key role in this phenomenon. We substantiate this with a Landau theory analysis of magneto-elastic coupling to strain gradients that generates the chiral Dzyaloshinskii-Moriya exchange required to stabilize skyrmions in our intermediate thickness films. A model of electrons coupled to a skyrmion crystal is found to exhibit a significant Kerr angle at a frequency scale set by the effective Hund's coupling, lending further support to our proposal. We term this observed optical incarnation of the topological Hall effect as the "topological Kerr effect".