Phenomenology of anomalous Kerr effect in SrRuO₃ thin films

Recent Hall experiments on ultrathin films of SrRuO₃ ferromagnet with several-unit-cell thickness have observed unusual hysteresis loops which display bump features near the coercive mangetic fields. This resembles the topological Hall effect induced by skyrmions which can nucleate during the magnetization reversal process and can arise from the interfacial Dzyaloshinskii-Moriya (IDM) interation at the film-substrate interface. A recent experiment on thicker films with more than 100 unit cells, where the IDM interation and skyrmions are not expected to be important, has also found the unusual hysteresis loops. Intriguingly, such unusual hystersis loops are also discovered in the optical Kerr effect. We formulate a phenomenological theory for the unusual Kerr effect which is shown to arise from the interplay between two non-skyrmion sources: (1) magnetic domains which are naturally present during the magnetization reversal and (2) an unsual nonmonotonic relation between the Kerr angle and the magnetization. Our work suggests that magnetic domains, instead of skyrmions, may provide a common origin for the unusual hysteresis loops in both Kerr and Hall effects in these thin films.