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The magnon dispersion of ferromagnetic SrRuO$_3$ was studied by inelasticneutron scattering experiments on single crystals as function of temperature.Even at low temperature the magnon modes exhibit substantial broadeningpointing to strong interaction with charge carriers. We find an anomaloustemperature dependence of both the magnon gap and the magnon stiffness, whichsoften upon cooling in the ferromagnetic phase. Both effects trace thetemperature dependence of the anomalous Hall effect. We argue that theseresults show that Weyl points and the anomalous Hall effect can directlyinfluence the spin dynamics in metallic ferromagnets.

Interplay of electronic and spin degrees in ferromagnetic SrRuO$_3$: anomalous softening of magnon gap and stiffness