One of the key goals in spintronics is to tame the spin-orbit coupling (SOC) that links spin and motion of electrons, giving rise to intriguing magneto-transport properties in itinerant magnets. Prominent examples of such SOC-based phenomena are the anomalous and topological Hall effects. However, controlling them with electric fields has remained unachieved since an electric field tends to be screened in itinerant magnets. Here we demonstrate that both anomalous and topological Hall effects can be modulated by electric fields in oxide heterostructures consisting of ferromagnetic SrRuO3 and nonmagnetic SrIrO3. We observe a clear electric field effect only when SrIrO3 is inserted between SrRuO3 and a gate dielectric. Our results establish that strong SOC of nonmagnetic materials such as SrIrO3 is essential in electrical tuning of these Hall effects and possibly other SOC-related phenomena.
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