Magnetic domain formation in the itinerant metamagnetic transition of Sr$_{4}$Ru$_{3}$O$_{10}$

We have performed systematic investigation on the electronic transport properties of the triple-layered ruthenate Sr$_{4}$Ru$_{3}$O$_{10}$. We observed surprising anomalous features near its itinerant metamagnetic transition, including ultrasharp magnetoresistivity steps and a non-metallic temperature dependence in resistivity for upward field sweeps. These features suggest that the metamagnetic transition of Sr$_{4}$Ru$_{3}$O$_{10}$ occurs via a phase separation process with magnetic domain formation. We have also identified the phase separated regime in the magnetic field-temperature phase diagram.