Electronic phase separation in the itinerant metamagnetic transition of Sr$_4$Ru$_3$O$_{10}$

Triple-layered ruthenate Sr$_4$Ru$_3$O$_{10}$ shows a first-order itinerant metamagnetic transition for in-plane magnetic fields. Our experiments revealed rather surprising behavior in the low-temperature transport properties near this transition. The in-plane magnetoresistivity $rho$$_{ab}$(H) exhibits ultrasharp steps as the magnetic field sweeps down through the transition. Temperature sweeps of $rho$$_{ab}$ for fields within the transition regime show non-metallic behavior in the up-sweep cycle of magnetic field, but show a significant drop in the down-sweep cycle. These observations indicate that the transition occurs via a new electronic phase separation process; a lowly polarized state is mixed with a ferromagnetic state within the transition regime.