  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.
