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We report electronic band structure calculations for Sr$_{4}$Ru$_{3}$O$_{10}$that displays both ferromagnetic and metamagnetic behavior. The densityfunctional calculations find the ground state to be ferromagnetic in agreementwith the experiment and we find that the inclusion of Coulomb Hubbardinteraction U applied to the Ru 4d states has dramatic effects on the Fermisurface, which reveal the role of Coulomb interactions and correlated many-bodyphysics. The minority spin bands are mainly empty with Fermi surfaces in theouter areas of the Brillouin zone away from the $\Gamma$ point with bands thatdisperse steeply upward. The majority spin bands are full or nearly fullyoccupied and form narrow bands near the Fermi energy around the $\Gamma$ point,which could be the electronic origin of the metamagnetism. The results are inqualitative agreement with recent angle resolved photoemission spectroscopy(ARPES) experiments and show the need for a combined theoretical study andexperimental ARPES investigation with better energy resolution to reveal thenature of the narrow bands close to the Fermi-level, which is critical forunderstanding the exotic magnetic properties observed in this material.

Electronic Structure and Magnetism of the Triple-layered Ruthenate Sr$_{4}$Ru$_{3}$O$_{10}$