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We show that the metamagnetic transition in Sr$_4$Ru$_3$O$_{10}$ bifurcatesinto two transitions as the field is rotated away from the conducting planes.This two-step process comprises partial or total alignment of moments inferromagnetic bands followed by an itinerant metamagnetic transition whosecritical field increases with rotation. Evidence for itinerant metamagnetism isprovided by the Shubnikov-de Hass effect which shows a non-trivial evolution ofthe geometry of the Fermi surface and an enhancement of the quasiparticleseffective-mass across the transition. The metamagnetic response ofSr$_4$Ru$_3$O$_{10}$ is orbital-dependent and involves ferromagnetic andmetamagnetic bands.Comment: Physical Review B (in press

physical review. b, condensed matter and materials physics

Orbital-dependent metamagnetic response in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mi>Sr</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:msub><mml:mi>Ru</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>10</mml:mn></mml:msub></mml:mrow></mml:math>

Orbital-dependent metamagnetic response inSr4Ru3O10