Anisotropy of magnetoresistivity in trilayered ruthenate Sr$_{4}$Ru$_{3}$O$_{10}$: Evidence for orbital dependent metamagnetism

Trilayered ruthenate Sr$_{4}$Ru$_{3}$O$_{10}$ is ferromagnetic with T$_{c}$ $\approx $ 100K and moderate in-plane magnetic field (B$_{c }\approx $ 2T) induces an itinerant metamagnetic transition [1,2]. Such metamagnetism within a FM ground state cannot be understood with a single band model of a field-tuned Stoner transition. We have measured azimuthal angular dependence of in-plane and out-of-plane magnetoresistivity ($\rho _{ab}(\phi $,B) and $\rho _{c}(\phi $,B)). We found that for B$<$B$_{c}$, at fixed field $\rho _{ab}(\phi )$ exhibits a two-fold anisotropy attributable to anisotropic behavior of an Ising ferromagnet, while $\rho _{c}(\phi )$ does not show such a behavior. For B$>$B$_{c}$, both $\rho _{ab}(\phi )$ and $\rho _{c}(\phi )$ exhibit a four-fold symmetry anisotropy, but the minimum value in $\rho _{ab}(\phi )$ and $\rho _{c}(\phi )$ occurs along different directions, i.e., [100] and [010] for $\rho _{ab}$, and [110] and [1$\overline{1}$0] for $\rho _{c}$. Such a difference in anisotropic behavior between $\rho _{ab}(\phi )$ and $\rho _{c}(\phi )$ provides strong support that metamagnetism in Sr$_{4}$Ru$_{3}$O$_{10}$ is orbital dependent, i.e., ferromagnetic and metamagnetic bands coexist. \\ $\left[1\right]$ Cao et al., Phys. Rev. B 68, 174409 (2003)\\ $\left[2\right]$ Mao et al., Phys. Rev. Lett. 96, 077205 (2006)\\ Work at Tulane is supported by NSF, DOE and the Research Corporation.