In-plane anisotropy of magnetoresistivity of tri-layered ruthenate Sr$_4$Ru$_3$O$_{10}$

The tri-layered ruthenate Sr$_4$Ru$_3$O$_{10}$ exhibits intriguing magnetic properties; its ferromagnetic transition at $T_c$ $\approx$ 105 K is followed by an additional magnetic phase transition at $T^*$ $\approx$ 50 K [1,2]. Below $T^*$, a first order metamagnetic transition is induced by a magnetic field applied in the plane. We have recently measured the in-plane angular dependence of magnetoresistivity of this material at various magnetic fields and temperatures. Our data reveal that the in-plane anisotropy of magnetoresistivity undergoes a transition from two-fold to four-fold symmetry across the metamagnetic transition of Sr$_4$Ru$_3$O$_{10}$. Such a transition can be well interpreted in terms of a multiple-band effect which involves the coexistence of ferromagnetic and metamagnetic bands.\\* $[1]$ G. Cao $et$ $al.$, Phys. Rev. B \textbf{68}, 174409 (2003). \\* $[2]$ Z.Q. Mao $et$ $al.$, Phys. Rev. Lett. \textbf{96}, 077205 (2006).