Probing orbital-dependent magnetism in layered perovskite ruthenates through angle-dependent magnetoresistivity

The orbital degree of freedom plays a very important role in layered perovskite ruthenates, leading to unusual magnetic states. The triple layered Sr$_{4}$Ru$_{3}$O$_{10}$ contains a ferromagnetic ground state, and undergoes a metamagnetic transition under moderate in-plane magnetic fields $\left[1\right]$. By analyzing the anisotropy in angle-dependent directional magnetoresistance measurements we can extract orbital information of magnetism. In Sr$_{4}$Ru$_{3}$O$_{10}$ we have found that below the metamagnetic transition the 4$d_{xy}$ orbitals are already polarized whereas the 4$d_{xz,yz}$ orbitals are not; \textit{$\rho $}$_{ab}$(H) exhibits 2-fold anisotropic symmetry indicating ferromagnetism and \textit{$\rho $}$_{c}$(H) exhibits anisotropy consistent with Fermi surface warping. Above the transition field, under polar rotation we observe a first order phase transition in \textit{$\rho $}$_{c}$(H) for angles close to the \textit{ab}-plane clearly indicating a polarization of the 4$d_{xz,yz}$ orbitals. Additionally, we have performed similar studies on Sr$_{3}$Ru$_{2}$O$_{7}$, and have observed preliminary evidence of orbital-dependent magnetic correlations. This work is supported by the NSF under grant DMR-0645305, the DOE under DE-FG02-07ER46358.\\ $\left[1\right]$ Cao \textit{et al}., Phys. Rev. B \textbf{68}, 174409 (2003)