Orbital Physics: Colossal Magnetoresistance and Quantum Oscillations in the Mott System Ca$_{3}$Ru$_{2}$O$_{7}$

Ca$_{3}$Ru$_{2}$O$_{7}$ features a Mott transition, colossal magnetoresistance and quantum oscillations. Ca$_{3}$Ru$_{2}$O$_{7 }$shows strikingly different behavior when the field is applied along the different crystal axes. A ferromagnetic (FM) state with full spin polarization is achieved for B$\vert \vert a-$axis, but colossal magnetoresistance is realized \textit{only} for B$\vert \vert b$-axis by avoiding the ferromagnetic state. For B$\vert \vert c$-axis, Shubnikov-de Haas oscillations are observed and followed by a less resistive state than for B$\vert \vert a$. Hence, in contrast to standard colossal magnetoresistive materials, the FM phase is the least \textit{favorable} for electron hopping. In addition, for B rotating within the \textit{ac}-plane, slow and strong Shubnikov-de Haas (SdH) oscillations periodic in 1/B are observed for T$\le $1.5 K in the presence of metamagnetism. These oscillations are highly angular dependent and intimately correlated with the spin-polarization of the ferromagnetic state. For B$\vert \vert $[110], oscillations are also observed \textit{but periodic in B }(rather than 1/B)\textit{ which persist up to 15 K. } While the SdH oscillations are a manifestation of the presence of small Fermi surface (FS) pockets in the Mott-like system, the B-periodic oscillations, an exotic quantum phenomenon, may be a result of anomalous coupling of the magnetic field to the $t_{2g}$-orbitals that makes the extremal cross-section of the FS field-dependent.