Metastable Magnetic states in Ca$_{3}$Ru$_{2}$O$_{7}$

We have performed systematic in-plane angle dependent c-axis transverse magnetotransport measurements on the double layered ruthenate Ca$_{3}$Ru$_{2}$O$_{7}$ throughout a broad field and temperature range. Our results reveal the magnetic states for $H\|b$ to be significantly more complex than for $H\|a$. When magnetic field is applied along the b-axis we probe several metastable magnetic states in close proximity to phase boundaries of long-range ordered antiferromagnetic (AFM) states previously revealed by neutron scattering, i.e. AFM states with magnetic moments oriented along the b-axis (AFM-b) and a-axis (AFM-a); canted AFM state (CAFM) (Wei Bao \textit{et al.}, Phys. Rev. Lett. \textbf{100}, 247203 (2006)). These metastable states are characterized by magnetoresistivity anisotropy distinct from that seen in the AFM-a, AFM-b, or CAFM phases, and switch either to a weakly ferromagnetic or AFM-b state when the magnetic field is rotated toward the \textit{a}-axis. Additionally, our results highlight the complex nature of the spin-charge coupling in Ca$_{3}$Ru$_{2}$O$_{7}$.