Singular angular magnetoresistance and sharp resonant features in a high-mobility metal with open orbits, ReO3

We report high-resolution angular magnetoresistance (AMR) experiments performed on crystals of ReO$_3$ with high mobility (90,000 cm$^2$/Vs at 2 K) and extremely low residual resistivity (5-8 n$\Omega$cm). The Fermi surface, comprised of intersecting cylinders, supports open orbits. The resistivity $\rho_{xx}$ in a magnetic field $B$ = 9 T displays a singular pattern of behavior. With $\bf E\parallel \hat{x}$ and $\bf B$ initially $\parallel\bf\hat{z}$, tilting $\bf B$ in the longitudinal $k_z$-$k_x$ plane leads to a steep decrease in $\rho_{xx}$ by a factor of 40. However, if $\bf B$ is tilted in the transverse $k_y$-$k_z$ plane, $\rho_{xx}$ increases steeply by a factor of 8. Using the Shockley tube integral approach, we show that, in ReO$_3$, the singular behavior results from the rapid conversion of closed to open orbits, resulting in opposite signs for AMR in orthogonal planes. The floor values of $\rho_{xx}$ in both AMR scans are identified with specific sets of open and closed orbits. Also, the "completion angle" $\gamma_c$ detected in the AMR is shown to be an intrinsic geometric feature that provides a new way to measure the Fermi radius $k_F$. However, additional sharp resonant features which appear at very small tilt angles in the longitudinal AMR scans are not explained by the tube integral approach.