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 intersecting cylinders, supports open orbits. $\rho_{xx}$ in a magnetic field $B$ = 9 T displays singular pattern behavior. With $\bf E\parallel \hat{x}$ B$ initially $\parallel\bf\hat{z}$, tilting the longitudinal $k_z$-$k_x$ plane leads to steep decrease by factor 40. However, if is tilted transverse $k_y$-$k_z$ plane, increases steeply 8. Using Shockley tube integral approach, we show that, ReO$_3$, behavior results from rapid conversion closed orbits, resulting opposite signs for AMR orthogonal planes. floor values both scans are identified specific sets Also, "completion angle" $\gamma_c$ detected shown be an intrinsic geometric feature that provides new way measure radius $k_F$. additional sharp resonant features which appear very small tilt angles not explained approach.