Critical Field Anisotropy and Muon Spin Relaxation Study of Superconducting Dirac-Semimetal CaSb$_2$

CaSb$_2$ has been identified as a bulk superconductor and a topological semimetal, which makes it a great platform for realizing topological superconductivity. In this work, we investigate the superconducting upper and lower critical field anisotropy using magnetic susceptibility, and study the superconducting state using muon spin-relaxation. The temperature dependence of transverse-field relaxation can be fitted with a single-gap model or two-gap model, consistent with previous tunnel-diode oscillator measurements. We highlight that the normal state of CaSb$_2$ shows a large diamagnetic signal, which is likely related to its Dirac semimetal nature. Zero-field relaxation shows little temperature dependence when the muon-spin is parallel to the $c*$-axis, while an increase in relaxation appears below 1~K when the muon-spin is parallel to the $ab$-plane. This may be related to a second superconducting phase appearing at low temperature below the bulk $T_c$ . However, we find no discernible anomaly in $\mu_{\rm{0}} H_{\rm{c1}}(0)$ around this temperature as has been seen in other superconductors with secondary superconducting states that appear at lower temperatures.