Angle dependence of Shubnikov-de Haas effect of filled skutterudite compounds CeOs$_4$Sb$_{12}$ and NdOs$_4$Sb$_{12}$

Intriguingly the three filled skutterudite compounds CeOs$_4$Sb$_{12}$, PrOs$_4$Sb$_{12}$, and NdOs$_4$Sb$_{12}$ span the range from the Kondo insulator with a 1K antiferromagnetic (AFM) order, a 1.85K unconventional superconductor (SC), to a 1K mean-field type ferromagnet (FM), indicating that they reside near quantum critical points of AFM and FM with unconventional SC induced within this regime. Therefore, understanding the Fermi surfaces of NdOs$_4$Sb$_{12}$ and CeOs$_4$Sb$_{12}$ becomes crucial in elucidating the superconducting pairing mechanism in PrOs$_4$Sb$_{12}$. Penetration depths of single crystals of CeOs$_4$Sb$_{12}$ and NdOs$_4$Sb$_{12}$ were measured for temperatures down to 1.3 K and magnetic fields up to 60 tesla by using proximity detection oscillators in the Pulsed Field Facility at NHMFL/LANL. Angle dependence of Shubnikov-de Haas oscillations was detected for rotating the field with respect to the crystalline orientations [010] and [0-10]. The results indicate that LaOs$_4$Sb$_{12}$, PrOs$_4$Sb$_{12}$ and NdOs$_4$Sb$_{12}$ have similar Fermi surfaces. The Fermi surface of CeOs$_4$Sb$_{12}$ is rather isotropic and is much different from the other three compounds.