The intrinsic electron spin $s=1/2$ and its orbital angular momentum $l$ are often blended due to relativistic orbital motion. This spin-orbit coupling (SOC) can be highly strong in compounds containing heavy elements, and therefore the total angular momentum, or effective spin, $j$, becomes the relevant quantum number. The band structure driven by strong SOC effect is fundamentally important in topological matters and is responsible for the quantum spin Hall effect, Weyl physics and high-spin topological superconductivity, which are promising platforms for the quantum devices. However, the high-spin Fermi surface in such systems has not been rigorously verified due to the inaccessible large-$j$ band. Here, we report compelling evidence for a coherent $j$=3/2 Fermi surface in the topological half-Heusler semimetal YPtBi via studies of the angle-dependent Shubnikov-de Haas effect, which exhibits an amplitude variation that is strikingly anisotropic for such a highly symmetric cubic material. We show that the unprecedented, anomalous anisotropy is uniquely explained by the spin-split Fermi surface of $j$=3/2 quasiparticles, and therefore confirm the existence of the long-sought high-spin nature of electrons in the topological RPtBi (R=rare earth) compounds. This work offers a thorough understanding of the $j$=3/2 fermiology in RPtBi, a cornerstone for realizing topological superconductivity and its application to fault-tolerant quantum computation.
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