Purely cubic spin splittings in the band structure of bulk insulators have not been extensively investigated yet despite the fact that they may pave the way for novel spin-orbitronic applications and can also result in a variety of promising spin phenomena. By symmetry analysis and first-principles simulations, we report symmetry-enforced purely cubic spin splittings (SEPCSS) that can even lead to persistent spin textures. In particular, these SEPCSS can be thought to be complementary to the cubic Rashba and cubic Dresselhaus types of spin splittings. Strikingly, the presently discovered SEPCSS are expected to exist in the large family of materials crystallizing in the $\overline{6}m2$ and $\overline{6}$ point groups, including the ${\mathrm{Ge}}_3{\mathrm{Pb}}_5{\mathrm{O}}_{11}$, ${\mathrm{Pb}}_7{\mathrm{Br}}_2{\mathrm{F}}_{12}$, and ${\mathrm{Pb}}_7{\mathrm{Cl}}_2{\mathrm{F}}_{12}$ compounds.

• Received 11 June 2020
• Revised 10 August 2020
• Accepted 9 October 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.216405