Zeeman-type spin splitting in non-magnetic three-dimensional compounds: Material prediction and electrical control*

Besides the Rashba and Dresselhaus effects, another kind of spin discrimination phenomena in non-magnetic inversion asymmetry (IA) compounds is the so-called Zeeman-type spin splitting, which exhibits a spin-texture similar to the one observed in the magnetic Zeeman effect. Despite its potential for device application, this non-magnetic effect has only been predicted and observed in the two-dimensional WSe₂ and MoS₂ materials. Here, we demonstrate that three-dimensional compounds can also exhibit this splitting. The required conditions for this effect are: valence band maximum or conduction band minimum in a non-time-reversal-invariant k-point, inversion asymmetry, and zero magnetic moment. Using these conditions as filters, we perform a material screening and high-throughput ab-initio calculations to systematically search for these materials in the ICSD database. We find 20 candidates featuring this splitting. Our calculated spin splittings can be as large as 433, 510, and 491meV for the compounds WN₂ (P6m1), WS₂ (R3m), and SnTe (F43m), respectively. We also demonstrate that the spin splitting in slabs of these compounds depends on the growth direction and can be controlled by an external electric field.