  Despite its potential for device application, the non-magnetic Zeeman effect
has only been predicted and observed in two-dimensional compounds. We
demonstrate that non-centrosymmetric three-dimensional compounds can also
exhibit a Zeeman-type spin splitting, allowing the splitting control by
changing the growth direction of slabs formed by these compounds. We determine
the required conditions for this effect: $i$) non-centrosymmetric including
polar and non-polar point groups, $ii$) valence band maximum or conduction band
minimum in a generic $k$-point, i.e., non-time-reversal-invariant momentum, and
$iii$) zero magnetic moment. Using these conditions as filters, we perform a
material screening to systematically search for these systems in the aflow-ICSD
database. We find 20 material candidates featuring the Zeeman-type effect. We
also found that the spin-splitting in confined systems can be controlled by an
external electric field, which in turns can induce a metal-insulator
transition. We believe that the Zeeman-type effect in three-dimensional
compounds can potentially be used for spin-filtering devices.
