Zeeman effect in centrosymmetric antiferromagnets controlled by an electric field

Centrosymmetric antiferromagnetic semiconductors, although abundant in nature, seem less promising than ferromagnets and ferroelectrics for practical applications in semiconductor spintronics. As a matter of fact, the lack of spontaneous polarization and magnetization hinders the efficient utilization of electronic spin in these materials. Here, we propose a paradigm to harness electronic spin in centrosymmetric antiferromagnets via Zeeman spin splittings of electronic energy levels -- termed as spin Zeeman effect -- which is controlled by electric field.By symmetry analysis, we identify twenty-one centrosymmetric antiferromagnetic point groups that accommodate such a spin Zeeman effect. We further predict by first-principles that two antiferromagnetic semiconductors, Fe$_2$TeO$_6$ and SrFe$_2$S$_2$O, are excellent candidates showcasing Zeeman splittings as large as $\sim$55 and $\sim$30 meV, respectively, induced by an electric field of 6 MV/cm. Moreover, the electronic spin magnetization associated to the splitting energy levels can be switched by reversing the electric field. Our work thus sheds light on the electric-field control of electronic spin in antiferromagnets, which broadens the scope of application of centrosymmetric antiferromagnetic semiconductors.