The control of spin-dependent properties by voltage, not involving magnetization switching, has significant advantages for low-power spintronics. Here, we predict that the interfacial crystal Hall effect (ICHE) can serve for this purpose. We show that the ICHE can occur in heterostructures composed of compensated antiferromagnetic metals and non-magnetic insulators due to reduced symmetry at the interface, and it can be made reversible if the antiferromagnet is layered symmetrically between two identical ferroelectric layers. We explicitly demonstrate this phenomenon using density functional theory calculations for three material systems: MnBi$_{2}$Te$_{4}$/GeI$_{2}$ and topological In$_{2}$Te$_{3}$/MnBi$_{2}$Te$_{4}$/In$_{2}$Te$_{3}$ van der Waals heterostructures, and GeTe/Ru$_{2}$MnGe/GeTe heterostructure composed of three-dimensional materials. We show that all three systems reveal a sizable ICHE, while the latter two exhibit a quantum ICHE and ICHE, respectively, reversible with ferroelectric polarization. Our proposal opens an alternative direction for voltage controlled spintronics and offers not yet explored possibilities for functional devices by heterostructure design.
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