Magnetoelectric Response of Antiferromagnetic Van der Waals Bilayers

We predict that antiferromagnetic bilayers formed from van der Waals (vdW) materials, like bilayer CrI$_3$, have a strong magnetoelectric response that can be detected by measuring the gate voltage dependence of Faraday or Kerr rotation signals, total magnetization, or anomalous Hall conductivity. Strong effects are possible in single-gate geometries, and in dual-gate geometries that allow internal electric fields and total carrier densities to be varied independently. We comment on the reliability of density-functional-theory estimates of interlayer magnetic interactions in van der Waals bilayers, and on the sensitivity of magnetic interactions to pressure that alters the spatial separation between layers.