Antiferromagnetic hall effect nonlinear in the electric current

A new galvanoantiferromagnetic effect is predicted—the Hall effect nonlinear in the electric current, i.e., a potential difference that is transverse to the current and is associated with the antisymmetric contribution to the resistivity tensor, which violates Ohm’s law, for example, of the form Δρij=?Δρji∝LE, where L is the antiferromagnetism vector and E is the electric field. The indicated contribution is characteristic for centrally antisymmetric antiferromagnets and can lead to a Hall field that is quadratic in the current: ΔE ^⊥ ∝ LJ ². Similarly, the effect ΔE ^⊥∝LJ ³ can exist in centrally symmetric antiferromagnets even in a state where the ordinary Hall effect, which is linear in J, is absent (for example, in hematite below the Morin point).