  We theoretically predict the existence of a non-zero magnetochiral
anisotropy-induced nonlinear Hall effect or a second harmonic Hall voltage
transverse to an applied current in spin-orbit coupled Rashba conductors in the
presence of an in-plane magnetic field B. This is distinct from the Berry
curvature dipole (BCD)-induced nonlinear Hall effect in systems with
non-trivial bandstructure because the former requires broken time-reversal
symmetry while the BCD-induced effect is non-zero even in time-reversal
symmetric systems. This result is independent of the existence of other types
of interactions, such as hexagonal warping or cubic Dresselhaus interactions.
We find that for E||B, the magnitude of the nonlinear Hall current flowing in a
direction perpendicular to the applied electric field is exactly 1/3 of the
magnitude of the non-linear rectification current responsible for
magnetoresistance parallel to the applied electric field obtained in the E\perp
B configuration.
