  The ordinary Hall effect refers to generation of a transverse voltage upon
exertion of an electric field in the presence of an out-of-plane magnetic
field. While a linear Hall effect is commonly observed in systems with breaking
time-reversal symmetry via an applied external magnetic field or their
intrinsic magnetization1, 2, a nonlinear Hall effect can generically occur in
non-magnetic systems associated with a nonvanishing Berry curvature dipole3.
Here we report, observations of a nonlinear optical Hall effect in a Weyl
semimetal WTe2 without an applied magnetic field at room temperature. We
observe an optical Hall effect resulting in a polarization rotation of the
reflected light, referred to as the nonlinear Kerr rotation. The nonlinear Kerr
rotation linearly depends on the charge current and optical power, which
manifests the fourth-order nonlinearity. We quantitatively determine the
fourth-order susceptibility, which exhibits strong anisotropy depending on the
directions of the charge current and the light polarization. Employing symmetry
analysis of Berry curvature multipoles, we demonstrate that the nonlinear Kerr
rotations can arise from the Berry curvature hexapole allowed by the
crystalline symmetries of WTe2. There also exist marginal signals that are
incompatible with the symmetries, which suggest a hidden phase associated with
the nonlinear process.
