  We study the Hall conductivity of a two-dimensional electron gas under an
inhomogeneous magnetic field $B(x)$. First, we prove using the quantum kinetic
theory that an odd magnetic field can lead to a purely nonlinear Hall response.
Second, considering a real-space magnetic dipole consisting of a sign-changing
magnetic field and based on numerical semiclassical dynamics, we unveil a
parametric resonance involving the cyclotron ratio and a characteristic width
of $B(x)$, which can greatly enhance the Hall response. Different from previous
mechanisms that rely on the bulk Berry curvature dipole, here, the effect
largely stems from boundary states associated with the real-space magnetic
dipole. Our findings pave a new way to engineer current rectification and
higher harmonic generation in two-dimensional materials having or not crystal
inversion symmetry.
