While plasma often behaves diamagnetically, we demonstrate that the laser irradiation of a thin opaque target with an embedded target-transverse seed magnetic field $B_mathrm{seed}$ can trigger the generation of an order-of-magnitude stronger magnetic field with opposite sign at the target surface. Strong surface field generation occurs when the laser pulse is relativistically intense and results from the currents associated with the cyclotron rotation of laser-heated electrons transiting through the target and the compensating current of cold electrons. We derive a predictive scaling for this surface field generation, $B_mathrm{gen} sim - 2 pi B_mathrm{seed} Delta x/lambda_0$, where $Delta x$ is the target thickness and $lambda_0$ is the laser wavelength, and conduct 1D and 2D particle-in-cell simulations to confirm its applicability over a wide range of conditions. We additionally demonstrate that both the seed and surface-generated magnetic fields can have a strong impact on application-relevant plasma dynamics, for example substantially altering the overall expansion and ion acceleration from a $mu$m-thick laser-irradiated target with a kilotesla-level seed magnetic field.
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