  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.
