  Magnetized high energy density physics offers new opportunities for observing
magnetic field-related physics for the first time in the laser-plasma context.
We focus on one such phenomenon, which is the ability of a laser-irradiated
magnetized plasma to amplify a seed magnetic field. We performed a series of
fully kinetic 3D simulations of magnetic field amplification by a
picosecond-scale relativistic laser pulse of intensity $4.2\times 10^{18}$
W/cm$^2$ incident on a thin foil. We observe axial magnetic field amplification
from an initial 0.1 kT seed to 1.5 kT over a volume of several cubic microns,
persisting hundreds of femtoseconds longer than the laser pulse duration. The
magnetic field amplification is driven by electrons in the return current
gaining favorable orbital angular momentum from the seed magnetic field. This
mechanism is robust to laser polarization and delivers order-of-magnitude
amplification over a range of simulation parameters.
