  Superconducting bulks, acting as high-field permanent magnets, are promising
for many applications. An important effect in bulk permanent magnets is
crossed-field demagnetization, which can reduce the magnetic field in
superconductors due to relatively small transverse fields. Crossed-field
demagnetization has not been studied in sample shapes such as rectangular
prisms or cubes. This contribution presents a study based on both 3D numerical
modelling and experiments. We study a cubic Gd-Ba-Cu-O bulk superconductor
sample of size 6 mm magnetized by field cooling in an external field of around
1.3 T, which is later submitted to crossed-field magnetic fields of up to 164
mT. Modelling results agree with experiments, except at transverse fields 50\%
or above of the initial trapped field. The current paths present a strong 3D
nature. For instance, at the mid-plane perpendicular to the initial magnetizing
field, the current density in this direction changes smoothly from the critical
magnitude, ${J_c}$, at the lateral sides to zero at a certain penetration
depth. This indicates a rotation of the current density with magnitude ${J_c}$,
and hence force free effects like flux cutting are expected to play a
significant role.
