  In this article, we calculate the magnetization and other thermodynamical
quantities for strongly magnetized quark matter within the Nambu-Jona-Lasinio
model at zero temperature. We assume two scenarios, chemically equilibrated
charge neutral matter present in the interior of compact stars and
zero-strangeness isospin-symmetric matter created in nuclear experiments. We
show that the magnetization oscillates with density but in a much more smooth
form than what was previously shown in the literature. As a consequence, we do
not see the unphysical behavior in the pressure in the direction perpendicular
to the magnetic field that was previously found. Finally, we also analyze the
effects of a vector interaction on our results.
