  While it is known that the QCD vacuum in a magnetic background exhibits both
diamagnetic and paramagnetic characteristics in the low-energy domain, a
systematic investigation of the corresponding phases emerging in the
pion-dominated regime is still lacking. Here, within two-flavor chiral
perturbation theory, taking into account the pion-pion interaction, we analyze
the subtle interplay between zero- and finite-temperature portions in the
magnetization and magnetic susceptibility. The dependence of the magnetic
susceptibility on temperature and magnetic field strength in the paramagnetic
and diamagnetic phase is non-monotonic. Our low-energy analysis complements
lattice QCD that is currently operating at higher temperatures and stronger
magnetic fields.
