  The symmetry considerations that imply a non-zero anomalous Hall effect (AHE)
in certain non-collinear antiferromagnets also imply both non-zero orbital
magnetization and a net spin magnetization. We have explicitly evaluated the
orbital magnetizations of several anomalous Hall effect antiferromagnets and
find that they tend to dominate over spin magnetizations, especially so when
spin-orbit interactions are weak. Because of the greater relative importance of
orbital magnetization the coupling between magnetic order and an external
magnetic field is unusual. We explain how magnetic fields can be used to
manipulate magnetic configurations in these systems, pointing in particular to
the important role played by the response of orbital magnetization to the
Zeeman-like spin exchange fields.
