  We predict from first principles an entirely topological orbital
magnetization in the noncoplanar bulk antiferromagnet $\gamma$-FeMn originating
in the nontrivial topology of the underlying spin structure, without any
reference to spin-orbit interaction. Studying the influence of strain,
composition ratio, and spin texture on the topological orbital magnetization
and the accompanying topological Hall effect, we promote the scalar spin
chirality as key mechanism lifting the orbital degeneracy. The system is thus a
prototypical topological orbital ferromagnet, the macroscopic orbital
magnetization of which is prominent even without spin-orbit coupling. One of
the remarkable features of $\gamma$-FeMn is the possibility for pronounced
orbital magnetostriction mediated by the complex spin topology in real space.
