  Using a semiclassical Green's function formalism, we discover the emergence
of chiral and topological orbital magnetism in two-dimensional chiral spin
textures by explicitly finding the corrections to the orbital magnetization,
proportional to the powers of the gradients of the texture. We show that in the
absence of spin-orbit coupling, the resulting orbital moment can be understood
as the electronic response to the emergent magnetic field associated with the
real-space Berry curvature. By referring to the Rashba model, we demonstrate
that by tuning the parameters of surface systems the engineering of emergent
orbital magnetism in spin textures can pave the way to novel concepts in
orbitronics.
