  We explore the spin density and charge currents arising on the surface of a
topological insulator and in a 2D Rashba metal due to magnetization gradients.
For topological insulators a single interconversion coefficient controls the
generation of both quantities. This coefficient is quantized to a value
proportional to the vorticity of the Dirac point which constitutes a hallmark
of parity anomaly at finite density. As such, it also unveils a robust route to
disentangle and detect the protected states of a topological insulator on a
given surface. In stark contrast, Rashba metals do not exhibit such anomalies
since they contain an even number of helical branches. Nonetheless, also these
are governed by quantized responses which, however, are not protected against
weak disorder. Furthermore, we find that for Rashba metals the interconversion
coefficients demonstrate discontinuities and a nontrivial interplay upon
varying the chemical potential, the strength of the spin-orbit coupling, and a
pairing gap. Our results have implications for the binding between magnetic
skyrmions and superconducting vortices, the emergence of Majorana zero modes,
and pave the way for superconducting diode effects mediated by out-of-plane
magnetization gradients.
