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We explore the spin density and charge currents arising on the surface of atopological insulator and in a 2D Rashba metal due to magnetization gradients.For topological insulators a single interconversion coefficient controls thegeneration of both quantities. This coefficient is quantized to a valueproportional to the vorticity of the Dirac point which constitutes a hallmarkof parity anomaly at finite density. As such, it also unveils a robust route todisentangle and detect the protected states of a topological insulator on agiven surface. In stark contrast, Rashba metals do not exhibit such anomaliessince they contain an even number of helical branches. Nonetheless, also theseare governed by quantized responses which, however, are not protected againstweak disorder. Furthermore, we find that for Rashba metals the interconversioncoefficients demonstrate discontinuities and a nontrivial interplay uponvarying the chemical potential, the strength of the spin-orbit coupling, and apairing gap. Our results have implications for the binding between magneticskyrmions and superconducting vortices, the emergence of Majorana zero modes,and pave the way for superconducting diode effects mediated by out-of-planemagnetization gradients.

Anatomy of Spin and Current Generation from Magnetization Gradients in Topological Insulators and Rashba Metals