Orbital angular momentum of a domain wall and geometrically twisted magnons*

We theoretically study the dynamics of a domain wall in a ferromagnetic nanotube driven by electrons and magnons by investigating the electron-domain-wall and magnon-domain wall interactions. Due to the geometry of the sample, domain walls are classified by the Skyrmion charge which counts the winding number of magnetic textures on the domain wall [1]. The domain wall with a non-zero Skyrmion charge generates an emergent magnetic field for interacting particles, which exerts the Lorentz force on moving electrons and magnons and thereby deflects their trajectories. This deflection is manifested as the generation of the finite orbital angular momenta of the electrons and magnons that traverse the domain wall [2,3]. For the case of electrons, we can interpret the exchange of orbital angular momenta between electrons and the domain wall as a current-induced torque. From this peculiar torque, the domain wall with the non-zero Skyrmion charge can be driven by an arbitrary small current without the Walker breakdown. For the case of magnons, we obtain the exact solution for the magnon on the Skyrmion-textured domain wall and also their scattering properties with the domain wall with the aid of supersymmetric quantum mechanics (SUSY QM) [4]. We also show that there is a critical wavenumber for the total reflection and it is discretized by the Skyrmion charge of the domain wall. Our results show that the orbital angular momenta of magnetic systems and quasi-particles can be intertwined in a curved geometry.