We develop a theory for the dynamics of a magnon on top of a domain wall in a ferromagnetic nanotube. Due to the geometry of the sample, domain walls are classified by the Skyrmion charge which counts the winding number of magnetic textures. The domain wall with a non-zero Skyrmion charge generates an emergent magnetic field for magnons, which exerts the Lorentz force on moving magnons and thereby deflects their trajectories. This deflection is manifested as the generation of the finite orbital angular momentum of the magnon that traverses the domain wall. We obtain exact solutions for the magnon on top of the Skyrmion-textured domain wall and also their scattering properties with the domain wall with the aid of supersymmetric quantum mechanics. We show that there is a critical wavenumber for the total reflection of magnons and it is discretized by the Skyrmion charge of the domain wall. Our results show that the orbital angular momenta of magnetic textures and magnons can be intertwined in a curved geometry.

We theoretically study the current-induced dynamics of a domain wall in a ferromagnetic nanotube by developing a theory for the orbital angular momentum of a domain wall and the current-induced torque on it. Specifically, a domain wall with nontrivial magnetization winding along the circumference is shown to possess finite orbital angular momentum, which is proportional to the product of its Skyrmion charge and position, and the current is shown to exert a torque changing the orbital angular momentum of the domain wall and thereby drives it. The current-induced torque is interpreted as the transfer of orbital angular momentum from electrons to the domain wall, which occurs due to the emergent magnetic field associated with the Skyrmion charge. Our results reveal a hitherto unrecognized utility of the orbital degree of freedom of magnetic solitons.

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