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Magnetic Weyl semimetals are unique among topological materials in possessing magnetic textures that are embedded directly into their topological structure and interact dynamically with it. The resulting interplay between non-trivial real-space and momentum-space topologies makes magnetic Weyl semimetals prominent candidates for the electrical manipulation of magnetic textures, with electrical control of local domain walls potentially enabling faster, lower power manipulation than conventional ferromagnetic metals. Since the magnetization, which is in general inhomogeneous, determines the location of the Weyl nodes, we demonstrate here that non-equilibrium carrier dynamics in the vicinity of the Weyl nodes in turn influences the magnetization, leading to a \textit{nodal spin-transfer torque} (NSTT) facilitated by charge accumulation on either side of a domain wall, with no counterpart in other materials. Using the Landau-Lifshitz-Gilbert equation we show that the nodal spin-transfer torque in real space results from the displacement of the Weyl nodes in momentum space mediated by the electrically-driven inhomogeneous magnetic texture, and is directly responsible for an electric field-induced structural transition in the magnetic configuration of one-dimensional domain walls and three-dimensional ferromagnetic domains. Remarkably, specific electric field orientations cause a N\'{e}el domain wall to vanish entirely, whereas a Bloch domain wall survives as the magnetization on either side of it is rotated. In order to examine the associated charge dynamics we develop a quantum kinetic theory for magnetic Weyl semimetals with dynamical domain walls under the influence of an external electric field, which captures the interplay between the driving force on the charge carriers, momentum-space topology and the real-space magnetic texture. We demonstrate that the presence of domain walls leads to non-linear anomalous drift and Hall currents, whose real-space profile can be used as a probe of the steady-state magnetic texture. For certain electric field orientations an \textit{electrical chiral anomaly} emerges, accompanied by the accumulation of extrinsic anomalous charge across the domain walls. We discuss experimental observation in state-of-the art samples and implications for magnetic memory and computing devices.
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