Electric transport in three-dimensional skyrmion/monopole crystal

We study theoretically the transport properties of a three-dimensional spin texture made from three orthogonal helices, which is essentially a lattice of monopole-antimonopole pairs connected by skyrmion strings. This spin structure is proposed for MnGe based on neutron scattering experiments as well as Lorentz transmission electron microscopy observations. Equipped with a sophisticated spectral analysis method, we adopt the finite temperature Green's function technique to calculate the longitudinal dc electric transport in such a system. We consider conduction electrons interacting with spin waves of the topologically nontrivial spin texture, wherein fluctuations of monopolar emergent magnetic fields enter. We study in detail the behavior of electric resistivity under the influence of temperature, external magnetic field, and a characteristic monopole motion, especially a novel magnetoresistivity effect describing the latest experimental observations in MnGe, wherein a topological phase transition signifying strong correlations is identified.