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Magnetic frustrated systems have resurged in spintronics as optimalcandidates for hosting three dimensional topological solitons, such as Shankarskyrmions and 4$\pi$-vortices, and other singular topological defects. Thesetopological excitations are encoded in the order-parameter connected to thespin-spin correlation of the system. The key challenge for their experimentaldiscovery is the lack of probes to observe them. We demonstrate here thatspin-transfer torque and topological Hall effect measurements can serve asprobes of magnetic disclinations and solitons in these systems, by means of apreviously unidentified contribution to them from these topological defects,with no analog in collinear magnetism. We present a minimal low-energylong-wavelength theory for the itinerant carriers and derive the effectiveemergent electrodynamics arising from the noncoplanar magnetic background withtopological defects and solitons. This opens new avenues for the detection oftopological defects in magnetic systems with order-parameter manifolds beyondthe conventional $S^{2}$ (unit sphere) ferromagnetic paradigm.

Spin-transfer and Topological Hall Effects as Novel Probes for Magnetic Disclinations in Frustrated Magnets