The nontrivial topology of spin systems such as skyrmions in real space can promote complex electronic states. Here, we provide a general viewpoint at the emergence of topological spectral gaps in spin systems based on the methods of noncommutative-theory. By realizing that the structure of the observable algebra of spin textures is determined by the algebraic properties of the noncommutative torus, we arrive at a unified understanding of topological electronic states which we predict to arise in various noncollinear setups. The power of our approach lies in an ability to categorize emergent topological states algebraically without referring to smooth real- or reciprocal-space quantities. This opens a way towards an educated design of topological phases in aperiodic, disordered, or nonsmooth textures of spins and charges containing topological defects.
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Published by the American Physical Society 2024 -
Abstract The emergence of spin‐orbit torques as a promising approach to energy‐efficient magnetic switching has generated large interest in material systems with easily and fully tunable spin‐orbit torques. Here, current‐induced spin‐orbit torques in VO2/NiFe heterostructures are investigated using spin‐torque ferromagnetic resonance, where the VO2layer undergoes a prominent insulator‐metal transition. A roughly twofold increase in the Gilbert damping parameter, α, with temperature is attributed to the change in the VO2/NiFe interface spin absorption across the VO2phase transition. More remarkably, a large modulation (±100%) and a sign change of the current‐induced spin‐orbit torque across the VO2phase transition suggest two competing spin‐orbit torque generating mechanisms. The bulk spin Hall effect in metallic VO2, corroborated by the first‐principles calculation of the spin Hall conductivity , is verified as the main source of the spin‐orbit torque in the metallic phase. The self‐induced/anomalous torque in NiFe, with opposite sign and a similar magnitude to the bulk spin Hall effect in metallic VO2, can be the other competing mechanism that dominates as temperature decreases. For applications, the strong tunability of the torque strength and direction opens a new route to tailor spin‐orbit torques of materials that undergo phase transitions for new device functionalities.