11 January 2022 Tue 4 pm

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We study the stability of topologically protected magnetic textures, such as skyrmions and antiferromagnetic skyrmions, in Hund’s insulators and metals. The study is motivated by (i) the technological importance of such magnetic textures in possible future devices, (ii) a lack of current theoretical understanding of formation of these textures at a microscopic level. Starting with ferromagnetic Kondo lattice model in the presence of Rashba spin-orbit coupling on a square lattice, we have derived a generalized classical super-exchange (CSE) Hamiltonian starting with large ferromagnetic Kondo coupling JH at half-filling. For large JH , the ground state corresponds to an insulator at half-filling (one electron per site), and the situation is similar to the Mott state in the Hubbard model. The elegant analogy with the effective quantum spin model originating from the Mott insulator suggests that Hund’s coupling can serve as a proxy for Hubbard interactions to understand the influence of spin-orbit coupling on magnetic ordering. In addition to the standard isotropic term, the anisotropic interactions of Dzyaloshinskii-Moriya and Kitaev-like form appear in this model. We show via explicit simulations that the model supports antiferromagnetic skyrmions and highly elusive skyrmion density wave states at low temperatures.

Further, we have investigated the effect on the ground state magnetic configurations by introducing geometric frustration in the effective CSE Hamiltonian on a triangular lat- tice. The large-scale Monte-Carlo simulation of this model leads to two antiferromagnetic skyrmion crystal (AF-SkX) phases that are understood to originate from a classical spin liquid state that exists at low but finite temperatures. Furthermore, these AF-SkX states can be easily distinguished in experiments as peaks characterize them at distinct momenta in the spin structure factor, directly measured in neutron scattering experiments.

Lastly, we have investigated how the spin-orbit coupling and the band structure details affect the underlying magnetic textures in the metallic limit. We have shown, the anti- ferromagnetic skyrmions can also be stabilized in a Hund’s metal by tuning the exchange coupling strength in a Dresselhaus spin-orbit coupled double exchange model. We pre- dict that this simple microscopic mechanism leads to antiferromagnetic skyrmions even in materials that conventionally host the ferromagnetic skyrmions. This work highlights the role played by the electron itinerancy in deciding the type of topological magnetic textures in metals and insulators.

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