Effective bilinear-biquadratic model for noncoplanar ordering in itinerant magnets

Noncollinear and noncoplanar magnetic textures including skyrmions and vortices act as emergent electromagnetic fields and give rise to novel electronic and transport properties. We here report a unified understanding of noncoplanar magnetic orderings emergent from the spin-charge coupling in itinerant magnets. The mechanism has its roots in effective multiple spin interactions beyond the conventional Ruderman-Kittel-Kasuya-Yosida (RKKY) mechanism, which are ubiquitously generated in itinerant electron systems with local magnetic moments. Carefully examining the higher-order perturbations in terms of the spin-charge coupling, we construct a minimal effective spin model composed of the bilinear and biquadratic interactions with particular wave numbers dictated by the Fermi surface. We find that our effective model captures the underlying physics of the instability toward noncoplanar multiple-$Q$ states discovered recently in itinerant magnets: a single-$Q$ helical state expected from the RKKY theory is replaced by a double-$Q$ vortex crystal with chirality density waves even for an infinitely small spin-charge coupling on generic lattices [R. Ozawa $\mathit{et \ al.}$, J. Phys. Soc. Jpn. $\mathbf{85}$, 103703 (2016)], and a triple-$Q$ skyrmion crystal with a high topological number of two appears with increasing the spin-charge coupling on a triangular lattice [R. Ozawa, S. Hayami, and Y. Motome, to appear in Phys. Rev. Lett. (arXiv: 1703.03227)]. We find that, by introducing an external magnetic field, our effective model exhibits a plethora of multiple-$Q$ states. Our findings will serve as a guide for exploring further exotic magnetic orderings in itinerant magnets.Comment: 22 pages, 19 figure

Engineering chiral density waves and topological band structures by multiple-QQ superpositions of collinear up-up-down-down orders

Magnetic orders characterized by multiple ordering vectors harbor noncollinear and noncoplanar spin textures and can be a source of unusual electronic properties through the spin Berry phase mechanism. We theoretically show that such multiple-$Q$ states are stabilized in itinerant magnets in the form of superpositions of collinear up-up-down-down (UUDD) spin states, which accompany the density waves of vector and scalar chirality. The result is drawn by examining the ground state of the Kondo lattice model with classical localized moments, especially when the Fermi surface is tuned to be partially nested by the symmetry-related commensurate vectors. We unveil the instability toward the multiple-$Q$ UUDD states with chirality density waves, using the perturbative theory, variational calculations, and large-scale Langevin dynamics simulations. We also show that the chirality density waves can induce rich nontrivial topology of electronic structures, such as the massless Dirac semimetal, Chern insulator with quantized topological Hall response, and peculiar edge states which depend on the phase of chirality density waves at the edges.Comment: 10 pages, 7 figure

On intrinsically knotted or completely 3-linked graphs

We say that a graph is intrinsically knotted or completely 3-linked if every embedding of the graph into the 3-sphere contains a nontrivial knot or a 3-component link any of whose 2-component sublink is nonsplittable. We show that a graph obtained from the complete graph on seven vertices by a finite sequence of $\triangle Y$-exchanges and $Y \triangle$-exchanges is a minor-minimal intrinsically knotted or completely 3-linked graph.Comment: 17 pages, 9 figure

スピン電荷結合が創発するトポロジカルなスピンテクスチャ

学位の種別: 課程博士審査委員会委員 : （主査）東京大学教授 求 幸年, 東京大学教授 今田 正俊, 東京大学教授 永長 直人, 東京大学教授 有馬 孝尚, 東京大学教授 川島 直輝University of Tokyo(東京大学