SpinOrbit Coupled Electrons on Kagome Lattice Give Rise to Various Magnetic Orderings
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Magnetic Orderings from SpinOrbit Coupled Electrons on Kagome Lattice
(JPSJ Editors' Choice)
J. Phys. Soc. Jpn. 91, 083702 (2022).
Diverse magnetic orderings are found to be produced by spinorbit coupled electrons on the kagome lattice. This finding provides a unified guiding principle for the design of magnetic topological materials.
Fig. 1: (a) Kagome lattice. The unit cell consists of three sublattices. (b) Electronic band structure with linear band touching points (Dirac points) and flat band. (c)(d) Obtained magnetic phase diagrams with spinorbit couplings and electron filling factor v. The spinorbit couplings (Rashba type λ_{R} and KaneMele type λ_{KM}) are scaled by the nearestneighbor hopping amplitude t on the kagome lattice. (e) Legends of magnetic orderings. Panels (c)(e) are adapted from Fig. 1 of J. Phys. Soc. Jpn. 91, 083702 (2022).
The kagome lattice [Fig. 1(a)] is one of the typical structures realized in twodimensional or layered materials. The study of the kagome lattice has a long history in the context of magnetism; the kagome lattice exhibits geometrical frustrations, which can give rise to various magnetic orderings. The recent discovery of topological features in the electronic band structure, known as a “Dirac point” or “Weyl point” [see Fig. 1(b)], of kagome layered materials renewed the interest in kagome lattices. For example, Mn_{3}Sn shows inplane 120degree antiferromagnetic ordering and exhibits Weyl points in the electronic bands. Co_{3}Sn_{2}S_{2 }also has Weyl points, whereas it shows outofplane ferromagnetic ordering. Fe_{3}Sn_{2 }exhibits inplane ferromagnetic ordering, yet its electronic bands exhibit massive Dirac dispersion. However, a unified understanding of the relationship between the magnetism and topological electronic states has not yet been established.
This study clarified the connection between these magnetic orderings and topological electronic structures in terms of spinorbit couplings. Spinorbit coupling is the relativistic interaction between the electron motion and electron spin, and plays an important role in realizing topological band structures. The magnetic phase diagrams of a kagome monolayer were numerically obtained by introducing spinorbit coupling in a model of the electron system coupled with localized spins (Kondo lattice model). The ground state magnetic ordering that minimizes the energy of the electron system depends on the electron filling factor and strength of spinorbit couplings. Typical spinorbit couplings resulting from the inversion symmetry breaking of the kagome lattice, namely the Rashba (λ_{R}) and KaneMele (λ_{KM}) types, were considered. As shown in Figs. 1(c) and 1(d), various magnetic orderings, such as ferromagnetic, 120degree antiferromagnetic, and magnetic spirals [see Fig. 1(e)], are realized. These magnetic orderings are related to the topological band structures in the kagome lattice; the ordering varies as the electron filling factor passes through the bandgap at the Dirac points opened by the spinorbit couplings. Noncollinear orderings, such as 120degree antiferromagnetic and spiral orderings, are also governed by the effective DzyaloshinskiiMoriya interaction of spins due to the spinorbit couplings.
Because both the electron filling factor and spinorbit couplings can be controlled by the substitution of elements, the obtained phase diagrams may be helpful for understanding the effects of the substitution on the magnetic orderings in various kagome materials. These findings provide a unified guiding principle for material design and will greatly accelerate the search for magnetic topological materials for device applications.
(Written by Y. Araki, K. Kobayashi, and A. Ozawa on behalf of all authors).
Magnetic Orderings from SpinOrbit Coupled Electrons on Kagome Lattice
(JPSJ Editors' Choice)
J. Phys. Soc. Jpn. 91, 083702 (2022).
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