Chirality Waves in Two-Dimensional Magnets

Abstract

We theoretically show that moderate interaction between electrons confined to move in a plane and localized magnetic moments leads to formation of a noncoplanar magnetic state. The state is similar to the skyrmion crystal recently observed in cubic systems with the Dzyaloshinskii-Moriya interaction; however, it does not require spin-orbit interaction. The non-coplanar magnetism is accompanied by the ground-state electrical and spin currents, generated via the real-space Berry phase mechanism. We examine the stability of the state with respect to lattice discreteness effects and the magnitude of magnetic exchange interaction. The state can be realized in a number of transition metal and magnetic semiconductor systems.Magnetism is a cooperative phenomenon where spins of magnetic ions spontaneously orient relative to each other below certain ordering temperature [1,2]. In principle, arbitrarily complex magnetic orderings are possible; however, the magnetic states encountered in nature tend to be simple, the most common being ferromagnetism (one atom in magnetic unit cell, Fig. 1a) and antiferromagnetism (two distinct atoms in magnetic unit cell, Fig. 1b). More complex orders [3][4][5][6], such as noncollinear spirals ( Fig. 1d) and various noncoplanar orders (e.g., Fig. 1e) are less common, typically arising from the interplay of magnetic exchange interactions, spin-orbit (SO) coupling [5], frustrated lattice structure [3], and magnetic field [6].Noncoplanar magnetism has a unique effect on electronic transport through coherently influencing the quantum-mechanical phase of electrons [7]. The phase accumulates when an electron moves through the magnetic texture and adjusts its spin according to the local magnetic environment. The resulting Berry phase is equal to half of the solid angle subtended by electron spin in the process of its evolution around a closed trajectory (Fig. 1c). This is similar to the Aharonov-Bohm phase induced by the electromagnetic vector potential which couples to electron charge. If the magnetic texture varies significantly on the scale of the material unit cell, the equivalent magnetic field strength can be gigantic, exceeding 10 4 Tesla. Consequently, in non-coplanar magnets one may find such exotic magneto-transport phenomena as the intrinsic anomalous Hall effect [8], Hall effect in the absence of net magnetization or magnetic field [9], or even quantum anomalous Hall effect [10,11].In the absence of SO coupling or magnetic field, the non-coplanar states have been believed to be very rare [12,13]. Recently, however, several examples have been found that show energetic preference for non-coplanar magnetic states [11,[14][15][16][17] in one of the simplest models of magnetism -the isotropic Kondo lattice modeleven in the absence of SO interaction. These noncoplanar states were found for particular lattice structures and electron densities, which leaves an open question: How common are the non-coplanar magnetic states? Here, we show that non-coplanar magnetic states occur in the lowdensity ...

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

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