Square skyrmion crystal in centrosymmetric systems with locally inversion-asymmetric layers

Abstract

We investigate an instability toward a square-lattice formation of the magnetic skyrmions in centrosymmetric layered systems. By focusing on a bilayer square-lattice structure with the inversion center at the interlayer bond instead of the atomic site, we numerically examine the stability of the square skyrmion crystal based on an effective spin model with the momentum-resolved interaction in the ground state through the simulated annealing. As a result, we find that a layer-dependent staggered Dzyaloshinskii-Moriya interaction built in the lattice structure becomes the origin of the square skyrmion crystal in an external magnetic field irrespective of the sign of the interlayer exchange interaction. The obtained square skyrmion crystal is constituted of the skyrmion crystals with different helicities in each layer due to the staggered Dzyaloshinskii-Moriya interaction. Furthermore, we show that the interplay between the staggered Dzyaloshinskii-Moriya interaction and the interlayer exchange interaction gives rise to a double-$Q$ state with a uniform component of the scalar chirality in the low-field region. The present results provide another way of stabilizing the square skyrmion crystal in centrosymmetric magnets, which will be useful to explore further exotic topological spin textures.

Degeneracy Lifting of Néel, Bloch, and Anti-Skyrmion Crystals in Centrosymmetric Tetragonal Systems

“…For example, the system with the chiral-type DM interaction under the D 4 (422) point group, which usually favors the Bloch SkX, can also lead to the hybrid SkX and anti-SkX once the ordering wave vectors lie at the low-symmetric ones. In addition, one can expect such generations of the hybrid SkX and anti-SkX induced by the DM interaction at low-symmetric wave vectors in centrosymmetric systems with the lack of local inversion symmetry [84][85][86][87]. In this case, the sublattice-dependent DM interaction becomes the origin of the above unconventional SkXs.…”

Skyrmion crystal and spiral phases in centrosymmetric bilayer magnets with staggered Dzyaloshinskii-Moriya interaction

“…The recent theoretical studies have revealed that the interplay between a layerdependent DM interaction and interlayer exchange interaction stabilizes the SkX with the net scalar chirality rather than the AF-SkX without the net scalar chirality under the out-of-plane magnetic field irrespective of the sign of the interlayer exchange interaction. [126][127][128][129] The model in Eq. ( 1) has five independent parameters: J, D, J ∥ , A ion , and H. Among them, we take J = 1 as the energy unit of the model.…”

“…For the ferromagnetic interlayer exchange interaction, i.e., J ∥ < 0, a ferro-type SkX with the same skyrmion number in both layers is stabilized as found in previous studies. [126][127][128][129] We construct the magnetic phase diagram of the model in Eq. ( 1) at low temperatures by performing simulated annealing.…”

Zero-Field Skyrmion, Meron, and Vortex Crystals in Centrosymmetric Hexagonal Magnets

“…1(a) within the nearestneighbor inter-sublattice interaction. They are distinguished by considering further-neighbor interactions in H inter and magnetic anisotropic interactions in H intra η , which are not taken into account in the present model in order to focus on the role of the competition between K and J inter [63,72,73]. Thus, the model in Eq.…”