Checkerboard bubble lattice formed by octuple-period quadruple-$Q$ spin density waves

TL;DR

This paper explores how superpositions of quadruple-Q spin density waves on a square lattice can create a checkerboard bubble lattice with unique spin textures, stabilized by small anisotropic interactions, and linked to charge density waves and flat electronic bands.

Contribution

It demonstrates that a checkerboard bubble lattice emerges from quadruple-Q spin density waves due to symmetry and geometry, stabilized by minimal interactions, offering a new route to exotic spin textures.

Findings

Checkerboard bubble lattice is stabilized by small anisotropic interactions.

The structure exhibits no high-harmonic wave vector intensities.

It is associated with charge density waves and flat electronic bands.

Abstract

We investigate multiple-$Q$ instability on a square lattice at particular ordering wave vectors. We find that a superposition of quadruple-$Q$ spin density waves, which are connected by fourfold rotational and mirror symmetries, gives rise to a checkerboard bubble lattice with a collinear spin texture as a result of the geometry among the constituent ordering wave vectors in the Brillouin zone. By performing the simulated annealing for a fundamental spin model, we show that such a checkerboard bubble lattice is stabilized under an infinitesimally small easy-axis two-spin anisotropic interaction and biquadratic interaction at zero field, while it is degenerate with an anisotropic double-$Q$ state in the absence of the biquadratic interaction. The obtained multiple-$Q$ structures have no intensities at high-harmonic wave vectors in contrast to other multiple-$Q$ states, such as a magnetic skyrmion lattice. We also show that the checkerboard bubble lattice accompanies the charge density wave and exhibits a nearly flat band dispersion in the electronic structure. Our results provide another route to realize exotic multiple-$Q$ spin textures by focusing on the geometry and symmetry in terms of the wave vectors in momentum space.