Checkerboard bubble lattice formed by octuple-period quadruple- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Q</mml:mi></mml:math> spin density waves

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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.

10 pages, 10 figures

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  • Physical Review B

    Physical Review B 108 (9), 2023-09-08

    American Physical Society (APS)

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