Skyrmion lattices (SkL) in centrosymmetric materials typically have a magnetic period on the nanometer-scale, so that the coupling between magnetic superstructures and the underlying crystal lattice cannot be neglected. We reveal the commensurate locking of a SkL to the atomic lattice in Gd₃Ru₄Al₁₂ via high-resolution resonant elastic x-ray scattering (REXS). Weak easy-plane magnetic anisotropy, demonstrated here by a combination of ferromagnetic resonance and REXS, penalizes placing a skyrmion core on a site of the atomic lattice. Under these conditions, a commensurate SkL, locked to the crystal lattice, is stable at finite temperatures – but gives way to a competing incommensurate ground state upon cooling. We discuss the role of Umklapp-terms in the Hamiltonian for the formation of this lattice-locked state, its magnetic space group, and the role of slight discommensurations, or (line) defects in the magnetic texture. We also contrast our findings with the case of SkLs in noncentrosymmetric material platforms.

中心对称材料中的斯格明子晶格（SkL）通常具有纳米级的磁周期，因此磁性超结构与底层晶格之间的耦合不容忽视。我们通过高分辨率共振弹性 X 射线散射 (REXS) 揭示了 SkL 与 Gd ₃ Ru ₄ Al ₁₂ 原子晶格的相应锁定。此处通过铁磁共振和 REXS 的组合证明了弱易平面磁各向异性，它会惩罚将斯格明子核放置在原子晶格的某个位置上。在这些条件下，锁定在晶格上的相称 SkL 在有限温度下是稳定的，但在冷却时就会让位于竞争性的不相称基态。我们讨论了哈密顿量中 Umklapp 项对于形成这种晶格锁定态、其磁性空间群的作用，以及磁性结构中轻微不通约或（线）缺陷的作用。我们还将我们的发现与非中心对称材料平台中的 SkL 案例进行了对比。