标题： 从分层三角自旋液体到自旋 GeFe$_2$O$_4$ 中的多$q$自旋纹理 显示英文标题

标题： From hierarchical triangular spin liquid to multi-$q$ spin texture in spinel GeFe$_2$O$_4$

摘要： 结合宏观测量、中子散射和建模，我们在 GeFe$_2$O$_4$ 尖晶石中识别出一种关联顺磁态，这是由第三近邻反铁磁相互作用占主导所导致的。 这些相互作用形成了 4 个孤立的三角平面家族，带有 120$^{\circ}$ 自旋从基础的萤石格子中显现出来。 在较低温度下，这种分层自旋液体经历了一次相变，转变成一种非共面自旋纹理，该纹理由 6 个传播矢量表征。 这种不寻常的多$q$ 序是由第六近邻较弱相互作用的存在触发的。 该系统在保持二维 120$^{\circ}$ 秩序的同时，成功地耦合了不同的三角平面。 我们的研究强调了 GeFe$_2$O$_4$ 中涉及的相互作用层次结构，这在尖晶石化合物中是独一无二的，因为第一近邻相互作用仅占主导的第三近邻相互作用的一小部分。 显示英文摘要

摘要： Combining macroscopic measurements, neutron scattering and modeling, we identify in the GeFe$_2$O$_4$ spinel a correlated paramagnetic state resulting from the predominance of third-neighbor antiferromagnetic interactions. These interactions materialize 4 isolated families of triangular planes with 120$^{\circ}$ spins emerging from the underlying pyrochlore lattice. At lower temperatures, a phase transition occurs from this hierarchical spin liquid to a non-coplanar spin texture that is characterized by 6 propagating vectors. This unusual multi-$q$ order is triggered by the presence of weaker interactions up to the sixth neighbors. The system is remarkably successful in coupling the different triangular planes while maintaining their two-dimensional 120$^{\circ}$ order. Our study highlights the hierarchy of interactions involved in GeFe$_2$O$_4$, which is singular among spinel compounds since first-neighbor interactions are only a small fraction of the dominant third neighbor ones.