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

L. Chaix; J. Robert; E. Chan; E. Ressouche; S. Petit; C. V. Colin; R. Ballou; J. Ollivier; L. -P. Regnault; E. Lhotel; V. Cathelin; S. Lenne; C. Cavanel; F. Damay; E. Suard; P. Strobel; C. Darie; S. deBrion; V. Simonet

arXiv · 2504.21142

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

L. Chaix·J. Robert·E. Chan·E. Ressouche·S. Petit·C. V. Colin·R. Ballou·J. Ollivier·L. -P. Regnault·E. Lhotel·V. Cathelin·S. Lenne·C. Cavanel·F. Damay·E. Suard·P. Strobel·C. Darie·S. deBrion·V. Simonet

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Abstract

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.

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L. Chaix, J. Robert, E. Chan, E. Ressouche, S. Petit, C. V. Colin, R. Ballou, J. Ollivier, L. -P. Regnault, E. Lhotel, V. Cathelin, S. Lenne, C. Cavanel, F. Damay, E. Suard, P. Strobel, C. Darie, S. deBrion, V. Simonet. 2025-04-29. From hierarchical triangular spin liquid to multi-$q$ spin texture in spinel GeFe$_2$O$_4$. https://arxiv.org/abs/2504.21142

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