From Triangular Correlated Paramagnet to Multi-q Noncoplanar Spin State in Spinel GeFe_{2}O_{4}

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 four interlaced families of triangular planes with 120° spins emerging from the underlying pyrochlore lattice. At lower temperatures, a phase transition occurs to a noncoplanar spin structure that is characterized by six propagation 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° order. Our Letter 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.