Emergent Vortex Ordering in a Multiflavor Pyrochlore-Lattice Compound GeCo${}_2$O${}_4$

Entangled spin and orbital degrees of freedom provide a multiflavor route to novel magnetic states inaccessible in conventional spin systems. Here, we report the experimental identification of an emergent vortex lattice in the multiflavor pyrochlore-lattice compound GeCo${}_2$O${}_4$. By combining comprehensive neutron scattering experiments with a regularized regression framework, we identify substantial Kitaev interactions among the nearest-neighboring Co${}^{2+}$ pseudospins, which cooperate with geometric frustration to stabilize the vortex order. These results reveal an unexpected route to vortex-lattice order in a three-dimensional Kitaev-frustrated magnet and demonstrate a regularized protocol for Hamiltonian determination in frustrated quantum materials.