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

TL;DR

This study reports the discovery of an emergent vortex lattice in GeCo$_2$O$_4$, a multiflavor pyrochlore compound, driven by Kitaev interactions and geometric frustration, using neutron scattering and a novel regression analysis.

Contribution

It uncovers a new vortex-lattice phase in a 3D Kitaev-frustrated magnet and introduces a regularized method for determining Hamiltonians in such complex systems.

Findings

Identification of a vortex lattice in GeCo$_2$O$_4$

Substantial Kitaev interactions among Co$^{2+}$ pseudospins

Demonstration of a regularized protocol for Hamiltonian determination

Abstract

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.