Relative orientation of Cu2OSeO3 tetrahedral moments

Determine the relative orientation of the ferrimagnetic Cu4 tetrahedra in Cu2OSeO3, which is not fixed by the nearly degenerate T and A response modes and remains unresolved by the linear-response calculation.

Background

Cu2OSeO3 has a 56-atom unit cell containing sixteen copper ions arranged into four Cu4 tetrahedra. The response calculation identifies a 3:1 ferrimagnetic configuration within each tetrahedron: the Cu1 moment is antiparallel to the combined moment of the three Cu2 sites. However, the dominant triply degenerate T mode and the nearly degenerate fully symmetric A mode differ in how the tetrahedral moments are arranged across the unit cell. The T mode produces a net ferrimagnetic moment, whereas the A mode has tetrahedral moments along four mutually cancelling ⟨111⟩ directions. Because these modes are nearly degenerate, the calculation establishes the intra-tetrahedral configuration but does not resolve the relative orientation of the tetrahedra.

References

The obtained response confirms the $3{:}1$ configuration within the strong tetrahedra, a feature characteristic of the first-principles spin model, also observed via neutron diffraction in the helimagnetic state, but leaves the relative orientation of the tetrahedra open.

— Magnetic Order from First-Principles Linear Response  (2610.10412 - Zhumagulov et al., 7 Oct 2026) in Section “Cu2OSeO3: ferrimagnetic order”