Origin of up-up-down-down magnetic order in Cu2GeO4

We use density-functional band-structure calculations to explore the origin of the up-up-down-down (UUDD) magnetic order in ${\mathrm{Cu}}₂{\mathrm{GeO}}₄$ with the frustrated ${J}₁\text{\ensuremath{-}}{J}₂$ spin chains coupled into layers within the spinel-like crystal structure. In contrast to earlier studies, we find that the nearest-neighbor coupling ${J}₁$ should be negligibly small, due to a nearly perfect compensation of the ferromagnetic direct exchange and antiferromagnetic superexchange. Under this condition, weak symmetric anisotropy of the exchange couplings gives rise to the UUDD order observed experimentally and also elucidates the nontrivial ordering pattern between the layers, whereas a small Dzyaloshinskii-Moriya interaction causes a spin canting that may generate local electric polarization. We argue that the buckling of the copper chains plays a crucial role in the suppression of ${J}₁$ in ${\mathrm{Cu}}₂{\mathrm{GeO}}₄$ and sets this compound apart from other ${J}₁\text{\ensuremath{-}}{J}₂$ chain magnets.