  GeCu2O4 exhibits a tetragonal spinel structure due to the strong Jahn-Teller
distortion associated with Cu2+ ions. We show that its magnetic structure can
be described as slabs composed of a pair of layers with orthogonally oriented
spin 1/2 Cu chains in the basal ab plane. The spins between the two layers
within a slab are collinearly aligned while the spin directions of neighboring
slabs are perpendicular to each other. Interestingly, we find that spins along
each chain form an unusual up-up-down-down (UUDD) pattern, suggesting a
non-negligible nearest-neighbor biquadratic exchange interaction in the
effective classical spin Hamiltonian. We hypothesize that spin-orbit coupling
and orbital mixing of Cu2+ ions in this system is non-negligible, which calls
for future calculations using perturbation theory with extended Hilbert (spin
and orbital) space and calculations based on density functional theory
including spin-orbit coupling and looking at the global stability of the UUDD
state.
