Ferromagnetic versus helical order in edge sharing CuO$_2$ chains - a computational study

The magnetic ground state of edge sharing CuO$_2$ spin 1/2 Heisenberg chains with nearest neighbor exchange $J_1$ and second neighbor exchange $J_2$ depends delicately on structural details of the crystal structure, like Cu-O-Cu bond angles, Cu-O distances and the position of the cations. Without taking into account a renormalization by the interchain coupling, a critical ratio $\alpha=-J_2/J_1$ separates a ferromagnetic from a helical ground state (FM for $\alpha < 1/4$, helical for $\alpha > 1/4$). Here, we present a density functional based band structure study that investigates the different influences of various structural parameters for Li$_2$ CuO$_2$ as example compound. We find that the ferromagnetic and antiferromagnetic contributions develop rather differently for the same structural changes. Therefore, the key parameter $\alpha$ for the ground state is especially sensitive for small structural changes that might be induced by temperature or pressure variation.