The route of frustrated cuprates from antiferromagnetic to ferromagnetic spin-1/2 Heisenberg chains: Li2ZrCuO4 as a missing link near the quantum critical point

From thermodynamics, LSDA+U calculations and exact diagonalization studies of a five-band Hubbard (Cu 3d, O 2p) model on CuO2 stripes we found that Li2ZrCuO4 (Li2CuZrO4 in traditional notation) is close to a ferromagnetic critical point. Analyzing its measured susceptibility chi(T) and specific heat cp(T,H) within a Heisenberg model, we show that the ratio of the 2nd to the 1st neighbor exchange integrals alpha=-J2/J1 of the order of 0.3, i.e. it is close to the critical value alpha_c=1/4. Comparing with related chain cuprates we explain the rather strong field dependence of cp, the monotonous down shift of the peak of chi(T), and its increase for alpha approaching 1/4 + 0.