The spin-1/2 alternating Heisenberg chain system ${\mathrm{Na}}_3{\mathrm{Cu}}_2{\mathrm{SbO}}_6$ features two relevant exchange couplings: $J_{1a}$ within the structural Cu${}_2$O${}_6$ dimers and $J_{1b}$ between the dimers. Motivated by the controversially discussed nature of $J_{1a}$, we perform extensive density-functional-theory (DFT) calculations, including DFT + $U$ and hybrid functionals. Fits to the experimental magnetic susceptibility using high-temperature series expansions and quantum Monte Carlo simulations yield the optimal parameters $J_{1a}=-217$ K and $J_{1b}=174$ K with the alternation ratio $\alpha =J_{1a}/J_{1b}\simeq -1.25$. For the closely related system Na${}_2$Cu${}_2$TeO${}_6$, DFT yields substantially enhanced $J_{1b}$, but weaker $J_{1a}$. The comparative analysis renders the buckling of the chains as the key parameter altering the magnetic coupling regime. Numerical simulation of the dispersion relations of the alternating-chain model clarify why both antiferromagnetic and ferromagnetic $J_{1a}$ can reproduce the experimental magnetic susceptibility data.

• Received 5 February 2014
• Revised 14 April 2014

DOI:https://doi.org/10.1103/PhysRevB.89.174403