#### Abstract

We have employed first principles calculations to study the electronic structure and magnetic properties of the low-dimensional phosphates, ${\mathrm{Ba}}_{2}\mathrm{Cu}{\left(\mathrm{P}{\mathrm{O}}_{4}\right)}_{2}$ and ${\mathrm{Sr}}_{2}\mathrm{Cu}{\left(\mathrm{P}{\mathrm{O}}_{4}\right)}_{2}$. Using the self-consistent tight-binding linearized muffin-tin orbital method and the $N\text{th}$ order muffin-tin orbital method, we have calculated the various intrachain as well as the interchain hopping parameters between the magnetic ions $\left({\mathrm{Cu}}^{2+}\right)$ for both the compounds. We find that the nearest-neighbor intrachain hopping $\left(t\right)$ is the dominant interaction suggesting the compounds to be indeed one dimensional. Our analysis of the band dispersion, orbital projected band structures, and the hopping parameters confirms that the ${\mathrm{Cu}}^{2+}\text{\u2212}{\mathrm{Cu}}^{2+}$ super-super exchange interaction takes place along the crystallographic $b$ direction mediated by O-P-O. We have also analyzed in detail the origin of short-range exchange interaction for these systems. Our *ab initio* estimate of the ratio of the exchange interaction of ${\mathrm{Sr}}_{2}\mathrm{Cu}{\left(\mathrm{P}{\mathrm{O}}_{4}\right)}_{2}$ to that of ${\mathrm{Ba}}_{2}\mathrm{Cu}{\left(\mathrm{P}{\mathrm{O}}_{4}\right)}_{2}$ compares excellently with available experimental results.

- Received 7 May 2007

DOI:https://doi.org/10.1103/PhysRevB.76.085104

©2007 American Physical Society