Electronic structure of spin-12Heisenberg antiferromagnetic systems:Ba2Cu(PO4)2andSr2Cu(PO4)2

Abstract

We have employed first principles calculations to study the electronic structure and magnetic properties of the low-dimensional phosphates, ${\mathrm{Ba}}_{2}\mathrm{Cu}{(\mathrm{P}{\mathrm{O}}_{4})}_{2}$ and ${\mathrm{Sr}}_{2}\mathrm{Cu}{(\mathrm{P}{\mathrm{O}}_{4})}_{2}$. 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 $({\mathrm{Cu}}^{2+})$ for both the compounds. We find that the nearest-neighbor intrachain hopping $(t)$ 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 ${\mathrm{Cu}}^{2+}\text{\ensuremath{-}}{\mathrm{Cu}}^{2+}$ 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 ${\mathrm{Sr}}_{2}\mathrm{Cu}{(\mathrm{P}{\mathrm{O}}_{4})}_{2}$ to that of ${\mathrm{Ba}}_{2}\mathrm{Cu}{(\mathrm{P}{\mathrm{O}}_{4})}_{2}$ compares excellently with available experimental results.