Sr$_2$Cu(PO$_4$)$_2$ - an unexpected one dimensional spin 1/2 Heisenberg system with isolated CuO$_4$ units*

Recently, Belik {\it et. al.} [1] reported synthesis and physical properties of the compound Sr$_2$Cu(PO$_4$)$_2$. The measured magnetic susceptibility [1] exhibits a broad maximum at 92 K characteristic for quasi-1D systems, but shows no long range magnetic ordering down to 0.45 K. Here, we present full potential electronic structure calculations within the local spin density approximation, followed by a subsequent mapping to a one-band tight-binding model and an extended Heisenberg model. Although the crystal structure of Sr$_2$Cu(PO$_4$)$_2$ is formed by unlinked CuO$_4$ units, we find a surprisingly pronounced one dimensional behaviour with substantial coupling between nearest neighbors (NN) only. The calculated NN exchange coupling J$_1$$\sim$180 K is in good agreement with the experimental estimate. It exceeds all other couplings by at least two orders of magnitude, placing the system in the forefront of 1D spin 1/2 model compounds. Model calculations using the derived exchange constants suggest that no long range magnetic ordering should be expected down to very low temperatures.\\[0pt] [1]Belik {\it et. al.}, J. of Sol. Stat. Chem. {\bf 177}, 883 (2004).