  We have employed first principles calculations to study the electronic
structure and magnetic properties of the low-dimensional phosphates,
Ba2Cu(PO4)2 and Sr2Cu(PO4)2. Using the self-consistent tight-binding lin-
earized muffin-tin orbital method and the Nth order muffin-tin orbital method,
we have calculated the various intrachain as well as the interchain hopping
parameters between the magnetic ions Cu2+ for both the com- pounds. 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 struc- tures, and the hopping parameters
confirms that the Cu2+-Cu2+ 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 inter- action of Sr2Cu(PO4)2 to
that of Ba2Cu(PO4)2 compares excellently with available experimental results.
