  We report magnetization measurements, full-potential band structure
calculations, and microscopic modeling for the spin-1/2 Heisenberg magnets
A2CuP2O7 (A = Na, Li). Based on a quantitative evaluation of the leading
exchange integrals and the subsequent quantum Monte-Carlo simulations, we
propose a quasi-one-dimensional magnetic model for both compounds, in contrast
to earlier studies that conjectured on the two-dimensional scenario. The
one-dimensional nature of A2CuP2O7 is unambiguously verified by magnetization
isotherms measured in fields up to 50 T. The saturation fields of about 40 T
for both Li and Na compounds are in excellent agreement with the intrachain
exchange J1 ~ 27 K extracted from the magnetic susceptibility data. The
proposed magnetic structure entails spin chains with the dominating
antiferromagnetic nearest-neighbor interaction J1 and two inequivalent,
nonfrustrated antiferromagnetic interchain couplings of about 0.01*J1 each. A
possible long-range magnetic ordering is discussed in comparison with the
available experimental information.
