  Resistivity, magnetic susceptibility, neutron scattering and x-ray
crystallography measurements were used to study the evolution of magnetic order
and crystallographic structure in single-crystal samples of the Ba1-xSrxFe2As2
and Sr1-yCayFe2As2 series. A non-monotonic dependence of the magnetic ordering
temperature T0 on chemical pressure is compared to the progression of the
antiferromagnetic staggered moment, characteristics of the ordering transition
and structural parameters to reveal a distinct relationship between the
magnetic energy scale and the tetrahedral bond angle, even far above T0. In
Sr1-yCayFe2As2, an abrupt drop in T0 precisely at the Ca concentration where
the tetrahedral structure approaches the ideal geometry indicates a strong
coupling between the orbital bonding structure and the stabilization of
magnetic order, providing strong constraints on the nature of magnetism in the
iron-arsenide superconducting parent compounds.
