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.
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