  In high Tc superconductors the magnetic and electronic properties are
determined by the probability that valence electrons virtually jump from site
to site in the CuO2 planes, a mechanism opposed by on-site Coulomb repulsion
and favored by hopping integrals. The spatial extent of the latter is related
to transport properties, including superconductivity, and to the dispersion
relation of spin excitations (magnons). Here, for three antiferromagnetic
parent compounds (single-layer Bi2Sr0.99La1.1CuO6+delta, double-layer
Nd1.2Ba1.8Cu3O6 and infinite-layer CaCuO2) differing by the number of apical
atoms, we compare the magnetic spectra measured by resonant inelastic x-ray
scattering over a significant portion of the reciprocal space and with
unprecedented accuracy. We observe that the absence of apical oxygens increases
the in-plane hopping range and, in CaCuO2, it leads to a genuine 3D
exchange-bond network. These results establish a corresponding relation between
the exchange interactions and the crystal structure, and provide fresh insight
into the materials dependence of the superconducting transition temperature.
