The compounds of the title series have been prepared from citrate precursors under moderate pressure conditions (P = 2 GPa) and 1000 degrees C in the presence of KClO(4) as oxidizing agent. The crystal structures are cubic, space group Im3 (No. 204); the unit cell parameters linearly vary from a = 7.3272(4) A (R = La) to a = 7.2409(1) A (R = Lu) at room temperature. A neutron or synchrotron X-ray diffraction study of all the members of the series reveals an interesting correlation between some structural parameters and the magnetic properties. The electron injection effect upon replacement of Ca(2+) with R(3+) cations in the parent CaCu(3)Mn(4)O(12) oxide leads to a substantial increment of the ferrimagnetic Curie temperature (T(C)). An essential ingredient is supplied by the internal pressure of the R(3+) cations upon a decrease in size along the rare-earth series, from La to Lu: the concomitant compression of the MnO(6) octahedral units for the small rare earths provides progressively shorter Mn-O distances and improves the overlapping between Mn and O orbitals, thereby promoting superexchange and enhancing T(C) by 50 K along the series. This interaction is also reinforced by a ferromagnetic component that depends on the local distortion of the MnO(6) octahedra, which also increases along the series, constituting an additional factor, via intersite virtual charge transfer t-e orbital hybridization, for the observed increment of T(C).