The remarkable sensitivity of the c-axis resistivity and magnetoresistance in cuprates to the spin ordering is used to clarify the doping-induced transformation from an antiferromagnetic (AF) insulator to a superconducting (SC) metal in RBa_2Cu_3O_{6+x} (R = Lu, Y) single crystals. The established phase diagram demonstrates that the AF and SC regions apparently overlap: the superconductivity in RBa_2Cu_3O_{6+x}, in contrast to La_{2-x}Sr_xCuO_4, sets in before the long-range AF order is completely destroyed by hole doping. Magnetoresistance measurements of superconducting crystals with low T_c<15-20 K give a clear view of the magnetic-field induced superconductivity suppression and recovery of the long-range AF state. What still remains to be understood is whether the AF order actually persists in the SC state or just revives when the superconductivity is suppressed, and, in the former case, whether the antiferromagnetism and superconductivity reside in nanoscopically separated phases or coexist on an atomic scale.
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