On the contrasting spin dynamics of La_2-xSr_xCuO ₄, Nd_2-xCe_xCuO₄ and YBa ₂Cu₃O_6+x near half filling

We present simple calculations which show that the incommensurability upon doping and the width of the magnetically ordered phase in Mott-Hubbard insulators depend strongly on the location of the hole/electron pockets in the Brillouin zone. For LaSrCuO systems, we found the pockets at (+or- pi /2,+or- pi /2), in which case the corrections to the antiferromagnetic spin stiffness rapidly grow with doping and destroy commensurate spin ordering even at a very small doping. On the other hand, in NdCeCuO, the hole pockets are located at ( pi ,0) and the symmetry-related points, in which case the corrections to the stiffness scale linearly with the density of carriers and do not destroy commensurate spin ordering. For YBCO systems, the situation is less certain, but our results favour hole pockets at ( pi /2, pi /2). We also briefly discuss the tendency towards phase separation.