Universal doping dependence of the ground state staggered magnetization in cuprates

Using muon spin rotation we determine the zero temperature staggered antiferromagnetic order parameter M0 versus hole doping measured from optimum Dp_m, in the (Ca_{x}La_{1-x})(Ba_{1.75-x}La_{0.25+x})Cu_{3}O_{y} system. In this system the maximum Tc and the superexchange J vary by 30% between families (x). M0(x,Dp_m) is found to be x-independent. Using neutron diffraction we also determine the lattice parameters variations for all x and doping. The oxygen buckling angle is found to change with x, implying a change in the holes kinetic energy. We discuss the surprising insensitivity of M0(x,Dp_m) to the kinetic energy variations in the framework of the t-J model.