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Doping dependence of long-range magnetic order in the t-J model.

The renormalization of the staggered-order parameter as a function of hole doping is studied for a two-dimensional doped antiferromagnet in the framework of the t-J model. The self-consistent Born approximation is used to calculate the Green's functions of holes and spin waves. It is shown that magnon softening is mainly due to the incoherent motion of the holes. The staggered-order parameter vanishes at a small critical density of holes δ c . The calculated value for δ c as well as the concentration dependence of both the staggered moment and spin-wave velocity are consistent with experimental data for La 2-δ Ba δ CuO 4 and YBa 52 Cu 3 O 6+x