OVERDAMPED MAGNONS IN A DOPED 2-DIMENSIONAL ANTIFERROMAGNET

Hole and magnon spectral functions of the 2D t-J model are calculated for a finite hole concentration x, using the self-consistent Born appr oximation. The magnon spectrum is shown to feature a branch of overdam ped magnons near the Gamma and M points of the Brillouin zone, if a cr itical concentration x(c) of mobile holes is exceeded. For parameters which are adequate for La2CuO4 we estimate x(c) approximate to 1.5%. T he appearance of such excitations means a sharp decrease of the instan taneous spin correlation length from a value determined by temperature fluctuations in the 2D system to a value which depends on x. We can r elate x(c) to the hole concentration at which the 3D long-range orderi ng is destroyed in La2-xSrxCuO4. The overdamped branch coexists with t he usual magnon branch. An overall softening of the latter branch with an increase of x is obtained.