MAGNETIC EXCITATIONS OF A DOPED 2-DIMENSIONAL ANTIFERROMAGNET

Magnetic excitations of the two-dimensional (2D) t-J model are conside red in the presence of a small concentration of holes c. The spin-wave approximation used implies long-range antiferromagnetic ordering from the beginning. Migdal's theorem is shown to be valid for the model co nsidered. The energy spectrum of the magnons is determined with the he lp of the one-pole approximation for the hole Green's function. If the concentration of mobile holes is larger than a critical value an addi tional branch of overdamped magnons arises near the GAMMA and M points of the Brillouin zone. This is connected with the generation of elect ron-hole pairs (the Stoner excitations) by magnons. The appearance of such excitations means the destruction of the long-range antiferromagn etic order. For parameters presumably realized in cuprate perovskites this happens for several percent of holes per site. The relation betwe en the critical concentration and the hole concentration destroying th e 3D long-range ordering in La2-xSrxCuO4 is discussed. The arising sho rt-range order is characterized by the instantaneous spin correlation length xi is similar to c-1/2, in coincidence with the experimentally observed dependence in this crystal.