SPIN EXCITATIONS IN A 2-DIMENSIONAL ANTIFERROMAGNET WITH MOBILE HOLES

The spin dynamics of a two-dimensional antiferromagnet doped with a finite concentration n of mobile holes is studied. The holes weaken the antiferromagnetic order by dilution, but more importantly by disrupting the antiferromagnetic order as they move. We calculate the renormalization of the spin excitations induced by hole motion. Spin-wave theory is applied to the t-J model and the range of small hole concentrations, n << 1, is considered. We find that the spin-wave spectrum is significantly softened upon doping, and that strong damping effects set in at a low concentration, resulting from decay of spin waves into "electron-hole" pair excitations. This implies that the spin-wave spectrum and eventually the antiferromagnetic order will collapse as the hole concentration increases. A comparison is made with measurements of spin-wave softening in doped copper oxide superconductors and other layered magnetic systems. Implications for hole motion are also briefly discussed.