Overdamped Magnons in a Doped Two‐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 approximation. The magnon spectrum is shown to feature a branch of overdamped magnons near the I and M points of the Brillouin zone, if a critical concentration x c of mobile holes is exceeded. For parameters which are adequate for La 2 CuO 4 we estimate x c ≈ 1.5%. The appearance of such excitations means a sharp decrease of the instantaneous spin correlation length from a value determined by temperature fluctuations in the 2D system to a value which depends on x. We can relate x c to the hole concentration at which the 3D long‐range ordering is destroyed in La 2‐x Sr x CuO 4 . The overdamped branch coexists with the usual magnon branch. An overall softening of the latter branch with an increase of x is obtained.