Theory of Two-Magnon Bound States in a Two-Dimensional Antiferromagnet

Two-magnon bound states are calculated for an antiferromagnetic spin system of the square lattice by the method developed by one of the authors in a previous paper. The calculations are carried out for the two cases; the total wave number K x = K y =0, and K x = K y =π/2. In both cases, two-magnon bound states exist in the Ising model, but they merge with the band as the anisotropy of exchange interactions, decreases, and there are no bound states in the Heisenberg model. The difference between the existence of two-magnon bound states in a ferromagnet and in an antiferromagnet is discussed.