Antiferromagnetic spin-wave states in a linear chain with nearest- and next-nearest-neighbour interactions

Abstract

The spectrum of short-closed chains up to N=12 are studied by exact diagonalization to obtain the spin-wave spectrum of the Hamiltonian H=2J Σ _i=1^Ns_i.s_i+1+2J α Σ _i=1^Ns_i.s_i+2, −1.0<or= α <or=1.0 with J<0. The spin-wave spectrum is fairly well described for small alpha by the spin-wave formula obtained by the Anderson approximation (1952). The results of short chains indicate that S=0 bound magnon states lie partly below the spin-wave states with S=1 only for α >or=0.3 and α <or=−0.5. A few remarks are made concerning the low-lying excitations.