Effect of next-nearest-neighbor hopping on the spin dynamics in antiferromagnets

Recently, inelastic-neutron-scattering (INS)experiments on the insulating parent compounds of high-T-c materials were analyzed to extract the value of the superexchange constant J. The starring point of the analysis was the nearest-neighbor Heisenberg model: Motivated by recent angle-resolved photoemission experiments, we consider the effects of a next-nearest-neighbor hopping, t', in the strong-coupling limit of the spin-density-wave formalism, where it leads to an antiferromagnetic exchange J'>0 between next-nearest-neighbor spins. We show that a finite J' (a) changes the spin-wave velocity and thus the value of J extracted from the INS data, yielding almost identical values for J in La2CuO4 and YBa2Cu3O6.15, and (b) leads to a considerable change in the high-frequency spin-dynamics. Finally, we calculate the 1/S quantum corrections in the presence of J' and discuss their relevance for the INS data. [S0163-1829(98)50826-0].