Three-dimensional generalization of theJ1-J2Heisenberg model on a square lattice and role of the interlayer couplingJc

Abstract

A possibility to describe magnetism in the iron pnictide parent compounds in terms of the two-dimensional frustrated Heisenberg ${J}_{1}$-${J}_{2}$ model has been actively discussed recently. However, recent neutron-scattering data have shown that the pnictides have a relatively large spin-wave dispersion in the direction perpendicular to the planes. This indicates that the third dimension is very important. Motivated by this observation we study the ${J}_{1}$-${J}_{2}$-${J}_{c}$ model that is the three-dimensional generalization of the ${J}_{1}$-${J}_{2}$ Heisenberg model for $S=1/2$ and $S=1$. Using self-consistent spin-wave theory we present a detailed description of the staggered magnetization and magnetic excitations in the collinear state. We find that the introduction of the interlayer coupling ${J}_{c}$ suppresses the quantum fluctuations and strengthens the long-range ordering. In the ${J}_{1}$-${J}_{2}$-${J}_{c}$ model, we find two qualitatively distinct scenarios for how the collinear phase becomes unstable on increasing ${J}_{1}$. Either the magnetization or one of the spin-wave velocities vanishes. For $S=1/2$ renormalization due to quantum fluctuations is significantly stronger than for $S=1$, in particular close to the quantum phase transition. Our findings for the ${J}_{1}$-${J}_{2}$-${J}_{c}$ model are of general theoretical interest; however, the results show that it is unlikely that the model is relevant to undoped pnictides.