Zero temperature phases of the frustrated [J.sub.1]-[J.sub.2] antiferromagnetic spin-1/2 Heisenberg model on a simple cubic lattice

At zero temperature magnetic phases of the quantum spin-1/2 Heisenberg antiferromagnet on a simple cubic lattice with competing first and second neighbor exchanges ([J.sub.1] and [J.sub.2]) is investigated using the non-linear spin wave theory. We find existence of two phases: a two sublattice Neel phase for small [J.sub.2] (AF), and a collinear antiferromagnetic phase at large [J.sub.2] (CAF). We obtain the sublattice magnetizations and ground state energies for the two phases and find that there exists a first order phase transition from the AF-phase to the CAF-phase at the critical transition point, [p.sub.c] = 0.56 or [J.sub.2]/[J.sub.1] = 0.28. We also show that the quartic 1/S corrections due spin-wave interactions enhance the sublattice magnetization in both the phases which causes the intermediate paramagnetic phase predicted from linear spin wave theory to disappear. Keywords Magnetism * Frustrated magnetic spin systems * Quantum phase transition * Heisenberg spin systems