Effect of Dzyaloshinskii-Moriya on Magnetic orders of J_1-J_2 Antiferromagnetic Heisenberg model

Motivated by recent experiments that detects Dzyaloshinskii-Moriya (DM) interaction in , we study the effects of DM interaction on magnetic orders of J1-J2 antiferromagnetic Heisenberg model. First, we find the classical phase diagram of the model using Luttinger-Tisza approximation. In this approximation, the classical phase diagram has two phases. For , the model has canted Neel and DM interaction cants the spins of one on the subluttices. The ground state of model is classically degenerate for , including infinit numbers of vorticity vectors that are able to minimize the model. This phase is important because of the probability of the existence of quantum spin liquid in this region. To investigate the effect of quantum fluctuation on the stability of the classical phase diagram, linear spin wave theory of Holstein-Primakoff is used. The results show that in the classical degeneracy regime, the quantum fluctuations for cause spiral order in this region. The ground state of model remains disorder for, and this region is a good place for finding quantum spin liquid