Critical and reentrant behavior of the spin quantum 1/2 anisotropic Heisenberg antiferromagnet model with Dzyaloshinskii–Moriya interaction in a longitudinal magnetic field

•Anisotropic Heisenberg antiferromagnet on a simple cubic lattice.•Effective-field theory.•Dzyaloshinskii–Moriya interaction.

In this paper we study the quantum spin-1/2 anisotropic Heisenberg antiferromagnet model in the presence of a Dzyaloshinskii–Moriya interaction (D) and a uniform longitudinal (H) magnetic field. Using the effective-field theory with a finite cluster N  =2 spin (EFT-2) we calculate the phase diagrams in the H−TH−T and D−TD−T planes on a simple cubic lattice (z  =6). We have only observed second order phase transitions for values between Δ∈[0,1]Δ∈[0,1], where the cases were analysed: Ising (Δ=1), anisotropic Heisenberg (Δ=0.6) and isotropic Heisenberg (Δ=0).