Influence of Dzyaloshinskii–Moriya interaction and ballistic spin transport in the two and three-dimensional Heisenberg model

Highlights: • The effect of Dzyaloshisnkii–Moriya (DM) interaction in XXZ model is analyzed in two and three dimensions. • The AC spin conductivity is calculated. • The influence of DM interaction on AC spin conductivity is analyzed. - Abstract: We study the effect of Dzyaloshisnkii–Moriya interaction on spin transport in the two and three-dimensional Heisenberg antiferromagnetic models in the square lattice and cubic lattice respectively. For the three-dimensional model, we obtain a large peak for the spin conductivity and therefore a finite AC conductivity. For the two-dimensional model, we have gotten the AC spin conductivity tending to the infinity at ω → 0 limit and a suave decreasing in the spin conductivity with increase of ω. We obtain a small influence of the Dzyaloshinskii–Moriya interaction on the spin conductivity in all cases analyzed.