Numerical Study of Weak Ferromagnetism in 2D J$\text{}_{1}$-J$\text{}_{2}$ Heisenberg Model with Dzyaloshinskii-Moriya Interaction

By means of exact diagonalization we consider the groundstate of the J$\text{}_{1}$-J$\text{}_{2}$ spin 1/2 Heisenberg model with an anisotropic interaction term of Dzyaloshinskii-Moriya type. We find that a Dzyaloshinskii-Moriya interaction may create a weak ferromagnetic moment. The interplay between the quantum nature of the groundstate of the pure J$\text{}_{1}$-J$\text{}_{2}$ model and the anisotropic Dzyaloshinskii-Moriya interaction favour energetically a well-defined direction of spin alignment creating anisotropic correlations.