Exchange frequencies and magnetic ground state of Wigner crystal in anisotropic two-dimensional electron systems

We investigate the effect of mass anisotropy on the magnetic structure of the Wigner crystal of low-density electron systems in two dimensions at T=0. The multiparticle exchange frequencies are calculated with effective mass anisotropy, with and without concomitant lattice distortions. Numerical diagonalization of small lattice sizes with two-, three-, and four-spin exchange terms shows a transition from a ferromagnetic to an antiferromagnetic ground state with increasing mass anisotropy. We map out this transition at various electron densities.