Novel magnetic structure of a vortex lattice in adsorbedHe3films

Stimulated by a recent finding of a sharp specific-heat anomaly at 2.5 mK in a second layer of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ adsorbed on Grafoil by Greywall et al., we studied a lattice-gas model or Hubbard model on a triangular lattice. We found a novel type of magnetic ordering of a vortex lattice, which is noncollinear with triple Q wave vectors and holds threefold symmetry, for nearly half fillings. The size of the unit cell varies with ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ coverages. This is a generic periodic pattern for neatly accommodating defects always present in an experiment.