Noncoplanar magnetism in the Hubbard model on frustrated lattices

Ferromagnets and staggered antiferromagnets are the most common forms of magnetic orderings that one comes across in models and materials. However, during the last few years non-collinear and non-coplanar magnetic states have been of special interest for condensed matter researchers due to their relevance to a variety of phenomena, such as, ferroelectricity, anomalous Hall effect, etc. A number of theoretical studies have shown that such magnetic states exist in Kondo-lattice model at special band-fillings on various geometrically frustrated lattices. It was recently shown that the Kondo-lattice model on a checkerboard lattice supports non-coplanar magnetic states which lead to a topologically non-trivial band gap in the electronic spectrum (PRL 109, 166405(2012)). We begin by asking if such magnetic ground-states can also be realized in a Hubbard model which, unlike the Kondo-lattice model, does not contain ``pre-formed'' localized magnetic moments. We make use of a mean-field decoupling scheme which allows for non-collinear and non-coplanar magnetic states in the Hubbard model. We show that the triangular lattice and the checkerboard lattice do support non-coplanar magnetic phases similar to the ones found in a Kondo-lattice model.