Itinerant Electron-Driven Chiral Magnetic Ordering and Spontaneous Quantum Hall Effect in Triangular Lattice Models

We study the Kondo Lattice and the Hubbard models on a triangular lattice. We find that at the mean-field level, these rotationally invariant models naturally support a noncoplanar chiral magnetic ordering. It appears as a weak-coupling instability at the band filling factor $3/4$ due to the perfect nesting of the itinerant electron Fermi surface. This ordering is a triangular-lattice counterpart of the collinear Neel ordering that occurs on the half-filled square lattice. While the long-range magnetic ordering is destroyed by thermal fluctuations, the chirality can persist up to a finite temperature, causing a spontaneous quantum Hall effect in the absence of any externally applied magnetic field.

Figure 1

Chiral spin ordering on a triangular lattice. (a) Four possible orientations of the local magnetic moments. They correspond to the normals to the faces of a regular tetrahedron. (b) Arrangement of the local moments on the real space lattice. ${\mathbf{a}}_1$ and ${\mathbf{a}}_2$ are the unit lattice vectors. (c) Momentum space. Unshaded hexagons define the Brillouin zones. $\mathbf{G}$ is one of the reciprocal lattice vectors. Vectors ${\mathbf{Q}}_{\eta }$ are the ordering vectors for the tetrahedral chiral order (${|\mathbf{Q}}_{\eta }|=G/2$). Note that ${\mathbf{Q}}_{\eta }$ perfectly nest the $3/4$-filled FS (shaded hexagons).

Figure 2

Band structure corresponding to Eq. (5). The coupling strength is $JS/t=1$. The axes are chosen along ${\mathbf{Q}}_a$ and ${\mathbf{Q}}_b$ and point (0,0) corresponds to the center of the first Brillouin zone.

Figure 3

Hubbard model, $U=4t$. The magnitude of the order parameter for noncoplanar $3q$ structure and Hall conductivity as a function of temperature.