Dirac Half-Metal in a Triangular Ferrimagnet

An idea is proposed for realizing a fully spin-polarized Dirac semimetal in frustrated itinerant magnets. We show that itinerant electrons on a triangular lattice exhibit the Dirac cone dispersion with half-metallic behavior in the presence of a three-sublattice ferrimagnetic order. The Dirac nodes have the same structure as those of graphene. By variational calculation and Monte Carlo simulation, we demonstrate that the ferrimagnetic order with the Dirac node spontaneously emerges in a simple Kondo lattice model with Ising anisotropy. The realization will be beneficial for spintronics as a candidate for a spin-current generator.

Figure 1

Schematic pictures of (a) a honeycomb ferromagnet, (b) kagome ferromagnet, and (c) three-sublattice triangular ferrimagnet. The arrows at each site represent localized spins.

Figure 2

Band structures of the model in Eq. (1) under the three-sublattice ferrimagnetic order at $J=2$. (a) The overall band structure of the three lower-energy bands at $J^{\prime }=0$, (b) the enlarged view near the Fermi level $\epsilon =-J$ at $n=1/3$ in the first quadrant, and (c) the cut along the symmetric lines. (d), (e) Results at $J^{\prime }=0.05$. The arrows indicate the spins for each band. In (a), the gray hexagon on the basal plane shows the first Brillouin zone for the magnetic supercell. The dashed line in (e) indicates the Fermi level in the MC simulation at $T=0.06$ and $N={18}^2$ shown in Fig. 4.

Figure 3

Ground state phase diagram obtained by variational calculation at (a) $J^{\prime }=0$ and (b) $J^{\prime }=0.05$. The schematic picture of magnetic structure in each phase is shown. The white region indicates the electronic phase separation (PS) and the dotted vertical lines indicate $n=1/3$.

Figure 4

MC results for (a) the pseudomoments $M_{xy}$ and $|M_z|$, (b) corresponding susceptibilities ${\chi }_{xy}$ and ${\chi }_z$, and (c) azimuth parameter $\psi$. The data are calculated at $n=0.34$.