Single-valley state in a two-dimensional antiferromagnetic lattice

We propose the concept of single-valley state in two-dimensional antiferromagnetic lattice, which intrinsically holds only one valley and thus robust valley-polarized physics. Using tight-binding model analysis, the physical mechanism to form the single-valley state is illustrated, and large magnetic moment and strong spin-orbit coupling are unveiled to define it. Furthermore, based on first-principles calculations, the single-valley state is predicted in a real material of single-layer $\mathrm{BiFe}{\mathrm{O}}_3$. The spontaneous valley polarization in single-layer $\mathrm{BiFe}{\mathrm{O}}_3$ is particularly huge, at least one order of magnitude higher than those of all the existing ferrovalley systems. Our work enriches the physics of two-dimensional valleytronics and provides a promising avenue to observe strong valley-polarized phenomena.

Figure 1

(a) Schematic of an antiferromagnetic honeycomb lattice. Red and orange circles represent up and down spins, respectively. (b) Energy bands of tight-bonding model with ${\lambda }_M=8$ as a function of ${\lambda }_{\mathrm{SOC}}$. (c) Phase diagram of the double-valley (DV) and single-valley (SV) states in terms of ${\lambda }_{\mathrm{SOC}}$ and ${\lambda }_M$. (d) Phase diagram of valley polarization (i.e., energy difference between the band edges at the K and K′). The black dotted lines divide this diagram into four parts: upper, lower, left and right.

Figure 2

(a) Crystal structure of single-layer $\mathrm{BiFe}{\mathrm{O}}_3$ from top and side views. Red, yellow, and blue spheres represent O, Fe, and Bi atoms, respectively. (b) 2D Brillouin zone of single-layer $\mathrm{BiFe}{\mathrm{O}}_3$. (c) Splitting of Fe-$d$ orbitals. (d) Different collinear magnetic configurations in the Fe hexagonal lattice. (e) Phonon bands of single-layer $\mathrm{BiFe}{\mathrm{O}}_3$. (f) Band structure of single-layer $\mathrm{BiFe}{\mathrm{O}}_3$ without considering SOC. (g) Band structure and (h) orbital-resolved band structure of single-layer $\mathrm{BiFe}{\mathrm{O}}_3$ with considering SOC. The Fermi level is set to 0 eV.

Figure 3

(a) Schematic of band structure around the valleys for single-layer $\mathrm{BiFe}{\mathrm{O}}_3$ with shifting the Fermi level in the K valley. (b) Diagram of valley and spin Hall effects for single-layer $\mathrm{BiFe}{\mathrm{O}}_3$ in the presence of an in-plane electric field.