Fig. 4: Schematic illustration of the NiO and MnO unit cell.

In the picture, the exchange interaction parameters \({J}_{1}^{+}\), \({J}_{1}^{-}\), and J2 introduced in Eq. (17), the lattice parameter a, and the angle ϑ quantifying the rhombohedral distortion are reported. Panel (a) shows the fcc cell, while (b) displays the rhombohedral cell employed in our first-principles calculations, and (c) is the Brillouin zone (BZ) corresponding to the rhombohedral cell. a1, a2, and a3 are the real-space primitive lattice vectors of the rhombohedral unit cell, while b1, b2, and b3 are the reciprocal-space primitive lattice vectors of the BZ. The high-symmetry points Γ, X, and M in the BZ are also highlighted.