Figure 8.

Mechanism of superplane formation in Na_xMnO₂. a) DOS of the d_z2 orbital of Mn³⁺ (red), the p_z orbital of JT long axis O(green), the p_x and p_y orbitals of two double-short axes O (orange) and the s orbital of Na(blue) in Na_1/3MnO₂. The two branches of positive and negative DOS correspond to two spin directions. The magnitude of the DOS in this figure is square root of the calculated actual value for better visualization. Inset shows charge density for a Mn³⁺ and surrounding oxygen. d and p orbitals are marked. b–e) Binding energy and DOS of Na or Na vacancy moving along b,c) JT long and d,e) double-short axes inside a Mn³⁺ superplane in Na_1/3MnO₂. DOS figure shows the hybridization peak positions of any Mn³⁺ in the original full Na superplane (green), two Mn^3.5+ marked by a₁ and a₂ in the left structure with vacancy distance 1 (orange), and four Mn^3.5+ marked by b₁ to b₄ in the right structure with vacancy distance 2 (blue). a₁ and a₂ show the same DOS while b₁ to b₄ show the same DOS. f) Binding energy of one Na moving 1 or 2 sites away from the Mn³⁺ superplane in a hypothetical Na_1/6MnO₂ structure. The Na rich Mn³⁺ planes are separated by three lattice constants, twice the distance in the Na_1/3MnO₂ ordering. g) DOS figure for inset (f) shows the hybridization peak positions of any Mn³⁺ in the original full Na superplane (green), four Mn³⁺ in the structure with the Na moving 1 site away (orange) marked by a₁ to a₄, and 3 Mn³⁺ (b₁, b₄, b₅) and 2 Mn^3.5+ (b₂, b₃) with the Na 2 sites away (blue). Note that the JT distortion of b₁–b₄ in inset (f) are changed from z direction to x direction (See inset (a) for definition of axes). For all other cases in this figure the JT distortion is always in the z direction. The energy reference in the DOS calculations in each model is the Fermi energy of the corresponding full-plane structure.