Bond Disproportionation, Ligand Holes, and Persistent Spin Textures in Ag$_2$BiO$_3$
The origin of the proposed bond disproportionated insulating state of the non-centrosymmetric ($Pnn2$) phase of Ag$_{2}$BiO$_{3}$ is explored using first principles electronic structure calculations. The novel insulating state is elucidated by first considering the initially proposed centosymmetric metallic ($Pnna$) phase of Ag$_{2}$BiO$_{3}$. Our calculations reveal that the valence skipping Bi$^{4+}$ ions in this phase are better described as Bi$^{3+}\underline{L}$ with completely filled Bi-(6$s$) states and a ligand hole. However, phonon calculations indicate that the metallic ($Pnna$) state is dynamically unstable. Structural stability is achieved through breathing distortions of the oxygen octahedra, resulting in two inequivalent Bi sites and a reduction of symmetry to the $Pnn2$ phase. Electronic structure calculations further reveal that the $Pnn2$ phase is a bond disproportionated insulator where the nominal charge state of Bi is described by : 2[Bi$^{3+}\underline{L}$ (Bi$^{4+}$)] $\rightarrow$ Bi$^{3+}\underline{L}^{2-\delta}$ (Bi1$^{5+}$) + Bi$^{3+}\underline{L}^{\delta}$ (Bi2$^{3+}$), highlighting the crucial role of ligand holes in driving the insulating state. Next we have investigated the electronic structure of Ag$_{2}$BiO$_{3}$ in the insulating ($Pnn2$) phase including spin-orbit coupling. Our density functional theory (DFT ) calculations complemented by ${\bf k.p}$ model Hamiltonian analysis reveal persistent spin-textures around the $X$ and $Y$ high symmetry points of the orthorhombic Brillouin zone imposed by non-symmorphic symmetry, positioning Ag$_{2}$BiO$_{3}$ as a promising candidate for spintronic applications.