${\mathrm{NaFe}}_{0.5}{\mathrm{Cu}}_{0.5}\mathrm{As}$ represents a rare exception in the metallic iron pnictide family, in which a small insulating gap is opened. Based on first-principles study, we provide a comprehensive theoretical characterization of this insulating compound. The ${\mathrm{Fe}}^{3+}$ spin degree of freedom is quantified as a quasi-one-dimensional (1D) $S=\frac{5}{2}$ Heisenberg model. The itinerant As hole state is downfolded to a $p_{xy}$-orbital hopping model on a square lattice. An orbital-dependent Hund's coupling between the spin and the hole is revealed. Several important material properties are analyzed, including (a) the factors affecting the small $p-d$ charge-transfer gap; (b) the role of extra interchain Fe atoms; and (c) quasi-1D spin excitation in the Fe chains. The experimental manifestations of these properties are discussed.

• Received 28 August 2017

DOI:https://doi.org/10.1103/PhysRevB.96.245128