Magnetic order and chemical bonding in the high-$T_C$ molecule-based cyanide magnets $\mathrm{Cs}M\left[{\mathrm{Cr}\left(\mathrm{CN}\right)\mathrm{}}_6\right]$ ($M=\mathrm{Mn},$ Ni) from first principles

We present the results of first-principles electronic-structure calculations for the molecule-based cyanide high-Curie-temperature magnetic insulators $\mathrm{Cs}M\left[{\mathrm{Cr}\left(\mathrm{CN}\right)\mathrm{}}_6\right],$ $M=\mathrm{Mn},$ Ni. The calculations are based on density-functional theory and the local-density approximation and employ the augmented-spherical-waves method. The electronic properties are found to be dominated by transition-metal $3d$ and ligand $2p$ orbitals. The chemical bonding is analyzed via an ab initio calculation of the crystal orbital overlap population (COOP). The magnetic properties are explained by the orthogonality/overlap of magnetically active orbitals as studied by the COOP. Possible pathways for the exchange interaction are identified. In particular the sign of the exchange integrals between different effective magnetic sites is deduced. Excellent agreement with experimental data is found. While proving essential for the consistent understanding of electronic, magnetic, and chemical properties of these materials our first-principles approach moreover allows for the prediction as well as the deeper understanding of the type of long-range magnetic order. Thereby it goes beyond the conclusions usually drawn from Goodenough-Kanamori superexchange rules or the model by Kahn and Briat.