Ferromagnetism and spin transitions in prussian blue: A solid-state hybrid functional study

The exchange interactions underlying the weak ferromagnetism of the prototypical mixed valence compound prussian blue (represented by K⁺Fe³⁺[Fe²⁺(CN)₆]) and a Cr³⁺ substituted analog are investigated within a series of solid-state hybrid density functional calculations. Weights of Hartree--Fock (HF) exchange in the range from 30% to 100% are used. The magnetic order in these compounds is shown to be dominated by the coupling of nearest-neighbor high spin (HS) Fe³⁺-Fe³⁺ and Cr³⁺-Cr³⁺ pairs, and not by the delocalization of spin along the ⋯NCFe²⁺CN⋯ pathways as previously proposed. The functional containing 35% HF exchange yields an estimated critical temperature for spin ordering and a magnitude for weak Fe²⁺ spin polarization in good agreement with experimental data. The energies of the Fe²⁺ low spin (LS)→HS (t2g⁶→t2g⁴eg²) and Fe³⁺ HS→LS (t2g³eg²→t2g⁵) excitations are determined and compared with the results obtained previously in a range of Fe²⁺ coordination compounds. It is concluded that the accurate description of these transitions requires the use of a weight of HF exchange below the stable limit of 35% attained in the current study. However, the trends in the present results indicate that the Fe³⁺ HS→LS excitation is lower in energy than the Fe²⁺ LS→HS, and also that there is no reasonable prospect of a temperature-induced spin crossover in either compound.