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 (t62g→t42ge2g) and Fe3+ HS→LS (t32ge2g→t52g) 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