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(+)Fe(3+)[Fe(2+)(CN)(6)]) and a Cr(3+) 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) Fe(3+)-Fe(3+) and Cr(3+)-Cr(3+) pairs, and not by the delocalization of spin along the center dot NC - Fe(2+)- CN center dot pathways as previously proposed. The functional containing 35% HF exchange yields an estimated critical temperature for spin ordering and a magnitude for weak Fe(2+) spin polarization in good agreement with experimental data. The energies of the Fe(2+) low spin (LS)-> HS (t(2g)(6)-> t(2g)(4)e(g)(2)) and Fe(3+) HS -> LS (t(2g)(3)e(g)(2)-> t(2g)(5)) excitations are determined and compared with the results obtained previously in a range of Fe(2+) 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 Fe(3+) HS -> LS excitation is lower in energy than the Fe(2+) LS -> HS, and also that there is no reasonable prospect of a temperature-induced spin crossover in either compound.