  The magnetic and electronic structures of Fe4O5 have been investigated at
ambient and high pressures via a combination of representation analysis,
density functional theory (DFT+U) calculations, and M\"ossbauer spectroscopy. A
few spin configurations corresponding to the different irreducible
representations have been considered. The total-energy calculations reveal that
the magnetic ground state of Fe4O5 corresponds to an orthogonal spin order.
Depending on the magnetic propagation vector k two spin ordered phases with
minimal energy differences are realized. The lowest energy magnetic phase is
related to k = (0, 0, 0) and is characterized by the ferromagnetic ordering of
the iron magnetic moments at prismatic sites along the b axis and
antiferromagnetic ordering of iron moments at octahedral sites along the c
axis. For the k = (1/2, 0, 0) phase, the moments in the prisms are
antiferromagnetically ordered along the b axis and the moments in the octahedra
are still antiferromagnetically ordered along the c axis. Under high pressure,
the Fe4O5 exhibits magnetic transitions with corresponding electronic
transitions of the metal-insulator type. At a critical pressure PC ~ 60 GPa the
Fe ions at the octahedral sites undergo a high-spin to low-spin state crossover
with a decrease in the unit-cell volume of ~ 4%, while the Fe ions at the
prismatic sites remain in the high-spin state up to 130 GPa. This
site-dependent magnetic collapse is experimentally observed in the
transformation of M\"ossbauer spectra measured at room temperature and high
pressures.
