The iron potassium fluorides with the general formula K${}_x$Fe${}^{\mathrm{II}}$${}_x$Fe${}^{\mathrm{III}}$${}_{5-x}$F${}_{15}$ (2 ≤ $x$ ≤ 3) are interesting multiferroic materials, for which the coexistence of all the three ferroic orders (elastic, electric, and magnetic) is simultaneously observed below the magnetic transition. Although the phase diagram has been previously defined, in particular for the potassium-rich K${}_3$Fe${}_5$F${}_{15}$ phase, its complex magnetic behavior has not been completely understood. In this paper, the information obtained by magnetization measurements carried out on an oriented single crystal, revealing high anisotropy with coercive field reaching 14 kOe on the easy axis, are combined with Mössbauer spectroscopy and powder neutron diffraction data to define the magnetic structure. The ferrimagnetic behavior of K${}_3$Fe${}_5$F${}_{15}$ arises from an antiferromagnetic triangular spin system, determined by neutron diffraction, frustrated by the difference in the magnetic contributions of adjacent structural layers, originated by Fe(II)/Fe(III) charge ordering. The atomic moments corresponding to the different iron sites, which cannot be reliably refined by neutron data, were evaluated from the hyperfine fields and quadrupolar parameters derived from Mössbauer measurements, by taking into account the saturation magnetization measured along the $b$ easy axis. The complexity of the M(H) and M(T) measurements in the H//a case is explained by the existence of an alternative magnetic solution, originated by the pseudotetragonal character of the structure, that is thermodynamically unfavorable in spontaneous magnetization, but becomes accessible when an external magnetic field is applied along a.

• Received 8 April 2011

DOI:https://doi.org/10.1103/PhysRevB.84.104418