Structural properties and multiferroic phase diagram of ${\text{K}}_{0.6}{\text{Fe}}_{0.6}^{\text{II}}{\text{Fe}}_{0.4}^{\text{III}}{\text{F}}_3$ fluoride with TTB structure

Iron fluorides with tetragonal tungsten bronze (TTB) structure, having general formula of ${\text{K}}_x{\text{Fe}}_x^{\text{II}}{\text{Fe}}_{1-x}^{\text{III}}{\text{F}}_3$ with $0.4<x<0.6$, are possible candidates for complete multiferroism (elastic, electric, and magnetic orders) coupled with charge ordering phenomena. Following the indication of a previous general work, we concentrated our attention on the potassium rich region of these bronzes where an orthorhombic distortion of the fundamental TTB structure takes place. We tried to define the complex phase diagram of ${\text{K}}_{0.6}{\text{FeF}}_3$, involving the different ordering phenomena in the range of 5–600 K, by using a series of characterization techniques such as transmission electron microscopy, x-ray and neutron diffractions, and magnetic measurements. The results revealed the coexistence of all these orders below the magnetic transition occurring at 118 K, showing the unique behavior of a system that can be considered a model for multiferroism.

Figure 1

(Color online) Charge ordering in the $ab$ plane of the COS cell. The layers at $z\approx 1/4$ and 3/4 are shown in (a) and (b), respectively. Coordination octahedra surrounding ${\text{Fe}}^{2+}$ and ${\text{Fe}}^{3+}$ ions are evidenced in dark red (dark gray) and yellow (light gray), respectively; orange (medium gray) indicates the mixed-valence sites.

Figure 2

Selected area electron-diffraction patterns collected in ${\left[110\right]}_{\text{TTB}}$ zone axis at 293 (left) and 220 K (right). Downward and upward arrows indicate FES and COS modulation satellites, respectively.

Figure 3

Intensity variation of two typical modulation satellites (513 and 431, indexed on the basis of the FES and COS cells, respectively). Lines are a guide to the eye.

Figure 4

(Color online) Relationships among the fundamental TTB lattice and the two possible twinning variants of FES.

Figure 5

Magnetization curves collected with applied field perpendicular and parallel (inset) to the $c$ axis; FC and ZFC refer to field and zero-field cooling measurements.

Figure 6

Neutron powder-diffraction patterns taken at different temperatures. The main magnetic contributions are indicated by arrows.

Figure 7

(Color online) Thermal evolution of the fundamental TTB cell parameters of ${\text{K}}_{0.6}{\text{FeF}}_3$ in the range of 5–700 K; structural modifications and existence regions of ordering phenomena (FM, FE, FEL, and CO) are reported.