Competing energetic states in $\gamma \text{−}{\mathrm{Fe}}_2\mathrm{W}{\mathrm{O}}_6$ with strong spin-charge-lattice coupling

We report magnetic and electronic properties of $\gamma \text{−}{\mathrm{Fe}}_2\mathrm{W}{\mathrm{O}}_6$ via neutron powder-diffraction measurements and first-principles density-function theory calculations. We reveal a magnetic ground state with two phases coexisting in which the minor phase is the same as an earlier report [Pinto et al., Acta Crystallogr., Sect. A 33, 663 (1977).], despite the fact that both materials studied have the same space group but with slightly different atomic positions. Interestingly, both magnetic phases are well captured by first-principles calculations. Furthermore, we show that these two magnetic phases are correlated with electronic properties, with one being insulating and the other being metallic. These features suggest that $\gamma \text{−}{\mathrm{Fe}}_2\mathrm{W}{\mathrm{O}}_6$ exhibits competing energetic states in which spin, charge, and lattice degrees of freedom are strongly coupled to each other.

Figure 1

Schematics of crystal and magnetic structures of $\gamma \text{−}{\mathrm{Fe}}_2\mathrm{W}{\mathrm{O}}_6$. (a) Crystal structure projected along [100] showing a single layer $\left(x\approx 0\right)$. (b) Crystal structure with labeled Fe-Fe couplings. (c), (d) Magnetic structures used for the DFT calculation: (c) structure reported by Pinto et al. [12] equivalent to ${\mathrm{\Psi }}_4\left({\mathrm{\Gamma }}_3\right)$, (d) the ${\mathrm{\Psi }}_6\left({\mathrm{\Gamma }}_4\right)$ component of our refinement.

Figure 2

(a) Magnetic susceptibility as a function of temperature measured with an applied field of 0.1 T. (b) Fe magnetic moment as a function of temperature calculated from the NPD intensity of the (110) Bragg peak measured on HB2A. (c), (d) Contour plots of selected Bragg reflections over a temperature range of 70 to 300 K measured on POWGEN.

Figure 3

NPD POWGEN data collected at different temperatures. (a) Overlaid diffraction patterns from $Q=1.2$ to $4.6{\AA }^{–1}$. (b) Overlaid diffraction patterns from $Q=1.35$ to $1.53{\AA }^{–1}$. (c), (d) Diffraction patterns and the refinements at 300 and 10 K, respectively. Black points represent experimental data. Red lines show Rietveld fitting. Vertical strokes label Bragg peak positions. The topmost row of strokes (green) labels $\gamma \text{−}{\mathrm{Fe}}_2\mathrm{W}{\mathrm{O}}_6$ nuclear peaks. The second row (orange) labels $\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$ nuclear peaks. The third row (pink) labels $\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$ magnetic peaks. The bottom row (gray) labels $\gamma \text{−}{\mathrm{Fe}}_2\mathrm{W}{\mathrm{O}}_6$ magnetic peaks. The bottom blue curve is the residual of the fit.

Figure 4

DFT results. DOS of type II (a) and type I (b) crystal structures projected on Fe1, Fe2, and W sites located on the top right corner of the unit cell shown in Fig. 1 (a). Red curves are the contributions from Fe1, green curves are from Fe2, blue curves are from W, and black curves are total DOS. Spin axis is taken along the $c$ axis. Band structure of the type II (c) and type I (d) crystal structures. The color scheme is the same as in (a), (b), and the linewidth is proportional to the sum of the weight of Fe1, Fe2, and W. The red arrow in (d) indicates bands with the mixed character of W and Fe1, which may be responsible for FM coupling on $J_3$ bonds. Energy is measured from the Fermi level. The inset of (c) shows the first octant of the first Brillouin zone.

Figure 5

Fermi surface of type I structure. The contribution from the highly dispersive band indicated in Fig. 4 is marked by a red circle, showing the largest Fermi velocity. The plot is made by using the fermisurfer package [27].