Coexistence of site- and bond-centered electron localization in the high-pressure phase of $\mathrm{LuF}{\mathrm{e}}_2{\mathrm{O}}_4$

Magnetic-electronic hyperfine interaction parameters of spectral components are obtained from in situ ${}^{57}\mathrm{Fe}$ Mössbauer spectroscopy pressure studies of the mixed-valence $\mathrm{LuF}{\mathrm{e}}_2{\mathrm{O}}_4$ multiferroic, up to $\sim 30\mathrm{GPa}$ and on recovered high-pressure phase samples. Temperature-dependent Mössbauer spectra of the low-pressure phase show that $\mathrm{F}{\mathrm{e}}^{2+}$ and $\mathrm{F}{\mathrm{e}}^{3+}$ sites are discernible, consistent with known site-centered charge order in the triangular (frustrated) Fe sublattice network. Magnetic spectra of the high-pressure phase, stabilized in a rectangular Fe sublattice network at $P>8\mathrm{GPa}$, exhibit fingerprints of iron in an intermediate valence state only. Temperature-dependent resistivity pressure studies evidence thermally activated small polaron motion in the high-pressure phase. These experimental signatures, complemented by ab initio calculations of electronic structure, are considered evidence of asymmetric dimer formation ${\mathrm{Fe}}^{(2+\mathrm{\Delta }+)}\iff {\mathrm{Fe}}^{(3-\mathrm{\Delta })+}$, where the minority-spin electron deconfinement coefficient is $\mathrm{\Delta }=0.3-0.4$. Bragg satellites discerned in electron diffraction patterns of the metastable high-pressure phase possibly stem from this admixture of site- and bond-centered localization (intermediate-state charge order) in a magnetic background. This breaks inversion symmetry and potentially renders $\mathrm{LuF}{\mathrm{e}}_2{\mathrm{O}}_4$ in its high-pressure phase as a new charge order instigated (electronic) ferroelectric.

Figure 1

Bilayers at 300 K involving (a) triangular networked Fe in the LP phase and (b) rectangular networked Fe in the HP structure where oxygen atoms (not shown) are at vertices of connecting bonds. Vectors on Fe show magnetic moments, and dashed lines represent shortest Fe-Fe distances. ${}^{57}\mathrm{Fe}$ Mössbauer spectra at 300 K of (c) paramagnetic LP phase and (d) magnetic HP phase. Solid lines through data points are overall fits to spectra. Deconvolution into subcomponents representing various charge states is discussed in the text.

Figure 2

${}^{57}\mathrm{Fe}$ Mössbauer spectra of (a) magnetic LP phase at 15 K and (b) recovered HP phase. Subcomponents representing $\mathrm{F}{\mathrm{e}}^{(3-\mathrm{\Delta })+}$ and $\mathrm{F}{\mathrm{e}}^{(2+\mathrm{\Delta })+}$ sites are discussed in the text. Solid lines through data points represent overall fit to a spectrum. Spectrum at 4 K was measured with a synchrotron Mössbauer source. (c) Valence separation representation, by comparison of isomer shifts (relative to α-Fe metal standard) of spectral subcomponents of $\mathrm{LuF}{\mathrm{e}}_2{\mathrm{O}}_4$ and $\mathrm{F}{\mathrm{e}}_2\mathrm{OB}{\mathrm{O}}_3$ reference. Bottom cartoon depicts minority-spin electron distribution/deconfinement at neighboring Fe-Fe sites. (d) Dimers forming Zener polarons along chains of ferromagnetic atomic spins in the $a$ direction. (e) Plot of $ln\left(\rho /T\right)$ versus inverse temperature. Solid gray line is a linear fit to HP data at $\sim 25\mathrm{GPa}$ in the range 180–320 K, representing thermally activated small polarons.

Figure 3

(a) Partial density of minority-spin 3d states at Fe(1) and Fe(2) sites of the HP phase. Inset depicts minority-spin electron hopping between neighboring sites. (b) Minority-spin band structure contribution from $3d$ states near the Fermi level of each Fe site (weighting contribution to a subband represented by line thickness). The Fe(1)-Fe(2) pair contributes higher weightings in upper subbands, while Fe(3)-Fe(4) weightings dominate lower subbands. Filled minority-spin states occur at all Fe sites (dashed line highlights). A higher weight of filled states occurs at one site in both pairs, indicating asymmetric dimer formation.