Incommensurate Charge Order Phase in ${\mathrm{Fe}}_2{\mathrm{OBO}}_3$ due to Geometrical Frustration

The temperature dependence of charge order in ${\mathrm{Fe}}_2{\mathrm{OBO}}_3$ was investigated by resistivity and differential scanning calorimetry measurements, Mössbauer spectroscopy, and synchrotron x-ray scattering, revealing an intermediate phase between room temperature and 340 K, characterized by coexisting mobile and immobile carriers, and by incommensurate superstructure modulations with temperature-dependent propagation vector $(\frac{1}{2},0,\tau )$. The incommensurate modulations arise from specific antiphase boundaries with low energy cost due to geometrical charge frustration.

Figure 1

Bulk physical properties of ${\mathrm{Fe}}_2{\mathrm{OBO}}_3$ indicating two phase transitions. (a)–(d) $T$ dependence of resistivity $\rho$ along $a$ (a), heat flow of differential scanning calorimetry (b), estimated monoclinic angle $\beta$ (c), and key parameters describing the Mössbauer spectra (d): fraction of the contribution to the spectra by Fe ions with no discernible electron hopping (■, left) and hopping frequency $\nu$ of the remainder (○, right). Inset in (a): Crystal structure at 355 K (after 11).

Figure 2

Mössbauer spectra at selected $T$ on powdered ${\mathrm{Fe}}_2{\mathrm{OBO}}_3$ crystals, modeled [16] with four contributions. At and below 325 K, the two nonelectron hopping doublets each for sites I, IV and II, III (labeled in the Fig. 1 inset) correspond to the two distinct Fe valences. Doublets with the larger (smaller) quadrupole splitting may be assigned to the site I, IV (II, III) [15]. The modeling indicates that the ${\mathrm{Fe}}^{2+}$ and ${\mathrm{Fe}}^{3+}$ quadrupole interactions have opposite sign for both the I, IV and the II, III site.

Figure 3

Commensurate and incommensurate superstructure reflections from synchrotron x-ray scattering. Fundamental reflections at integers $(h,k,\ell )$ typically have peak intensities in excess of ${10}^4\mathrm{\text{counts}}/\mathrm{\text{monitor}}$. (a) Scattered intensity at $(\frac{1}{2},k,\ell )$ and 100 K, showing one of the superstructure peaks corresponding to the doubled unit cell [11]. Black line: half-maximum-intensity contour. (b) Intensity at $(\frac{3}{2},3,\ell )$ vs $T$. An estimated beam heating of 5 K was corrected. Inner white ticks indicate $T$ at which data were taken. (c) Intensity after background subtraction at $(\frac{3}{2},0,\ell )$ measured every 1 K in a different experimental setup with an image plate system. (d) $h$, $k$, and $\ell$ scans through $(\frac{3}{2},3,\frac{5}{2})$ at 350 K.

Figure 4

Different charge order configurations within the four-chain ribbons of the ${\mathrm{Fe}}_2{\mathrm{OBO}}_3$ structure (Fig. 1 inset). ${\mathrm{Fe}}^{3+}$ (${\mathrm{Fe}}^{2+}$) are drawn as filled (open) circles. (a) Diagonal CO, the ground state. Degeneracy of the two configurations leads to domain formation, with opposite sense of monoclinic distortion [11]. (b) Alternative “zigzag” CO with only slightly higher energy than the diagonal ground state. All other configurations are intermediate between diagonal and zigzag.

Figure 5

Impact of geometrical frustration on the charge order. (a),(b) Phase relationship between two charge-ordered chains: For chains offset by $\frac{a}{2}$ (a), interchain electrostatic interactions are frustrated, and two configurations are degenerate in energy. Without offset (b), the antiphase configuration has lower energy. (c) $bc$ projection of the ${\mathrm{Fe}}_2{\mathrm{OBO}}_3$ structure. The arrangement of chains leads to geometrical frustration even for interactions (thick lines) between chains with possible phase relationships as in (b) (the other chains are crossed out). Dashed line: possible antiphase boundary (see text).