Structural and spectroscopic investigation of the charge-ordered, short-range ordered, and disordered phases of the ${\mathrm{Co}}_3{\mathrm{O}}_2{\mathrm{BO}}_3$ ludwigite

Charge ordering is prone to occur in crystalline materials with mixed-valence ions. It is presumably accompanied by a structural phase transition, with possible exceptions in compounds that already present more than one inequivalent site for the mixed-valence ions in the charge-disordered phase. In this work, we investigate the representative case of the homometallic Co ludwigite ${\mathrm{Co}}_2^{2+}{\mathrm{Co}}^{3+}{\mathrm{O}}_2{\mathrm{BO}}_3$ ($Pbam$ space group) with four distinct Co crystallographic sites [$M1$–$M4$] surrounded by oxygen octahedra. The mixed-valent character of the Co ions up to at least $T=873$ K is verified through x-ray absorption near-edge structure (XANES) experiments. Single crystal x-ray diffraction (XRD) and neutron powder diffraction (NPD) confirm that the Co ions at the $M4$ site are much smaller than the others at low temperatures, consistent with a ${\mathrm{Co}}^{3+}$ oxidation state at $M4$ and ${\mathrm{Co}}^{2+}$ at the remaining sites. The size difference between the Co ions in the $M4$ and $M2$ sites is continuously reduced upon warming above $\approx 370$ K, indicating a gradual charge redistribution within the $M4-M2-M4$ (424) ladder in the average structure. Minor structural anomalies with no space group modification are observed near 475 and 495 K, where sharp phase transitions were previously revealed by calorimetry and electrical resistivity data. An increasing structural disorder, beyond a conventional thermal effect, is noted above $\approx 370$ K, manifested by an anomalous increment of XRD Debye-Waller factors and broadened vibrational modes observed by Raman scattering. The local Co-O distance distribution, revealed by Co $K$-edge extended x-ray absorption fine structure (EXAFS) data and analyzed with an evolutionary algorithm method, is similar to that inferred from the XRD crystal structure below $\approx 370$ K. At higher temperatures, the local Co-O distance distribution remains similar to that found at low temperatures, at variance with the average crystal structure obtained with XRD. We conclude that the oxidation states ${\mathrm{Co}}^{2+}$ and ${\mathrm{Co}}^{3+}$ are instantaneously well defined in a local atomic level at all temperatures, however the thermal energy promotes local defects in the charge-ordered configuration of the 424 ladders upon warming. These defects coalesce into a phase-segregated state within a narrow temperature interval ($475<T<495$ K). Finally, a transition at $\approx 500$ K revealed by differential scanning calorimetry (DSC) in the iron ludwigite ${\mathrm{Fe}}_3{\mathrm{O}}_2{\mathrm{BO}}_3$ is discussed.

Figure 1

(a) Polyhedral representation of the ludwigite structure (space group $Pbam$) projected in the $ab$ plane. This arrangement is simply repeated along the c direction. Metal sites $M$ are numbered from 1 to 4. The five oxygen sites are indicated by red circles and black dots represent the boron ions. The solid rectangle represents the unit cell. Thick lines indicates two crystal subunits, namely the 424 and 313 three-legged ladders that run along c, which are also displayed in more detail in (b) and (c), respectively, with the corresponding $M-M$ average bond length obtained with x-ray diffraction data at 300 K.

Figure 2

(a)–(d) $\mathrm{Co}i-\mathrm{O}j$ bond lengths obtained from single crystal x-ray diffraction data. (e) Mean $\langle \mathrm{Co}i-\mathrm{O}\rangle$ bond length for each $\mathrm{Co}i$ site averaged over the neighboring oxygen atoms. Filled and empty markers represent data collected in the low- and high-temperature regime on different crystals (see Sec. 2). Statistical errors are smaller than the symbol size.

Figure 3

Debye-Waller factors ${\sigma }^2$ for (a)–(d) Co1–Co4 and (e)–(i) O1-O5 sites obtained with single crystal x-ray diffraction data. Solid lines show theoretical curves according to the Debye model (see text) where the value for ${\theta }_D$ for each site is indicated. The dashed line in (d) is the Debye model fit for site Co3, shown for comparison purposes. Filled and empty markers represent data collected in the low- and high-temperature regime on different crystals (see Sec. 2).

Figure 4

(a)–(d) $\mathrm{Co}i-\mathrm{O}j$ bond lengths obtained using Rietveld refinement results for neutron powder diffraction data. (e) Mean $\langle \mathrm{Co}i-\mathrm{O}\rangle$ bond length for each $\mathrm{Co}i$ site averaged over the neighboring oxygen atoms. Statistical errors are smaller than the symbol size.

Figure 5

Raman spectra at selected temperatures. The spectra were vertically translated for clarity. The dashed vertical lines mark the frequency positions of selected peaks at 15 K. Fits of the observed spectra with Lorentzian peaks are shown in red solid lines.

Figure 6

Temperature dependence of (a)–(d) the frequency positions and (e)–(h) the corresponding linewidths of the peaks at $\approx 430$, 560, 618, and 665 ${\mathrm{cm}}^{-1}$. The insets show zoom outs that highlight low-temperature anomalies.

Figure 7

(a) Co $K$-edge $k^3$-weighted EXAFS transmission spectra at selected temperatures and (b) their Fourier transform. The spectra were vertically translated in (a) for clarity. The first Co-O and second Co-Co coordination shells are indicated in (b).

Figure 8

Bars: local Co-O bond length distribution of ${\mathrm{Co}}_3{\mathrm{O}}_2{\mathrm{BO}}_3$ obtained from RMC simulation of Co $K$-edge EXAFS data (see text) at (a) 125 K, (b) 300 K, (c) 573 K, and (d) 873 K. The vertical dashed lines in (a)–(c) represent the crystallographic $\mathrm{Co}i-\mathrm{O}j$ bond lengths obtained with x-ray diffraction data, where the color scheme is the same as in Figs. 2–(d). The red solid lines in (a)–(c) are the Gaussian-broadened XRD $\mathrm{Co}i-\mathrm{O}j$ bond length distributions at similar temperatures.

Figure 9

(a) Normalized XAS spectra at the Co $K$-edge of ${\mathrm{Co}}_3{\mathrm{O}}_2{\mathrm{BO}}_3$ and reference compounds ${\mathrm{Co}}_5\mathrm{Sn}{\left({\mathrm{O}}_2{\mathrm{BO}}_3\right)}_2, {\mathrm{LaCoO}}_3$ and CoO at room temperature measured with membrane samples. Arrows indicate the general notion that higher (or lower) valence states shifts the spectral “center of gravity” to higher (or lower) energies. (b) Normalized XAS spectra at the Co $K$-edge of ${\mathrm{Co}}_3{\mathrm{O}}_2{\mathrm{BO}}_3$ at 300 K, 623 K, and 873 K, where arrows indicate visually detectable changes in the spectra going from low to high temperature.

Figure 10

Heat flow as a function of temperature for a ${\mathrm{Fe}}_3{\mathrm{O}}_2{\mathrm{BO}}_3$ single crystal, taken on heating and cooling with a rate of 10 K/min. Dashed curve displays the data obtained upon heating multiplied by $-1$ to facilitate comparison.

Figure 11

Schematic charge arrangements for $M_2^{2+}{M}^{3+}{\mathrm{O}}_2{\mathrm{BO}}_3$ homometallic ludwigites inside the 424 ladders for $M$=Fe and Co at low temperatures, and for $M$=Co at higher temperatures. Filled and empty symbols represent $M^{3+}$ and $M^{2+}$ ions, respectively. (a) $M$=Fe charge-ordered state ($T<283$ K) [6, 7, 8, 9, 10]. (b) $M$=Co charge-ordered state ($T\lesssim 370$ K). (c) $M$=Co charge-ordered state with uncorrelated “defective rows” (blue boxes, $370\lesssim T<475$ K). (d) The defects become denser upon warming and finally coalesce into defect-rich regions through a phase transition, forming a short-range zigzag pattern (light red boxes) coexisting with defect-free regions (dark red boxes, $475<T<495$ K). (e) At higher temperatures ($T>495$ K), the thermal energy disrupts the defective-row correlations, returning the system to an uncorrelated defect state that is qualitatively similar to (c) but with higher density of defects, through a reentrant phase transition.