Understanding the Mössbauer spectrum of magnetite below the Verwey transition: Ab initio calculations, simulation, and experiment

Magnetite is often the subject of Mössbauer spectroscopy experiments either as a part of fundamental research of this compound or during various geological studies. However, the complicated structure of the low-temperature phase of magnetite exhibits 24 crystallographic iron sites, which presents a considerable obstruction for spectrum interpretation. In this work, we carried out ab initio calculations to obtain a complete set of hyperfine parameters of all the sites, and we used these parameters to simulate the corresponding Mössbauer spectrum. Simulation analysis suggested an approximation of the spectrum by four sextets. Parameters of these four sextets were calculated, and the approximation was shown to be appropriate. Further, the Mössbauer spectrum of a high-quality synthetic single crystal of magnetite was measured at 4 K, allowing for a comparison of the theoretical results with the experimental data. Finally, the four-sextet approximation was successfully applied to fit the measured spectrum.

Figure 1

Isomer shift calibration. The values from Table 2 are represented by the points; the line corresponds to a fit of expression (2). The $a$ and $d$ crystallographic sites of yttrium iron garnet (YIG) are distinguished. The labels ${\mathrm{Fe}}_3{\mathrm{O}}_4$ (A) and ${\mathrm{Fe}}_3{\mathrm{O}}_4$ (B) refer to the A and B sites of the high-temperature phase of magnetite, respectively. ($a_0\approx 5.292\times {10}^{-11}$ m is the Bohr radius.)

Figure 2

Visualization of the EFG tensors at Fe(B) sites in the elementary cell (scaling coefficient $C=0.05$ Å $\times 10{}^{-21} {\mathrm{V}}^{-1}$  ${\mathrm{m}}^2$). Trimerons [15] are highlighted by the green lines. The site numbering is the same as in Ref. [2] and corresponds to site listing order in Ref. [15]; primes denote the sites generated by the ac-glide symmetry. (Surface color corresponding to the z coordinate is to improve clarity.)

Figure 3

Renormalized isotropic and anisotropic parts of the hyperfine magnetic field $V_{\text{ani}}=\sqrt{V_{zz}^2+V_{yy}^2+V_{xx}^2\phantom{{}^l}}$ parameter of EFG and isomer shift $\delta$ of the B-site iron ions plotted as a function of oxidation state determined by the AIM method in Ref. [2]. The site numbering is the same as in Ref. [2] and corresponds to site listing order in Ref. [15]. The lines serve only to guide the eye.

Figure 4

Simulation of a zero-field ${}^{57}\mathrm{Fe}$ Mössbauer spectrum (referenced to $\alpha$-Fe) of a single-domain single-crystal sample of magnetite (in the low-temperature phase) oriented in the [201] direction along the incident $\gamma$ ray. The site numbering is the same as in Ref. [2] and corresponds to site listing order in Ref. [15]. Black, red, and blue indicate the three groups of Fe(B) subspectra corresponding to the three groups of Fe(B) ions identified in Ref. [2]. The experimental data (see Sec. 4) are given for comparison.

Figure 5

Comparison of the four-sextet approximation (thick lines) with the subspectra calculated by considering individual sites in the groups (thin lines); see text for details. Black, red, and blue indicate the three groups of Fe(B) subspectra corresponding to the three groups of Fe(B) ions identified in Ref. [2]. The experimental data (see Sec. 4) are given for comparison. The spectra are referenced to $\alpha$-Fe.

Figure 6

The four-sextet approximation improved by taking the average hyperfine magnetic fields directly from the zero-field NMR measurement at 4.2 K [12]; see text for details. Black, red, and blue indicate the three groups of Fe(B) subspectra corresponding to the three groups of Fe(B) ions identified in Ref. [2]. The experimental data (see Sec. 4) are given for comparison. The spectra are referenced to $\alpha$-Fe.

Figure 7

Experimental Mössbauer spectrum (referenced to $\alpha$-Fe) of magnetite at 4 K decomposed into four sextets by the fit (see text). The gray line denotes the sextet corresponding to the group of Fe(A) ions, while the black, red, and blue lines indicate the three sextets representing the three groups of Fe(B) ions identified in Ref. [2].