Light scattering from the critical modes of the Verwey transition in magnetite

We present inelastic light scattering data on a single crystal of magnetite (${\mathrm{Fe}}_3{\mathrm{O}}_4$) across the Verwey transition. We identify anomalies of the lattice vibrations that originate from strong coupling to electronic excitations. We reveal spectroscopic signatures of diffusive modes in the electronic contribution to the Raman response function. We thereby provide information on the critical dynamics and the hierarchy of the structural and electronic modes in the mechanism of the Verwey transition.

Figure 1

Complete data sets of Raman spectra as a function of nominal temperature for (a) 2.4 and (b) 3.1 eV excitation. Data are normalized to the background intensity integrated between 800 and $810{\mathrm{cm}}^{-1}$. Red (green) arrows indicate magnetite (hematite) phonon modes in the monoclinic phase. Blue-to-red color coding refers to increasing nominal temperature. Black denotes the Verwey temperature.

Figure 2

Pictorial representation of the different contributions to the Raman response function of magnetite from phonons, magnons, and electrons, with diffusive or propagating dynamics.

Figure 3

Spectral response obtained for 2.4 eV excitation at (a) 293 and (b) 5 K, and for 3.1 eV excitation at the same reduced temperatures. Red (green) arrows indicate magnetite (hematite) phonon modes. Labels in red refer to the cubic counterparts of the phonon modes in the monoclinic phase. For better comparison, data are normalized to the background intensity integrated between 800 and $810{\mathrm{cm}}^{-1}$.

Figure 4

(a) Temperature dependence of the intensity of the critical modes for 3.1 eV excitation. Reference data for the $A_{1g}$ mode are also plotted. Temperature dependence of the (b) area and (c) center of gravity of the background distribution in the $240–500{\mathrm{cm}}^{-1}$ Raman shift range. Violet (green) symbols refer to 3.1 eV (2.4 eV) excitation. Lines are guides to the eye. Vertical dashed lines denote the Verwey temperature.

Figure 5

Temperature dependence of the frequency and linewidth of the (a,b) $A_{1g}$, (c,d) $T_{2g}^2$, and (e,f) $T_{2g}^1$ modes of the cubic phase, visible in the form of single peaks both above and below $T_V$. Violet (green) symbols refer to 3.1 eV (2.4 eV) excitation. A vertical dashed line denotes the Verwey temperature. The lower horizontal axis is the nominal temperature for 3.1 eV excitation and our approximate estimate of the effective temperature at the laser spot for 2.4 eV excitation.

Figure 6

Temperature dependence of the frequency and linewidth of Raman-active modes of the monoclinic phase. Violet (green) symbols refer to 3.1 eV (2.4 eV) excitation. The shoulder mode of the $A_{1g}$ mode in panels (a) and (b) is clearly observable only for 3.1 eV excitation. A vertical dashed line denotes the Verwey temperature. The lower horizontal axis is the nominal temperature for 3.1 eV excitation and our approximate estimate of the effective temperature at the laser spot for 2.4 eV excitation.

Figure 7

Temperature dependence of phonon modes and background intensity in the $240–500{\mathrm{cm}}^{-1}$ Raman shift range for (a) 2.4 and (b) 3.1 eV excitation. Red (green) arrows indicate magnetite (hematite) phonon modes. A blue arrow denotes the central energy of the higher-energy acoustic magnon at the $\mathrm{\Delta }$ point at 115 K $<T_V$ from INS [42]. Data are offset for clarity. Temperature dependence of the monoclinic modes at (c) 470 and (d) $160{\mathrm{cm}}^{-1}$ for 3.1 eV excitation. Red (blue) refers to the cubic (monoclinic) phase. For better comparison, data are normalized to the background intensity integrated between 800 and $810{\mathrm{cm}}^{-1}$. For clarity, data are offset and multiplied by a factor 5 close to the Verwey temperature. Data and fitting functions are plotted with colored symbols and lines, respectively. Black lines represent separate fit components.

Figure 8

Comparison between the spectral response, $R{\chi }^{\prime \prime }\left(\omega \right)$ (black), at the transition temperature and in the (a) (blue) monoclinic and (b) (red) cubic phase. The fitting functions to the background intensity defined in Eq. (3) are plotted together with the data, with the same color coding. Shaded areas highlight the diffusive contribution to the spectral response. (c)–(e) (black symbols): Temperature dependence of the fit parameters. The reduced temperature dependence of the dc conductivity of our sample is also plotted with a red line in panel (d). The lower horizontal axis of panels (c)–(e) is the nominal temperature. Vertical dashed lines denote $T_V^{*}$. To account for the effects of laser heating, fits are repeated for $R{\chi }^{\prime \prime }\left(\omega \right)$ computed from $S\left(\omega \right)$, respectively, with reference to our estimate of the effective temperature, $T$, and the nominal temperature, $T^{*}$. Error bars correspond to the differences between the fit parameters in the above two cases. Data points are average values.

Figure 9

Comparison between the spectral response, $R{\chi }^{\prime \prime }\left(\omega \right)$ (black), at the transition temperature and in the (a) (blue) monoclinic and (b) (red) cubic phase. The fitting functions to the background intensity defined in Eq. (5) are plotted together with the data, with the same color coding. Shaded areas highlight the electronic contribution to the spectral response. (c) Our data from spontaneous Raman scattering (SRS, green symbols and shaded area) are compared with data from INS (black symbols and shaded area) [7]. The black line is the theoretical prediction for the correlation time of polaron fluctuations of ${\mathrm{\Delta }}_5$ symmetry at (0,0,0.75) r.l.u. based on experimental estimates of the microscopic parameters of Yamada's model [49]. The lower horizontal axis of panel (c) is the nominal temperature. Vertical dashed lines denote $T_V$. As in Figs. 8–8, data points and error bars account for the uncertainty from the effects of laser heating.