Temperature dependence of the local electromagnetic field at the Fe site in multiferroic bismuth ferrite

In this paper, we present a study of the temperature-dependent characteristics of electromagnetic fields at the atomic scale in multiferroic bismuth ferrite (${\mathrm{BiFeO}}_3$ or BFO). The study was performed using time differential perturbed angular correlation (TDPAC) spectroscopy on implanted ${}^{111}\mathrm{In}$ (${}^{111}\mathrm{Cd}$) probes over a wide temperature range. The TDPAC spectra show that substitutional ${}^{111}\mathrm{In}$ on the ${\mathrm{Fe}}^{3+}$ site experiences local electric polarization, which is otherwise expected to essentially stem from the ${\mathrm{Bi}}^{3+}$ lone pair electrons. Moreover, the TDPAC spectra show combined electric and magnetic interactions below the Néel temperature $T_N$. This is consistent with simulated spectra. X-ray diffraction (XRD) was employed to investigate how high-temperature TDPAC measurements influence the macroscopic structure and secondary phases. With the support of ab initio DFT simulations, we can discuss the probe nucleus site assignment and can conclude that the ${}^{111}\mathrm{In}$ (${}^{111}\mathrm{Cd}$) probe substitutes the Fe atom at the B site of the perovskite structure.

Figure 1

(a) Unit cell representation of BFO where the Bi-O bonds are not shown. (b) Magnified view of two neighboring, interconnected ${\mathrm{FeO}}_6$ octahedra. (c) ${\mathrm{FeO}}_6$ octahedra viewed along the threefold axis to emphasize octahedral tilting. This picture was reproduced based on the work of Ruchi et al. (Fig. 1) [3] using the vesta program [4].

Figure 2

Simulated time differential perturbed angular correlation (TDPAC) spectra of combined hyperfine interactions in the electric coordinate systems (left) and their corresponding fast Fourier transforms (FFTs; right).

Figure 3

The eigenvalues of the combined hyperfine interaction Hamiltonian are plotted as functions of $y$, with $\gamma ={60}^{\circ }, \beta ={30}^{\circ }$, and $\eta =0.5$, in the electric coordinate system. Note that the eigenvalues are in units of $\hslash {\omega }_Q$.

Figure 4

Temperature dependence of the quadrupole (${\omega }_{\mathrm{Q}}$) and Larmor (${\omega }_{\mathrm{L}}$) frequencies according to the KATAME and K1 machines. The α phase is shown in orange ($T>T_{\mathrm{N}}$) and light blue ($T<T_{\mathrm{N}}$) layers, whereas the β phase is shown in the brick red layer. The red and blue dotted curves are shown for visual guidance.

Figure 5

(left) KATAME perturbed angular correlation (PAC) spectra at various measurement temperatures (370–835 °C) and (right) the corresponding fast Fourier transforms (FFTs). The α phase is shown in orange layers, whereas the β phase is shown in the brick red layer.

Figure 6

(left) K1 perturbed angular correlation (PAC) spectra at various measurement temperatures (370–840 °C) and (right) the corresponding fast Fourier transforms (FFTs). The α phase is shown in orange layers, whereas the β phase is shown in the brick red layer.

Figure 7

Temperature dependence of the asymmetry parameter (η) according to KATAME and K1. The α phase is shown in orange ($T>T_{\mathrm{N}}$) and light blue ($T<T_{\mathrm{N}}$) layers, whereas the β phase is shown in the brick red layer. The blue dotted curve is shown for visual guidance.

Figure 8

Temperature dependence of the damping parameter (δ) for KATAME and K1. The α phase is shown in orange ($T>T_{\mathrm{N}}$) and light blue ($T<T_{\mathrm{N}}$) layers, whereas the β phase is shown in the brick red layer.

Figure 9

(left) KATAME perturbed angular correlation (PAC) spectra at various measurement temperatures [room temperature $\left(\mathrm{RT}\right)=360{}^{\circ }\mathrm{C}$] and (right) the corresponding fast Fourier transforms (FFTs).

Figure 10

Temperature dependence of the Larmor frequencies. The fitting function is derived from the analytical solution of the Weiss equation as shown in Eqs. (6) and (7).

Figure 11

Configuration for polarization direction, effective magnetic field direction and cycloid orientation in BFO pseudocubic unit cell as resulting from our data. This figure was made based on the source [42].

Figure 12

Euler angles γ and β.

Figure 13

Comparison of the Mathematica calculations and the fittings performed using pacfit for our perturbed angular correlation (PAC) measurements at various temperatures. The red curves are plotted up to 170 ns intentionally to note the degree of overlap between the artificial time differential PAC (TDPAC) spectra and our experimental fits.

Figure 14

X-ray diffraction (XRD) spectrum of BFO at room temperature, before the time differential perturbed angular correlation (TDPAC) measurements.

Figure 15

X-ray diffraction (XRD) measurements at room temperature after time differential perturbed angular correlation (TDPAC) for (a) KATAME and for (b) K1.

Figure 16

Quadrupole interaction frequencies for BFO (${}^{111}\mathrm{In}$) and BFO (${}^{111m}\mathrm{Cd}$). The phase transition disorder interval is displayed in purple.

Figure 17

Temperature dependence of $V_{zz}$ for KATAME and K1 and a fit produced using Landau theory. The inset shows linear dependence of local electric field gradients (EFGs) on the square of polarization.

Figure 18

$R$($t$) spectra comparing the α-β phase transition of (a) BFO (${}^{111}\mathrm{In}$) and (b) BFO (${}^{111m}\mathrm{Cd}$).

Figure 19

Changes in the coordination and ion bond lengths of Bi-O (top) and changes in the bond lengths of Fe-O (bottom) with the phase transition from $R3c$ to $Pbnm$ symmetry. Made with vesta [4].