Multiferroic bismuth ferrite: Perturbed angular correlation studies on its ferroic $\alpha -\beta$ phase transition

Work of numerous research groups has shown different outcomes of studies of the transition from the ferroelectric $\alpha$-phase to the high temperature $\beta$-phase of the multiferroic, magnetoelectric perovskite Bismuth Ferrite (${\mathrm{BiFeO}}_3$ or BFO). Using the perturbed angular correlation (PAC) method with ${}^{111m}\mathrm{Cd}$ as the probe nucleus, the $\alpha$ to $\beta$ phase transition was characterized. The phase transition temperature, the change of the crystal structure, and its parameters were supervised with measurements at different temperatures using a six detector PAC setup to observe the $\gamma -\gamma$ decay of the ${}^{111m}\mathrm{Cd}$ probe nucleus. The temperature dependence of the hyperfine parameters shows a change in coordination of the probe ion, which substitutes for the bismuth site, forecasting the phase transition to $\beta$-BFO by either increasing disorder or formation of a polytype transition structure. A visible drop of the quadrupole frequency ${\omega }_0$ at a temperature of about $T_c\approx {820}^{\circ }\mathrm{C}$ indicates the $\alpha -\beta$ phase transition. For a given crystal symmetry, the DFT-calculations yield a specific local symmetry and electric field gradient value of the probe ion. The $Pbnm$ ($\beta$-BFO) crystal symmetry yields calculated local electric field gradients, which very well match our experimental results. The assumption of other crystal symmetries results in significantly different computed local environments not corresponding to the experiment.

Figure 1

Summary of selected works addressing the crystallographic settings of the $\beta$-phase of BFO.

Figure 2

Change of sublevel energies $E_Q\left(M\right)$ with increasing asymmetry parameter. Reference values only valid for $I=5/2$.

Figure 3

Resulting change of angular frequencies ${\omega }_n$ calculated with Eqs. (4) to (6). Reference values only valid for $I=5/2$.

Figure 4

TDPAC spectra with fitting functions in red and FFT showing the measured EFGs.

Figure 5

Three distinctive PAC spectra showing single $\alpha$-phase on top, the disordered range with a combination of $\alpha$ and $\beta$ coordination in the middle, and pure $\beta$-phase in the bottom spectrum. Specific Bi(Cd)-O polyhedra with symmetry elements to the right.

Figure 6

Temperature dependence of the quadrupole interaction frequency ${\omega }_0$. The blue area shows the rhombohedral $\alpha$-phase region and the red area the orthorhombic $\beta$-phase region with the area of disordered coordination in purple in between. If no errorbars are visible, the symmetrical error is smaller than the marker size.

Figure 7

Temperature dependence of the asymmetry parameter $\eta$. The blue area shows the rhombohedral $\alpha$-phase region and the red area the orthorhombic $\beta$-phase region with the area of disordered coordination in purple in between. If no errorbars are visible, the symmetrical error is smaller than the marker size.

Figure 8

Temperature dependence of the damping parameter $\delta$. The blue area shows the rhombohedral $\alpha$-phase region and the red area the orthorhombic $\beta$-phase region with the area of disordered coordination in purple in between. If no errorbars are visible, the symmetrical error is smaller than the marker size.

Figure 9

Temperature dependence of the frequency fraction $f$. The blue area shows the rhombohedral $\alpha$-phase region and the red area the orthorhombic $\beta$-phase region with the area of disordered coordination in purple in between. If no errorbars are visible, the symmetrical error is smaller than the marker size.

Figure 10

Temperature dependence of x-ray diffractograms measured between ${20}^{\circ }$–${70}^{\circ }$ (graphs are only shown up to ${60}^{\circ }$ as no information gain is achieved from reflections above ${60}^{\circ }$) at increasing temperatures around the phase transition temperature. The top and bottom graphs show calculated diffractograms of BFOs R3c and Pbnm structure, respectively. The intensities are normalized to the highest intensity.

Figure 11

Reflection behavior at the phase transition. $\alpha$-phase in blue, mixed phase in green, and $\beta$-phase in red. Reflection descriptions of the $\beta$-phase are italic. (a) The top diffractogram shows the reflection merging during the heating cycle, (b) the lower diffractogram shows the reflection splitting during the cooling cycle.

Figure 12

Temperature development of the Rietveld refinement phase fractions given in weight percent showing a clear hysteresis. The heating cycle is depicted in red and the cooling cycle in blue.

Figure 13

Peak growth of ternary phases ${\mathrm{Bi}}_{25}{\mathrm{FeO}}_{39}$ (italic) and ${\mathrm{Bi}}_2{\mathrm{Fe}}_4{\mathrm{O}}_9$ with temperature. The color gradient corresponds to the temperature change.