Chemical compression and ferroic orders in La substituted $\mathrm{BiFe}{\mathrm{O}}_3$

Chemical compression effects on the ferroic orders in La substituted $\mathrm{BiFe}{\mathrm{O}}_3$ are studied by atomic pair distribution function analysis and structure modeling. While rhombohedral $\mathrm{BiFe}{\mathrm{O}}_3$ exhibits ferroelectricity and antiferromagnetism (AF) with a cycloidal Fe spin arrangement leading to zero magnetization, La substituted $\mathrm{BiFe}{\mathrm{O}}_3$ exhibits a reduced lattice polarization, strengthened AF order, and an apparently suppressed spin cycloid leading to nonzero magnetization. The observed changes in the ferroic orders arise from the chemical compression induced changes in the octahedral rotation and ferroelectric displacement of Bi atoms, which appear as lattice degrees of freedom entangling the electronic and magnetic orders in $\mathrm{BiFe}{\mathrm{O}}_3$.

Figure 1

(a) Fragment from the rhombohedral structure of $\mathrm{BiFe}{\mathrm{O}}_3$ projected down the $\langle 001{\rangle }_R$ direction, featuring corner shared Fe (brown circles)–oxygen (blue circles) octahedra with Bi (red circles) atoms positioned in the cavities between them. The octahedra are rotated with respect to each other and Bi atoms are displaced from the geometrical center of the cavities, rendering the material ferroelectric. (b) XRD patterns, (c) room temperature hysteresis curves, and (d) total atomic PDFs $G$($r$) for pure and La substituted $\mathrm{BiFe}{\mathrm{O}}_3$. The PDFs are offset vertically for clarity.

Figure 2

(a) Computed total and Bi-differential atomic pair correlation functions (PCFs) $g$($r$) (black) for pure $\mathrm{BiFe}{\mathrm{O}}_3$. The individual partial PCFs are also shown, each in a different color. (b) Energy dependence of the real dispersion correction $f^{\prime }$ for Bi. The energies below the $K$ edge of Bi used in the present experiments are marked with arrows. Values for $f^{\prime }$ and $f^{\prime \prime }$ at these energies are also given. (c) XRD patterns for $\mathrm{BiFe}{\mathrm{O}}_3$ taken and at 25 eV (red) and 500 eV (black) below the $K$ edge of Bi (90.524 keV). Their difference (blue) multiplied by a factor of 3 is also given. (d) Experimental Bi-differential atomic PDFs $G$($r$) for pure and La substituted $\mathrm{BiFe}{\mathrm{O}}_3$. The PDFs are offset vertically for clarity. Note that, as defined, the PCF $g\left(r\right)=\rho \left(r\right)/{\rho }_o$, oscillates about 1 while the PDF $G\left(r\right)=4\pi r{\rho }_o\left[\rho \left(r\right)\text{−}1\right]$ oscillates about zero. Here ρ($r$) and ${\rho }_o$ are the local and average atomic number density, respectively.

Figure 3

Rietveld fits (black) to XRD patterns (red) for La substituted ${\mathrm{Bi}}_{1-\mathrm{x}}{\mathrm{La}}_{\mathrm{x}}\mathrm{Fe}{\mathrm{O}}_3$ based on a S.G. $R3c$ model. Vertical green bars show the position of Bragg peaks. The residual difference (blue) is shifted by subtracting a constant for clarity. The goodness-of-fit indicator, $R_{\mathrm{wp}}$, is about 6% for the $x=0.1$ and $x=0.2$ samples. It is about 13% and 16% for the $x=0.3$ and $x=0.4$ samples, respectively.

Figure 4

Rietveld fits (black) to XRD patterns (red) for La substituted ${\mathrm{Bi}}_{1-\mathrm{x}}{\mathrm{La}}_{\mathrm{x}}\mathrm{Fe}{\mathrm{O}}_3$ based on a S.G. $P1$ model. Vertical green bars show the position of Bragg peaks. The residual difference (blue) is shifted by subtracting a constant for clarity. The goodness-of-fit indicator, $R_{\mathrm{wp}}$, is about 7% and 9% for the $x=0.3$ and $x=0.4$ samples, respectively.

Figure 5

Crystallographic (small unit cell) fits (black) to experimental PDFs $G$($r$) (red) for La substituted ${\mathrm{Bi}}_{1-\mathrm{x}}{\mathrm{La}}_{\mathrm{x}}\mathrm{Fe}{\mathrm{O}}_3$ based on a S.G. $P1$ model. The residual difference (blue) is shifted by subtracting a constant for clarity. The goodness-of-fit indicator, $R_{\mathrm{wp}}$, for the fits is about 13%.

Figure 6

RMC (large model based) fits (black) to experimental PDFs $G$($r$) (red) for La substituted ${\mathrm{Bi}}_{1-\mathrm{x}}{\mathrm{La}}_{\mathrm{x}}\mathrm{Fe}{\mathrm{O}}_3$. The initial configuration is based on a S.G. $P1$ type structure. The residual difference (blue) is shifted by subtracting a constant for clarity. The goodness-of-fit indicator, $R_{\mathrm{wp}}$, for the fits is about 6%.

Figure 7

RMC (large model based) fits (black) to experimental Bi-differential PDFs $G$($r$) (red) for La substituted ${\mathrm{Bi}}_{1-\mathrm{x}}{\mathrm{La}}_{\mathrm{x}}\mathrm{Fe}{\mathrm{O}}_3$. The initial configuration is based on a S.G. $P1$ type structure. The residual difference (blue) is shifted by subtracting a constant for clarity. The goodness-of-fit indicator, $R_{\mathrm{wp}}$, for the fits is about 6%.

Figure 8

Projection of the RMC refined model for (a) $\mathrm{BiFe}{\mathrm{O}}_3$ and (b) ${\mathrm{Bi}}_{0.6}{\mathrm{La}}_{0.4}\mathrm{Fe}{\mathrm{O}}_3$ onto the ${\left(001\right)}_R$ atomic plane of the perovskite lattice. For simplicity, Fe atoms are not shown. Bi atoms are in brown and oxygen atoms are in blue. The gray shaded contour boundaries include 99% of all atoms at the particular lattice sites. The blue/orange-colored regions include all atoms at the particular site, where atoms that are closer than $0.5\AA$ are merged. Bi atoms in ${\mathrm{Bi}}_{0.6}{\mathrm{La}}_{0.4}\mathrm{Fe}{\mathrm{O}}_3$ appear less displaced from the geometrical centers of the oxygen polyhedron that encloses them in comparison to a Bi atom in pure BFO (compare the positions of the crosshair type projection of the unit cell edges on the distribution of Bi atoms at the center of the plots, which, for clarity, is also shown enlarged on their left side). Partial (c) Bi-O and (d) Bi-Fe PDFs $G$($r$) computed from the RMC refined models for ${\mathrm{Bi}}_{1-\mathrm{x}}{\mathrm{La}}_{\mathrm{x}}\mathrm{Fe}{\mathrm{O}}_3$ ($x=0$, 0.1, 0.2, 0.3, and 0.4). (e) Distribution of Fe-O-Fe bond angles computed from the RMC models; (f) our experimental data for the coercive field $H_c$ and remanent magnetization $M_r$ for pure and La substituted BFO. (g) RMC model averaged Fe-O-Fe bond angles (black) and experimental Néel temperature $T_N$ (red) for La substituted BFO. (h) Change in computed spontaneous (blue) and experimental saturation (red) and remanent (black) polarization in La substituted BFO. Broken lines in (f)–(h) are a guide to the eye. Arrows in (c)–(e) highlight trends in the shown data sets with increasing La content $x_{\mathrm{La}}$ from $x=0$ (black) to $x=0.4$ (green).