$\beta$ phase and $\gamma \text{−}\beta$ metal-insulator transition in multiferroic $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_3$

We report on extensive experimental studies on thin film, single crystal, and ceramics of multiferroic bismuth ferrite $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_3$ using differential thermal analysis, high-temperature polarized light microscopy, high-temperature and polarized Raman spectroscopy, high-temperature x-ray diffraction, dc conductivity, optical absorption and reflectivity, and domain imaging, and show that epitaxial (001) thin films of $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_3$ are clearly monoclinic at room temperature, in agreement with recent synchrotron studies but in disagreement with all other earlier reported results. We report an orthorhombic order-disorder $\beta$ phase between 820 and 925 $(\pm 5)°\mathrm{C}$, and establish the existence range of the cubic $\gamma$ phase between 925 $(\pm 5)$ and 933 $(\pm 5)°\mathrm{C}$, contrary to all recent reports. We also report the refined ${\mathrm{Bi}}_2{\mathrm{O}}_3\text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$ phase diagram. The phase transition sequence rhombohedral-orthorhombic-cubic in bulk [monoclinic-orthorhombic-cubic in $\left(001\right)\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_3$ thin film] differs distinctly from that of $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$. The transition to the cubic $\gamma$ phase causes an abrupt collapse of the band gap toward zero (insulator-metal transition) at the orthorhombic-cubic $\beta \text{−}\gamma$ transition around $930°\mathrm{C}$. Our band structure models, high-temperature dc resistivity, and light absorption and reflectivity measurements are consistent with this metal-insulator transition.

Figure 1

As-grown dendrites of $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_3$: (a) bunch of leaves grown in a Pt crucible; (b) individual leaf, axis parallel to ⟨110⟩pc, plane of leaf parallel to (110)pc. The horizontal axis is $\sim 2.5$ and $1\mathrm{cm}$ in (a) and (b), respectively.

Figure 2

(a) Comparison of unpolarized Raman spectra along ⟨001⟩ direction of (100)STO single crystal substrate, SRO/STO, and (001)BFO/SRO/STO thin film at room temperature. Lines are drawn as a guide for the eyes. (b) Deconvolution of the BFO peak around $74{\mathrm{cm}}^{-1}$ at RT shows the evolution of two peaks at 71.6 and $76.3{\mathrm{cm}}^{-1}$. The “dotted line with empty circle” shows the fitting after the deconvolution of these two peaks. The STO(100) single-crystal substrate shows one peak at $79.8{\mathrm{cm}}^{-1}$ at RT, plotted for comparison.

Figure 3

(a) Polarized Raman spectra of (001)BFO thin film on SRO/STO in $\mathrm{Z}\left(\mathrm{XX}\right)\overline{\mathrm{Z}}$ and $\mathrm{Z}\left(\mathrm{XY}\right)\overline{\mathrm{Z}}$ scattering configurations. (b) Polarized Raman spectra of (100)STO substrate given for comparison.

Figure 4

(Color online) Temperature-dependent Raman spectra of (001)BFO thin film on SRO/STO substrates.

Figure 5

(Color online) (a) Phase diagram of the ${\mathrm{Bi}}_2{\mathrm{O}}_3\text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$ system. Open circles show the data points obtained by DTA. The dotted line above the liquidus represents the approximate temperature limit not to be surpassed for avoiding decomposition, otherwise correct equilibrium DTA peaks are no longer observed upon a second heating. The $\alpha$, $\beta$, and $\gamma$ phases are rhombohedral, orthorhombic, and cubic, respectively. (b) DTA studies on crushed dendritic single crystal (dotted points) and target material of thin film (solid line) of $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_3$. Signal has been inverted and offset for clarity. Peak heights are proportional to the temperature difference between sample and reference.

Figure 6

(Color online) Temperature variation of lattice parameters for rhombohedral (pseudocubic setting), orthorhombic, and cubic phases of $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_3$. At $825°\mathrm{C}$, the lattice constant $a=4.0011\mathrm{\AA }$ splits into a triplet (open circles, squares, and triangles), which combines again at about $925(\pm 5)°\mathrm{C}$ in the cubic phase (solid square), where $a=3.9916\mathrm{\AA }$.

Figure 7

(Color online) $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_3$ (111)pc cut in transmission with crossed polarizers, thickness about $9\mu \mathrm{m}$. (a) Orthoscopy; black isotropic stripe in middle with $P_s$ perpendicular to plane. (b) Uniaxial conoscopy figure with crossed polarizers of black stripe in (a) between the two clear ones, with $P_s$ inclined at 34° ${16}^{\prime }$ with respect to the surface. The length of the part of the crystal plate shown is $\sim 3\mathrm{mm}$.

Figure 8

Cross section through a leaf of dendrite, parallel to a (110)pc plane: polished surface (a) in unpolarized light and (b) with crossed polarizers for two domains with $P_s$ in plane. (c) After etching, sharp spikes point in the direction of $P_s$. (d) Schematic; the crosses corresponding to the black and white domain fields in (b) represent the orientation of the principal section of the reflectivity ovaloid (principal $\text{bireflectance}=R_{\gamma }-R_{\alpha }$). The approximately vertical, thick, irregular trace (indicated with white arrow), visible in (a)–(c), represents an inclusion of flux. The horizontal extension of the crystal’s cross section is $\sim 2.5\mathrm{mm}$.

Figure 9

Evolution of domain structure in polished pseudocubic (111)pc cut of dendritic BFO single crystal (Fig. 1) (Ref. 16) at different temperatures: (a) at $27°\mathrm{C}$, ferroelastic domains of $\alpha$ phase, separated by traces of (110)pc walls. Reflected, polarized light, dark domains in extinction position; nearly crossed polarizers (for contrast formation in reflection, consult Ref. 57. (b) At $820°\mathrm{C}$, ferroelastic domains of $\beta$ phase; majority of rectilinear traces due to (110)pc walls. A few lines, perpendicular to the former ones, are due to traces of (100)pc walls. Specular reflection with polarizer only; contrast due to puckered surface. Small dark dots indicate nuclei of starting decomposition. (c) At $820°\mathrm{C}$, showing the coexistence of $\alpha$ and $\beta$ phases, separated by a sharp first-order phase boundary. The horizontal extension of the visible part of the crystal is $\sim 3\mathrm{mm}$.

Figure 10

(Color online) Band-gap energy in $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_3$ from room temperature to its peritectic decomposition point. The data show a linear decrease from about $2.5\mathrm{eV}$ at ambient temperature to about $1.5\mathrm{eV}$ at $550°\mathrm{C}$, followed by a discontinuous drop at the $\beta \text{−}\gamma$ transition near zero (metallic). For the lower-temperature data points, the gap is arbitrarily assigned as the energy (wavelength) at which the absorption exceeds $100{\mathrm{cm}}^{-1}$; this is probably about $0.15\mathrm{eV}$ below the true band gap. The broken (dotted) line was drawn to infer the nature of band-gap change. (b) Temperature vs reflective intensity of BFO thin film. The intensity was normalized to its room-temperature intensity $\left(I_{\mathrm{RT}}\right)$ and the wavelength used was $514.5\mathrm{nm}$.

Figure 11

Two-point resistance measurement $R\left(T\right)$ of $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_3$ single crystal. The resistance drops by ${10}^9$ between $20°\mathrm{C}$ and about $920°\mathrm{C}$ in this sample. We interpret the change in sign of $dR∕dT$ at $920°\mathrm{C}$ as from semiconducting (negative) to metallic (positive). The discontinuity at about $930–940°\mathrm{C}$ in this sample is presumably phase decomposition. The few degrees difference between the apparent metal-insulator transition in this specimen and that in Fig. 10 may be the different morphology of the sample, which is a bulk single crystal rather than a strained film.

Figure 12

Band-gap energy calculation for $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_3$ using screened exchange method for different structures: (a) cubic and (b) orthorhombic. Fermi level is at $0\mathrm{eV}$ in (a), and the valence band maximum is at $0\mathrm{eV}$ in (b).