Phase separation and electrical switching between two isosymmetric multiferroic phases in tensile strained ${\text{BiFeO}}_3$ thin films

Phase separation of two different isosymmetric phases can occur as a result of their similar ground state energies. We have found such phase separation in a multiferroic system at a tensile-strain-driven morphotropic phase boundary of rhombohedral and orthorhombic bismuth ferrite. We utilize the emergent phase competition in order to implement three-step electric switching of ferroelectric polarization as well as rotation of the magnetic easy axis using electric fields. This observation provides a pathway to phase-competition-driven magnetoelectric devices.

Figure 1

Schematic diagram of electrically switchable R-BFO and O-BFO with possible ferroelectric polarizations in a tensile strained (110)${}_{\mathrm{pc}}$ BFO thin film on a GSO substrate. To express both ferroelectric and ferroelastic domains simultaneously, we used $r_i^{\pm }$ notation where $i$ = 1 or 2 indicates rhombohedral variants and the $+$ or $-$ sign refers to upward or downward polarization. $o^{\pm }$ notation is for orthorhombic variants. ${\vec{P}}_{\widehat{n}}$ denotes the projected ferroelectric polarization along the film normal direction ($\widehat{n}\parallel$[110${\text{]}}_{\mathrm{pc}}$). ${\vec{E}}_1$ and ${\vec{E}}_2$ describe the switching fields between R-BFO and O-BFO.

Figure 2

(a) Conventional θ-2θ scan for a BFO film grown on a (110)${}_{\mathrm{pc}}$ GSO substrate. Circles and diamonds indicate R-BFO peaks and O-BFO peaks, respectively. (b) RSMs for (110)${}_{\mathrm{pc}}$ and (221)${}_{\mathrm{pc}}$ peaks with a horizontal reciprocal axis aligned to [001${\text{]}}_{\mathrm{pc}}$. (c) RSMs for (110)${}_{\mathrm{pc}}$ and (210)${}_{\mathrm{pc}}$ peaks with a horizontal reciprocal axis aligned to [$1\overline{1}0$${\text{]}}_{\mathrm{pc}}$. (d) Schematic displaying a monoclinic unit cell (colored red) which has twice larger volume relative to a pseudocubic unit cell (colored black). An olive-colored plane represents the $a_m$-$b_m$ plane of GSO substrate. The lattice parameters and volumes are determined; $a_m$ = 3.96(7) Å, $b_m$ = 5.6(5) Å, $c_m$ = 5.57(4) Å, ${\beta }_m$ = 90.(0)°, and $V_m$ = 124.(9) Å${}^3$ for O-BFO; $a_m$ = 3.96(7) Å, $b_m$ = 5.61(1) Å, $c_m$ = 5.62(5) Å, ${\beta }_m$ = 89.1(2)°, and $V_m$ = 125.(2) Å${}^3$ for R-BFO; $a_m$ = 3.96(7) Å, $b_m$ = 5.74(5) Å, $c_m$ = 5.48(0) Å, ${\beta }_m$ = 90.0(0)°, and $V_m$ = 124.(9) Å${}^3$ for GSO. We note that all the $a_m$ IP lattice parameters are matched exactly but the other $b_m$ IP parameters are relaxed as a result of uniaxial misfit strain.

Figure 3

(a) Topographic image of an as-grown (110)${}_{\mathrm{pc}}$ BFO thin film. Crystal axes are indicated. (b) OOP PFM image exhibiting needle-shaped O-BFO areas with zero OOP polarization (brown, ${\vec{P}}_{\widehat{n}}=0$) surrounded by the matrix areas of R-BFO with downward polarization (black, ${\vec{P}}_{\widehat{n}}<0$). (c) IP-PFM real part image discriminating downward polarization (${\vec{P}}_{\widehat{n}}<0$) regions including $r_1^{-}$ (brown) and $r_2^{-}$ (yellow) domains and zero OOP polarization (${\vec{P}}_{\widehat{n}}=0$) regions including $o^{+}$ (white) and $o^{-}$ (black) domains. Scale bars represent 1 μm. (d) Schematic diagram of IP component ferroelectric polarizations for the R-BFO and O-BFO phases. A PFM tip along the black dashed line depicts the fast scan direction oriented 45° to the crystalline [001${\text{]}}_{\mathrm{pc}}$ axis.

Figure 4

(a) XAS at Fe $L$ edges with a σ-polarized x-ray beam where its electric field ($\overleftrightarrow{E}$) is aligned to [001${\text{]}}_{\mathrm{pc}}$. In the inset, the enlarged $L_2$-edge spectra and their differences are presented. (b) OOP PFM image. (c) IP-PFM image. At the same region, a series of PEEM images were acquired by using linearly polarized x rays with the incident electric field along (d) [001${\text{]}}_{\mathrm{pc}}$, (e) [$1\overline{1}0$${\text{]}}_{\mathrm{pc}}$, (f) an in-plane axis rotated 45° from [001${\text{]}}_{\mathrm{pc}}$, and (g) an axis 30° off from the surface normal. Contrast of the PEEM images represents the relative intensity of two $L_2$ subpeaks ($I_B-I_A$). Red dashed ovals indicating $o^{-}$ domains in (c) and (g) are drawn to address the correlation between ferroelectric domains of O-BFO and their PEEM contrast with the π-polarized x ray. Scale bars represent 1 μm. Schematics on the right-hand side describe the ferroelectric polarization and the proposed magnetic easy axis of (h) R-BFO and (i) O-BFO. The spectra in (a) were obtained by means of microspectroscopy, i.e., integrating the intensities from two different domains in a stack of images.

Figure 5

(a) Topographic image after the electric switching. (b) OOP PFM image which shows three different OOP ferroelectric polarization regions: as-grown R-O mixed BFO region, O-BFO dominant region with little OOP polarization (inside the outer box), and R-BFO dominant region with upward polarization (inside the inner box). (c) IP-PFM image of the same area. Scale bars indicate 2 μm.