Capturing ultrafast photoinduced local structural distortions of BiFeO3

The interaction of light with materials is an intensively studied research forefront, in which the coupling of radiation energy to selective degrees of freedom offers contact-free tuning of functionalities on ultrafast time scales. Capturing the fundamental processes and understanding the mechanism of photoinduced structural rearrangement are essential to applications such as photo-active actuators and efficient photovoltaic devices. Using ultrafast x-ray absorption spectroscopy aided by density functional theory calculations, we reveal the local structural arrangement around the transition metal atom in a unit cell of the photoferroelectric archetype BiFeO3 film. The out-of-plane elongation of the unit cell is accompanied by the in-plane shrinkage with minimal change of interaxial lattice angles upon photoexcitation. This anisotropic elastic deformation of the unit cell is driven by localized electric field as a result of photoinduced charge separation, in contrast to a global lattice constant increase and lattice angle variations as a result of heating. The finding of a photoinduced elastic unit cell deformation elucidates a microscopic picture of photocarrier-mediated non-equilibrium processes in polar materials.


Static x-ray diffraction of BiFeO3 thin film
The x-ray reflectivity around BiFeO3 (BFO) (002)pc peak shows the film is a crystalline film, evident by clear Kiessig fringes in Fig. S1(a). The splitting of (113)pc Bragg peaks shown in Fig.  S1(b) supports that the BFO film has multi-domain structures in which the remnant ferroelectric polarization points to four possible directions along the <111>pc-axis ). 2. The structure of the ground state of BiFeO3 as used in the calculations: For the calculations of x-ray BFO spectrum, we have used a modified version of the bulk structure as referenced by Moreau et al. [Ref S1]. The principal modification made to the original bulk BFO structure was on the value of the octahedral tilt angle, θ, defined by O-O-O alignment as shown in Fig. S2(a) and Fig. S2(b). In the original bulk structure, the octahedron tilt is about 10 degrees, while in thin film the octahedron tilt is about 7 degrees [Ref S2]. Based on 7 degree octahedron tilt angle, we have adjusted the lattice parameters of the modified BFO structure in order to keep the Fe-O bond length within each octahedron the same as those in the original structure. Table S1 shows structural characteristics of the original and modified BFO bulk structures. The latter has been used as the reference ground state of the thin film for the calculation of x-ray spectrum shown in Fig. S2(c), which agrees well with the measured ground state spectrum shown in Fig. 1a.   Table S1: Some characteristics of the initial and modified bulk BFO structures. The latter has been used as the reference ground state for the calculation of x-ray spectrum.

3.
The correspondence between electronic density of state and Fe K-edge XANES spectra.

Effects of an increased broadening of the density of states on the XANES spectra:
In order to improve the qualitative agreement between the calculated and experimental difference spectra, we have tested the effect of a slight uniform increased broadening on the density of states. This effect as a result of temperature increase are mainly responsible for damping the absorption variations by homogeneously reducing (increasing) the intensity of the absorption peak (valley) without introducing any energy shift to the XANES spectra. As shown in Fig. S4, we found that the difference spectra can be improved a bit around the A1 peak region, without significantly modifying the rest of the difference spectra, especially the |A3|/|A4| ratio. Fig. S4: Effect of increasing the DOS broadening on the XANES and differential spectra. For clarity purpose, we show a plot of the XANES spectra (left panel) with a much larger broadening increase than that used to calculate the difference spectra (right panel).

The calculation of octahedron rotation:
To investigate the effect of a variation of the oxygen octahedron tilt angle on the spectral features, we have generated a series of structures from the modified ground state of the BFO pseudo-cubic unit cell. Since the average Fe-O bond length should remain unchanged (Fig 2b), we have assumed each FeO6 octahedron as rigid octahedron while performing the rotation. This induces a slight volume increase of the pseudo-cubic unit cell, as the octahedron tilt angle reduces. The rotation of the oxygen octahedron around each Fe atom has been done for two cases: (i) a rotation within the [110, 001] plane (see Fig. S5

The simulation of thermally induced spectrum:
Lattice deformations and atomic reorganizations play a crucial role in modifying the relative peak intensities of the main edge. In particular, the calculations show that keeping the average Fe-O bond length constant is essential to avoid energy shifts of the XANES spectra. If any energy shifts occur, the difference spectrum would be more complicated to calculate and interpret. As shown in Fig.2b, the variation of the average Fe-O bond length obtained experimentally for the thermal excitation case is negligible. All these elements suggest that the cell deformations and atomic reorganizations occurring during thermal excitation are not simple since they must induce an increase of the cell volume, as expected under heating conditions, but also keep relatively constant the average Fe-O bond length. In that regards, finding the exact lattice deformations involved in thermal excitation is a tedious work since many degrees of freedom are available for cell modification upon temperature increase, such as isotropic or non-isotropic variation of length and angles between the lattice vectors and the atomic reorganization in the oxygen octahedrons.
In our study, we simplified the calculation of thermal induced spectra using a constant volume deformation model (c-axis expansion and a, b-axis contraction) in the hexagonal frame. This simplification is justified by the small temperature rise (250K) that does not yield a significant volume changes (Ref. [22] in the main text). A constant volume deformation in the hexagonal frame results in a global increase of the lattice vectors and a modification of the unit cell angles in the pseudo-cubic frame. This type of cell deformation allows us to include the contributions from lattice and unit cell angle variation (key parameter to switch the A3/A4 ratio compared to the photoexcited case). In this case, constant volume deformation in the hexagonal frame is a good approximation to the much more complicated real case cell deformation with regards to the A3/A4 ratio.

Data analysis of EXAFS:
The Athena program is used to process experimental XAS data to extract the normalized oscillation amplitude  exp (k) and the photoelectron wave number k is defined by , where E0 is the absorption edge energy. The theoretical calculated  th (k) is given by EXAFS equation, where j indicates a shell with identical backscatters, Nj is the coordination n umber of jth shell, fj is the backscattering amplitude, Rj is the average distance, σj is the mean square variation, j is the scattering phase shift,  is the effective mean free path and 2 0 S is the amplitude reduction factor. FEFF6 is used to calculate fj, j and . Fitting to the experimental data to refine the structure parameters 2 0 S , Rj, j 2 is done using the Artemis program. Crystal structure as detailed in Supplemental Materials Note 1 is used as the starting structure for fitting of all spectra. The k 3 -weighted Fourier transformed EXAFS spectra with k ranging from 2 to 7.8 Å -1 are fitted in R space in the range of 0.8 -2.2 Å (Fig.S6). Due to the limited k range used in the fitting, only the first Fe-O shell has been fitted. Based on the crystal structure, the first Fe-O shell split into two sets Fe-O (1.915 Å) and Fe-O (2.072 Å), both with triple-degeneracy. The same  2 and distance changes from both paths were used in the fitting.
Four EXAFS spectra were fitted: XTA spectra before (t<0) and after (t=100 ps) laser excitation and two static XA spectra measured at 300 K and 550K.  Table S2. The average Fe-O bond lengths of 4 EXAFS spectra are the same within statistical frame. Fig. S7: The Fourier transformed Fe-K edge EXAFS spectra and best fit of (a) XTA spectra before (t<0) and after (t=100 ps) laser excitation; (b) Static XA spectra taken at 300 and 550K respectively. The spectra are phase uncorrected, so the distances R shown in the figure are smaller than the actual best fitting values. The imaginary parts of were offset by -2 for clarity.