Photostriction in Ferroelectrics from Density Functional Theory

International audienceAn ab initio procedure allowing the computation of the deformation of ferroelectric-based materials under light is presented. This numerical scheme consists in structurally relaxing the system under the constraint of a fixed n e concentration of electrons photoexcited into a specific conduction band edge state from a chosen valence band state, via the use of a constrained density functional theory method. The resulting change in lattice constant along a selected crystallographic direction is then calculated for a reasonable estimate of n e. This method is applied to bulk multiferroic BiFeO 3 and predicts a photostriction effect of the same order of magnitude than the ones recently observed. A strong dependence of photostrictive response on both the reached conduction state and the crystallographic direction (along which this effect is determined) is also revealed. Furthermore, analysis of the results demonstrates that the photostriction mechanism mostly originates from the screening of the spontaneous polarization by the photoexcited electrons in combination with the inverse piezoelectric effect. The coupling of ferroelectric or multiferroic materials with light is currently attracting a lot of attention [1], as, e.g., demonstrated by the above-band-gap photovoltages found in BiFeO 3 (BFO) thin films [2], the search of low band gap materials for photovoltaic applications [3], or the recent development in the so-called hybrid perovskite solar cells [4]. Beyond the photovoltaic effect, there is another coupling between light and properties of ferroelectrics or multiferroics that is of current interest, namely, the so-called photostriction effect, a deformation of the material under illumination [5]. The photostriction phenomenon opens new perspectives for combining several functionalities in future generations of remote switchable devices and is promising for the realization of light-induced actuators [5]. It has been recently observed in BFO under visible light [6,7]. A giant shear strain generated by femtosecond laser pulses was also reported [8,9], and time-resolved synchrotron diffraction reported a shift of the Bragg peak on a picosecond time scale in both bismuth ferrite [10] and lead titanate [11]. However, the microscopic mechanism responsible for photostriction is poorly understood [8,9]. Obviously, having accurate numerical techniques able to tackle photostriction will allow us to " shed some light " on this effect. However, to the best of our knowledge, such numerical tools allowing a systematic study of the photostriction phenomenon and its atomistic origin are not available yet, despite recent attempts to use Density Functional Theory (DFT) as a tool to fit x-ray absorption spectra in pump-probe photostriction experiments [12]. Here, we report the development of an ab initio procedure to compute photostriction from first principles. This procedure not only reproduces the order of magnitude of the observed change of lattice constant in BFO [6], but also reveals that photostriction mostly originates from the combination of the screening of the polarization by the electrons photoejected in the conduction band and the inverse piezoelectric effect. It is also found that photo-striction depends on the precise conduction state the electron is excited into, and on the crystallographic direction along which the effect is studied. In order to realize the difficulty in mimicking photo-striction, let us start by recalling that the Kohn-Sham (KS) implementation of DFT [13] reformulates the many-body problem of interacting electrons into many single-body problems, and " only " guarantees that the model noninter-acting KS Hamiltonian yields the same ground state density and energy as the real interacting Hamiltonian. Such a fact, therefore, leaves the description of unoccupied states within traditional DFT an unanswered question, and the determination of excitation energies remains the privilege of rather costly techniques, such as time-dependent DFT [14] or the GW approximation [15]. However, an alternative formulation of DFT that treats ground and excited states on the same footing has been proposed [16]. In particular, Ref. [16] connected each eigenstate of a real interacting Hamiltonian with the eigenstate of a model noninteracting Hamiltonian through a generalized adiabatic connection (GAC) scheme. The so-called ΔSCF method [17] takes advantage of this GAC scheme, and assumes an one-to-one correspondence between the excited states of a single Kohn-Sham system and the real system [16]. This ΔSCF scheme has proved successful and computationall