Ultrafast transient increase of oxygen octahedral rotations in a perovskite

TL;DR

This study demonstrates that femtosecond photodoping can temporarily enhance oxygen octahedral rotations in EuTiO3, revealing a novel ultrafast structural control mechanism in perovskites with potential for functional state manipulation.

Contribution

It provides the first evidence of ultrafast photoinduced increase in structural order parameter in a perovskite, linked to charge-transfer effects and tolerance factor reduction.

Findings

Transient increase in oxygen octahedral rotations observed

Ultrafast charge transfer reduces Goldschmidt tolerance factor

Structural order parameter enhancement occurs on femtosecond timescales

Abstract

The ability to control the structure of a crystalline solid on ultrafast timescales bears enormous potential for information storage and manipulation or generating new functional states of matter [1]. In many materials where the ultrafast control of crystalline structures has been explored, optical excitation pushes materials towards their less ordered high temperature phase [2{9] as electronically driven ordered phases melt and possible concomitant structural modifications relax. Nonetheless, for a few select materials it has been shown that photoexcitation can slightly enhance the amplitude of an electronic ordering phenomenon (i.e. its electronic order parameter) [9{13]. Here we show via femtosecond hard X-ray diffraction that photodoping of the perovskite EuTiO3 transiently increases the order parameter associated with a purely structural [14] phase transition represented by the antiferrodistortive rotation of the oxygen octahedra. This can be understood from an ultrafast charge-transfer induced reduction of the Goldschmidt tolerance factor [15], which is a fundamental control parameter for the properties of perovskites

Full text

Phase transitions are commonly described by an order parameter (OP) that represents the degree of order in the system. Within the ordered phase, the OP quantifies the amplitude of an ordering phenomenon or the distance to the critical point with respect to a tuning parameter such as temperature, structural parameters or the electronic chemical potential. Examples of OPs include the amplitude of a symmetry-breaking distortion of a crystal structure and the amount of charge carriers in a charge/orbital-density wave or a superconducting condensate. In correlated materials, structural or electronic ordering phenomena often occur simultaneously or compete with each other morosan2012 . Slight changes of a tuning parameter can induce a phase transition with potentially useful functionality. Optical control of such tuning parameters opens up the possibility to manipulate an OP and thereby control possibly connected macroscopic material properties on ultrafast timescales. Novel routes to optically increase an OP have been explored recently with the goal of enhancing or inducing functional properties. Examples include light enhanced superconductivity mitrano2016 ; fausti2011 , increased charge singer2016 or spin kim2012 density wave amplitudes. Significant potential exists for increasing an order parameter by coherently controlling the structural parameters mankowsky2014 ; subedi2014 ; mankowsky2017 ; kozina2019 .

Second-order purely structural phase transitions are driven by anharmonic interactions within the phonon system cowley1980 ; dove1997 . When a tuning parameter reaches the critical point, the structure spontaneously distorts along a vibrational coordinate which lowers the symmetry of the crystal. The corresponding OP is the mean displacement amplitude dove1997 . At the critical point of a displacive dove1997 structural transition, the eigenfrequency of the respective vibrational mode, called softmode, approaches zero and the susceptibility of the OP with respect to the tuning parameter diverges.

EuTiO3 is a cubic perovskite (Pm$\overline{3}$m) at high temperature which undergoes a structural phase transition around $T\approx 290K$ driven by an acoustic softmode at the $R$-point which manifests as an antiferrodistortive (AFD) rotation of the oxygen octahedra (Fig. 1a) , very similar to that in SrTiO3 ellis2012 ; goian2012 ; bettis2011 . The rotation angle $\varphi$ is the order parameter of the transition dove1997 . Here we photoexcite EuTiO3 in its low temperature structurally distorted phase (I4/mcm) via ultrafast optical excitation across its direct band gap of  0.9 eV lee2009 (see Methods). Via subsequent femtosecond hard X-ray pulses we monitor the intensities of AFD induced X-ray superlattice (SL) reflections (Fig. 1b) which are proportional to $\varphi^{2}$ porer2018 .

Figure 1c shows the normalised intensity of the (5/2 3/2 1/2) SL reflection as a function of the pump-probe delay for a series of excitation conditions. The green/blue/red data points show the transient SL intensity obtained for excitation with photon energies of 4.65/3.1/1.55 eV for an absorbed fluence of 2.0/3.66/3.86 mJ/cm2 injecting a density (see Methods) of 0.04/0.11/0.23 electron-hole (eh) pairs per formula unit (FU), respectively. Independent of the pump photon energies and fluences/injected carrier densities, we observe a transient increase of the superlattice diffraction intensity ($I\textsubscript{AFD}$) within an initial sub-ps time window. The enhancement is similar for another AFD-induced SL reflection with different X-ray momentum transfer (Supplementary Figure S2). Quantitatively, the maximum observed enhancement factor of $I\textsubscript{AFD}$ is 1.4 for the highest injected density with 1.55 eV photons. The subsequent decay of $I\textsubscript{AFD}$ intersects the initial baseline. For excitation with photon energies below 4.65 eV the decay exhibits a superimposed strongly damped oscillatory component with a frequency of approximately $4\,\mathrm{THz}$. Furthermore, when lowering the excitation intensity we find that the decay slows down and the lifetime of the enhanced diffraction intensity increases (Fig. 2). The base temperature does not significantly influence the dynamics (Fig. S3). As $I\textsubscript{AFD}$ scales with $\varphi^{2}$, the enhanced diffraction efficiency may originate from an increase of the OP.

To describe this behavior we calculate the total energy within the I4/mcm unit cell at a series of fixed rotation angles (Fig. S4) and from there we derive the double-well potential of the AFD mode (SI). Fig. 3b shows the resulting potential for various doping levels. We obtain a rotation angle for zero doping of $\varphi_{0}=6.3^{\circ}$. With increasing $\rho$, we find both a deepening of the potential and, importantly, an increasing displacement of the potential minimum from $\varphi_{0}$. The latter yields a driving force towards an increased AFD rotation which can explain the increase of SL diffraction intensity during the initial time-window (Fig. 1c). An increased excess energy of the doped carriers, implemented via an elevated electronic temperature, is predicted to further enhance the effect (Fig. S5). This trend agrees with our experimental observation that fewer eh pairs are needed to generate equivalent enhancements at higher excitation frequencies, e.g. $0.11$ eh pairs per FU generated by 3.1 eV pump photons yield a similar enhancement as $0.23$ eh pairs per FU injected by 1.55 eV photons (Fig. 1c, blue and red datapoints).

In principle, deepening of the soft-mode potential with constant $\varphi$ could also enhance the reflection intensity by reducing the average incoherent thermal displacements of the local rotations. This would increase the Debye-Waller factor (DWF) and consequently the reflection efficiency. For our experimental conditions, we expect an initial DWF of $>0.99$ for the (5/2 3/2 1/2) SL reflection based on the thermal displacement parameters of EuTiO3 allieta2012 . This rules out an increase of $I\textsubscript{AFD}$ by more than 1% from changes in the DWF. Furthermore, the scaling of the DWF with the X-ray momentum transfer $\mathbf{q}$ implies that the reflection efficiency would be more strongly enhanced at larger $\mathbf{q}$, which is not observed (Fig. S2). Both arguments exclude a significant influence of photoinduced deepening of the double-well potential on the observed dynamics of $I\textsubscript{AFD}$.

While the observed photoinduced increase of the OP is contrary to its evolution for increasing temperature (and phonon entropy) in thermal equilibrium, it does however not imply an actual decrease of phonon entropy. The increase of $\varphi$ can be understood intuitively in terms of a reduction of the Goldschmidt tolerance factor goldschmidt1926 : Photoexcitation across the Eu $4f$ - Ti $3d$ charge-transfer gap of EuTiO3 (indicated by the top three arrows at the bottom of Fig. 3a) removes $f$-electrons from the Eu2+ A-site ions and shrinks the surrounding electron clouds. Analogously, the Ti4+ B-site ions expand due to their additional electronic charge. Both size effects decrease the tolerance factor, which is known to cause a more distorted perovskite structure in the static case. We illustrate this in Fig. 3a right inset, the calculated change in charge density in the (101) plane (cubic notation). We see that the electron density decreases approximately spherically at the Eu sites and increases at the Ti sites. This unusual decrease in electron density on the Eu2+ ion on photodoping is the origin of the stark contrast in behavior between EuTiO3 and SrTiO3 on photoexcitation, in spite of their similar crystallographic structures and O $2p$ – Ti $3d$ electronic bands bettis2011 ; birol2013 . In the case of EuTiO3, the largely unhybridized Eu $4f$ states form an additional set of occupied bands above the oxygen $2p$ valence band; these localized $4f$ states are electron depleted by charge-transfer excitation reducing the size of the Eu2+ cation. In contrast, charge transfer excitation across the O $2p$ -Ti $3d$ band gap of SrTiO3 reduces the octahedral distortion porer2018 .

Following the excitation, both phonon-mediated eh recombination and cooling of the electronic system via electron-phonon scattering reduce the electronically driven enhancement of $\varphi$ and heat the phonon system. A rapidly increased temperature of the vibrational system can be expected to further relax the distortion via anharmonic phonon-phonon interactions, similar to a thermally driven phase transition.

All optical experiments on a EuTiO3 film (Methods, SI) show a decay dynamics of the photoinduced reflectivity change for 1.55 eV probe photons that resembles a bimolecular decay dynamics. Similar dynamics is observed when probed in the multi-THz regime. We ascribe this decay to an excitation-dependent carrier recombination process (SI).

To model the dynamics of chemical potential $\varphi$, we introduce a time dependency of chemical potential $V(\varphi,\rho)$ via a transient doping level $\rho(t)$. The onset dynamics of $\rho(t)$ reflects the pump pulse duration and injected number of eh pairs and the decay dynamics accounts for the recombination process (SI). The temperature increase of the lattice is included via an additional relaxation of $V(\varphi,\rho)$ towards the high temperature phase along its dependency on $\rho$. We scale this additional component phenomenologically with the amount of recombined charge carriers at time $t$ (SI). Solving the equation of motion for a time-dependent potential $V(\varphi(t),\rho(t))$ yields $\varphi(t)$ porer2018 (SI) which we numerically fit via $\varphi(t)^{2}/\varphi_{0}(t)^{2}$ to the experimental data (solid lines, Fig. 1c (red and blue curves), and Fig. 2).

The model reproduces the slow down of the decay dynamics for lowering the excitation fluence. As the slow down is described by an eh density-dependent carrier recombination, we conclude that the lifetime of the enhanced octahedral rotation is mainly governed by the lifetime of the photoinjected carriers. The weak oscillatory component on the decay dynamics of $I\textsubscript{AFD}$ (Fig. 1 (c), red and blue curves) is well reproduced by a model consiting of a displacive excitation caused by a shift of the potential minimum, with the correct phase and frequency and thus further supports a displacively driven structural dynamics initiated by the optical excitation. The damping of the soft mode is fixed to yield a coherence lifetime of $0.14\,\mathrm{ps}$. The absence of an oscillation after excitation with 4.65 eV photons is possibly related to a delayed build-up of the displacive force due to the opposite effects of the simultaneous O$2p$-Ti$3d$ and Eu$4f$-Ti$3d$ charge transfer excitations.

Ultrafast control of a structural distortion in the opposite direction to its thermal transition by optical excitation opens up new possibilities for ultrafast tuning of electronic and magnetic properties imada1998 ; aken2004 ; varignon2017 . In particular, the ability to tune rotations of oxygen octhahedra, allows in turn the tuning of magnetic and electronic properties that are strongly correlated with the tolerance factor and structural distortions, such as magnetic orderings or electric polarization, on ultrafast timescales.

I Methods

EuTiO3 films were grown by Pulsed Laser Deposition (PLD) at the PLD facility of the Surface/Interface Spectroscopy (SIS, X09LA) beamline at the Swiss Light Source (SLS) - Paul Scherrer Institute. The films were deposited on commercial SrTiO3 (001) substrates (purchased from SurfaceNet GmbH) in a very low oxygen partial pressure of $10^{-7}$ mbar (base pressure of the PLD chamber $10^{-9}$ mbar) and at a temperature of $750\,\mathrm{{}^{\circ}C}$. The phase transition of the 40 nm film was characterised using static X-ray diffraction (Figures 1b and S1). Compared to EuTiO3 ceramic material goian2012 , we find the critical temperature to be elevated to $T_{c}\approx 650\,\mathrm{K}$ which we attribute to oxygen defects goian2012 and/or residual strain ryan2013 .

For time resolved X-ray diffraction experiments, we photoexcite the EuTiO3 thin film with  50 fs long pulses derived either from the fundamental ($\left<E_{p}\right>=1.55\,\mathrm{eV}$), the second harmonic ($\left<E_{p}\right>=3.1\,\mathrm{eV}$) or the third harmonic ($\left<E_{p}\right>=4.65\,\mathrm{eV}$) of a Ti:Sapphire amplifier system. We estimate the absorbed fluence in the film via an optical transfer matrix formalism pettersson1999 based on the the optical constants of EuTiO3 and the SrTiO3 substrate (SI). The injected densities of eh pairs for the laser harmonics are $6\cdot 10^{-2}$, $3\cdot 10^{-2}$ and $2\cdot 10^{-2}$ per formula unit and 1 mJ/cm2 absorbed fluence of 1.55 eV, 3.1 eV and 4.65 eV excitation energies, respectively.

Approximately 50 fs long X-ray pulses with 9.5 keV photon energy delivered by LCLS (SLAC) were used to probe the SL reflection intensity after excitation (SI). The sample was cooled with a N2 cryo-blower to $T=120\,\mathrm{K}$ to remain above the critical temperature for the AFD transition of the SrTiO3 substrate at $T=105\,\mathrm{K}$ bettis2011 .

Supplementary optical pump-probe studies were performed at the FEMTO-facility at Swiss Light Source using  80 fs long pulses with a central photon energy of 1.55 eV. Additional time resolved optical-pump/multi-THz probe studies were performed at the University of Regensburg (SI).

The density functional theory (DFT) computations are carried out utilizing the all-electron full-potential linearised augmented-plane wave implementation within the elk code elk . As an approximation for the exchange-correlation functional we apply a generalised gradient approach plus U (GGA+U) and apply a $U=6.2\,\mathrm{eV}$ and $J=1\,\mathrm{eV}$, respectively on the Eu $4f$-states. The muffin tin radii for Eu, Ti and O are set to $1.3\,\mathrm{\AA}$, $0.9\,\mathrm{\AA}$ and $0.75\,\mathrm{\AA}$. We used a basis set of $l_{lmax_{\mathrm{APW}}}=10$, $8\times 8\times 6$ k-point sampling of the Brillouin zone and took the product of the average muffin tin radius and the maximum reciprocal lattice vector to be 8.5. Further numerical parameters are adjusted to the high-quality (’highq .true.’) settings within the Elk code.

II Acknowledgements

We thank H. Lemke for support in processing data acquired at LCLS. Static X-ray characterization of the sample was performed at the X04SA beamline (SLS) with technical assistance from D. Meister. We thank J. L. Mardegan, J. Raab and M. Furthmeier for technical assistance on the all-optical studies. The research leading to these results has received funding from the Swiss National Science Foundation and its National Centers of Competence in Research, NCCR MUST and NCCR MARVEL. E.M.B. acknowledges funding from the European Community’s Seventh Framework Programme (FP7/2007-2013) under grant agreement No. 290605 (PSI-FELLOW/COFUND). Computing resources were provided by the MERLIN cluster at the Paul Scherrer Institute.

III Author contributions

M. P., S. L. J. and U. S. conceived the experiment. M. P., M. K., M. J. N., S. P., S. L. J. and U. S. performed the time-resolved diffraction experiment together with J. M. G, S. S. and T. S.. M. R. grew the sample. M. P., M. J. N., M. K., and S. P. analysed FEL data. M. P. performed supplementary time-resolved optical experiments. M. P., S. L. J, M. F. and U. S. interpreted the data with support from N. A. S.. E. M. B., V. E., M. K., M. J. N. and M. P. characterised the static diffraction properties of sample candidates. M. P. implemented the DFT constraints in the elk-package and performed calculations in collaboration with M. F., support from A. N. and input from N. A. S.. A. N. performed additional DFT calculations. M. P., M. F., S. L. J. and U. S. wrote the paper and all authors contributed to the final version.