Ultrafast structural dynamics of the Fe-pnictide parent compound BaFe{}_{2}As{}_{2}

Ultrafast structural dynamics of the Fe-pnictide parent compound BaFeAs

Abstract

Using femtosecond time-resolved x-ray diffraction we investigate the structural dynamics of the coherently excited A phonon mode in the Fe-pnictide parent compound BaFeAs. The fluence dependent intensity oscillations of two specific Bragg reflections with distinctly different sensitivity to the pnictogen height in the compound allow us to quantify the coherent modifications of the Fe-As tetrahedra, indicating a transient increase of the Fe magnetic moments. By a comparison with time-resolved photoemission data we derive the electron-phonon deformation potential for this particular mode. The value of is comparable with theoretical predictions and demonstrates the importance of this degree of freedom for the electron-phonon coupling in the Fe pnictides.

pacs:
78.47.J-, 74.70.Xa, 61.05.C-, 63.20.K-

In the Fe pnictides, the complex interplay of the electronic, spin, orbital/ising-nematic and lattice degrees of freedoms leads to the emergence of a complex phase diagram, including structural transitions, spin-density wave (SDW) phases and high-temperature superconductivity. These phases emerge for electron and hole doping, but also for isovalent doping and external pressure Mazin (2010); Johnston (2010). The electronic structure and the magnetic properties depend very sensitively on the exact shape and size of the Fe-As tetrahedra, where an important degree of freedom is the pnictogen height above the Fe layers, which changes the Fe-As tetrahedra angle (see Fig. 1(a)). A high sensitivity of the Fe magnetic moments on the pnictogen height with a rate of has been predicted Yin et al. (2008), signifying a strong magneto-structural coupling Yildirim (2009); Egami et al. (2010); Johnston (2010). Similarly, an increase of the electron-phonon (e-ph) coupling strength was been found in calculations including magnetic ordering Yndurain and Soler (2009); Boeri et al. (2010). Indeed, a universal relation between the Fe-As tetrahedra angle and the superconducting critical temperature has been proposed for the Fe pnictides Lee et al. (2008); Johnston (2010), underlining the importance of structural degrees of freedom in these compounds.

The role of e-ph coupling for the mechanism of superconductivity in the Fe pnictides is still controversial. The average e-ph coupling constant has been found to be relatively weak both experimentally Stojchevska et al. (2010); Mansart et al. (2010); Rettig et al. (2013) and theoretically Boeri et al. (2008, 2010) with , insufficient to explain the high critical temperatures found in the pnictides in a conventional pairing scheme. However, due to the strong interplay of structural and magnetic degrees of freedom, a few phonon modes with enhanced magneto-structural coupling could still play an important role in the superconducting pairing mechanism Egami et al. (2010); Yndurain (2011).

One such mode is the Raman active A mode at the zone center corresponding to a displacement of the As ions perpendicular to the Fe layers with (Fig. 1(a)). This mode directly modulates the pnictogen height and thereby the Fe-As tetrahedra angle . Coherent excitation of this mode has recently been observed using femtosecond (fs) time-resolved optical spectroscopy Mansart et al. (2009), and time-resolved THz spectroscopy demonstrated a transient resurrection of the magnetically ordered state during the coherent oscillations Kim et al. (2012). In addition, using time- and angle-resolved photoemission spectroscopy, a strong modulation of the chemical potential by the coherent A mode has been observed Avigo et al. (2013); Yang et al. (2014). These observations demonstrate a significant coupling of the A mode to both the electronic and the spin system, which is also the subject of recent theoretical investigations Yndurain (2011); García-Martínez et al. (2013); Lee et al. (2014).

So far no quantitative information about the ultrafast structural motions of the Fe-As lattice has been available. Structural information is crucial for determining the coupling of the various degrees of freedom to this coherent mode, and previous estimates of the structural displacement amplitudes relied solely on theoretical considerations. As such, even the direction of the displacive excitation towards smaller or larger tetrahedra angle is controversial in the literature. Some papers argue that the excitation leads to a larger Fe-As distance and an increase of  Kim et al. (2012); Yang et al. (2014), while a recent theoretical investigation predicts a transient resurrection of the SDW state for a decrease in  Lee et al. (2014).

In this letter, we investigate the structural dynamics of the coherently excited A mode in the Fe-pnictide parent compound BaFeAs using fs time-resolved x-ray diffraction. We observe the fluence dependent intensity oscillations of two specific Bragg reflections with opposite sensitivity to the pnictogen height. Calculations of the structure factor allow us to quantify the coherent displacement and oscillation amplitudes, yielding a transient increase of the tetrahedra angle as large as , compatible with a transient increase of the Fe magnetic moment. In addition, by comparing our results to the transient chemical potential shift observed in trARPES, we are able to quantify the e-ph deformation potential and determine the e-ph coupling constant for this particular mode.

Figure 1: (color online) (a) Unit cell of BaFeAs with an Fe-As tetrahedron indicated. Red arrows show the atomic displacements of the A phonon mode, which modulates the Fe-As tetrahedra angle . (b) Sketch of the experimental geometry. (c) Time-resolved rocking curves of the (1 0 5) and (2 0 6) reflection before (black) and at after excitation (red).

High-quality single crystals of BaFeAs were grown by a self-flux method Hardy et al. (2010). Time-resolved x-ray diffraction experiments were performed at the hard x-ray FEMTO slicing facility at the Swiss Light Source Beaud et al. (2007) in an asymmetric diffraction configuration Johnson et al. (2010) (Fig. 1(b)). The (0 0 1) surface of the cleaved BaFeAs single crystal was kept at during the measurements using a cryogenic nitrogen blower. This is above the Néel temperature and avoids a splitting of the Bragg peaks due to the orthorhombic distortion below . The sample was excited at a repetition rate by laser pulses with a duration of full-width at half maximum (FWHM). The sliced x-ray pulses ( FWHM) were incident on the sample at a grazing angle of , matching the x-ray penetration depth to the optical penetration depth of at the x-ray energy of ( at ). The x-ray beam was focused to vertically and horizontally to ensure a homogenous excitation of the probed volume. The overall time resolution was . The diffracted x-ray photons were detected by a fast avalanche photodiode (APD).

Time-resolved rocking curves for a rotation about the sample surface normal for the (1 0 5) and (2 0 6) lattice reflections are shown in Fig. 1(c) before (black) and at after excitation (red). The rocking curves are well described by a squared Lorentzian function (lines), which demonstrates the homogeneity and high crystal quality of the sample. The two reflections show a distinctly different response to the pump pulse: Whereas the (1 0 5) reflection shows a significant increase after excitation, the (2 0 6) reflection is decreased by the pump pulse. This indicates an ultrafast increase of the Fe-As tetrahedra angle due to the displacive excitation of the coherent A mode (see below). Both peak position and width remain constant for both peaks for up to , indicating little influence of strain for these early times 1.

Figure 2: (color online) (a) Pump-induced change of the peak intensity of the (1 0 5) reflection as a function of pump-probe delay for an absorbed fluence of . (b) Oscillatory component after subtracting an exponential fit to the data (orange line in (a)). The blue line is a fit of a damped oscillator. (c) FFT spectrum of the data in (b), showing a clear peak at .

The normalized pump-induced intensity change of the (1 0 5) reflection is shown in Fig. 2(a) as a function of pump-probe delay. After the ultrafast increase of the diffraction signal by at within the experimental time resolution, the signal shows an exponential decay with a sub-ps timescale, superimposed by an oscillatory component. Such a behavior is typical for the displacive excitation of a coherent phonon. An abrupt change of the atomic potential landscape induced by the pump laser results in a new position of the potential minimum and leads to coherent oscillations around this new minimum Zeiger et al. (1992). The exponential decay of the intensity change reflects the relaxation of the excited energy potential surface, as well as the influence of lattice heating, which influences the x-ray signal via the Debye-Waller effect.

The oscillatory component is extracted from the data by subtracting an exponential function (orange line), and is shown in Fig. 2(b). A fit of a damped cosine function to the data yields a frequency of , which is corroborated by the clear peak in the Fast Fourier Transformation (FFT) of the data shown in Fig. 2(c), centered at . This value is in very good agreement with the frequency of the coherent A mode observed by time-resolved optical Mansart et al. (2009), THz Kim et al. (2012) and photoemission Rettig et al. (2012); Avigo et al. (2013); Yang et al. (2014) experiments. The displacive nature of the excitation is supported by the phase of the oscillation, which is very close to a pure cosine-like excitation, characteristic for the displacive excitation of coherent phonons (DECP) Zeiger et al. (1992).

Figure 3: (color online) Pump-induced change of the peak intensity for (a) the (1 0 5) reflection and (b) the (2 0 6) reflection for various absorbed pump fluences. Lines are fits to equation (1).

For a more quantitative analysis of the coherent phonon oscillations, the pump-induced intensity change is shown for various fluences as a function of pump-probe delay for the (1 0 5) and (2 0 6) reflections in Fig. 3(a) and (b), respectively. In agreement with our observation in Fig. 1(c), the two reflections show an opposite behavior after excitation, with a displacive increase in intensity for (1 0 5) and a decrease for (2 0 6), superimposed by the coherent oscillations of the A mode.

In order to determine the amplitudes of displacement and oscillations, we model the transient change in diffraction signal by the following expression for a displacively excited mode, consisting of a displacive and an oscillatory component:

(1)

Here, and are the amplitudes of displacive and oscillatory components, and the relaxation timescales of the displacive and oscillatory part, and and the frequency and phase of the oscillation, respectively. In order to take the finite temporal resolution of the experiment into account, equation (1) is convolved by a Gaussian profile with FWHM. Due to the limited time window of the data in Fig. 3, the frequency and phase of the oscillations have been fixed at the values determined from Fig. 2.

Figure 4: (color online) Displacement amplitudes (circles) and oscillation amplitudes (squares) for the (1 0 5) (red) and (2 0 6) reflection (black), derived from the fits in Fig. 3. Error bars are 95 confidence intervals, and lines are linear fits. Inset: Calculated normalized diffraction intensity of the (1 0 5) (red) and (2 0 6) reflection (black) as a function of Fe-As tetrahedra angle . The vertical line marks the equilibrium position.

Fits of the data to equation (1) are shown in Fig. 3 as lines and reproduce the data very nicely. Figure 4(a) summarizes the amplitudes for the displacive and oscillatory components and as solid and open symbols, and for the (1 0 5) (red) and (2 0 6) (black) reflection, respectively. Both components show a linear behavior for low fluences (), and saturate for the largest fluences. Remarkably, the amplitudes of the oscillatory and displacive components agree very well within the accuracy of the experiment, as expected from the DECP model of coherent phonon excitation Zeiger et al. (1992); Huber et al. (2014). The larger error bars for are due to the deconvolution with the limited time resolution, which suppresses the experimentally observed oscillation amplitudes. The saturation behavior observed for the highest pump fluences indicates a nonlinear response of the excited atomic potential to the electronic excitation level or anharmonicities in the atomic potential DeCamp et al. (2001); Fritz et al. (2007).

In order to relate the amplitudes to the microscopic atomic displacements and the modification of the Fe-As tetrahedra, we calculate the diffraction intensities of the (1 0 5) and (2 0 6) reflections as a function of the Fe-As tetrahedra angle in the kinematic approximation SOM (). The calculated normalized intensities are shown in the inset of Fig. 4 and nicely reproduce the opposite slope of the two reflections with respect to . We find a relative intensity change of for the (1 0 5) reflection, and for the (2 0 6) reflection. Comparison with the experimental amplitudes allows us to quantitatively determine the average atomic displacement induced by the coherent A mode (right axis of Fig. 4). For the highest fluence of , we find displacement and oscillation amplitudes as large as , corresponding to an initial displacement of the As atoms by , more than of the equilibrium pnictogen height. A linear fit at low fluences yields an amplitude of () for the (1 0 5) reflection, and () for the (2 0 6) reflection. The slight difference of the values found for the two reflections could be due to the limits of the kinematic approximation, or indicate further structural components in the coherent oscillations beyond the vertical motion of the As coordinate Avigo et al. (2013).

The quantification of the absolute oscillation amplitude of the coherent A mode offers important insight into the interplay of structural and electronic degrees of freedom, by comparison to the imprint of the same coherent phonon oscillation on the electronic structure observed by time-resolved photoemission spectroscopy. Yang et al. Yang et al. (2014) report a coherent modulation of the chemical potential of . Comparing this with the structural information obtained here, and taking the different probe depth of the x-rays and the photoemission process into account SOM (), we estimate a deformation potential of the As A mode of or . This value is in reasonable agreement with the deformation potentials predicted by density functional theory for variation of the As heights in various FeAs compounds Singh (2008); Yndurain and Soler (2009); Yndurain (2011); Dhaka et al. (2013); Lee et al. (2014), which are on the order of . The deformation potential is also comparable to the deformation potential of the coherent A mode in Bismuth Papalazarou et al. (2012).

The e-ph deformation potential allows us to determine the e-ph coupling constant for the A mode, which is related to the electronic deformation potential as Yndurain (2011):

(2)

where is the As atomic mass, the A phonon frequency and the electronic density of states at the Fermi level. Using from density functional theory Singh (2008), we obtain . This value for is in the same range as the total e-ph coupling constant in BaFeAs, as predicted theoretically Boeri et al. (2010), and measured by time-resolved optics and photoemission Mansart et al. (2010); Rettig et al. (2013). The total e-ph coupling is the sum of the coupling to all modes in the system. Thus, our finding of indicates that the A mode plays a major role for the e-ph coupling in BaFeAs.

Finally, the observation of a displacive excitation towards larger pnictogen height and larger tetrahedra angles implies an ultrafast increase of the Fe magnetic moments Yin et al. (2008); Yildirim (2009); Egami et al. (2010); Johnston (2010). This enhanced magnetic moments could in principle be responsible for the ultrafast resurrection of the SDW order Kim et al. (2012). However, the atomic displacement at the fluence of based on band structure calculations Yin et al. (2008) yields a maximal increase of the magnetic moment of , which corresponds to a relative change of  Avci et al. (2012). This leads to an increase of T by , if we consider the ratio of the SDW transition temperature and the Fe magnetic moments of observed in BaKFeAs Avci et al. (2012) and BaFe(AsP) Allred et al. (2014). Given the fact that the transient magnetic ordering has also been observed above  Kim et al. (2012), the increased magnetic moments cannot be solely responsible for the resurrection of SDW order, but the transiently modified nesting properties of the band structure need to be also considered Kim et al. (2012).

In conclusion, using time-resolved x-ray diffraction, we investigated the coherent structural dynamics of the displacively excited A phonon mode oscillations in BaFeAs. Based on structure factor calculations we determine the absolute oscillation and displacement amplitudes, and the direction of the modulation. Comparison of the absolute oscillation amplitude of the As coordinate to time-resolved photoemission experiments allows us to determine the A deformation potential . An estimate of the e-ph coupling constant underlines the importance of this structural degree of freedom in the Fe pnictides. Our findings are consistent with a transient increase of the Fe magnetic moment, which however is predicted to be too small to explain the observed transient resurrection of the SDW phase in BaFeAs.

Acknowledgements.
Time-resolved x-ray diffraction experiments were performed on the X05LA beamline at the Swiss Light Source, Paul Scherrer Institut, Villigen, Switzerland. We thank I. Eremin for stimulating discussions, and J. Fink for support in sample supply. We acknowledge support in sample characterization from C. Bernhard and M.A. Uribe-Laverde, and we thank D. Grolimund for experimental support. We acknowledge financial support by the NCCR Molecular Ultrafast Science and Technology (NCCR MUST), a research instrument of the Swiss National Science Foundation (SNSF).

Footnotes

  1. For , a strain wave is observed, which shifts the peak position and width. Therefore, we limit the analysis to early times.

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