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Time-resolved X-ray diffraction study of the ferroelectric phase-transition in DKDP
Chemical Physics 299 (2004) 157–161 www.elsevier.com/locate/chemphys
Time-resolved X-ray diffraction study of the ferroelectric phase-transition in DKDP J. Larsson
a,b,*
, P. Sondhauss a,c, O. Synnergren b, M. Harbst a, P.A. Heimann d, A.M. Lindenberg e, J.S. Wark c
a
c
Atomic Physics Division, Lund Institute of Technology, P.O. Box 118, S-221 00 Lund, Sweden b Technology and Society, Malm€o University, 20506 Malm€o, Sweden Department of Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK d Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA e Department of Physics, University of California, Berkeley, CA 94720, USA Received 18 September 2003; accepted 24 November 2003
Abstract We have performed experiments where DKDP has been irradiated by short (100 fs), laser pulses. Subsequently X-ray pulses with a duration of 100 ps were used as a probe. Time-resolved X-ray diffraction enables monitoring of the transitions between the paraelectric and ferroelectric phases. By recording the intensity of a peak only present in the paraelectric phase, we observe indications of a phase-transition following laser-irradiation of DKDP in the ferroelectric phase. We have estimated the laser heating effect, by measuring the strain (peak shifts) in the diffraction patterns. Furthermore, the orientation of the ferroelectric domains has been observed. In spite of the fact that the temperature did not rise above the Curie temperature, following interaction with this radiation, the polarization of ferroelectric domains was modified. This indicates a mechanism where short pulses impulsively excite phonons, which enable either reversal of entire domains, the shift of domain walls and/or the broadening of the domain wall widths. Ó 2003 Elsevier B.V. All rights reserved.
1. Introduction A considerable effort has been made over the last half century in order to understand the ferroelectric phasetransition in KDP, DKDP and similar ferroelectric crystals [1–6]. The first order phase-transition is of a mixed displacive and order–disorder type. It is explained by the thermal and tunnelling behaviour of a hydrogen ion in a double-well potential, which constitutes the hydrogen bond between phosphate groups and an interaction involving optical phonon modes. Experimental data that have been used for comparisons are the phasetransition temperatures for different ratios of the hydrogen isotopes [7–9]. The strong correlation between the hydrogen isotope and the Curie temperature has been known since the 1940s when X-ray studies for * Corresponding author. Address: Atomic Physics Division, Lund Institute of Technology, P.O. Box 118, S-221 00 Lund, Sweden. Tel.: +46-46-222-3099; fax: +46-46-222-4250. E-mail address: [email protected] (J. Larsson).
0301-0104/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2003.11.019
KDP as well as DKDP had been performed. The role of the hydrogen atoms has been studied mainly using neutron diffraction [7]. In a relatively recent study, not only the isotope of the hydrogen, but also those of potassium and oxygen were changed but no strong influence on the Curie temperature was found [10]. Over the last 10 years, impulsive Raman scattering [11] has been used to follow softening of the modes near the phasetransition temperature in real time [12,13]. We have today a very detailed understanding of materials on the atomic level and are able to measure experimentally and calculate from first principles many of the static properties with very high precision. The dynamics in these materials span from ultrafast electronic responses and rearrangements of the unit cells to the formation and alignment of domains. In this paper we draw attention to the possibility to manipulate domains with light. Domain formation in KDP has been extensively studied. A review showing the state-of-theart in 1986 was written by Bornarel [14]. Later studies using optical techniques, most recently in [15] have given
J. Larsson et al. / Chemical Physics 299 (2004) 157–161
more insight into the size of the domains and shown how an external electric field and temperature influence them. Coherent X-ray probing [16] has not yet been used to study KDP. A full theoretical description of the macroscopic domains presents some major challenges. In a recent letter by Fahy et al. [17], it was suggested that phonons might be responsible for domain reversal. In experiments described here, we observe a partial alignment of ferroelectric domains in DKDP due to the external influence of a short-pulse laser. In this paper we demonstrate the feasibility of performing measurements where the time-dependence of the phase-transition is mapped out using time-resolved X-ray diffraction. We discuss the implications from the obtained results and how the measurements can be improved in future studies.
2. Experimental conditions The sample was a disc with a 10-mm diameter and a thickness of 3 mm. The surface normal was along the caxis. For technical reasons, the deuterated compound with higher Curie temperature was used. The deuterated compound is referred to as DKDP in this paper. The manufacturer (Cleveland crystals) specified the degree of deuteration to be 98%. However, we note that the measured Curie temperature was 212 K, which implies a lower degree of deuteration. The laser transmission could not be measured on-line, since the sample holder was a solid piece of copper upon which the sample was glued with heat conducting paste. The crystal is transparent for both 400 and 800 nm, but near the intensities at which we were operating, multi-photon effects start to become important. However, the intensities are similar to those used for frequency doubling and in these cases, multi-photon absorption can be neglected. An upper bound for the mosaicity of the sample can be estimated from the width of the rocking curve which is 2 eV corresponding to an angular width of 1.3 mrad.
3. Method With the recent availability of high-brightness, shortpulse, hard X-ray sources, including third generation synchrotron sources and optical laser based sources [18– 21], the direct observation of structural dynamics on an ultrafast time-scale has become feasible [22,23]. A range of phenomena such as non-thermal melting [24,25], generation and propagation of acoustic phonons [26–28] and optical phonons [29] can now be probed by X-ray methods in the time domains. Studies of photo-dissociation of iodine [30] have also been performed. More recently, collective phenomena in ferroelectric crystals
25
20
Intensity
158
15
10
5
0 3530
3540
3550
3560
3570
Energy (eV) Fig. 1. Rocking curves of the sample. The three peaks are the paraelectric phase (center) and ferroelectric phase (right and left). The dashed curve was recorded at the temperature of 220 K, which is above the measured temperature at which we observed the phase-transition T ¼ 212 K. The solid line was recorded at 195 K.
have been studied using tine-resolved X-ray diffraction in Laue geometry [31]. In the present study we use Xrays to study the phase-transition of DKDP and the orientation of domains in the ferroelectric phase. As in many of the experiments described above, we observe only the vicinity of one diffraction order. By choosing a reflection where the two first indices differ, we have different 2D spacing for the two different domain polarizations, due to the fact that the a- and b-axes differ in length. In the paraelectric phase, the a- and b-axis have the same length. Therefore we observe three diffraction peaks two originating from the two different polarizations of the ferroelectric phase corresponding to (2 3 3) and (3 2 3) (indices given in the base of the ferroelectric unit cell) and one from the paraelectric phase. The two different domain orientations, with domain walls either in [1 1 0] or ½1 1 0 direction, are indistinguishable in the chosen diffraction geometry. The corresponding small orientational difference of the (2 3 3) lattice planes is perpendicular to the diffraction plane, the plane spanned by the vectors [2 3 3] and [0 0 1], and thus does not express itself by a shift of the rocking curve. Such a rocking curve is shown in Fig. 1. The dashed curve was obtained at 220 K, which is above the Curie temperature (212 K) and the solid curve was obtained at 195 K well below the Curie temperature. Similar studies have been undertaken previously and by using a different geometry, it is possible to observe domains with different domain wall orientation as well as the polarisation [32]. 4. Experimental setup We utilise a Ti:Al2 O3 -based 100 fs, 1 kHz laser synchronised to an electron storage ring with jitter less than
J. Larsson et al. / Chemical Physics 299 (2004) 157–161
10 ps. The bending magnet beamline source provides tuneable X-rays using a two-crystal monochromator. In the present study we used an X-ray energy of 3.5 keV. The X-rays are focused using a toroidal mirror. The Xray beamsize on the sample was approximately 0.1 mm2 , and the divergence of the beam was 0.3 mrad perpendicular to the diffraction plane. The delay between the laser and the X-ray pulse could be varied using an electronic phase shifter. X-rays were detected by a X-ray sensitive avalanche photodiode which has a yield of about 105 electrons per incident X-ray photon. The response time of this detector is 10 ns which is fast enough to enable integration of the X-ray intensity from one isolated bunch in the storage ring. The signal was recorded using a gated-integrator connected to a computer allowing us to record data at 1 kHz as determined by the laser repetition rate. In order to maintain detector alignment, rocking curves were obtained by scanning the photon energy rather than rotating the crystal.
tion. When irradiating the sample, which was in the ferroelectric state (T ¼ 198 K), with the fundamental, the intensity of the paraelectric peak increase and recover within a few nanoseconds, as seen in Fig. 2. We interpret this as evidence that following the interaction with the laser radiation, the paraelectric phase is present and subsequently, the structure recovers. Using second harmonic radiation, we were not able to see any rapid changes of the sample. However, as the sample (T ¼ 200 K) was radiated for several minutes, we could observe a change in polarisation of the ferroelectic domains. As can be seen in Fig. 3, the left-hand peak is increased in width at the expense of the height of the right hand peak. The integrated intensity as function of time is shown in Fig. 4. To our knowledge, alignment
1.6 1.4
Experiments were performed both with fundamental (800 nm) and second harmonic (400 nm) laser radia3.0
0 minutes 15 minutes 30 minutes 45 minutes
1.2
X-ray intensity (arb units)
5. Results
159
1.0 0.8 0.6 0.4 0.2 0.0 -0.2 3535
2.5
3540
3545
3550
3555
3560
3565
3570
3575
Fig. 3. Rocking curve after irradiating the sample with 400 nm radiation for 0, 15, 30 and 45 min. The sample temperature was 200 K.
2.0
22 20
1.5 Integrated reflectivity (arb.units)
Diffracted intensity (relative units)
Photon energy (eV)
1.0
0.5
18 16 14
Ferroelectric peak 1 Paraelectric peak Ferroelectric peak 2
12 10 8 6 4 2
0.0 -4
-2
0
2 4 Time (ns)
6
8
Fig. 2. Temporal recording of the intensity at the peak of the rocking curve for the paraelectric phase following laser-irradiation. The sample temperature was 198 K.
0 0
10
20
30
40
50
Time (minutes)
Fig. 4. Integrated intensity of the peaks corresponding to the paraelectric and two ferroelectric peaks as function of irradiation time. The sample temperature was 200 K.
160
J. Larsson et al. / Chemical Physics 299 (2004) 157–161
of ferroelectric polarisation using radiation has not previously been observed experimentally, but has been considered for a model system consisting of arrays of coupled oscillators by Fahy and Merlin [17].
6. Mechanism driving the phase-transition In the following section we will discuss the possibility that either the sample is heated above the Curie temperature or that sufficient energy for the hydrogen atoms is given to the sample via other processes. The baseline temperature was 198 K (14 K below the Curie temperature). We do not observe a DC temperature increase as we irradiate the sample with the laser. The heating effect occurs on a rapid (ns) timescale and the heat is then dissipated into the sample and the cryogenic system on a ms/ls timescale. The crystal was pumped by pulses containing an energy of 800 lJ and the radiation was focused to a 0.25 mm2 spot on the sample. The instantaneous temperature effect is estimated based on the time-resolved wavelength scans where we can see a shift of the peaks by 0.5 eV. From that and from a calibration of the recorded static shifts with temperature, we estimate the temperature increase to be about 5 K. The crystal was mounted on a cryogenic heat sink with active temperature stabilisation and there was no recorded rise in average temperature. In particular we note that the shifts are small enough that the equilibrium temperature is not above the Curie temperature. The mechanism explaining the phase-transition which is discussed in [33] relates to the double-well potential of the bonding hydrogen atoms. When the thermal energy is sufficient to allow for hopping between two possible sites, the material goes to the paraelectric phase. With the single laser pulse employed in this experiment one excites coherent phonons predominantly in the centre of the Brillouin zone via impulsive stimulated Raman scattering (ISRS) [34]. Amongst the excited modes is the mode, which includes the ‘‘hopping’’ movement of the bonding hydrogen atoms, i.e. the mode, which drives the phase-transition. In particular since the laser pulse duration is relatively long (100 fs) it is very likely that in particular this mode is excited. This is because close to the Curie temperature, this mode is considerably softened and thus the condition for ISRS that the pulse duration of the exciting laser is small compared to the inverse phonon frequency is best fulfilled. Our results suggest that via laser excitation of the soft mode detectable fractions of the ferroelectric phase are transformed temporarily into the paraelectric phase, leading to an increase of the paraelectric Bragg peak in Fig. 2. On a longer timescale the unstable paraelectric phase relaxes back to the ferroelectric phase.
7. Mechanism driving the domain polarisation change When considering what is driving the domain polarisation change with second harmonic radiation we consider two possibilities and evaluate the possibility of it either being a purely thermal mechanism or that it is a process based on impulsive scattering. It could be that we observe a thermal effect where two-photon processes excite the sample, heat it above the Curie temperature and effectively destroy the domain structure, which upon cooling, reforms with different polarisation. In order to see if this is at least energetically possible we make a simple estimation. We use radiation with 100 lJ pulse focused into a 0.25 mm2 area. The duration of the pulse is about 100 fs. The laser absorption depth can be estimated from the two-photon cross-section of KDP (we have not found that of DKDP for this wavelength). From the cross-section of 0.02 cm/ GW [35] and the intensity 4 1011 W/cm2 we find the penetration depth to be 1.2 mm. The pulse energy is assumed to be deposited into a volume defined by the spot size and the penetration depth. This gives an absorbed energy per unit volume of 0.4 J/cm3 . With the KDP heat capacity of 0.3 J/g/K at 20 K below the Curie temperature and the density of 2.4 g/ cm3 , we would at most get an instantaneous temperature rise of 0.5 K, which would dissipate quickly through heat diffusion. The crystal was mounted on a cryogenic heat sink with active temperature stabilisation and there was no recorded rise in temperature. The temperature would still be below the Curie temperature. We therefore do not believe that this could be the mechanism. However, a possible explanation is that the thermal energy and strain deposited may give rise to shifting of domain walls, making domains of one particular polarisation grow on the expense of the other in the probed volume. A more speculative explanation is based on the paper by Fahy and Merlin [17] in which they suggest a mechanism, which could explain the observed domain polarisation change. The laser energy is coupled into phonon modes and cooperative motion can reverse an entire domain if the laser energy per unit area is above 1% of the thermal energy. The pulse duration should be short compared to the phonon dissipation time, which is fulfilled in the discussed experiment. An estimate of the laser energy per unit area needed for the domain reversal via this mechanism should tell us whether this mechanism is at least energetically possible. However, that estimation requires knowledge of the susceptibility change due to phonon displacement, which is not known for KDP. An estimate valid for all transparent materials was made by Fahy and Merlin. According this a fluence of 10 mJ/cm2 to 1 J/cm2 are typical values for domain reversal. Our experimental fluence of 40 mJ/cm2 falls into this regime.
J. Larsson et al. / Chemical Physics 299 (2004) 157–161
8. Conclusions In this paper we show the possibility of simultaneously measuring, microscopic properties (atom positions), while measuring mesoscopic properties (domain polarisation) and macroscopic properties such as the phase and temperature. Overall we see the power of time-resolved X-ray diffraction. We see indications of the fact that the ferroelectric phase-transition can be mediated by excitation of phonons. In future studies we plan to excite particular phonon modes using impulsive excitation and follow the transitions using time-resolved X-ray diffraction. Acknowledgements J.L. would like to thank The Swedish Science Council (VR) and the Swedish Foundation for Strategic Research (SSF). The authors would like to acknowledge the financial contribution of the European Commission. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]
J.C. Slater, J. Chem. Phys. 9 (1941) 16. R. Blinc, J. Phys. Chem. Solids 13 (1960) 204. K.K. Kobayashi, J. Phys. Soc. Jpn. 24 (1968) 497. A. Bussnabb-Holder, K.H. Michael, Phys. Rev. Lett. 80 (1998) 2173. D. Merunka, B. Rakvin, Phys. Rev. B 66 (2002) 174101. S. Koval, J. Kohanoff, R.L. Migoni, E. Tosatti, Phys. Rev. Lett. 89 (2002) 187602. R.J. Nelmes, Ferroelectrics 71 (1986) 87. H. Sugimoto, S. Ikeda, Phys. Rev. Lett. 67 (1991) 1306. S.J. van Reeuwijk, A. Puig-Molina, H. Graafsma, Phys. Rev. B 62 (2000) 6192. A. Bussmann-Holder, N. Dalal, AIP Conf. Proc. 582 (2001) 127. Y.-X. Yan, J. Edward, B. Gamble, K.A. Nelson, J. Chem. Phys. 83 (1985) 5391. S. Yoshioka, Y. Tsujimi, T. Yagi, J. Phys. Soc. Jpn. 67 (1998) 2178. T. Yagi, T. Watanuki, S. Yoshioka, Ferroelectrics 239 (2000) 173. J. Bornarel, Ferroelectrics 71 (1987) 255. J. Bornarel, R. Cach, Phys. Rev. B 60 (1999) 3806. Z.H. Hu, P.A. Thomas, A. Snigirev, I. Snigireva, A. Souvorov, P.G.R. Smith, G.W. Ross, S. Teat, Nature 392 (1998) 690.
161
[17] S. Fahy, R. Merlin, Phys. Rev. Lett. 73 (1994) 1122. [18] M.M. Murnane, H.C. Kapteyn, M.D. Rosen, R.W. Falcone, Science 251 (1991) 531. [19] R. Schoenlein, W.P. Leemans, A.H. Chin, P. Volfbeyn, T.E. Glover, P. Balling, M. Zolotorev, K.-J. Kim, S. Chattopadhyay, C.V. Shank, Science 274 (1996) 236. [20] R.W. Schoenlein, S. Chattopadhyay, H.H.W. Chong, T.E. Glover, P.A. Heimann, C.V. Shank, A.A. Zholent, M.S. Zolotorev, Science 287 (2000) 2237. [21] J. Larsson, Z. Chang, E. Judd, P. Schuck, R. Falcone, P. Heimann, H.A. Padmore, H.C. Kapteyn, P. Bucksbaum, M. Murnane, R.W. Lee, A. Machachek, J. Wark, Opt. Lett. 22 (1997) 1012. [22] C. Rischel, A. Rousse, I. Uschmann, P.-A. Albouy, J.-P. Geindre, P. Audebert, J.C. Gauthier, E. F€ orster, J.-L. Martin, A. Antonetti, Nature 390 (1997) 490. [23] J. Larsson, P.A. Heimann, A. Lindenberg, P.J. Schuck, P.H. Bucksbaum, R.W. Lee, H.A. Padmore, R.W. Falcone, Appl. Phys. A 66 (1998) 587. [24] A.H. Chin, R.W. Schoenlein, T.E. Glover, P. Balling, W.P. Leemans, C.V. Shank, Phys. Rev. Lett. 83 (1999) 336. [25] A. Rousse, C. Rischel, S. Fourmaux, I. Uschmann, S. Sebban, G. Grillon, Ph. Balcou, E. F€ orster, J.P. Geindre, P. Audebert, J.C. Gauthier, D. Hulin, Nature 410 (2001) 65. [26] C. Rose-Petruck, R. Jimenez, T. Guo, A. Cavalleri, C.W. Siders, F. Raksi, J.A. Squier, B.C. Walker, K.R. Wilson, C.P.J. Barty, Nature 398 (1999) 310. [27] A.M. Lindenberg, I. Kang, S.L. Johnson, T. Missalla, P.A. Heimann, Z. Chang, J. Larsson, P.H. Bucksbaum, H.C. Kapteyn, H.A. Padmore, R.W. Lee, J.S. Wark, R.W. Falcone, Phys. Rev. Lett. 84 (2000) 111. [28] D. Reis, M. DeCamp, P.H. Bucksbaum, R. Clarke, E. Dufresne, M. Hertlein, R. Merlin, R. Falcone, H. Kapteyn, M. Murnane, J. Larsson, Th. Missalla, J. Wark, Phys. Rev. Lett 86 (2001) 3072. [29] K. Sokolowski-Tinten, C. Blome, J. Blums, A. Cavalleri, C. Dietrich, A. Tarasevitch, I. Uschmann, E. F€ orster, M. Horn-vonHoegen, D. von der Linde, Nature 422 (2003) 287. [30] R. Neutze, R. Wouts, S. Techert, J. Davidsson, M. Kocsis, A. Kirrander, F. Schotte, M. Wulff, Phys. Rev. Lett. 87 (2001) 195508. [31] E. Collet, M.H. Lemee-Cailleau, M. Buron-Le Cointe, H. Cailleau, M. Wulff, T. Luty, S.Y. Koshihara, M. Meyer, L. Toupet, P. Rabiller, S. Techert, Science 300 (2003) 612. [32] P.M. Bastie, J. Bornarel, J. Phys. C: Solid State. Phys. 12 (1979) 1785. [33] B.A. Strukov, A.P. Levanyuk, Ferroelectric Phenomena in Crystals, Springer-Verlag, Berlin, Heidelberg, 1998, p. 151ff , ISBN 3540-63132-1. [34] R. Merlin, Solid State Commun. 102 (1997) 207. [35] A.D. Walser, A. Bouselhami, M. Yan, R. Dorsinville, Proc. SPIE – The Int. Soc. Opt. Eng. 3793 (1999) 157.
Time-resolved X-ray diffraction study of the ferroelectric phase-transition in DKDP J. Larsson
a,b,*
, P. Sondhauss a,c, O. Synnergren b, M. Harbst a, P.A. Heimann d, A.M. Lindenberg e, J.S. Wark c
a
c
Atomic Physics Division, Lund Institute of Technology, P.O. Box 118, S-221 00 Lund, Sweden b Technology and Society, Malm€o University, 20506 Malm€o, Sweden Department of Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK d Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA e Department of Physics, University of California, Berkeley, CA 94720, USA Received 18 September 2003; accepted 24 November 2003
Abstract We have performed experiments where DKDP has been irradiated by short (100 fs), laser pulses. Subsequently X-ray pulses with a duration of 100 ps were used as a probe. Time-resolved X-ray diffraction enables monitoring of the transitions between the paraelectric and ferroelectric phases. By recording the intensity of a peak only present in the paraelectric phase, we observe indications of a phase-transition following laser-irradiation of DKDP in the ferroelectric phase. We have estimated the laser heating effect, by measuring the strain (peak shifts) in the diffraction patterns. Furthermore, the orientation of the ferroelectric domains has been observed. In spite of the fact that the temperature did not rise above the Curie temperature, following interaction with this radiation, the polarization of ferroelectric domains was modified. This indicates a mechanism where short pulses impulsively excite phonons, which enable either reversal of entire domains, the shift of domain walls and/or the broadening of the domain wall widths. Ó 2003 Elsevier B.V. All rights reserved.
1. Introduction A considerable effort has been made over the last half century in order to understand the ferroelectric phasetransition in KDP, DKDP and similar ferroelectric crystals [1–6]. The first order phase-transition is of a mixed displacive and order–disorder type. It is explained by the thermal and tunnelling behaviour of a hydrogen ion in a double-well potential, which constitutes the hydrogen bond between phosphate groups and an interaction involving optical phonon modes. Experimental data that have been used for comparisons are the phasetransition temperatures for different ratios of the hydrogen isotopes [7–9]. The strong correlation between the hydrogen isotope and the Curie temperature has been known since the 1940s when X-ray studies for * Corresponding author. Address: Atomic Physics Division, Lund Institute of Technology, P.O. Box 118, S-221 00 Lund, Sweden. Tel.: +46-46-222-3099; fax: +46-46-222-4250. E-mail address: [email protected] (J. Larsson).
0301-0104/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2003.11.019
KDP as well as DKDP had been performed. The role of the hydrogen atoms has been studied mainly using neutron diffraction [7]. In a relatively recent study, not only the isotope of the hydrogen, but also those of potassium and oxygen were changed but no strong influence on the Curie temperature was found [10]. Over the last 10 years, impulsive Raman scattering [11] has been used to follow softening of the modes near the phasetransition temperature in real time [12,13]. We have today a very detailed understanding of materials on the atomic level and are able to measure experimentally and calculate from first principles many of the static properties with very high precision. The dynamics in these materials span from ultrafast electronic responses and rearrangements of the unit cells to the formation and alignment of domains. In this paper we draw attention to the possibility to manipulate domains with light. Domain formation in KDP has been extensively studied. A review showing the state-of-theart in 1986 was written by Bornarel [14]. Later studies using optical techniques, most recently in [15] have given
J. Larsson et al. / Chemical Physics 299 (2004) 157–161
more insight into the size of the domains and shown how an external electric field and temperature influence them. Coherent X-ray probing [16] has not yet been used to study KDP. A full theoretical description of the macroscopic domains presents some major challenges. In a recent letter by Fahy et al. [17], it was suggested that phonons might be responsible for domain reversal. In experiments described here, we observe a partial alignment of ferroelectric domains in DKDP due to the external influence of a short-pulse laser. In this paper we demonstrate the feasibility of performing measurements where the time-dependence of the phase-transition is mapped out using time-resolved X-ray diffraction. We discuss the implications from the obtained results and how the measurements can be improved in future studies.
2. Experimental conditions The sample was a disc with a 10-mm diameter and a thickness of 3 mm. The surface normal was along the caxis. For technical reasons, the deuterated compound with higher Curie temperature was used. The deuterated compound is referred to as DKDP in this paper. The manufacturer (Cleveland crystals) specified the degree of deuteration to be 98%. However, we note that the measured Curie temperature was 212 K, which implies a lower degree of deuteration. The laser transmission could not be measured on-line, since the sample holder was a solid piece of copper upon which the sample was glued with heat conducting paste. The crystal is transparent for both 400 and 800 nm, but near the intensities at which we were operating, multi-photon effects start to become important. However, the intensities are similar to those used for frequency doubling and in these cases, multi-photon absorption can be neglected. An upper bound for the mosaicity of the sample can be estimated from the width of the rocking curve which is 2 eV corresponding to an angular width of 1.3 mrad.
3. Method With the recent availability of high-brightness, shortpulse, hard X-ray sources, including third generation synchrotron sources and optical laser based sources [18– 21], the direct observation of structural dynamics on an ultrafast time-scale has become feasible [22,23]. A range of phenomena such as non-thermal melting [24,25], generation and propagation of acoustic phonons [26–28] and optical phonons [29] can now be probed by X-ray methods in the time domains. Studies of photo-dissociation of iodine [30] have also been performed. More recently, collective phenomena in ferroelectric crystals
25
20
Intensity
158
15
10
5
0 3530
3540
3550
3560
3570
Energy (eV) Fig. 1. Rocking curves of the sample. The three peaks are the paraelectric phase (center) and ferroelectric phase (right and left). The dashed curve was recorded at the temperature of 220 K, which is above the measured temperature at which we observed the phase-transition T ¼ 212 K. The solid line was recorded at 195 K.
have been studied using tine-resolved X-ray diffraction in Laue geometry [31]. In the present study we use Xrays to study the phase-transition of DKDP and the orientation of domains in the ferroelectric phase. As in many of the experiments described above, we observe only the vicinity of one diffraction order. By choosing a reflection where the two first indices differ, we have different 2D spacing for the two different domain polarizations, due to the fact that the a- and b-axes differ in length. In the paraelectric phase, the a- and b-axis have the same length. Therefore we observe three diffraction peaks two originating from the two different polarizations of the ferroelectric phase corresponding to (2 3 3) and (3 2 3) (indices given in the base of the ferroelectric unit cell) and one from the paraelectric phase. The two different domain orientations, with domain walls either in [1 1 0] or ½1 1 0 direction, are indistinguishable in the chosen diffraction geometry. The corresponding small orientational difference of the (2 3 3) lattice planes is perpendicular to the diffraction plane, the plane spanned by the vectors [2 3 3] and [0 0 1], and thus does not express itself by a shift of the rocking curve. Such a rocking curve is shown in Fig. 1. The dashed curve was obtained at 220 K, which is above the Curie temperature (212 K) and the solid curve was obtained at 195 K well below the Curie temperature. Similar studies have been undertaken previously and by using a different geometry, it is possible to observe domains with different domain wall orientation as well as the polarisation [32]. 4. Experimental setup We utilise a Ti:Al2 O3 -based 100 fs, 1 kHz laser synchronised to an electron storage ring with jitter less than
J. Larsson et al. / Chemical Physics 299 (2004) 157–161
10 ps. The bending magnet beamline source provides tuneable X-rays using a two-crystal monochromator. In the present study we used an X-ray energy of 3.5 keV. The X-rays are focused using a toroidal mirror. The Xray beamsize on the sample was approximately 0.1 mm2 , and the divergence of the beam was 0.3 mrad perpendicular to the diffraction plane. The delay between the laser and the X-ray pulse could be varied using an electronic phase shifter. X-rays were detected by a X-ray sensitive avalanche photodiode which has a yield of about 105 electrons per incident X-ray photon. The response time of this detector is 10 ns which is fast enough to enable integration of the X-ray intensity from one isolated bunch in the storage ring. The signal was recorded using a gated-integrator connected to a computer allowing us to record data at 1 kHz as determined by the laser repetition rate. In order to maintain detector alignment, rocking curves were obtained by scanning the photon energy rather than rotating the crystal.
tion. When irradiating the sample, which was in the ferroelectric state (T ¼ 198 K), with the fundamental, the intensity of the paraelectric peak increase and recover within a few nanoseconds, as seen in Fig. 2. We interpret this as evidence that following the interaction with the laser radiation, the paraelectric phase is present and subsequently, the structure recovers. Using second harmonic radiation, we were not able to see any rapid changes of the sample. However, as the sample (T ¼ 200 K) was radiated for several minutes, we could observe a change in polarisation of the ferroelectic domains. As can be seen in Fig. 3, the left-hand peak is increased in width at the expense of the height of the right hand peak. The integrated intensity as function of time is shown in Fig. 4. To our knowledge, alignment
1.6 1.4
Experiments were performed both with fundamental (800 nm) and second harmonic (400 nm) laser radia3.0
0 minutes 15 minutes 30 minutes 45 minutes
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X-ray intensity (arb units)
5. Results
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1.0 0.8 0.6 0.4 0.2 0.0 -0.2 3535
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3560
3565
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Fig. 3. Rocking curve after irradiating the sample with 400 nm radiation for 0, 15, 30 and 45 min. The sample temperature was 200 K.
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1.5 Integrated reflectivity (arb.units)
Diffracted intensity (relative units)
Photon energy (eV)
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Fig. 2. Temporal recording of the intensity at the peak of the rocking curve for the paraelectric phase following laser-irradiation. The sample temperature was 198 K.
0 0
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Fig. 4. Integrated intensity of the peaks corresponding to the paraelectric and two ferroelectric peaks as function of irradiation time. The sample temperature was 200 K.
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of ferroelectric polarisation using radiation has not previously been observed experimentally, but has been considered for a model system consisting of arrays of coupled oscillators by Fahy and Merlin [17].
6. Mechanism driving the phase-transition In the following section we will discuss the possibility that either the sample is heated above the Curie temperature or that sufficient energy for the hydrogen atoms is given to the sample via other processes. The baseline temperature was 198 K (14 K below the Curie temperature). We do not observe a DC temperature increase as we irradiate the sample with the laser. The heating effect occurs on a rapid (ns) timescale and the heat is then dissipated into the sample and the cryogenic system on a ms/ls timescale. The crystal was pumped by pulses containing an energy of 800 lJ and the radiation was focused to a 0.25 mm2 spot on the sample. The instantaneous temperature effect is estimated based on the time-resolved wavelength scans where we can see a shift of the peaks by 0.5 eV. From that and from a calibration of the recorded static shifts with temperature, we estimate the temperature increase to be about 5 K. The crystal was mounted on a cryogenic heat sink with active temperature stabilisation and there was no recorded rise in average temperature. In particular we note that the shifts are small enough that the equilibrium temperature is not above the Curie temperature. The mechanism explaining the phase-transition which is discussed in [33] relates to the double-well potential of the bonding hydrogen atoms. When the thermal energy is sufficient to allow for hopping between two possible sites, the material goes to the paraelectric phase. With the single laser pulse employed in this experiment one excites coherent phonons predominantly in the centre of the Brillouin zone via impulsive stimulated Raman scattering (ISRS) [34]. Amongst the excited modes is the mode, which includes the ‘‘hopping’’ movement of the bonding hydrogen atoms, i.e. the mode, which drives the phase-transition. In particular since the laser pulse duration is relatively long (100 fs) it is very likely that in particular this mode is excited. This is because close to the Curie temperature, this mode is considerably softened and thus the condition for ISRS that the pulse duration of the exciting laser is small compared to the inverse phonon frequency is best fulfilled. Our results suggest that via laser excitation of the soft mode detectable fractions of the ferroelectric phase are transformed temporarily into the paraelectric phase, leading to an increase of the paraelectric Bragg peak in Fig. 2. On a longer timescale the unstable paraelectric phase relaxes back to the ferroelectric phase.
7. Mechanism driving the domain polarisation change When considering what is driving the domain polarisation change with second harmonic radiation we consider two possibilities and evaluate the possibility of it either being a purely thermal mechanism or that it is a process based on impulsive scattering. It could be that we observe a thermal effect where two-photon processes excite the sample, heat it above the Curie temperature and effectively destroy the domain structure, which upon cooling, reforms with different polarisation. In order to see if this is at least energetically possible we make a simple estimation. We use radiation with 100 lJ pulse focused into a 0.25 mm2 area. The duration of the pulse is about 100 fs. The laser absorption depth can be estimated from the two-photon cross-section of KDP (we have not found that of DKDP for this wavelength). From the cross-section of 0.02 cm/ GW [35] and the intensity 4 1011 W/cm2 we find the penetration depth to be 1.2 mm. The pulse energy is assumed to be deposited into a volume defined by the spot size and the penetration depth. This gives an absorbed energy per unit volume of 0.4 J/cm3 . With the KDP heat capacity of 0.3 J/g/K at 20 K below the Curie temperature and the density of 2.4 g/ cm3 , we would at most get an instantaneous temperature rise of 0.5 K, which would dissipate quickly through heat diffusion. The crystal was mounted on a cryogenic heat sink with active temperature stabilisation and there was no recorded rise in temperature. The temperature would still be below the Curie temperature. We therefore do not believe that this could be the mechanism. However, a possible explanation is that the thermal energy and strain deposited may give rise to shifting of domain walls, making domains of one particular polarisation grow on the expense of the other in the probed volume. A more speculative explanation is based on the paper by Fahy and Merlin [17] in which they suggest a mechanism, which could explain the observed domain polarisation change. The laser energy is coupled into phonon modes and cooperative motion can reverse an entire domain if the laser energy per unit area is above 1% of the thermal energy. The pulse duration should be short compared to the phonon dissipation time, which is fulfilled in the discussed experiment. An estimate of the laser energy per unit area needed for the domain reversal via this mechanism should tell us whether this mechanism is at least energetically possible. However, that estimation requires knowledge of the susceptibility change due to phonon displacement, which is not known for KDP. An estimate valid for all transparent materials was made by Fahy and Merlin. According this a fluence of 10 mJ/cm2 to 1 J/cm2 are typical values for domain reversal. Our experimental fluence of 40 mJ/cm2 falls into this regime.
J. Larsson et al. / Chemical Physics 299 (2004) 157–161
8. Conclusions In this paper we show the possibility of simultaneously measuring, microscopic properties (atom positions), while measuring mesoscopic properties (domain polarisation) and macroscopic properties such as the phase and temperature. Overall we see the power of time-resolved X-ray diffraction. We see indications of the fact that the ferroelectric phase-transition can be mediated by excitation of phonons. In future studies we plan to excite particular phonon modes using impulsive excitation and follow the transitions using time-resolved X-ray diffraction. Acknowledgements J.L. would like to thank The Swedish Science Council (VR) and the Swedish Foundation for Strategic Research (SSF). The authors would like to acknowledge the financial contribution of the European Commission. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]
J.C. Slater, J. Chem. Phys. 9 (1941) 16. R. Blinc, J. Phys. Chem. Solids 13 (1960) 204. K.K. Kobayashi, J. Phys. Soc. Jpn. 24 (1968) 497. A. Bussnabb-Holder, K.H. Michael, Phys. Rev. Lett. 80 (1998) 2173. D. Merunka, B. Rakvin, Phys. Rev. B 66 (2002) 174101. S. Koval, J. Kohanoff, R.L. Migoni, E. Tosatti, Phys. Rev. Lett. 89 (2002) 187602. R.J. Nelmes, Ferroelectrics 71 (1986) 87. H. Sugimoto, S. Ikeda, Phys. Rev. Lett. 67 (1991) 1306. S.J. van Reeuwijk, A. Puig-Molina, H. Graafsma, Phys. Rev. B 62 (2000) 6192. A. Bussmann-Holder, N. Dalal, AIP Conf. Proc. 582 (2001) 127. Y.-X. Yan, J. Edward, B. Gamble, K.A. Nelson, J. Chem. Phys. 83 (1985) 5391. S. Yoshioka, Y. Tsujimi, T. Yagi, J. Phys. Soc. Jpn. 67 (1998) 2178. T. Yagi, T. Watanuki, S. Yoshioka, Ferroelectrics 239 (2000) 173. J. Bornarel, Ferroelectrics 71 (1987) 255. J. Bornarel, R. Cach, Phys. Rev. B 60 (1999) 3806. Z.H. Hu, P.A. Thomas, A. Snigirev, I. Snigireva, A. Souvorov, P.G.R. Smith, G.W. Ross, S. Teat, Nature 392 (1998) 690.
161
[17] S. Fahy, R. Merlin, Phys. Rev. Lett. 73 (1994) 1122. [18] M.M. Murnane, H.C. Kapteyn, M.D. Rosen, R.W. Falcone, Science 251 (1991) 531. [19] R. Schoenlein, W.P. Leemans, A.H. Chin, P. Volfbeyn, T.E. Glover, P. Balling, M. Zolotorev, K.-J. Kim, S. Chattopadhyay, C.V. Shank, Science 274 (1996) 236. [20] R.W. Schoenlein, S. Chattopadhyay, H.H.W. Chong, T.E. Glover, P.A. Heimann, C.V. Shank, A.A. Zholent, M.S. Zolotorev, Science 287 (2000) 2237. [21] J. Larsson, Z. Chang, E. Judd, P. Schuck, R. Falcone, P. Heimann, H.A. Padmore, H.C. Kapteyn, P. Bucksbaum, M. Murnane, R.W. Lee, A. Machachek, J. Wark, Opt. Lett. 22 (1997) 1012. [22] C. Rischel, A. Rousse, I. Uschmann, P.-A. Albouy, J.-P. Geindre, P. Audebert, J.C. Gauthier, E. F€ orster, J.-L. Martin, A. Antonetti, Nature 390 (1997) 490. [23] J. Larsson, P.A. Heimann, A. Lindenberg, P.J. Schuck, P.H. Bucksbaum, R.W. Lee, H.A. Padmore, R.W. Falcone, Appl. Phys. A 66 (1998) 587. [24] A.H. Chin, R.W. Schoenlein, T.E. Glover, P. Balling, W.P. Leemans, C.V. Shank, Phys. Rev. Lett. 83 (1999) 336. [25] A. Rousse, C. Rischel, S. Fourmaux, I. Uschmann, S. Sebban, G. Grillon, Ph. Balcou, E. F€ orster, J.P. Geindre, P. Audebert, J.C. Gauthier, D. Hulin, Nature 410 (2001) 65. [26] C. Rose-Petruck, R. Jimenez, T. Guo, A. Cavalleri, C.W. Siders, F. Raksi, J.A. Squier, B.C. Walker, K.R. Wilson, C.P.J. Barty, Nature 398 (1999) 310. [27] A.M. Lindenberg, I. Kang, S.L. Johnson, T. Missalla, P.A. Heimann, Z. Chang, J. Larsson, P.H. Bucksbaum, H.C. Kapteyn, H.A. Padmore, R.W. Lee, J.S. Wark, R.W. Falcone, Phys. Rev. Lett. 84 (2000) 111. [28] D. Reis, M. DeCamp, P.H. Bucksbaum, R. Clarke, E. Dufresne, M. Hertlein, R. Merlin, R. Falcone, H. Kapteyn, M. Murnane, J. Larsson, Th. Missalla, J. Wark, Phys. Rev. Lett 86 (2001) 3072. [29] K. Sokolowski-Tinten, C. Blome, J. Blums, A. Cavalleri, C. Dietrich, A. Tarasevitch, I. Uschmann, E. F€ orster, M. Horn-vonHoegen, D. von der Linde, Nature 422 (2003) 287. [30] R. Neutze, R. Wouts, S. Techert, J. Davidsson, M. Kocsis, A. Kirrander, F. Schotte, M. Wulff, Phys. Rev. Lett. 87 (2001) 195508. [31] E. Collet, M.H. Lemee-Cailleau, M. Buron-Le Cointe, H. Cailleau, M. Wulff, T. Luty, S.Y. Koshihara, M. Meyer, L. Toupet, P. Rabiller, S. Techert, Science 300 (2003) 612. [32] P.M. Bastie, J. Bornarel, J. Phys. C: Solid State. Phys. 12 (1979) 1785. [33] B.A. Strukov, A.P. Levanyuk, Ferroelectric Phenomena in Crystals, Springer-Verlag, Berlin, Heidelberg, 1998, p. 151ff , ISBN 3540-63132-1. [34] R. Merlin, Solid State Commun. 102 (1997) 207. [35] A.D. Walser, A. Bouselhami, M. Yan, R. Dorsinville, Proc. SPIE – The Int. Soc. Opt. Eng. 3793 (1999) 157.