We report a detailed high pressure study on Eu1−xSrxTiO3 polycrystalline samples using synchrotron x-ray diffraction. We have observed a second-order antiferrodistortive phase transition for all doping levels which corresponds to the transition that has been previously explored as a function of temperature. The analysis of the compression mechanism by calculating the lattice parameters, spontaneous strains and tilt angles of the TiO6 octahedra leads to a high pressure phase diagram for Eu1−xSrxTiO3.
I. INTRODUCTION
Perovskite materials of the ABO3 general formula are often sensitive to structural changes with temperature and pressure because of the tilting of BO6 octahedra. SrTiO3 (STO) is one of the most studied perovskites that undergoes such an antiferrodistortive structural phase transition at 105 K1 or 9.5 GPa2 from cubic Pm-3m to tetragonal I4/mcm. EuTiO3 (ETO) on the other hand has attracted a lot of interest only recently, mainly due to the recent discovery of strong magneto-electric coupling at low temperature in this compound.3 The comparison of STO and ETO is very important since these compounds share many common properties: they crystallize in the cubic ABO3 perovskite structure, they share similar lattice constants and ionic radii for Eu2+ and Sr2+, and the Ti4+ ion is in the d0 configuration. The latter is a crucial condition for ferroelectricity, and both compounds show the tendency to a ferroelectric instability as evidenced by a transverse optic mode softening.4–6 Their main difference lies in the magnetic nature of 4f7 Eu2+ ion with strongly localized spins of S=7/2, which is responsible for the appearance of a G-type antiferromagnetism (AFM) below TN=5.5 K.3,7,8
It has been recently shown by several different experimental techniques9–15 that the same structural phase transition as observed in STO at TS = 105K, is also present in ETO, but at much higher temperature, namely TS = 220 – 285 K. We also showed recently that, as in the case of STO, there is a pressure-induced transition in ETO starting roughly at ∼2.7 GPa.16 The phase transition of ETO is not very well understood, and depends on the synthesis conditions,5 the presence of mixed valence states for Eu,11 or oxygen vacancies.11 In any case, the large difference in the critical temperature/pressure for the phase transitions in STO and ETO is unexpected and it is possible that spin-phonon coupling effects govern the structural instability of the latter.3,9
The peculiar property of ETO to show “hidden” magnetism far above the AFM state together with the suppression of AFM order by Sr doping17 is expected to reveal novel states when being driven into the vicinity of a quantum critical point. The close analogy of ETO with STO suggests that the multiple application properties of STO should also be present in ETO based materials where the additional spin degree of freedom offers new perspectives and functionalities as compared to STO. In this work we fill in the gap of information between STO and ETO by carrying out a thorough synchrotron x-ray diffraction (XRD) study under hydrostatic pressure for the solid solution Eu1−xSrxTiO3. Our data clearly show the antiferrodistortive phase transition as a function of x and establish a new pressure phase diagram of Eu1−xSrxTiO3.
II. EXPERIMENTAL
Polycrystalline samples of Eu1−xSrxTiO3 (x=0.25, 0.50, 0.75 and 0.97), with crystallite sizes 2-5 μm have been prepared as described in Ref 9. The synchrotron x-ray diffraction experiments were performed on the ID27 beamline at the ESRF, using a monochromatic wavelength of 0.3738 Å (33.168 keV). The beam size was focused to a spot of about 3x3 μm2. The samples were loaded in Le Toullec type membrane diamond anvil cells (DACs) with diamond culets of 300 μm in diameter. The rhenium gaskets were pre-indented to a thickness of 50 μm, while the sample chamber was created by drilling a 150 μm hole in the gasket with a Nd:YAG pulsed laser. Helium gas has been used as a pressure transmitting medium (PTM), thus minimizing the non-hydrostatic stresses that could modify the onset or the sequence of the phase transitions in perovskites. The pressure has been measured using the fluorescence lines of ruby. The data were collected with a Perkin Elmer flat panel detector and the acquired images have been integrated using the Dioptas software.18 The diffractograms were indexed using DICVOL91 software.19 The Lebail refinements have been carried out with the Fullprof software package.20
III. RESULTS AND DISCUSSION
The Eu1−xSrxTiO3 samples have been measured at room temperature up to a maximum pressure of 48 GPa. The phase transition from cubic to tetragonal in perovskites can be followed by x-ray diffraction either by the splitting of Bragg peaks or by the appearance of superstructure reflections. In Fig. 1 we display the evolution of the (200) peak in the diffraction patterns of all four samples for some selected pressures. The data clearly show the splitting of the (200) reflection to (220) and (004), that accounts for the tetragonal distortion in Eu1−xSrxTiO3. The same phase transition has been detected under pressure for pure EuTiO316 and SrTiO3.2 As in the case of EuTiO3, the transition is fully reversible as can be seen in the decompression data in the supplementary material.21 The phase transition is generated by the tilting of the TiO6 octahedra with a tilting scheme a0a0c- in the Glazer notation,22 i.e. an out-of-phase rotation of the c axis with no rotation of the a and b axes.
Evolution of the (200) diffraction peak of Eu1−xSrxTiO3 with pressure for a) x=0.25, b) x=0.50, c) x=0.75 and d) x=0.97.
Evolution of the (200) diffraction peak of Eu1−xSrxTiO3 with pressure for a) x=0.25, b) x=0.50, c) x=0.75 and d) x=0.97.
In order to accurately define the onset of the pressure-induced transition, we plot the normalized linewidth of the (200) reflection with pressure, as shown in Fig. 2(a). The same method has also been followed in the case of EuTiO3,16 since it minimizes any resolution issues that could delay the emergence of the transition. Fitting the (200) peak with a single profile function will result in an abrupt increase in the FWHM at the pressure where the tetragonal phase appears, and the (200) reflection becomes a doublet. The kinks observed in the FWHM plots of Fig. 2 clearly demonstrate that the critical transition pressure Pc increases for increasing Sr content in Eu1−xSrxTiO3. In a high pressure diffraction experiment peak broadening can occur due to the hardening of PTM or the squeezing of the sample between the diamonds (“bridging”). Both of these possibilities are excluded in our experiments: First of all, He used in this study is the best quasi-hydrostatic PTM that remains in the liquid phase liquid until ∼12 GPa. Second, the gasket thickness before and after the experiment was far superior than the initial thickness of the sample, meaning that bridging has been prevented. Moreover, the transition is found to be reversible in our experiments without any significant hysteresis, confirming the absence of peak broadening due to non-hydrostatic stresses. A second criterion in the definition of the onset for the phase transition has been the Lebail refinements, which are much better fitted with the tetragonal pattern I4/mcm beyond the critical pressures. Refinements of the x-ray data using both the cubic and tetragonal models are shown in the supplementary material.21
a. Normalized FWHM of the (200) diffraction peak, indicating the onset of the phase transition in Eu1−xSrxTiO3. b. Pseudo-cubic volume vs pressure at room temperature for Eu1−xSrxTiO3. The open symbols correspond to the cubic phase and the closed ones to the tetragonal phase. The dashed-dotted lines represent the BM2 fits. The errors bars are smaller than the symbols.
a. Normalized FWHM of the (200) diffraction peak, indicating the onset of the phase transition in Eu1−xSrxTiO3. b. Pseudo-cubic volume vs pressure at room temperature for Eu1−xSrxTiO3. The open symbols correspond to the cubic phase and the closed ones to the tetragonal phase. The dashed-dotted lines represent the BM2 fits. The errors bars are smaller than the symbols.
The normalized (pseudo-cubic) cell volumes with respect to pressure are given in Fig. 2(b). The pseudo-cubic plots of the lattice constants vs pressure for all samples are shown in the supplementary material.21 Using an F-f plot (see supplementary material21), our data in the tetragonal phase can be represented with a straight horizontal line, indicating that a 2nd order Birch-Murnaghan (BM2) equation of state (EoS) is sufficient to reproduce the data. We obtain the bulk moduli for both cubic and tetragonal phases that are summarized in Table I together with the critical pressures Pc of the transition for each of the four investigated samples. The BM2 EoS yields bulk moduli between 168-175 GPa for the cubic phase and 177-187 GPa for the tetragonal phase, values that are comparable with previous experimental and theoretical studies of EuTiO3 or SrTiO3.2,16,23–25 The higher values for the tetragonal phase are reasonable since the material becomes less compressible at higher pressures. No discontinuities have been observed in the pseudo-cubic volume evolution with pressure, indicating that the nature of the transition is of second order. It is important to emphasize however that despite the apparently second order nature of the phase transition in our work, recent thermal expansion measurements support the first order character of it.15
Critical transition pressures and bulk moduli for Eu1−xSrxTiO3.
x . | Pc (GPa) . | K0 Pm-3m (GPa) . | K0 I4/mcm (GPa) . |
---|---|---|---|
0.25 | 3.7 | 168.7 (8) | 177.8 (7) |
0.50 | 4.6 | 172.5 (6) | 181.0 (3) |
0.75 | 5.5 | 175.4 (9) | 187.8 (9) |
0.97 | 7.6 | 174.3 (5) | 183.0 (4) |
x . | Pc (GPa) . | K0 Pm-3m (GPa) . | K0 I4/mcm (GPa) . |
---|---|---|---|
0.25 | 3.7 | 168.7 (8) | 177.8 (7) |
0.50 | 4.6 | 172.5 (6) | 181.0 (3) |
0.75 | 5.5 | 175.4 (9) | 187.8 (9) |
0.97 | 7.6 | 174.3 (5) | 183.0 (4) |
The tetragonal distortion in perovskites can be quantified by the use of symmetry-adapted spontaneous strains, ea = (2e1 + e3) (volume strain) and et = 2(e3 − e2) (tetragonal strain), where e1 and e2 are the strain components calculated by using the pseudo-cubic lattice constants apc and cpc: e1 = e2 = (apc − a0)/a0 and e3 = (cpc − a0)/a0. In Fig. 3(a) we present the evolution of the spontaneous strains with pressure for x=0.25. The volume strain is very small in all cases and can be considered negligible within error bars for all studied pressures, meaning that the elongation of the octahedra along the c axis compensates almost completely the volume reduction caused by the tilts. The tilt angles can be obtained by the exact atomic positions since they depend on the displacements of O atoms. However, in our data, the polycrystalline nature of the samples made it difficult to obtain Rietveld refinements with satisfying uncertainties at high pressures. Alternatively, the tilt angles can be calculated by the lattice constants by assuming the octahedra to remain undistorted (i.e. octahedral that maintain their corner-sharing connectivity). For a tetragonal lattice the octahedral tilting can be expressed by the relation . The tilt angle, which is the order parameter of the observed structural transition, clearly shows that the tetragonal distortion is small for low pressures and strongly increases at higher pressures, reaching a maximum value of ∼12o for the maximum pressure (Fig. 3(b)). The data for the remaining samples are presented in the supplementary material.21
a. Evolution of spontaneous strains with pressure for x=0.25. b. Evolution of the octahedral tilt angle with pressure for x=0.25. The error bars are smaller than the symbols.
a. Evolution of spontaneous strains with pressure for x=0.25. b. Evolution of the octahedral tilt angle with pressure for x=0.25. The error bars are smaller than the symbols.
From our data it is possible to construct a high pressure phase diagram of Eu1−xSrxTiO3, as shown in Fig. 4. We add also for comparison the data points for pure EuTiO316 and SrTiO3.2 Our data can be fitted with a straight line with a positive slope dPc/dx = 5.2 GPa. Extrapolating to x=0 (pure EuTiO3) gives a transition pressure of Pc=2.2 GPa, which is close to the 2.7 Gpa of our previous work.16 However, by extrapolating for x=1 we obtain Pc= 7.6 GPa for pure SrTiO3, which is substantially lower than 9.6 GPa as reported by Guennou et al.2 The difference can most likely be ascribed to the different PTM used in the two experimental works (He in our work and Ne in Guennou et al.2). Oxygen deficiencies or oxygen excess accompanied by the presence of small amounts of Eu3+ ions in the Eu1−xSrxTiO3 samples are additional error sources leading to slight variation of the lattice parameters and thus different transition pressures.11 These problems have not been encountered in pure SrTiO3. A previous work on the low temperature phase diagram of Eu1−xSrxTiO3 using electron paramagnetic resonance (EPR) and resistivity measurements26 show a non-linear behavior of TS with x, which is unexpected given the many structural similarities between the two end members, mainly the similar ionic radii between Sr and Eu. Since the non-linear behavior cannot be due to a lattice mismatch, the authors concluded that there is a change in the dynamics around x=0.75 that is dependent on the next-nearest neighbor spin-phonon interactions. If this is the case, our x-ray diffraction measurements at room temperature are not sensitive to such an effect since Bragg reflections are a lot stronger than any spin-related effects and therefore, a linear behavior with pressure is observed, as in the case of pure EuTiO316 and SrTiO3.2
Phase diagram of Eu1−xSrxTiO3. Our present work (circles) is compared with our previous work on pure EuTiO3 (rectangle) and the work of Guennou et al. (triangle) on pure SrTiO3.
Phase diagram of Eu1−xSrxTiO3. Our present work (circles) is compared with our previous work on pure EuTiO3 (rectangle) and the work of Guennou et al. (triangle) on pure SrTiO3.
IV. CONCLUSION
To summarize, we have made a detailed high pressure synchrotron x-ray diffraction study of Eu1−xSrxTiO3. We have observed the antiferrodistortive cubic-to-tetragonal phase transition in the whole doping regime which is identical to the phase transition observed in both end members either under high pressure or at low temperature and corresponds to the tilting of TiO6 octahedra. No further phase transitions have been observed up to 48 GPa within the resolution limits of our experiment. We conclude with a P-x structural phase diagram for Eu1−xSrxTiO3, which exhibits a linear behavior with x.