Pressure-induced transformations of multiferroic relaxor PbFe_0.5Nb_0.5O₃

Multiferroic materials exhibit two or more ferroic features, such as ferro- or anti-ferromagnetism, ferroelectricity, or ferroelasticity. Recently, there has been increased interest in multiferroics, toward efforts to understand both the essential aspects of the unique mechanism giving rise to magnetoelectric coupling and the important possibility of using the coupled order parameters in technological applications. One of the most well-studied multiferroic materials is BiFeO₃, in which the magnetoelectric coupling is weak, and the origin of the ferroelectricity is different from that of the magnetism.¹ Lead ferroniobate, Pb(Fe_0.5Nb_0.5)O₃ (PFN), not only exhibits strong coupling but also displays relaxor, piezoelectric, and pyroelectric properties, making it a promising material for multi-functional devices.² At ambient conditions, PFN has an ABO₃ perovskite structure with a local disorder on the B sites, which are occupied by either Fe³⁺ or Nb⁵⁺, which leads to a local charge imbalance. To avoid this charge imbalance, the system generates regions with short-range order known as polar nanoregions. Such a signature of ordered regions has been observed in Pb(Mg_1/3Nb_2/3)O₃.³ These polar nanoregions are the origin of relaxor behavior in ferroelectric materials such as PFN.⁴ 

PFN undergoes several temperature-dependent structural transitions. Above the Curie temperature T_c (376 K), the material is cubic (paraelectric $Pm3¯m$⁠), whereas below T_c, the stable phase is tetragonal (ferroelectric, P4mm).^5,6 Although there is some disagreement concerning its structure in the temperature range of 153–355 K, the R3m structure, supported by observation of the quadratic paramagnetoelectric effect, is the generally accepted one.^7,8 Below its Néel temperature T_N (153 K), PFN is orthorhombic and exhibits antiferromagnetic ordering.⁸ An anomaly in the value of the dielectric constant observed at T_N strongly indicates magnetoelectric coupling between the ferroelectric and the antiferromagnetic order.⁹ Furthermore, PFN forms magnetic superclusters above T_N, adding complexity to the high temperature behavior of the material.

High pressure x-ray diffraction in conjunction with neutron diffraction and Raman spectroscopy carried out by Kozlenko et al.¹⁰ indicate two structural phase transitions—from the ambient rhombohedral R3m phase to a monoclinic Cm phase at 5.5 GPa followed by another transition to a monoclinic Pm phase at 8.5 GPa. The authors argue that all the observed pressure-induced monoclinic phases are polar and allow ferroelectricity. In another study, Wilfong et al.¹¹ probed the P-T phase diagram using Raman spectroscopy and found three pressure-induced phase transitions at 5.6, 7.9, and 27 GPa at room temperature. The temperature-dependent, high-pressure measurements revealed transitions at 1.5 GPa at 335 K and 365 K, which were suggested to involve a tetragonal phase forming between the ferroelectric and paraelectric phases. At higher pressures, the tetragonal phase was not observed. Transitions at pressures similar to those obtained by Kozlenko et al.¹⁰ were reported, but it was also argued that further experiments are required to identify the high-pressure phase as ferroelectric. X-ray diffraction, particularly powder diffraction as used in Ref. 10, is not generally sufficient for identifying polar phases; additional determination of the dielectric response^12–14 or second-harmonic generation (SHG) optical measurements at high pressure are required.^15,16

Here, we report the results of measurements on PFN using second-harmonic generation (SHG) and x-ray diffraction to study the nature of the ferroelectric–paraelectric phase transition in PFN at high pressure. SHG arises from the second-order nonlinear dependence of the polarization on the electric field, which is forbidden in centrosymmetric materials or a medium with inversion symmetry.¹⁷ The linear response connects the polarization at frequency ω and the field at the same frequency, and the nonlinear response produces polarization harmonics. As such, the second harmonic is the polarization at the doubled frequency, the appearance of which results from the product of two components of the field generated at frequency ω,

where β is the third-rank tensor of the nonlinear polarizability. For centrosymmetric materials, β is zero.¹⁷ In ideal ferroelectric crystals, light is scattered by the set of uniformly displaced ions, and the corresponding peak is very sharp. Thus, a temperature- or pressure-induced transition from the polar to non-polar symmetry can be observed by the disappearance of the SHG signal. A number of such temperature-dependent polar to nonpolar transitions identified by SHG measurements have been reported previously (e.g., Ref. 18).

PFN was synthesized using two-stage ceramic technology as outlined previously.¹⁰ High pressure SHG and powder x-ray diffraction were measured in diamond anvil cells (DACs) with culet sizes 300–350 μm. For the SHG experiments, Boehler-Almax¹⁹ DACs and rhenium gaskets were used. The sample PFN and reference sample (LiTaO₃ or LT) were pressed into pellets, 2–3 μm thick, and loaded in the DAC [Fig. 1(a) at 1.7 GPa] with argon (99.999% purity), as a pressure transmitting medium. Ruby grains, 2–3 μm in size, were placed close to the sample for pressure determination, with an uncertainty of 0.2 GPa. The SHG intensities were measured in a transmission geometry using an IR (λ_ω = 1064 nm), 5–8 ns pulsed YAG laser with a 10 kHz repetition rate. The SHG intensity was observed at λ_2ω = 532 nm. A dedicated spectrograph equipped with a charge-coupled-device detector synchronized with the laser pulse²⁰ was used to record the SHG signal. All measurements were performed at room temperature, and the laser power and sample orientation were consistent throughout all experiments. The laser focus spot was about 5 μm, and the SHG signal was collected separately from PFN and the reference sample. One of the issues faced in the SHG measurements was absorption of the IR laser by the PFN sample. This problem dictated us to make the sample as thin as possible without compromising on the SHG signal intensity. However, preparing a thin sample from the single crystal was not possible due to constant fracturing of the pellet while polishing. Therefore, we decided to make thin pellets from the powder sample.

High pressure x-ray diffraction measurements were carried out at beamline 16-BM-D (HPCAT sector) at the Advanced Photon Source, Argonne National Laboratory, using 29.2 keV (λ = 0.4246 Å) photons. Symmetric DACs and stainless-steel gaskets were used for the diffraction measurements. Finely powdered samples from a single crystal of PFN and a few ruby grains were loaded with argon as the pressure transmitting medium. FIT2D²¹ was used to integrate two-dimensional diffraction images and produce intensity versus 2θ profiles. GSAS²² was employed for the Le Bail refinements.²³ EosFit was used to determine the equation-of-state parameters.²⁴ 

The variation in the measured intensities of the SHG signal from PFN and LT with pressure is plotted in Fig. 1(a), and the SHG intensity at each pressure, relative to that obtained at ambient conditions (I_amb) in the same time interval, is shown in Fig. 1(b). The intensity of the SHG signal decreases with pressure and disappears completely above 7.1 GPa. This reduction in SHG intensity strongly indicates a decrease in polarization followed by its complete disappearance, suggesting that the system has transformed from a polar to a non-polar structure. The simultaneous measurement of the SHG signal from LT shows a similar behavior. However, the SHG intensity persists well beyond 7 GPa, which is expected, as the ferroelectric–paraelectric transition for LT occurs at 30 GPa.²⁵ This confirms that the disappearance of the SHG signal from PFN is not an experimental artifact.

For a crystal of thickness (l), the second harmonic intensity (I) is given by

where I_in, f(n), d_eff, and Δl are the incident light intensity, a function of the refractive indices, the effective nonlinear coefficient, and the coherence length, respectively. Calculating the nonlinear optical coefficients in our measurements is not straightforward because of (i) using a powder sample (since d_eff is generally calculated for single crystals) and (ii) the dependence of f(n) on pressure. Therefore, we semi-quantitatively determined the effective non-linear coefficient by considering some approximations for both materials. Equation (2) can be rewritten as

where A = $Δl2 sin2πl2Δl$ and is approximated as a constant value at high pressures. $Iin2$ is calculated from the measured incident laser power and the beam spot size. We approximate f(n) to be the refractive index of PFN at ambient conditions and assume it to be constant at high pressures. The average d_eff calculated is plotted against pressure in Fig. 1(c). As expected, the d_eff values for both samples decreased with pressure. For PFN, d_eff again disappears around 7.1 GPa, indicating a transition to a non-polar structure, whereas d_eff for LT persisted to the highest pressure of our study. A similar SHG study was performed on LiNbO₃ and LiTaO₃ to measure the non-linear coefficient, d₃₃.¹⁸ It was observed that d₃₃ continuously decreases to zero at the Curie temperature, indicating a transition to a paraelectric centrosymmetric phase.

Representative x-ray diffraction patterns for PFN are shown in Fig. 2. At ambient and moderate pressures, the experimental data are consistent with a rhombohedral R3m structure. For the results obtained at approximately 7.9 GPa, where we observe the disappearance of SHG intensities, we attempted fitting with various polar and non-polar symmetries. After several iterations, we narrowed down our search to the following symmetries: polar rhombohedral R3m, monoclinic Cm, and non-polar rhombohedral $R3¯m$⁠. The weighted R-factor values obtained are R_wp = 3% (R3m), 3.1% (⁠$R3¯m$⁠,) and 4.65% (Cm). We observe that the difference in values of R_wp between the two rhombohedral symmetries is very small. Given that SHG data indicate that the system transforms to a non-polar symmetry at approximately this pressure, we accepted the non-polar rhombohedral $R3¯m$ space-group as the correct model to fit the pattern above 7 GPa. A further increase in pressure results in a subtle phase transition as observed from the change in diffraction peak widths, which, as discussed below, are consistent with previous observations.^10,11 However, to identify this subtle structural phase transition, higher resolution x-ray diffraction measurements are required. Furthermore, we add that the monoclinic Cm phase could have been present within the narrow pressure range of 5–7 GPa. Second harmonic measurements are not sensitive enough to detect this change, and no x-ray data in this region could be obtained. Nevertheless, the disappearance of the SHG intensities above 7 GPa clearly indicates a transition to non-polar symmetry irrespective of the preceding structure.

The variation with pressure for the lattice parameters and unit cell volume, converted to those of a pseudo-cubic unit cell, are shown in Fig. 3. The lattice parameters and pressure-volume data are shown in Table I. Anisotropic compression is indicated by the greater compression of the c-axis as compared to the a-axis. We also fitted the P-V data to the third-order Birch–Murnaghan (BM) equation of state (EOS)²⁶ and obtained a bulk modulus K₀ = 136 (±2) GPa, K₀′ = 4.0 (±0.2), and the initial volume V₀ = 64.5 (±0.1) ų. An alternative EOS function proposed by Vinet et al.²⁷ has been shown to be reliable for both predicting zero-pressure elastic properties and for extrapolation to higher pressure.²⁸ Therefore, we also fitted our P-V data to the Vinet EOS for comparison and obtained similar values of K₀ (136 (±2) GPa), K₀′ (4.0 (±0.2)), and V₀ (64.5 (±0.1) ų). The bulk modulus value of PFN is comparable to those of similar ferroelectric systems. For example, K₀ is 119 (±10) GPa for PbSc_0.5Nb_0.5O₃ (PSN), 104 (±5) GPa for PbMg_1/3Nb_2/3O₃ (PMN), and 120 (±9) GPa for Pb(Mg_1/3Nb_2/3)O₃-(0.22)PbTiO₃ (PMN-0.22PT).^29–31 Even though the initial volumes of these systems differ (Table II), the compression curves are similar to those of PFN (Fig. 4). Comparing the volume data from Ref. 10, we observed a significant divergence in the volume from 7 GPa onwards [Fig. 3(b)]. We suggest that the difference may be due to the use of an incorrect space group assignment in that study. Diffraction linewidths for reflections (101), (202), and (21$2¯$⁠) with increasing pressure are plotted in Fig. 5. We observe a marked increase in the diffraction linewidth at around 5 to 7 GPa, which is consistent with a phase change at this pressure. We also observe a change in the slope of this plot at around 20 GPa, suggesting another structural transition at higher pressure, as observed in previous studies.^10,11

The measured SHG results reveal that PFN undergoes a ferroelectric to paraelectric transition above 7 GPa. The assignment of polar symmetry to the high pressure phase above 7 GPa for PFN in Ref. 10 is based on x-ray diffraction measurements. It is generally accepted that two competing forces, long range Coulomb attraction and short range repulsive forces, determine the distortion, octahedral tilt, and structural transitions in oxide perovskite systems.³² The resulting distortion or tilting is typically small, and thus, the profile fitting of powder diffraction data provides rather similar R values for several possible symmetries. As noted above, we obtained very similar R_wp for the three symmetries at 7.9 GPa. Similarly, R-factor values close to each other for different symmetries were obtained in Ref. 10. Consequently, in the absence of complementary measurements, an incorrect symmetry assignment is possible if the determination is based only on powder diffraction.

Polar nanoregions (PNRs) in relaxors are known to excite the SHG signal; however, the intensity is not as strong as that emitted from the ferroelectric state. In a recent measurement on Pb(Mg_1/3Nb_2/3)O₃ (unpublished), we observed a weak signal intensity from the sample because the origin of the signal was PNRs. Additionally, the correlations between the PNRs and the polar nature of the PNRs weaken rapidly as observed from x-ray diffuse scattering at high pressure.³³ Venturini et al.³⁴ showed that the behavior of PNRs is pronounced at pressures well below 7–8 GPa. The transition observed in PFN above 7 GPa is ferroelectric to paraelectric transformation rather than pressure induced suppression of PNRs. Furthermore, the two pressure dependent Raman studies on PFN^10,11 did not observe a soft-optical-mode which is generally associated with the structural transition in ferroelectrics, for example, in PbTiO₃.³⁵ However, in relaxor ferroelectrics, because of the structural and chemical disorder and PNRs, those short range ordered clusters will over-damp the soft-mode, and any mode softening will not be observed with conventional light-scattering methods.

There are two possible experimental techniques that can be successfully exploited to identify the high-pressure ferroelectric phase. Dielectric spectroscopy has been successfully employed by Venturini et al.³⁴ to study the pressure-induced ferroelectric to relaxor transition in Pb(Sc_1/2Nb_1/2)O₃ and by Deguchi et al.³⁶ to study the P-T phase diagram of Pb(Mg_1/3Nb_2/3)O₃. However, dielectric spectroscopy measurements to date have been limited to modest pressures (2–3 GPa) due to technical difficulties. Furthermore, dielectric measurements at room temperature on various oxide dielectric systems have been reported using a large volume toroidal cell up to 8 GPa,^12–14 and extending this method to higher P-T conditions remains a challenge. Another important technique, which is rarely used at high pressure,¹⁵ is SHG. The present work successfully corroborates that SHG measurements can be coupled to high-pressure and are effective in detecting the polarization properties of materials at extreme conditions.

In conclusion, we have elucidated the considerable effects of pressure on the dielectric properties and phase behavior of PFN. Using a combination of SHG and x-ray diffraction measurements, we show that pressure induces an R3m - $R3¯m$ structural transition in this material at room temperature and 7.9 GPa. This report contradicts a recent high-pressure study on PFN and presents the advantage of SHG measurements over x-ray diffraction alone in detecting polar phases. The disappearance of the SHG signal for PFN at high pressures supports the conventional understanding that ferroelectricity disappears at high pressures. This technique can be successfully extended to several other ferroelectric systems to more fully understand the effects of pressure on this class of materials.

We are grateful to A. Karandikar, Z. Geballe, M. Somayazulu and S. A. Gramsch for helpful discussions and comments on the manuscript. This research was supported by Energy Frontier Research in Extreme Environments (EFree), an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, under Award No. DE-SC0001057 (partial salary support for A.B. and M.A.). This work was also supported by the U.S. National Science Foundation through Grant No. EAR1248553 and by the Office of Naval Research through Grant No. N00014-14-1-0561. HPCAT was supported by DOE/NNSA (No. DE-NA0001974) at the Advanced Photon Source, Argonne National Laboratory (Contract No. DE-AC02-06CH11357). Additional infrastructure and facilities were supported by the Carnegie-DOE Alliance Center (CDAC, No. DE-NA-0002006).