1. Introduction
In sharp contrast to normal ferroelectric (for example BaTiO3), relaxors show unusually large dielectric constant over a large temperature range (~100 K) (Fig. 1 (a)) [1,2]. Such large dielectric response is strongly dependent on the frequency. Its origin has been the focus of interest in the solid-state physics. Unlike the dielectric anomaly in BaTiO3, which is associated with a ferroelectric phase transition, the maximum of dielectric response in relaxor does not indicate the occurrence of a ferroelectric phase transition. Such huge dielectric response suggests that local polarization might occur in the crystal. This was envisioned by Burns and Dacol from the deviation from linearity of refractive index
Another longstanding issue on relaxors is how PNRs interact at low temperature. There are two acceptable models: (1) dipole glass model [2,8-11], and (2) random-field model [12,13]. In spherical random-bond–random-field (SRBRF) model, Pirc and Blinc assumed that PNRs are spherical and interact randomly and proposed a frozen dipole glass state for relaxor (Fig. 2(a)) [10,11]. It predicts that the scaled third-order nonlinear susceptibility
Combining our recent results [15] from the electrical polarization, Raman scattering, TEM measurements and those reported in the literature, here, we propose a physical picture to understand the dielectric behaviors of Pb(Mg1/3Nb2/3)O3 (PMN) relaxor.
2. Multiple inhomogeneities in relaxors
PMN is a prototypical relaxor with A(B’,B”)O3 perovskite structure (Fig. 3), in which B-sites are occupied by two kinds of heterovalent cations. Such chemical inhomogeneity is a common feature of relaxor crystals. Although it remains an average centrosymmetric cubic structure down to 5 K [16], local structural inhomogeneity has been detected in PMN relaxor. In addition to PNR mentioned above, chemically ordering region (COR) [17-19] with size of several nm has been observed in PMN crystal by TEM. It should be noticed that PNR and COR belong to different symmetry groups and are considered to have non-centrosymmetry of
3. Evolution of the electrical polarization and origin of the huge dielectric responses
In order to understand the nature of the huge dielectric response and the ground state of the electrical polarization in PMN, it is essential to know the polarization hysteresis of all states including virgin state in PMN crystal. Although there are many reports on the polarization hysteresis of PMN crystal, there is a lack of understanding of the polarization hysteresis of the virgin state. In our polarization measurements, in order to access the virgin state of the crystal at a temperature, it was firstly annealed at 360 K and then cooled to the desired temperature for the measurements.
Figure 4 shows the
Upon further cooling to temperatures lower than ~220 K,PMN shows polarization hysteresis similar to that of normal ferroelectric [22]. Fig. 4(a) shows an example of the characteristic hysteresis loop in this temperature range. In the virgin state as indicated by the thick red line, it appears that there is no remnant polarization in the crystal at zero electric field. However, as increasing the electric field, we can see the gradual growth of the polarization. This is a characteristic behavior of the polarization reversal (switching) in ferroelectric. When the applied field is larger than the coercive field
There are many reports on the electric-field induced phase transition in PMN. On the basis of the change of dielectric constant under the application of a DC electric field, Colla et al. proposed an
As discussed in following, ferroelectric micro-domain and soft-mode behaviors have also been observed at zero field in PMN in our measurements. Also, lowering of symmetry of local structure at zero field was also revealed around 210 K by a NMR study [21]. All these results direct to the fact of occurrence of a ferroelectric state at zero field in PMN crystal. We therefore consider that it is more rational to attribute
The high-resolution data of the polarization obtained by a 14-bit oscilloscope allow us to calculate the linear and nonlinear dielectric susceptibilities (defined by the expansion
The nonlinear dielectric susceptibility
In the random field model, the ferroelectric phase transition is suggested to be smeared due to the quenched random fields, but it may be visible if the random fields are overcome by an external electric field [12]. This ferroelectric phase transition has been convincingly shown by the sharp peak of the linear dielectric susceptibility
Here, we can see that there are two characteristic temperatures in relaxors: Burns temperature
4. Soft mode behaviors in PMN relaxor
In the displacive-type ferroelectrics, soft-modes should occur in the lattice dynamics of the crystal. Actually, in a study of neutron inelastic scattering, a FE soft mode was revealed to recovers, i. e., becomes underdamped, below 220 K, and from there its energy squared (
In Raman scattering studies for relaxors, the multiple inhomogeneities due to the coexistence of different symmetry regions such as the PNR and COR has been a tremendous barrier to clarify the dynamical aspect of relaxor behavior in PMN. In particular, the intense temperature-independent peak at 45 cm−1 (indicated by↓in Fig. 6(a)), which stems from the COR with
Such special configuration allows us to observe the other low-wave number modes easily. Fig. 6 (d) shows the spectra obtained by this configuration. At the lowest temperature, a well-defined mode can be seen from the spectrum, which softens as increasing the temperature, indicating the occurrence of FE soft mode in PMN relaxor. Due to the multiple inhomogeneities of the system, the shape of soft-mode of PMN relaxor is not as sharp as that observed in normal displacive-type ferroelectrics. However, we still can estimate its frequency reliably from the careful spectrum analysis. Its temperature dependence is shown in Fig. 6(e) (indicated by ●) in comparison with the results obtained by neutron inelastic scattering (○) [31].
We find that the soft-mode exhibits softening towards
In a short summary, we may say that the polarization in PMN is induced by the soft mode. This interpretation is essentially consistent with the results described in the polarization measurements, and the results obtained in previous neutron studies [36, 37], in which the crystallographic structure of PNR is attributed to the displacement pattern of the soft mode. The results of the Raman study also support that a ferroelectric state exists in PMN even at the zero-bias field.
5. Ferroelectric domain structures observed by TEM
In order to understand the microstructures of COR and PNR together with the domain structures and its evolution with temperature in the ferroelectric phase of PMN relaxor, we have carried out a detailed TEM observation. The typical results are summarized in Fig. 7. As shown in Fig. 7 (a”)-(c”), COR was found to be spherical shape and has size less than 5 nm. It is very stable and remains unchanged within the temperature range of 130 K-675K. In the TEM observation, large amount of CORs were found to distribute in the PMN crystal. In a previous HRTEM study, its volume fraction has been estimated to be ~1/3 of the crystal [18]. CORs are thus considered to be the intense sources of the strong random fields.
In contrast to CORs, PNRs exhibit remarkable change with temperature. As shown in Fig. 7(a’)-(c’) and Fig. 8, PNRs with size of several nm were found to occur in the crystal for
Associating with the change in the number and the shape of PNR, micrometric ferroelectric domains were found to occur for
The occurrence of micrometric domains, the soft-mode observed by Raman scattering, and the macroscopic polarization all direct to the same conclusion: PMN is essentially ferroelectric but not dipole-glass at
Here, we made a discussion on the volume fraction of PNRs in PMN crystal. Neutron scattering technique has been used to estimate the volume fraction of PNRs. Fig. 9 replots two results reported by Jeong et al. [37] and Uesu et al. [39], respectively. Both studies indicate that PNRs occupy a volume fraction > 25% at the lowest measurement temperature. This volume fraction is larger than the threshold of 22% to form a percolated ferroelectric state with an ellipsoidal-shape [40], supporting again the picture of a ferroelectric state in PMN relaxor.
6. A physics picture of relaxor
In summary, we propose a physics picture for relaxors. Figure 10 schematically shows a model of structure evolution in PMN relaxor. Since COR has been observed at
Acknowledgements
We thank Mr. M. Yoshida, Prof. N. Yamamoto and Prof. Shin-ya Koshihara of Tokyo Institute of Technology for their contributions in this work. We acknowledge the support of a Grant-in-Aid for Scientific Research, MEXT, Japan.
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