A combinatory ferroelectric compound bridging simple ABO3 and A-site-ordered quadruple perovskite

The simple ABO3 and A-site-ordered AA′3B4O12 perovskites represent two types of classical perovskite functional materials. There are well-known simple perovskites with ferroelectric properties, while there is still no report of ferroelectricity due to symmetry breaking transition in A-site-ordered quadruple perovskites. Here we report the high pressure synthesis of an A-site-ordered perovskite PbHg3Ti4O12, the only known quadruple perovskite that transforms from high-temperature centrosymmetric paraelectric phase to low-temperature non-centrosymmetric ferroelectric phase. The coordination chemistry of Hg2+ is changed from square planar as in typical A-site-ordered quadruple perovskite to a rare stereo type with 8 ligands in PbHg3Ti4O12. Thus PbHg3Ti4O12 appears to be a combinatory link from simple ABO3 perovskites to A-site-ordered AA′3Ti4O12 perovskites, sharing both displacive ferroelectricity with former and structure coordination with latter. This is the only example so far showing ferroelectricity due to symmetry breaking phase transition in AA′3B4O12-type A-site-ordered perovskites, and opens a direction to search for ferroelectric materials. There are few reports of ferroelectricity due to symmetry breaking transition in A-site-ordered quadruple perovskites. Here, the authors find one with phase transition from a high-temperature centrosymmetric paraelectric phase to a low-temperature non-centrosymmetric ferroelectric phase in a high pressure synthesized compound.

P erovskites and their derivatives show many interesting physical, chemical and mineral properties such as ferromagnetism, ferroelectricity, piezoelectricity, ion conductivity, photocatalysis and superconductivity [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] that can be modified dramatically by the coordination chemistry for a given composition. There is a special class of perovskite-type materials with the general chemical formula AA′ 3 B 4 O 12 , named Asite-ordered, or quadruple perovskites, which received much attention owing to their fascinating structural and wide varieties of physical properties 10 , including colossal magnetoresistance under weak field 11 , charge disproportionation 12 and giant dielectric constant over a wide temperature range 13,14 . For the simple ABO 3 perovskite, the 12-fold coordinated A-site is often occupied by large size ions such as alkali metal, alkaline earth or lanthanide cations and the 6-fold coordinated B-site is often occupied by transition metals (TMs) to satisfy the so called tolerance factor t = (r A + r O )/√2(r B + r O ) (r A , r B , & r O represent for the ion radius of A, B, and O, respectively) with t usually in the range of 0.75 to 1.05 for stable perovskite compounds 1,18 . However in the A-site-ordered perovskite AA′ 3 B 4 O 12 , three quarters of the A-site is substituted by a TM, A′ with much smaller ionic radius [16][17][18][19] . Generally, TM ions with strong Jahn-Teller distortions like Mn 3+ and Cu 2+ preferentially occupy the A′-site with square-planar coordination [20][21][22][23][24] . The small TM ion at the A′-site causes the distortion of BO 6 octahedron in AA′ 3 B 4 O 12 perovskite, usually resulting in a cubic crystal structure with space group Im-3 25 . From a structural point of view, the flexibility for tilting the BO 6 octahedra in AA′ 3 B 4 O 12 perovskite is limited in order to maintain the square-planar coordination at the originally 12-fold coordinated A-site in the simple perovskite structure 21 .
Ferroelectricity is one of the most important properties for application in actuators, sensors, and memory storage devices, etc. Large numbers of ferroelectric materials possess simple perovskite structures, such as BaTiO 3 , PbTiO 3 , Pb(Ti, Zr)O 3 , BiFeO 3 [26][27][28][29][30] . The origin of ferroelectricity is due to either the lone pair 6s 2 effect of cations (Pb 2+ , Bi 3+ ), or the second-order Jahn-Teller active cations with electron configuration of d 0 (Ti 4+ , Zr 4+ ); these compounds are usually referred to as displacive-type ferroelectrics. However, ferroelectricity is seldom observed in AA′ 3 B 4 O 12 type A-site-ordered compounds, even when they contain second-order Jahn-Teller active cations or lone pair effect cations 28 . One reason for the absence of ferroelectricity in this series of compounds is the usual presence of a centrosymmetric structure, and the variation of temperature generally causes isostructural or centrosymmetricto -centrosymmetric phase transition 12,21,25 , hence there cannot be spontaneous polarization. Currently the rare examples in this series that show ferroelectricity are AMn 7 O 12 (A = Ca, Bi or Pb) [31][32][33] and AMn 3 Cr 4 O 12 (A = La or Bi) 20,22 . Although these compounds have centrosymmetric structures, all are spindriven multiferroic systems, due to strong magnetoelectric coupling effects 20,22,32 . Up to now, there is still no report of ferroelectricity from symmetry breaking transition in A-site-ordered perovskite compounds.
In this work, an AA′ 3 B 4 O 12 type A-site-ordered perovskite oxide, PbHg 3 Ti 4 O 12 (henceforth PHTO) was designed and synthesized at high pressure and high temperature conditions. It is found that the Hg 2+ ion occupies the A′-site in AA′ 3 B 4 O 12 type perovskite in sharp contrast to previous reports where 3d TM ions (Cu 2+ , Mn 3+ ) usually locate at the A′-site. Moreover, ferroelectricity was observed in PHTO, when its ambient centrosymmetric phase transformed to a non-centrosymmetric phase at 250 K. The origins of ferroelectricity are discussed based on the comprehensive characterizations of crystal structure using both neutron and synchrotron x-ray diffractions and density functional theory (DFT) calculation.

Results and Discussion
Crystal structure. The NPD refinements are shown in Fig. 1a, which confirm that PHTO crystallizes in the AA′ 3 B 4 O 12 type Asite-ordered perovskite. The refined structure parameters of PHTO based on NPD data collected at 295 K are listed in Table 1. No anomaly is observed in the occupation parameters at any site, including full occupancy for the oxygen site as well. Thus, PHTO should have stoichiometric composition. Bond valence sum (BVS) calculations based on the refined structure from NPD data give valences of +2.26 for Pb ions, +1.99 for Hg ions and +3.88 for Ti ions (see Table 1), which are consistent with x-ray absorption spectroscopy (XAS) results discussed later. Hence the obtained sample is an A-site-ordered perovskite with stoichiometric Pb 2+ Hg 2+ 3 Ti 4+ 4 O 12 formula and space group Im-3 as shown in Fig. 1b. The structure model is consistent with the refinements of SXRD data as shown in Supplementary Fig. S1 Figure 2 shows the tolerance factor t versus average ionic radius of A-site ions for simple perovskites ATiO 3 and A-site-ordered perovskites AA′ 3 Ti 4 O 12 where the t factor is calculated assuming a simple ABO 3 form with the average ionic size at A site. It is found that from CaTiO 3 to BaTiO 3 , the ionic radius of A-site increases from 1.34 Å to 1.61 Å while the tolerance factor t increases from 0.97 to 1.07. The simple perovskites ATiO 3 are located at the upper right panel of Fig. 2. For most of the AA′ 3 Ti 4 O 12 compounds, the average ionic radius of A-site is about 0.8 Å and the tolerance factor t is around 0.77. Therefore, AA′ 3 Ti 4 O 12 perovskites are located at the lower left panel of the Fig. 2. However, different from these ATiO 3 and AA′ 3 Ti 4 O 12 compounds, the average ionic radius of A-site ion for PHTO is large, about 1.1 Å and the tolerance factor t is about 0.88. Moreover as aforementioned, the coordination number for Hg ions at the A′-site in PHTO is eight, not square planar as in A′-TM quadruple perovskites AA′ 3 Ti 4 O 12 , and it is located in the middle area of Fig. 2, between those of simple ATiO 3 (coordination number 12) and AA′ 3 Ti 4 O 12 quadruple perovskites (coordination number 4). Thus, PHTO appears to be a link from simple ATiO 3 perovskite to AA′ 3 Ti 4 O 12 type A-site-ordered perovskite (Fig. 2). The A-site coordination number for ABO 3 perovskite is 12 while the A-site and A'-site coordination numbers in the A-site-ordered quadruple perovskite AA' 3 B 4 O 12 compound are 12 and 4 respectively. However in PHTO, the coordination number of A′ (Hg 2+ ) is 8, which is just in between that for simple ATiO 3 and AA' 3 Ti 4 O 12. This result provides further evidence supporting the scenario aforementioned. Considering that the ionic size of Sr 2+ (1.45 Å) is similar to that Pb 2+ (1.49 Å), we also fabricated the A-site-ordered perovskite compound SrHg 3 Ti 4 O 12 , which is isostructural with PHTO, but without the observation of ferroelectricity. The result about SrHg 3 Ti 4 O 12 will be published elsewhere. According to the previous report 37 , the low energy level of d 10 orbital prefers a relatively high coordination number owing to the weak d-s and dp hybridization in perovskite compounds. As to PHTO system, the first principles calculation result indicates that the energy level 155.83 (6)   of d 10 for Hg 2+ has a lower energy for 8 coordination than that for 4 coordination (See Supplementary Fig. S2a). Moreover PHTO also shows a low total energy in the state of 8 coordination of Hg 2+ (See Supplementary Fig. S2b). Thus 8-fold coordination of Hg 2+ is more stable than 4-fold in the PHTO system.
Valence state analysis. Soft X-ray absorption spectroscopy at the L 2,3 edge of TM 3d ions 38 is a highly sensitive method to determine the valence state 39,40 , local environment 41 , and orbital occupation 42 of the ions. Figure 3a shows the Ti-L 2,3 XAS spectra of PHTO together with SrTiO 3 as a pure  45 , which suggests a weaker crystal field effect in PHTO. Figure 3b shows the Pb-L 3 XAS spectra of PHTO together with PbTiO 3 as a Pb 2+ and PbNiO 3 as Pb 4+ reference. The weak pre-edge feature in PbNiO 3 due to excitation from a 2p core electron to the 6s orbital. It has been established that this weak pre-edge feature is a sensitive finger-print of the Pb valence state in solid state materials 46 . The reason is that the Pb 5d 10 orbitals are fully occupied, the valence state is then reflected by the 6s occupation. However, as shown in the inset, PHTO has the Pb-L 3 XAS profile similar to the Pb 2+ reference PbTiO 3 in detail, no 2p-6s related excitation is observed in PHTO, which indicates the valence state of Pb 2+ with fully occupied 6s 2 state in this compound. Figure 3c shows the Hg-L 3 XAS spectra of PHTO as well as HgO. Magnetic and transport characterizations. The magnetic susceptibility χ is almost constant and negative near zero from 300 K to 30 K, while χ increases rapidly on further decrease of temperature as shown in Supplementary Fig. S3. These results revealed that PHTO is nonmagnetic due to the 3d 0 , 5d 10 and 6s 2 electron configuration for Ti 4+ , Hg 2+ and Pb 2+ , respectively, and consistent with the BVS calculations and XAS results. The resistance of PHTO at room temperature is too large to be measured, indicating the high electrical insulating property and few vacancies in the sample. Supplementary Fig. S4a shows the Ultraviolet-Visible-Near Infrared (UV-Vis-NIR) absorption spectrum of PHTO. The curve exhibits a steep decrease from 420 to 640 nm, which is a typical optical response of semiconductors. The optical band gap of the PHTO was estimated to be 2.12 eV. The first principles calculations show that PHTO is a direct gap insulator with 1.70 eV gap at the H point shown in Supplementary Fig. S4b. The gap might be underestimated in DFT calculations, nevertheless, it reveals the wide gap nature of PHTO. The obtained PHTO sample is stable at ambient up to 973 K as revealed by thermogravimetry analysis measurements shown in Supplementary Fig. S5.
Dielectricity and ferroelectricity. The permittivity and dielectric loss measured with different frequencies from 2 K to 300 K are shown in Fig. 4a, b, respectively. The relative dielectric constant, ε r of PHTO is over 220 in the measured temperature range. The temperature dependence of ε r shows a clear peak around 250 K at all the frequencies of measurements. The overall temperaturedependent ε r strongly indicates a low-temperature ferroelectric phase transition to a high-temperature paraelectric phase at T FE ≈ 250 K. Furthermore, the transition temperature is independent of measurement frequency, indicating that PHTO is not a relaxor-type ferroelectric material. The relative increase of the dielectric loss around 250 K is consistent with the paraelectricferroelectric transition. Moreover the dielectric loss keeps at a very low value (<0.03) with all of frequency in the whole measurement range, which indicate the intrinsic dielectric property of PHTO. In order to further identify the ferroelectricity of PHTO, the isothermal polarizations were measured by the PUND method 20 . No loops of polarization versus electric field (P-E) were observed in polycrystalline PHTO at room temperature. However, canonical P-E hysteresis loops were observed below 250 K as shown in Fig. 4c, d. It is clear that polarization is enhanced at low temperature. At fixed temperature, the P-E loops significantly expand with increasing electric field. For example, the P value increases from 0.028 to 0.11 µC cm −2 as the maximum electric field changes from 17 to 32 kV cm −1 at 10 K. As known, PbTiO 3 is a classic and extensively studied ferroelectric material with Curie temperature about 763 K, which excludes the possibility that the ferroelectricity of PHTO originated from PbTiO 3 . Thus it can be concluded that the ferroelectricity is due to PHTO.
Temperature dependent crystal structure transition. To further understand the mechanism of ferroelectricity from the structure point of view, we performed the temperature dependent SXRD, as shown in Supplementary Fig. S6. The characteristic (400) diffraction peak at different temperatures is collected in Fig. 5a. It is obvious that the diffraction peaks split into two sub-peaks between 240 K and 260 K, which indicates the occurrence of temperature induced phase transition at 250 K is due to symmetry reduction from a cubic -to -orthorhombic phase. Checking the SXRD data measured at 300 K and 90 K, all the high symmetry diffraction peaks, such as (200), (220), (222), (400) and (402) of the high temperature phase, are split into two sub-peaks on cooling to low temperature (see Supplementary Fig. S7). There is a clear long-range structural transition with decreasing temperature. The SXRD data collected at 90 K is presented in Fig. 5b. The crystal structure of PHTO can be fitted very well by an orthorhombic phase of noncentrosymmetric space group Imm2 (No.44). The inset shows the crystal structure of the low temperature phase. The Rietveld refinement results are listed in Supplementary Table S2. Figure 5c shows variation of the lattice parameters based on refinements of SXRD data. The lattice parameter a decrease lineally from 300 K to 250 K. Below the temperature of the phase transition, the lattice parameter b and c continue to decrease while parameter a increases. Figure 5d shows the evolution of TiO 6 octahedron before and after phase transition. In the high temperature phase, TiO 6 Supplementary Fig. S8 illustrates the evolution of HgO 8 during the paraelectricferroelectric transition. Therefore, PHTO is a displacive-type ferroelectric. The ionic spontaneous polarization can be calculated by multiplying the effective charges and the distance between the negative and positive valence weighted mean center along the c-axis then divided by the volume of the unit cell 47 . Based on the refined results of NPD data collected at 5 K in Table 3, the calculated polarization value is about 13.65 μC cm −2 . Although temperature-dependent phase transition is typical in A-site-ordered perovskites, it is usually isostructural or centrosymmetric -to -centrosymmetric phase transition    Table 3 Refined structure parameters of PHTO based on NPD data collected at 5 K. First principles calculations. In order to get a deeper insight into the ferroelectricity of PHTO at low temperature, first principles calculations have been performed. Supplementary Fig. S9 shows the phonon spectrum for the cubic structure of PHTO: three imaginary frequency modes with irreducible representation T u degenerate at Γ point. By moving atoms along these soft phonon modes, the noncentrosymmetric crystal structure with space group Imm2 can be obtained. Free energy per primitive cell versus moving amplitude of atoms along one of the soft modes is plotted in Fig. 6. The energy well suggests a spontaneous structure phase transition with the biggest contribution coming from the Ti-O mode. The imaginary modes at H point only consist of the Ti-O phonon modes, which are consist with the experimental conclusion. In addition, the 6s 2 lone pair electrons of Pb 2+ also contribute to the site instability according to the theory analysis. However, the contribution from the lone pair mechanism does not play a dominant role from the energy perspective (see Fig. 6). Using Berry phase method, the polarization of ferroelectric structure and Born effective charge have been calculated. The calculated polarization value is about 16.87 μC cm −2 , which can also be obtained by multiplying the Born effective charge tensor with the corresponding atom displacements. This result is roughly in agreement with that ionic spontaneous polarization calculation result of 13.65 μC cm −2 based on neutron diffraction measurements. Both values are larger than the experimental result. This is because the calculated value is based on single crystal data, while the experimental measured value is from a polycrystalline sample of randomly distributed grains. For example, in ceramic samples of BiFeO 3 , much lower values of about 8.9 μC cm −2 of polarization have been measured at room temperature while in single crystals the polarization is up to 60 μC cm −2 along [012] axis and 100 μC cm −2 along [001] axis 48,49 . Another reason for the low experimental value of polarization may be due to the grain boundary effect and/or leaking current issue preventing the application of maximum electric field in the experiment 48,50 . Supplementary Fig. S10 shows the SEM image of the polycrystalline sample of PHTO. It can be seen that the grain size distributes around several microns to nearly 20 microns and generates a large amount of grain boundaries. Those grains are disorderly distributed, which will severely affect the polarization.
The A-site-ordered perovskite PbHg 3 Ti 4 O 12 was synthesized at high pressure and high temperature. PbHg 3 Ti 4 O 12 is a nonmagnetic insulator with a direct energy gap of~2.12 eV and relative dielectric constant larger than 220. PbHg 3 Ti 4 O 12 undergoes a transition from a high temperature centrosymmetric, cubic and paraelectric phase to a low temperature non-centrosymmetric, orthorhombic and ferroelectric phase with a record high Curie temperature at 250 K for an A-site-ordered quadruple perovskite. The ferroelectric distortion is dominated by Ti-O phonon mode anomaly. Because of the large average size of the A-site cation~1.1 Å in PHTO, the coordination of Hg 2+ is not square planar as in typical A-site-ordered quadruple perovskites, but closer to 8. Therefore PHTO can be considered to be structurally linking ABO 3 simple and AA′ 3 B 4 O 12 quadruple perovskites. The established A-site-ordered perovskites AHg 3 B 4 O 12 may provide a potential pathway to find a class of ferroelectric materials of high Curie temperature. The work provides one of unique examples that high pressure synthesis can lead to the compounds with unique properties that are otherwise hard to get access at ambient. Moreover perovskites are the most abundant minerals in the broad lower Mantle of the Earth where high pressure is prevailing. Hence it might shed lights to further understand the coordination chemistry of perovskites like compounds at high pressures.

Methods
Sample fabrication. The polycrystalline sample of PHTO was synthesized by a solid state reaction under high pressure of 6 GPa and high temperature of 1273 K. The starting materials HgO (Aldrich, 99.0% pure), PbO (Alfa, 99.995% pure) and TiO 2 (Alfa, 99.995% pure) were mixed homogenously in a molar ratio 1:3:4 and pressed into a pellet with diameter of 6 mm in an argon gas protected glove box with oxygen and H 2 O level of less than 1 ppm. The pre-pressed pellet was sealed in a gold capsule. High pressure experiments were performed with the cubic anvil type high pressure apparatus 51,52 . After the pressure was gradually increased to 6 GPa, the sample was heated to 1273 K and maintained for 30 min. Then the temperature was quenched to ambient before the release of pressure. In this process, yellow polycrystalline PHTO was obtained.
Structure characterization. The crystal structure was characterized by neutron powder diffraction (NPD) with the BT-1 high-resolution neutron powder diffractometer with a Ge (311) monochromator at the Center for Neutron Research (NCNR) of the National Institute of Standard & Technology (NIST). The neutron wavelength was 2.0774 Å. The intensities were measured with steps of 0.05°in the 2θ range of 10°-160°. The sample was also measured by synchrotron x-ray diffraction (SXRD) at the 11-BM-B at the Advanced Photon Source (APS) in Argonne National Laboratory. The X-ray wavelength was 0.412726 Å. Diffraction data were collected in the angle (2θ) range from 0.5°to 50°with steps of 0.002°. The obtained NPD and SXRD data were analyzed by the Rietveld method with the GSAS program 53 .
Valences determination. The valence states of the Ti, Pb and Hg ions were determined by x-ray absorption spectroscopy (XAS). The soft XAS at the Ti-L 2,3 edge was measured with total the electron yield mode at the Dragon beamline while the hard XAS at the Pb-L 3 and Hg-L 3 edge were measured with transmission geometry at the BL07A beamline at National Synchrotron Radiation Research Center (NSRRC) of Taiwan. SrTiO 3 , PbTiO 3 , PbNiO 3 and HgO were also measured at the respective Ti-L, Pb-L and Hg-L edges as reference materials.
Permittivity and ferroelectricity characterization. The permittivity was measured with different frequency by an Agilent-4980A LCR meter on a solid pellet with 4.0 mm in diameter and 230 μm in thickness. The ferroelectric hysteresis loops were measured at 20 Hz with a Radiant Precision Premier-II Ferroelectric Test System at different temperatures based on the proposed positive-up negative-down (PUND) method. Detailed experimental descriptions can be found in Ref. 20 .

Data availability
The data that support the findings of this study are available from the corresponding authors upon reasonable request.