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Polar Order and Frustrated Antiferromagnetism in Perovskite Pb2MnWO6 Single Crystals Sergey A. Ivanov,†,‡ Alexander A. Bush,§ Adam I. Stash,† Konstantin E. Kamentsev,§ Valerii Ya. Shkuratov,§ Yaroslav O. Kvashnin,∥ Carmine Autieri,∥ Igor Di Marco,∥ Biplab Sanyal,∥ Olle Eriksson,∥ Per Nordblad,‡ and Roland Mathieu*,‡ †

Center of Materials Science, Karpov Institute of Physical Chemistry, Vorontsovo pole 10, 105064 Moscow, K-64, Russia Department of Engineering Sciences, Uppsala University, Box 534, SE-751 21 Uppsala, Sweden § Moscow State Institution of Radio Engineering, Electronics and Automation, RU-119434 Moscow, Russia ∥ Department of Physics and Astronomy, Uppsala University, Box 516, SE-751 20 Uppsala, Sweden ‡

S Supporting Information *

ABSTRACT: Single crystals of the multiferroic double-perovskite Pb2MnWO6 have been synthesized and their structural, thermal, magnetic and dielectric properties studied in detail. Pure perovskite-phase formation and stoichiometric chemical composition of the as-grown crystals are confirmed by X-ray single-crystal and powder diffraction techniques as well as energy-dispersive X-ray and inductively coupled plasma mass spectrometry. Detailed structural analyses reveal that the crystals experience a structural phase transition from the cubic space group (s.g.) Fm3̅m to an orthorhombic structure in s.g. Pn21a at about 460 K. Dielectric data suggest that a ferrielectric phase transition takes place at that same temperature, in contrast to earlier results on polycrystalline samples, which reported a transition to s.g. Pnma and an antiferroelectric low-temperature phase. Magnetic susceptibility measurements indicate that a frustrated antiferromagnetic phase emerges below 8 K. Density functional theory based calculations confirm that the cationic order between Mn and W is favorable. The lowest total energy was found for an antiferromagnetically ordered state. However, analyses of the calculated exchange parameters revealed strongly competing antiferromagnetic interactions. The large distance between the magnetic atoms, together with magnetic frustration, is shown to be the main reason for the low value of the ordering temperature observed experimentally. We discuss the structure−property relationships in Pb2MnWO6 and compare these observations to reported results on related Pb2BWO6 perovskites with different B cations.

1. INTRODUCTION In recent years, research on materials showing multiferroicity has increased dramatically, and new complex metal oxides with intrinsic spin and dipole coupling have been discovered.1−8 Multiferroic (MF) materials have intriguing fundamental physical properties4−6 and offer an exciting platform for novel technological applications.3,8 A number of design strategies toward the creation of new MF materials have been suggested.9 Magnetism requires d electrons, while these electrons also have a tendency to maintain center of symmetry and eliminate spontaneous polarization.3−5 Therefore, ABO3 perovskite oxides containing cations with lone electron pairs (such as Pb2+ or Bi3+) have attracted much attention because such cations increase the chances of violating the centrosymmetric tendency. A promising way to obtain materials with both spin and dipole ordering is the synthesis of double perovskites combining the presence of stereochemically active cations on the A sites and magnetic cations on the B sites. A double perovskite is described by the formula A2B′B″O6 in order to emphasize the long-range ordering of the B sites following a rock-salt pattern.10−15 Large differences between the cations on © XXXX American Chemical Society

the B′ and B″ sites, in either the oxidation state or size, favor such ordering. Several double perovskites composed of two cations with partially filled d shells are ferro- or ferrimagnets.15 In addition, the presence of Pb2+ on the A site promotes the appearance of polar structures. This is due to the 6s2 lone pairs and the strong covalent character of the Pb−O bonds, which stabilize a noncentrosymmetric-distorted environment.15 The coexistence of (anti)ferromagnetism and (anti)ferroelectricity thus occurs in some Pb-based complex metal oxides.7,10−12,16,17 The structural and dielectric properties of Pb2MnWO6 (PMWO) ceramics were first reported in the mid-1960s,18−21 during which it was established that this compound has a monoclinically distorted perovskite-type structure in which Mn2+ and W6+ regularly occupy octahedral positions. However, the symmetry of the room temperature phase remains controversial because different authors have reported contradicting crystal structures.21−28 Dielectric measurements indicate that PMWO undergoes a first-order phase transition from a Received: November 12, 2015

A

DOI: 10.1021/acs.inorgchem.5b02577 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Figure 1. Photographs of single crystals of PMWO formed around the wall of the crucible. corundum crucible at 900 °C in a stream of argon gas. The growth experiments were carried out in a muffle furnace equipped with an automatic temperature controller. The melts, after being held at 900 °C for 1 h, were cooled for 4 h to 700 °C and then to room temperature in the switched-off oven. The crystallized products consisted of an intergrowth of crystals, from which it was possible to isolate perfect ruby-colored octahedral single crystals of fully faceted and well-developed morphology with dimensions of up to 1 mm diameter. On the walls of the crucible, it was also possible to observe the formation of faceted crystals (cf. Figure 1). The main form of crystal growth is represented by {111} faces (using the pseudocubic axes of the basic perovskite cell). The grown crystals were harvested and then boiled in 30% acetic acid for several hours. Some of the crystals were ground into fine powders for powder XRD measurements. A typical ruby-colored PMWO single crystal (1 × 1 × 0.5 mm3) was used for inductively coupled plasma mass spectrometry (ICP-MS) analysis in order to detect the local cation composition. Analyses were performed on 10 different points on the crystal surface. It was found that the average composition of the crystal is very close to the nominal stoichiometric composition. For light-red crystals, the concentration of the B-site ions exhibits some fluctuation, varying by up to 1% around the nominal composition. Such a composition fluctuation is supposed to result from an unequal occupation of the B site by the competitive cations (Mn and W) during crystal growth. This seems to be a common phenomenon in crystals with multiple-site occupancy grown from a multicomponent system.29 2.2. Single-Crystal XRD. A suitable red plate-shaped single crystal of PMWO (0.085 × 0.055 × 0.014 mm) was selected for XRD analysis. No signs of twinning were observed. Integrated intensity data were collected on an Enraf-Nonius CAD-4 diffractometer with Mo Kα (λ = 0.71073 A; β filter) radiation using the ω−2θ scan mode at room temperature. The scan speed and time for each reflection were varied so as to obtain σI/I = 0.01. The unit cell was determined from a leastsquares fit to positions of 25 high-2θ reflections. The ranges of hkl values measured are −16 < h < 18, −12 < k < 12, and −8 < l < 9, giving a total number of measured reflections of 6468. Three standard reflections were measured every 60 min during data collection. The importance of weak reflections in resolving the centrosymmetric− noncentrosymmetric ambiguity was considered. Out of the measured 2633 independent reflections, there were 1072 for which Iobs > 2σ(I) and that could be used for refinement. Four standard reflections were measured; the variation in Iobs was around 1%. Each reflection was centered at eight different equivalent positions. The intensities were corrected for Lorentz−polarization effects and subsequently for absorption using the ABSORB program.30 The structures were solved by direct methods and refined on F2 with full-

high-temperature cubic paraelectric phase to a low-temperature antiferroelectric (AFE) phase at 425 K.18,19 In ref 25, it was inferred that the room temperature structure of PMWO is orthorhombic with the Pnma space group (s.g.). An additional structural investigation26 established that two orthorhombic structures with different s.g.’s (centrosymmetric Pnma and noncentrosymmetric Pn21a) fitted the powder X-ray diffraction (XRD) data with similar R values for both structural models. On the basis of analyses of some additional physical properties, it was finally claimed that it was most suitable to assign room temperature PMWO the centrosymmetric s.g. Pnma. Although historically there has been dispute on the superstructure of the PMWO crystal and the assignment of the s.g., all recent reports are consistent on orthorhombic unit cell parameters, which are related to the cubic perovskite primitive unit cell parameter ac, with a = 2√2ac, b = 2ac, and c = √2ac. Recent XRD and neutron diffraction data of ceramics and microcrystals of PMWO confirm orthorhombic distortions at room temperature but assign them to the noncentrosymmetric s.g. Pmc21.27,28 There are some differences in the reported values of Tc for PMWO,18−28 which vary in the range 425−450 K, but it is clear that this transition is coupled to a structural phase transformation from a high-temperature cubic to a low-temperature orthorhombic structure. Most of the previous results on the structure and properties of PMWO have been derived from studies of ceramic polycrystalline samples. Here we report a comprehensive study of PMWO single crystals using a variety of complementary techniques including high-resolution single-crystal and powder XRD, electron microscopy, and dielectric, magnetic, heat capacity, and nonlinear-optical (NLO) measurements. It is found that the room temperature structure is noncentrosymmetric Pn21a with a spontaneous ferrielectric moment. The system is paramagnetic at room temperature; however, a frustrated antiferromagnetic (AFM) order is established below 8 K.

2. EXPERIMENTAL PROCEDURES 2.1. Crystal Growth and Sample Preparation. Crystal growth was carried out by crystallization of the melt upon cooling in an argon atmosphere. As initial reagents, PbO, Mn2O3, and WO3 oxides were used. A homogenized mixture of 4PbO·Mn2O3·2WO3 was melted in a B


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Inorganic Chemistry

2.7. Electrophysical Measurements. Platelets of various thicknesses were cut from the PMWO ingots. These were finely polished with diamond paste and then covered with silver paste. The dielectric constant and loss tangent at different frequencies (ranging from 100 Hz to 1 MHz) were derived from an Agilent 4284A impedance analyzer. To determine Tc, capacitance measurements were made as a function of the temperature in an automated temperaturecontrolled furnace interfaced with a computer for data acquisition. Dielectric hysteresis loops of the samples were measured in the Sawyer−Tower mode at an electric-field frequency of 50 Hz. The temperature dependence of the pyroelectric current was measured on a plate with dimensions 1 × 4 × 8 mm, which was prepared from aggregates of several PMWO crystals. 2.8. Specific Heat Measurements. Specific heat measurements were performed using a relaxation method between 3 and 60 K on a PPMS6000 system from Quantum Design Inc. Heat capacity data in the temperature range 295−600 K were obtained by differential scanning calorimetry (DSC) using a DSC Q-20 from TA-Instruments with samples sealed in aluminum pans under a nitrogen atmosphere. The scanning rate was 10 K min−1. 2.9. X-ray Photoelectron Spectroscopy (XPS). XPS measurements were acquired with a UK Kratos Axis Ultra spectrometer with an Al Kα X-ray source operated at 15 kV and 15 mA. 2.10. Computational Details. First-principles density functional theory (DFT) calculations were performed using the VASP37 package based on a plane-wave basis set and a projector-augmented wave method.38 A plane-wave energy cutoff was set to 450 eV. The Perdew−Burke−Ernzerhof39 exchange-correlation functional, based on the generalized gradient approximation (GGA), was used. The effects of strong correlations were treated on a static mean-field level by employing the GGA+U approach.40 For 3d states of Mn, we have chosen U = 6.0 eV and J = 0.9 eV. The k-point grid of 4 × 6 × 8 was taken to produce all of the results. The calculations for the intersite exchange parameters (Jij’s) were done within a full-potential realization of the linear muffin-tin orbital method (FP-LMTO), as implemented in the “RSPt” program code.41 The Jij parameters were calculated by means of the magnetic force theorem.42 The parameters were extracted for the Heisenberg Hamiltonian of the shape Ĥ = −∑i ≠ j Jij ei⃗ · ej⃗ where ei⃗ is the unit vector pointing along the direction of the spin moment at the Mni site. Further details of the implementation can be found in ref 43. Having the Jij’s at hand, the critical temperatures were estimated using a mean-field model.44,45

matrix least-squares methods using the SHELXS-97 and SHELXL-97 programs, respectively.31 Scattering factors and anomalous dispersion terms for Pb, Mn, W, and O were taken from ref 32. The Pb, Mn, and W atoms were first located, and the O atoms were found subsequently in the difference Fourier maps. 2.3. Powder XRD. The phase formation and impurity levels of the crystals were examined using powder XRD. The patterns were obtained with a D-5000 diffractometer using Cu Kα radiation. Crystals of PMWO were crushed into powder in an agate mortar and suspended in ethanol. A Si single-crystal substrate was covered with several drops of the resulting suspension, leaving randomly oriented crystallites after drying. The powder XRD data for Rietveld analyses were collected at room temperature on a Bruker D8 Advance diffractometer (Ge-monochromatized Cu Kα1 radiation, Bragg− Brentano geometry, DIFFRACTplus software) in the 2θ range 10− 152° with a step size of 0.02° (the counting time was 15 s/step). The slit system was selected to ensure that the X-ray beam was completely within the sample for all 2θ angles. The high-temperature XRD studies were conducted on a Philips X’Pert Pro instrument [2θ = 10−140°; step 0.02°; Anton Paar HTK2000 heating stage at 295−550 K under vacuum (total pressure was 5 × 10−7 atm)]. The equilibration time was around 1 h. The experimental powder XRD patterns were analyzed with the Rietveld profile method using the FULLPROF program.33 The diffraction peaks were described by a pseudo-Voigt profile function, with a Lorentzian contribution to the Gaussian peak shape. A peak asymmetry correction was made for angles below 35° (2θ). Background intensities were estimated by interpolating between up to 40 selected points (temperature-dependent powder XRD experimental data) or described by a polynomial with six coefficients. During the refinements, the metal-site occupations of Pb, Mn, and W cations were allowed to vary. The IVTON software34 was employed to characterize the coordination spheres of the A- and B-site cations and to obtain bond lengths, volumes of the coordination polyhedra, and displacements of cations from the centers of the coordination polyhedra. Several structural models were tried in the refinement. Each structural model was refined to convergence, with the best result selected on the basis of the agreement factors and stability of the refinement. 2.4. Chemical Composition. The chemical composition of PMWO single crystals was analyzed by energy-dispersive spectroscopy (EDS) using a JEOL 840A scanning electron microscope and INCA 4.07 (Oxford Instruments) software. The EDS conditions were 20 kV accelerating voltage and 14.7 mm working distance. The analyses performed on several particles showed that the concentration ratios of Pb, Mn, and W are stoichiometric, and no compositional inhomogeneity was detected in the tested crystals within the limits of experimental uncertainty. EDS analyses of selected regions of the samples showed the presence of all cations with a constant ratio between all of them, which indicates that the crystals are uniform in composition. An independent determination of the concentration of Pb, Mn, and W cations in the PMWO crystals was made by the ICPMS method (IY ULTRACE 238 spectrometer). 2.5. Second Harmonic Generation (SHG) Measurements. SHG measurements were performed in reflection geometry, using a pulsed Nd:YAG laser (λ = 1.064 μm). The room temperature SHG signal I2ω was measured from the polycrystalline samples relative to an α-quartz standard in the Q-switching mode with a repetition rate of 4 Hz. The SHG efficiency has been shown to strongly depend on the particle size;35,36 to make relevant comparisons, the α-quartz standard was therefore sieved into the same particle size range as that of the PMWO microcrystalline powders. In order to classify a material as centrosymmetric using the absence of SHG, a sensitivity of I2ω/ I2ω(quartz) < 0.01 is necessary. 2.6. Magnetic Measurements. The magnetization measurements were performed on an MPMSXL SQUID magnetometer from Quantum Design Inc. The temperature dependence of the magnetization was recorded as a function of the temperature in magnetic fields of H = 50 Oe and 5 kOe using zero-field-cooled (ZFC) and field-cooled (FC) protocols.

3. RESULTS 3.1. Single Crystals. The PMWO single crystals grew in the form of ruby-colored oriented intergrown aggregates in the shape of cubes of 0.5−1 mm edge length (see Figure 1). These aggregates disintegrated into many small crystal fragments after treatment in HNO3. Examined under an optical microscope in reflected light, these crystal fragments show a very smooth surface free from fissures. The growth morphology of PMWO was related to the cooling rate of the growth solution. A high cooling rate favors the presence of (111) faces, whereas the crystals show quasicubic (100) growth at a lower cooling rate. According to EDS analyses done on 20 different crystallites of each sample, the metal compositions are close to the nominal values. They correspond to the following formula: Pb1.993(6)Mn0.997(6)W1.010(6)O6. No peaks representing impurities could be resolved. Scanning electron micrographs showed a uniform distribution of grains of average size between 1.2 and 1.5 μm. The oxygen content, determined with iodometric titration, was between 5.96(4) and 6.02(4) for the different samples. Differential thermal analysis (DTA) measurements also revealed that the PMWO crystals are near oxygen stoichiometric; however, a tendency toward minor anion C


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Inorganic Chemistry

Figure 2. Temperature dependence of (top panels) the dielectric permittivity ε and (bottom panels) the tangent of dielectric loss tan δ of PMWO, measured at frequencies of 2 (1), 10 (2), 50 (3), 100 (4), and 200 (5) kHz. The inset shows an enlarged view of ε(T) near the transition at 460 K and tan δ near the 138 K anomaly.

Figure 3. Dielectric hysteresis loop of PMWO at room temperature, recorded using Sawyer−Tower ’s scheme (U = voltage on the reference condensator C0 = 1 μF; S = area of the electrodes on the PMWO sample): (a) polarization and (b) current density through the sample during an electric-field cycling of increasing amplitude.

Figure 4. Temperature dependence of the thermally stimulated current in the sample upon heating. Left panel: (1) after cooling from room temperature without an applied electric field; (2) after cooling under an applied voltage of 300 V. Right panel: (3) after cooling from 500 to 295 K under a poling voltage of 10 V. Sample thickness = 1.15 mm.

within the frame of the reproducibility error and comparable to other possible experimental uncertainties. A sharp peak observed in the DTA curve at 854 °C corresponds to the

deficiency was observed for crystals with light-red color (the measured values of nonstoichiometry vary in the range 0.002− 0.005). These deviations from stoichiometry are, however, D


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Inorganic Chemistry melting of this perovskite phase. The Mn ions were confirmed by X-ray fluorescence analysis to be divalent. 3.2. Electrophysical Studies. Figure 2 shows the temperature variation of the dielectric permittivity (ε) and tangent of the dielectric loss (tan δ) of a single crystal of PMWO at various frequencies upon heating; the left panel shows the behavior below and the right panel that above room temperature. A sharp knee in the permittivity occurs at 458 K, indicating that a long-range electrical dipole order is established below this temperature. The inset in the upper right panel shows that this feature is reproduced under cyclic measurements upon heating and cooling of the sample, with a thermal hysteresis of 4 K, indicating that the transition is of first order.46 The temperature of this anomaly does not depend on the frequency of the measuring field, so we can conclude that it is related to the orthorhombic-to-cubic phase transition in the PMWO crystal near 450 K.25,26 As seen in the left panels of Figure 2, two additional frequency-independent anomalies, at 138 and 185 K, are observed in the temperature dependences of ε(T) and tan δ(T). Figure 3 shows the results from room temperature dielectric hysteresis measurements on the same single crystal; the left panel shows polarization versus electric field loops and the right panel the current density through the sample on the same electric-field cycling protocol. As seen in the figures, the dielectric hysteresis loops of the crystal are affected by the nonlinear conductivity σ(E) of the material, so that the expected ferrielectric response of the material is masked in the observed hysteresis loops.27 Figure 4 shows the thermally stimulated current in a PMWO crystal, at temperatures below (left panel) and above (right panel) room temperature. The measurement labeled 1 was carried out upon heating of a PMWO crystal that had been cooled to 100 K in zero electric field. There is a broad peak in the current centered at about 175 K [cf. the 185 K anomaly detected in the ε(T) curves]; a corresponding anomaly is described in ref 27. When the current through the sample is measured after cooling to 100 K in an electric voltage of 300 V, a peak occurs already at 137 K, i.e., in the vicinity of the second anomaly in the ε(T) curves. The left panel of Figure 4 shows the thermally stimulated current measured upon heating of a sample that has been prepolarized by application of a voltage of 10 V at 295 K. A pronounced peak is seen at 457 K, i.e., at the temperature onset of dipole order. The increased conductivity does not allow (from disruption of the crystals at high voltages) derivation of the polarization of the samples from the pyroelectric current data. 3.3. DSC Studies. Figure 5 shows a DSC curve (heating scan), where a pronounced endothermic peak related to the phase transition is seen at about 455 K. This temperature agrees with the one obtained from powder XRD and dielectric measurements. Upon heating and cooling scans at a speed of 10 K min−1, a shift of the position of the anomaly of around 8 K was recorded. The observed phase-transition temperature is higher than the phase-transition temperature reported in the literature for ceramic samples.25 This difference is possibly due to the difference of the processing method adopted by us compared to the method used in earlier studies. We have adopted single-crystal growth to synthesize PMWO instead of ceramic technology as used in earlier work.18−28 Further, formation of the secondary PbWO4 phase often occurs when the samples are prepared by ceramic technology, and this may

Figure 5. DSC heat flow recorded at high temperatures upon heating.

introduce some deviation from the stoichiometry of the PMWO material and could cause a shift of Tc. 3.4. Magnetic Properties. The temperature dependence of the low-field magnetization of the crystals is shown in the top panel of Figure 6. The magnetization curves suggest an

Figure 6. Top panel: Temperature dependence of the low-field ZFC and FC magnetization (H = 50 Oe) and heat capacity C (plotted as C/ T) for single crystals. Lower panel: Temperature dependence of the FC magnetization recorded in a higher magnetic field (H = 5 kOe). Inset: associated Curie−Weiss analysis.

AFM transition at 8 K (using the maximum slope of the (M/H) T versus T curve to determine the Néel temperature). The occurrence of this transition is confirmed by the heat capacity data also plotted in the upper frame of Figure 6 and evidenced by the sharp peak in C/T versus T at 8 K. A weak irreversibility is observed below ∼45 K in the magnetization curves. It has earlier been suggested that the PMWO system shows an onset of ferrimagnetism in the vicinity of that temperature.28 However, there is no anomaly in the heat capacity data in that temperature range. Also, if the magnetization is measured in larger magnetic fields, as shown in the lower panel of Figure 6, only the AFM transition at 8 K is observed. Hence, the irreversibility observed in smaller fields E


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Inorganic Chemistry

distortion is found to be orthorhombic and the systematic absence of reflections constrains the possible s.g.’s of PMWO to Pnma or Pn21a. The XRD pattern of Figure 7b can be readily indexed with an orthorhombic cell with a = 11.6336(4) Å, b = 8.0227(5) Å, and c = 5.7819(5) Å. The orthorhombic lattice parameters are, as already mentioned, related to lattice parameter ac of the basic cubic perovskite structure via the relationsships a = 2√2ac, b = 2ac, and c = √2ac. Thermal evolution of the cell parameters of PMWO has been investigated between 295 and 550 K. Temperature evolution of the powder XRD patterns confirms the presence of a first-order phase transition Pn2 Ia → Fm3̅ m around 460 K. An orthorhombic unit cell can be derived from the doubleperovskite Fm3̅m using the lattice vectors (1, 0, −1), (0, 1, 0), and (1/2, 0, 1/2). The orthorhombic distortion of the unit cell decreases with increasing temperature and around 460 K transforms into a cubic cell. Figure 8 shows the derived

might instead be related to minute amounts of Mn3O4 impurities in the sample contributing a weak ferromagnetic moment below 45 K.47 While the magnetic signal is dominated by the AFM response of the material at high fields, the ferrimagnetic response of Mn3O4 is uncovered in low magnetic fields and may mistakenly be attributed to ferrimagnetism or canted antiferromagnetism of the main phase.48 Above 10 K, the high-field susceptibility (M/H) data closely follow Curie−Weiss behavior. The linear fit of the H/M versus T data yields a Curie−Weiss temperature θCW of −26 K, i.e., more than three times TN, suggesting an AFM interaction and significant magnetic frustration. The associated effective Bohr magneton number peff amounts to 6.2, in agreement with that expected for Mn2+ cations in the high-spin configuration (3d5, S = 5/2, L = 0, peff = 5.92). 3.5. Powder XRD. The powder XRD patterns of PMWO measured at 500 and 295 K are shown in parts a and b of Figure 7, respectively. They exhibit typical perovskite characteristics. In

Figure 8. Temperature dependence of the lattice parameters and associated cell volume.

temperature dependence of the lattice parameters and the cell volume. The strong variation of the cell parameters at the transition is notable: the b axis abruptly enlarges, while the a and c parameters are strongly contracted. The unit cell volume increases at the transition with about 2 Å3, and the volume of the orthorhombic phase is bigger than the corresponding cubic one. Moreover, temperature evolution of the unit cell volume is different for the two phases. The volume of the orthorhombic phase increases as the temperature decreases, whereas the cubic phase shows a normal expansion with increasing temperature. According to well-established phenomenological theory and experimental studies of paraelectric-to-AFE phase transitions,49−51 the unit cell volume should decrease upon cooling below the transition temperature Tc. For PMWO, however, the transition behavior around the transition is opposite to the phenomenology and theoretical prediction. In fact, the observed transition in PMWO rather mimics a paraelectricto-ferrielectric transition behavior. Structural refinement of the powder XRD pattern at 500 K was performed in s.g. Fm3̅m with Pb atoms located at the 8c position, Mn at 4a, W at 4b, and O at 24e. An excellent fit was obtained for this model, as shown in Figure 7a. In the final refinement, the possibility of antisite disorder was checked by assuming that some Mn atoms could occupy W sites, and vice versa. Refinement of the inversion degree led to less than 1% of antisite disorder. Refinement of the oxygen occupancy revealed

Figure 7. Observed, calculated, and difference XRD Rietveld profiles for PMWO collected at (a) 500 K and (b) 295 K.

addition, several types of superstructure reflections can be seen in the room temperature pattern of Figure 7b. The presence of superlattice reflections suggests that the prototypic crystal structure is an ordered perovskite with an effective unit cell elongated in size in all crystallographic axis directions of a cubic perovskite cell. PMWO has a pronounced long-range order in the B sublattice that arises from Mn2+ and W6+ cations. As is evidenced from the split in the fundamental lines, the lattice F


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Inorganic Chemistry Table 1. Summary of the Results of the Structural Refinements Using Single-Crystal and Powder XRD Data crystal experiment

powder experiment

295 K

295 K

295 K

500 K

a [Å] b [Å] c [Å] V [Å]3 s.g.

11.640(2) 8.0198(16) 5.7809(12) 539.65(19) Pn21a

11.6336(4) 8.0227(5) 5.7819(5) 539.6(1) Pn21a

8.1358(6)

x y z Uiso,a Bb [Å2]

0.6462(2) 0.1206(5) 0.7182(6) 0.0180(4)

11.640(2) 8.0198(16) 5.7809(12) 539.65(19) Pnma Pb1 0.3559(3) 0.4937(7) 0.7133(8) 0.0274(3) Pb2

0.6444(8) 0.1213(7) 0.7198(8) 1.85(5)


0.64206(19) 0.6342(3) 0.7088(5) 0.0156(4)


0.6192(3) 0.3730(15) 0.240(2) 0.0044(3)


0.61775(7) 0.8827(8) 0.2485(7) 0.00568(14)


0.731(1) 0.872(1) 0.533(1) 0.011(5)

crystal experiment 295 K

538.5(1) Fm3m ̅


0.751(1) 0.893(1) 0.047(1) 0.011(5)

0.25 0.25 0.25 1.93(6)


0.515(1) 0.896(1) 0.010(1) 0.006(5)


0.633(1) 0.655(1) 0.270(1) 0.021(9)

0.6417(7) 0.6361(9) 0.7096(8) 1.51(4) Mn 0.6196(4) 0.2500 0.7565(11) 0.0094(5) W 0.3823(4) 0.2500 0.2474(5) 0.0089(4) O1 0.2485(9) 0.2500 0.0468(8) 0.016(3)

0.6175(5) 0.3718(6) 0.2413(5) 0.48(4)

0.5 0.5 0.5 0.53(4)


0.639(1) 1.124(1) 0.278(1) 0.023(8)

0.6186(6) 0.8818(5) 0.2493(6) 0.29(5)

0 0 0 0.32(8)

0.504(1) 0.859(1) 0.481(1) 0.014(6)

0.7305(7) 0.8728(8) 0.5338(8) 1.05(5)

0.2421(8) 0 0 1.32(8)

x y z Uiso,a Bb [Å2] Rp [%] Rwp [%] RB [%] χ2 a

2.31 1.06

powder experiment

295 K

295 K

O2 0.3653(7) 0.0148(9) 0.2793(7) 0.021(2) O3 0.2685(8) 0.2500 0.5320(9) 0.014(3) O4 0.4941(9) 0.2500 0.4822(8) 0.024(5) O5 0.4867(7) 0.2500 0.0139(9) 0.020(4) O6

500 K

0.7498(7) 0.8943(8) 0.0446(7) 1.26(4) 0.5157(8) 0.8939(9) 0.0112(9) 0.89(4) 0.6313(9) 0.6531(7) 0.2692(8) 1.06(5) 0.6371(8) 1.1213(7) 0.2769(9) 0.94(5) 0.5062(8) 0.8578(7) 0.4821(8) 0.86(5) 3.61 5.06 2.24 2.23

2.89 1.14

4.33 5.38 2.43 2.09

Single-crystal XRD data. bPowder XRD data.

crystals should be contained in the “probability distribution” of the observed intensities. For example, the ratio ρ may indicate the presence (=0.637) or absence (=0.785) of a center of symmetry.56 The ρ value calculated for PMWO is 0.531. Another effect can be detected in particular projections of the s.g.’s Pnma and Pn21a. The presence of the mirror plane should be expected to increase the average intensity of the h0l reflections. Therefore, it is interesting to estimate the ratio Sh0l = ⟨I⟩h0l/⟨ I⟩hkl. The experimental ratio of Sh0l is close to 1, which indicates the absence of the mirror element.57 From statistical tests on the distribution of the structure factor |E| (following refs 31 and 57), |EE−1| = 0.690 (expected 0.968 for centrosymmetric and 0.736 for noncentrosymmetric) clearly indicates the absence of an inversion center, thus suggesting the s.g. to be Pn21a. During refinement, the atoms related by the “pseudo” center of symmetry were not simultaneously varied, in order to avoid the problem of high correlation between coefficients. In the Pn21a structure, both the A- and B-sublattice atoms are slightly displaced, thus lifting the center of inversion. In order to check the reliability of the model, the site occupancy of the cation positions was allowed to vary. During initial refinements, the occupancies of Pb, Mn, and W cations converged respectively to 0.99(1), 0.99(1), and 1.00(1). Henceforth, the occupancies of both the A- and B-site atoms were fixed to unity. It is worth noting that the acentric structural model obtained here does not show high values in the correlation matrix between pairs of ions that are equivalent

no deficiency within the standard deviation. The most important structural parameters of the crystallographic structure at both 295 and 500 K and the discrepancy factors after refinement are listed in Table 1. The main interatomic distances are included in Table 3. The very large isotropic temperature factor for Pb atoms is noticeable. The structural disorder of Pb is a common feature of most Pb-based complex perovskites,52−54 where the Pb2+ cation is not found on the special Wyckoff position but statistically split over several neighboring sites. Three types of displacements for the Pb atoms, along the [100], [110], and [111] directions, leading to 6, 12, and 4 local disorder positions, respectively, were analyzed. For the Pb atoms, the differences between these types of displacements are quite small, and there was a strong correlation between the thermal parameters and positional disorder. During our refinements, the [110] model has shown the deepest minimum in the R factor versus the Pb-atom position. 3.6. Single-Crystal XRD and Noncentrosymmetricity. The collected intensity data verified that the Laue symmetry of each crystal is mm2 and the systematic absences are no conditions on hkl, k = 2n on 0kl, h + l = 2n on hk0, and no conditions on h0l. The observed reflection conditions allowed two possible s.g.’s, Pnma (No. 62) and Pn21a (No. 33; standard set Pna21).55 We assumed that the s.g. was Pn21a, which is further justified below. Independent important information about the probable presence or absence of a center of symmetry in PMWO G


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Inorganic Chemistry

Figure 9. Polyhedral representation of the crystal structure of PMWO used in the calculations, drawn using VESTA.69 The Mn atoms are shown with magenta spheres, W atoms are green, Pb atoms are black, and O atoms are red.

Table 2. Anisotropic Displacement Parameters (Å2) for Cations in the PMWO Structure atom

U11

U22

U33

U23

U13

U12

Pb1 Pb2 Mn W

0.0171(7) 0.0146(6) 0.0042(6) 0.0055(2)

0.0200(7) 0.0190(7) 0.0037(9) 0.0049(3)

0.0170(9) 0.0132(9) 0.0061(9) 0.0066(3)

−0.0018(8) −0.0011(7) −0.001(3) 0.0017(1)

0.0011(7) 0.0049(7) −0.0003(9) 0.0003(2)

0.0021(10) 0.0009(9) 0.0017(16) 0.0001(8)

to the centrosymmetric s.g. Pnma. The observed value of the Flack parameter (see ref 58), which often is used to indicate noncentrosymmetric structures, was obtained as 0.113(62), indicating that the acentric model is the correct choice. The refinements were made using models for both Pnma and Pn21a for comparison. It should be noted that the difference in the atomic coordinates between centrosymmetric and noncentrosymmetric PMWO models is relatively small and the refinements converged with very close R factors (0.022 and 0.028, respectively). The results of the structural refinements for PMWO are given in Table 1, which includes atomic coordinates and temperature factors. Difference Fourier syntheses calculated after the final refinements showed minimum and maximum values of −1.4 and +1.3 e Å−3, respectively. Our results from dielectric and SHG experiments also support the noncentrosymmetric structure. If the PMWO crystals belong to s.g. Pn21a at room temperature, they should show a pyroeffect. Several of our tests on different crystals were positive, which suggests that the crystals are noncentrosymmetric. This result is consistent with the results reported in ref 27. SHG on crystalline powders gives useful information on the NLO properties of crystals and makes possible the detection of small deviations from centrosymmetry.58,59 At room temperature, the SHG efficiency of PMWO was found to be at least one-third of the magnitude of an α-quartz standard [I2ω/ I2ω(quartz) ∼ 0.3−0.4 at 295 K; noise signal ∼ 0.1]. The registered SHG response may also reflect some degree of acentric nature of the crystals. Because PMWO is colored (ruby), the lower SHG value could be associated with optical absorption. Crystals with moderate absorption coefficients at

the second harmonic can be examined for noncentrosymmetry with approximately an order of magnitude decrease in sensitivity.35,36,59,60

4. DISCUSSION The PMWO structure can be viewed (see Figure 9) as a regular arrangement of ordered corner-sharing MnO6 and WO6 octahedra, alternating along the three directions of the crystal with the voluminous Pb cations occupying the voids between the octahedra. The Mn and W atoms occupy the octahedral sites in the B-perovskite sublattice in an ordered fashion. All atoms are located at general positions, and the refined structural parameters (coordinates and temperature factors) are summarized in Tables 1 and 2. The room temperature PMWO structure is characterized by the relative cation shifts and octahedral tilts and distortions from its prototype hightemperature Fm3̅m cubic structure. In that cubic phase above Tc , Pb cations are 12-fold coordinated by O anions. Considering the Pb−O polyhedron, the theoretical distance, 2.87 Å,61 agrees nicely with the experimental value reported in Table 3. However, as the temperature is lowered to room temperature, the displacements of certain ions give rise to a highly asymmetric Pb−O bond arrangement (see Table 3) with four bonds considerably shortened; the Pb1 and Pb2 cations are found at the apex of a pyramid. When the Pb displacements from their original cubic positions (see Table 4) are examined, it is illuminating to divide the displacements into the corresponding shifts along the main crystallographic directions. These shifts are listed in Table 5. Several important pieces of information may be extracted from this table. First, the major shifts of Pb1 are in the plane perpendicular to the polar axis; H


Article

Inorganic Chemistry

Table 5. Atomic Displacements Related with Fm3m ̅ → Pna21 Phase Transition in PMWOa

Table 3. Selected Bond Lengths (Å) of PMWO Pb1−O1 Pb1−O5 Pb1−O4 Pb1−O2 Pb1−O6 Pb1−O2 Pb1−O3 Pb1−O6 Pb1−O1 Pb1−O5 Pb1−O4 Pb1−O3 Pb2−O1 Pb2−O2 Pb2−O4 Pb2−O5 Pb2−O6 Pb2−O6 Pb2−O3 Pb2−O3 Pb2−O2 Pb2−O1 Pb2−O4 Pb2−O5 Mn−O5 Mn−O1 Mn−O3 Mn−O6 Mn−O4 Mn−O2 W−O3 W−O4 W−O6 W−O2 W−O5 W−O1

295 K

500 K

2.475(1) 2.544(1) 2.602(6) 2.680(7) 2.835(1) 2.900(4) 2.904(4) 3.004(3) 3.064(4) 3.240(3) 3.259(4) 3.294(3) 2.396(6) 2.483(7) 2.544(6) 2.581(6) 2.751(6) 2.992(5) 3.102(4) 3.105(6) 3.120(4) 3.180(5) 3.251(4) 3.269(6) 2.023(1) 2.115(7) 2.136(8) 2.161(7) 2.274(8) 2.336(7) 1.828(6) 1.839(6) 1.896(7) 1.942(6) 1.958(7) 2.110(6)

2.878(1) × 12

atomic displacements

x (Å)

Pb1 Pb2 Mn W

12 12 6 6

0.068 0.124 0.126 0.063

ξ (Å)

uy

uz

|u|

0.021 0.017 −0.006 −0.007 −0.015 0.005 0.011 −0.008 −0.014 0.000

0.032 0.041 0.010 0.002 0.041 −0.039 0.002 −0.020 0.028 0.011

0.010 −0.003 0.008 −0.002 0.009 −0.013 −0.015 −0.016 −0.001 0.022

0.316 0.309 0.109 0.085 0.298 0.251 0.174 0.195 0.226 0.188

times smaller than that of Pb1. Second, the values of the polyhedral volume of Pb1 and Pb2 are very similar; for instance, the average Pb1−O and Pb2−O distances are almost identical: 2.901 and 2.898 Å, respectively. The cation displacement from the polyhedron center is more pronounced for Pb2 than Pb1, yielding a more distorted anion environment. The observed Pb−O bond ranges reflect a high degree of covalency of this asymmetric bonding. As for the B-site cations, both Mn2+ and W6+ exhibit main shifts in the plane perpendicular to the polar axis, as well as uncompensated antiparallel shifts along the polar axis. These displacements are small, almost within the size of the experimental errors; thus, this result has to be viewed with some caution. The Mn−O and W−O bond lengths in the paraelectric phase (2.115 and 1.953 Å) are in reasonable agreement with the values derived from tabulated ionic radii,61 which are 2.21 Å for Mn2+−O (Mn2+ in the high-spin state) and 1.98 Å for W6+−O. However, at room temperature, the deviation from this expected bond length shows a significant increase, and a set of longer and shorter bonds have been formed. Pb-cation displacements and B-type octahedral tilting play a significant role in the formation of a specific type of pseudosymmetric PMWO structure. Pb polyhedron deformation and octahedral tilting are probably strongly related to the noncentrosymmetric nature of the Pb−O bonding. The driving forces for the phase transition in PMWO at 460 K may be related with the tendency of the lone electron pairs to localize into lobes in a ferrodistortive manner and the tendency of MnO6 and WO6 octahedra with different sizes to tilt in a cooperative manner (driven by a tolerance factor of less than 1). During this phase transition, the coordination number of the Pb2+ cations is reduced from 12 to 8 because of octahedral tilting. It is interesting to note that Pb shifts seems to appear because of interaction with its lone pair or with the O anions that are linked to the lone pair. At the same time, the Mn and W sublattices are also displaced, making a smaller contribution to the total electric polarization. A central consequence of our structure determination of PMWO is the s.g. assignment Pn21a. There has been much argument on whether the true s.g. is centrosymmetric or noncentrosymmetric. Upon acceptance of a noncentrosymmetric structure, there is still a discrepancy between our current assignment and s.g. Pmc2I recently reported in ref 27, an assignment that was based on a limited number of reflections registered from a microcrystal inside a powder PMWO sample.

2.115(1) × 6

1.953(1) × 6

T = 295 K, s.g. Pn21a cn

ux

Pb1 Pb2 Mn W O1 O2 O3 O4 O5 O6

a ux, uy, and uz are given in relative units, and |u| is the absolute distance given in angstroms.

Table 4. Polyhedral Analysis of PMWO at Different Temperaturesa cation

atom

ω

valence

0.067 0.068 0.013 0.008

1.87 2.04 2.16 6.06

V (Å3)

2.901 ± 0. 283 56.86 (1) 2.898 ± 0.324 56.95 (1) 2.174 ± 0.114 13.39(1) 1.928 ± 0.103 9.40(1) T = 500 K, s.g. Fm3m ̅

cation

cn

x (Å)

ξ (Å)

V (Å3)

ω

Pb Mn W

12 6 6

0.0 0 0.0

2.878 2.115 1.953

56.04 (1) 12.62(1) 9.93(1)

0.073 0.0 0.0

cn = coordination number, x = shift from the centroid, ξ = average bond length, V = polyhedral volume, and ω = polyhedral volume distortion.

a

these displacements are much greater than the shifts along the polar axis. However, this difference does diminish as the temperature increases, and the sites gradually move to their high-temperature high-symmetry positions. The main shifts of Pb2 are similar, but the displacement along the polar axis is 3 I


Article

Inorganic Chemistry If the true s.g. of PMWO at room temperature is Pn21a, then the cations should be shifted along the polar axis. Our refinement of the cation positions in s.g. Pn21a indicated such shifts. Furthermore, if the real s.g. is Pn21a, then there are two independent Pb positions, which are replaced by one when the structure is refined in Pnma. The averaging of the positional parameters then leads not only to large errors but also to large displacement parameters. In our refinements of the PMWO diffraction patterns using Pnma, the accuracy of the cation positions was quite low, and the thermal parameters were clearly larger compared to those obtained using s.g. Pn21a. The bond valence sums62,63 are in good agreement with the expected bond valences calculated from the composition of Pb2+2Mn2+W6+O6 (see Table 4). Also, the XPS results confirm that W is in the W6+ state and that Mn is in the Mn2+ state, as was also suggested by Curie−Weiss analysis of the magnetic susceptibility. The uncommon structural properties of PMWO are likely to appear because of the 6s2 lone electron pair of the Pb2+ cation, which induces an additional distortion of the lattice and gives rise to polar characteristics due to the off-center atomic displacements. The role of lone pairs in structural chemistry is well-known, and the geometry of the coordination polyhedra including lone pairs has been intensively discussed.64−68 Lone pairs may be considered as pseudoligands that can occupy a volume corresponding to the volume commonly required by an O atom. The unit cell contains four formula units and is depicted in Figure 9. We have compared the total energies for a set of structures considering all possible ways of distributing Mn and W atoms in the cell. According to our results, the lowest energy of the system is reached for the modulated structure, where each Mn-centered octahedron is surrounded by W-centered octahedra. In this way, the cationic order is stabilized in PMWO. After identification of the cationic order, we have investigated the magnetic ground state within a given Pn21a crystal structure. The differences in the total energies of various magnetic configurations were found to be very small, indicating the weakness of the magnetic interactions in the system. The lowest energy was obtained for an “↑↓↓↑” AFM state, where the arrows denote the directions of the spin moments of each Mni (i ∈ [1, 4]) cation. The values of the calculated magnetic moments per Mn were found to be 4.55 μB, which is rather close to the value 5 μB, expected from a simple ionic picture. In order to assess the stability of the obtained ground state, we computed the effective Jij parameters. The calculated Jij values as a function of the intersite distance are shown in Figure 10a. As seen in the figure, the magnetic interactions between the Mn atoms in PMWO are quite small. This is because the Mn atoms are second-nearest neighbors (NNs) with respect to each other in the B sublattice. All couplings are AFM, with the largest Mn−Mn interaction reaching the value of −0.78 meV. This is in agreement with the Kanamori rules applied to the first and second neighbors, where the rule states that the d5−d5 magnetic interaction is always AFM. The primary reason for the smallness of Jij in PMWO is the fact that Mn ions do not share any bonds with the same O atoms (see Figure 9). As a result, the superexchange paths are relatively long compared with, for example, MnO. The results shown in Figure 10a indicate that the Jij parameters in PMWO are short-ranged, being negligible after the second coordination shell (corresponding to distances around dij = 0.707; see Figure 10). Thus, it is of primary importance to discuss the NN interactions in this system. For

Figure 10. (a) Calculated exchange parameters in PMWO as a function of the intersite distance. The latter one is in the units of the a lattice parameter determined experimentally. The NNs are located around dij = 0.5. (b) PMWO lattice with the NN exchange interactions. The color of each bond denotes to the strength of the corresponding exchange interaction, listed on the left-hand side of the graph. In the obtained lowest-energy state, four Mn spin moments are aligned as ↑↓↓↑.

this purpose, we show the graph with all NN Mn−Mn couplings in Figure 10b. An inspection of the figure reveals that Mn ions form a distorted face-centered-cubic lattice. It is well-known that for the AFM sign of NN interactions such a lattice is frustrated, so that all bonds cannot be satisfied at the same time. However, as one can see from Figure 10b, there are six independent Jij values for the various pairs of Mn cations. This is a consequence of the lattice distortions, which makes all of the bonds inequivalent. Depending on the bond, the magnitudes of the NN exchange interactions are spread in the range between −0.78 and −0.20 meV. Because of such large differences in the Jij values, the competition between AFM interactions is effectively reduced, so that some interactions dominate over others. In this case, the three weakest interactions (−0.37, −0.36, and −0.20 meV) are left unsatisfied. For instance, the NN Mn1−Mn4 interactions were found to be the weakest ones, and therefore they are left unsatisfied within the obtained “↑↓↓↑” state. Thus, our results provide a clear picture of the nature of the lattice distortions in PMWO and the role they play in stabilization of the AFM order. In PMWO, the lattice distortions give rise to anisotropy in the Jij values. As a result, the continuous degeneracy of the ground state is lifted. However, the system still has two sources of frustration, which most probably lead to the emergence of a noncollinear magnetic configuration. The first is the presence of triangles of Mn cations, where all of the spins are aligned in the collinear ground state (see Figure 10b). A second source of J


Article

Inorganic Chemistry frustration comes from the second neighbors that are also antiferromagnetically coupled, with the values of the secondneighbor couplings being comparable to those of the firstneighbor couplings. Hence, the presence of the spin spiral structure reported in ref 28 for this compound is possible. The ferromagnetic couplings found in ref 28 may correspond to the weakest couplings (black and blue bonds in our Figure 10b). The spins with black and blue couplings are antiferromagnetically coupled but are effectively ferromagnetically aligned in the frustrated magnetic ground state. The exchange parameters shown in Figure 10a were used to calculate the critical temperature of the “↑↓↓↑” state. Our MFbased estimates provide the value of the ordering temperature of 23 K. This is quite a small value, meaning that the stability of the state is subtle. Typically, for the employed MF approximation, the estimated critical temperature is larger than the experimental one, here experimentally determined to be 8 K. We also investigated the electronic properties of the AFM phase of PMWO. The calculated polarization, related to the displacement of Pb cations, is 8.7 μC/cm2 per formula unit along the b direction. The occurrence of phase transition between Pn21a and Fm3̅m has been theoretically considered in ref 70. The symmetry-breaking static distortions underlying displacive phase transition can be understood as distortion modes acting on a cubic prototype structure. The static frozen distortions present in the distorted orthorhombic structure can be described by collective atomic displacements. Displacive modes responsible for the symmetry reduction owing to the observed phase transition Fm3m ̅ → Pn21a were examined using a crystallographic mode-based analysis and representation theory utilizing the AMPLIMODES program to analyze the transition pathways.71,72 The only input data provided for the analysis were the crystal structures of the distorted and parent structures in their conventional settings and the unit cell transformation that relates the two. On the first stage, a standard setting of the orthorhombic PMWO structure (s.g. 33) was obtained using the transformation Pn21a → Pna21 (abc → ac-b). The program identifies pairs of atoms that correspond to each other in both structures and calculates the atomic displacements. In order to obtain results independent of the lattice strain, it is advisible to adapt the reference structures to the unit cell parameters of the distorted structures. The amplitudes of the modes active across the transition are summarized in Table 6 and correspond to the atomic movements in the mode exemplified in Figure 11.

Figure 11. Representation of the main distortion modes (SM2, SM4, and X5−) considered during symmetry analysis, which was drawn using VESTA.69

Symmetry analysis reveals that the Pna21 distortion mainly can be decomposed into eight different modes corresponding to several different symmetry points. The global distortion amplitude is 0.72 Å. After the unit cell origin is shifted along the polar axis in order to eliminate global translation of the polar phase (the center of inertia may be shifted because of the arbitrary choice of the origin along the polar axis), one can then distinguish primarily and secondarily induced distortions, which will have, in general, quite different weights in the structure. Considering the relative amplitude of the irreducible representations (IRs), one can see that three distortion amplitudes are much higher: SM2, X5−, and SM4 (see Table 6), indicating that these symmetry components of global distortion are the primary ones. The rest of the identified modes are secondary ones allowed by symmetry and play a marginal role in phase stabilization. A schematic diagram representing the relationship between the subgroups connecting the Pn21a and Fm3̅m s.g.’s is displayed in Figure 12. It can be seen that a single IR distortion component is not sufficient to explain the full symmetry break of the transformation from the cubic phase to the orthorhombic

Table 6. Summary of Mode Decomposition of the PMWO Structure (in the Standard Pna21 Setting), Indicating the Amplitude (Å) of All Intervening IR Distortion Components at 295 K (Amplitudes Normalized with Respect to the Primitive Unit Cell of the High-Symmetry Structure) K vector

IR

isotropy subgroup

dimension

amplitude (Å)

(0, 0, 0) (0, 0, 0) (0, 0, 0) (0, 0, 0) (1/2, 1/2, 0) (1/2, 1/2, 0) (0, 1, 0) (0, 1, 0)

GM1+ GM3+ GM5+ GM4− SM2 SM4 X5+ X5−

Fm3m ̅ I4/mmm Immm I4mm Pnma Pccn Pnnm Pmmn

1 1 2 5 8 4 3 6

0.139 0.008 0.099 0.126 0.519 0.250 0.071 0.375 K


Article

Inorganic Chemistry

Other Pb-based A2B′B″O6 perovskites such as Pb2BWO6 (B = Cd2+, Mn2+, Cr2+, Fe2+, Co2+, Zn2+, Cu2+, Mg2+, or Ni2+)13,74−80 also show ferroic properties. For the MF design, it is important to understand the influence of the B-site cations on these properties. In Figure 13, literature values of the

Figure 12. Diagram showing the group−subgroup relationships connecting Fm3m ̅ and Pna21 s.g.’s.

Figure 13. (top panel) Variation of the dielectric transition temperature (ferrielectric Tc for B = Mn2+ and antiferroelectric TAFE for the other compounds) and (bottom panel) AFM transition temperatures (TN) as a function of the B-cation radius RB52 for different Pb2BWO6 perovskites. The line in the top panel is a guide for the eye.

phase. That is, the Pn21a phase cannot be generated by a singlemode distortion, and at least one set of different normal modes must be active; i.e., several order parameters must be involved. In contrast to the centrosymmetric Pnma model in which the Pb atoms exhibit antiparallel displacements, the Pn21a structure shows nonequivalent Pb displacements along the polar axis, which lead to spontaneous polarization in the crystal. Besides Pb2+ ions, there are additional antiparallel shifts of 2− O anions along the polar direction that also are unbalanced (see Table 5). This structural study revealed a possible ferrielectric character of the electric-dipole order for PMWO, where the cationic displacements are still antiparallel to each other as in an AFE crystal but the associated dipole moments do not cancel each other completely. This group of materials, which exhibit an unbalanced antidipole structure representing an incompletely compensated AFE material, is well-known among perovskites.73 In the family of perovskite compounds, a wide variety of distorted variants of the nonpolar cubic structure are observed as a function of the composition and temperature. The structural relationships of PbZrO3 and PMWO perovskites are similar (concerning, e.g., lattice symmetry and metrics). A detailed comparison of our results with data previously obtained for the model AFE PbZrO3 shows that the change of a single constituent Zr to a combination of Mn and W cations has profound effects on the dielectric responses of these compounds. The creation of a long-range order in the B sublattice in PMWO has a significant influence only on the most active dipolar interactions, leaving most of these interactions strikingly similar. It is evident that B−O interactions depend strongly on the B cation, being quite different in PbZrO3 and PMWO. On the other hand, the A−O interaction is similar owing to the covalent character of the bonding between Pb and O. The A sublattice is directly responsible for the polar instability in both compounds, but the delicate nature of the observed difference arises from the dipolar contribution of additional A−B, A−A, B−B, and O−O couplings, which are not the same for both compounds.

transition temperatures for dipole (ferrielectric Tc or antiferroelectric TAFE) and spin (AFM TN) orders are plotted versus the ionic size of the B cation on the B′ sites. A roughly linear dependence of the (anti)ferroelectric transition temperature on the size of B2+ is observed. The increase of Tc/TAFE with increasing size of the B cation may be related to a facilitated displacement of the Pb ions in a larger unit cell. It should be emphasized that only a few of the compounds order antiferromagnetically.12,77,79,80 While the compounds with B = Fe2+ and Co2+ order at temperatures similar to that of PMWO (TN ∼ 8−9 K), the compounds with B = Cr2+ and Ni2+ were reported to order at higher temperatures, 33 and 56 K. Concerning the B″ sublattice, exchanging, e.g., W for the smaller Re cation, Pb2MnWO6−Pb2MnReO6, increases TN from 8 to 100 K and lowers Tc from 460 to 410 K.81−83 The ferroic properties are also strongly dependent on the cation ordering on B′−B″ sites.84 There is little experimental data on how Tc/TAFE and TN are influenced by exchange of Pb on the A sublattice. The existence of any kind of dipole ordering has yet to be confirmed experimentally in Cd-, Ca-, Sr-, and Ba-based compounds.48,85,86

5. CONCLUSIONS Single crystals of PMWO, which belong to the family of double perovskites with an ordered arrangement of Mn2+ and W6+ cations, have been successfully grown directly from the mixture of starting chemicals by a gradually accelerated slow-cooling technique from a high-temperature solution in sealed Al2O3 crucibles. Room temperature X-ray structural analysis of single crystals and Rietveld analysis of the powder XRD data reveal that the L


Article

Inorganic Chemistry structure of PMWO is ortorhombic in the Pn21a s.g. EDS and ICP-MS studies confirmed nominal values for the cation concentrations with quite low experimental uncertainty. This compound undergoes a structural phase transition at Tc (460 K), which is coupled to a sharp knee in the dielectric permittivity. DSC measurements revealed an anomaly around Tc, and thermal hysteresis of the transition confirmed its firstorder character. Below Tc, PMWO is orthorhombic and ferrielectric, and above Tc , it is cubic and paraelectric. The magnetic susceptibility of PMWO follows Curie−Weiss law in a broad temperature range above 10 K. The measured effective paramagnetic moment indicates the presence of high-spin Mn 2+ ions. The Mn moments are found to order antiferromagnetically below 8 K, in the presence of significant magnetic frustration. DFT-based calculations confirm the presence of a low-temperature magnetic ordering and competing AFM exchange interactions between Mn magnetic moments. PMWO undergoes a structural phase transition from the orthorhombic ferrielectric phase with symmetry Pn21a to the cubic paraelectric phase with symmetry Fm3m ̅ . As a result of the phase transition, the average Pb−O interatomic distance decreases significantly (by almost 30%); at the same time, the average Mn−O and W−O interatomic distances change remarkably less. This character of the structural changes is related to the fact that formation of the ferrielectric state in PMWO is mainly due to the displacements of the Pb cations from centrosymmetric positions; these displacements disappear in the paraelectric cubic phase. The dielectric properties of PMWO are determined by the strong competition between ferroelectric and AFE ordering. Our results suggest that PMWO single crystals are ferrielectric rather than AFE at room temperature, owing to the polarization of two nonequivalent sublattices with unbalanced antidipole structure. The polar structure of PMWO may be described as a combination of several order parameters that correspond to antiparallel shifts of Pb ions accompanied by oxygen octahedral tilts. There are two sets of experimental data obtained earlier on the PMWO perovskite: one with a centrosymmetric crystal structure (powder sample25) and one with a noncentrosymmetric crystal structure (powder/micro single crystal27). Using our single crystals, we have confirmed that the PMWO structure is without a center of symmetry but in a different s.g. than that reported in ref 27. The crystals have high quality and perfect stoichiometry, and we are confident that we are investigating and reporting the intrinsic structural and physical properties of PMWO. Diffraction data include a relatively large number of reflections, and its refinement unequivocally yields a Pn21a s.g. In contrast to earlier reports, we show that there is only one intrinsic magnetic phase transition, the AFM transition at 8 K, and that the observed excess moment appearing at 44 K necessarily is related to impurities (Mn3O4). Last, our experimental study is supported by DFT calculations considering cationic and magnetic order.

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CIF file for the crystal structure PMWO reported in the manuscript (CIF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Author Contributions

Experimental results were obtained by S.A.I., A.A.B., A.I.S., K.E.K., V.Ya.S., P.N., and R.M. Theoretical results were contributed by Y.O.K., C.A., I.D., B.S., and O.E. All authors have contributed to the discussion and writing of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support from the Swedish Research Council (VR), the Swedish Foundation for International Cooperation in Research and Higher Education (STINT), and the Russian Foundation for Basic Research is gratefully acknowledged. Thanks also go to S. Yu. Stefanovich for his kind help and technical assistance during SHG measurements and to N. Sadovskaya for general service related with EDS analysis. The authors are grateful for the very helpful discussions with M. I. Aroyo and J. M. Perez-Mato concerning AMPLIMODES software. C.A. and B.S. acknowledge financial support from Carl Tryggers Stiftelse (Grants CTS 12:419 and 13:413). Computational resources provided by Swedish National Infrastructure for Computing are acknowledged. Bengt Gö tesson is thanked for his expert help with crystal photographs.

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