Magnetic and Electrical Characteristics of Nd3+-Doped Lead Molybdato-Tungstate Single Crystals

Single crystals of Pb1−3x▯xNd2x(MoO4)1−3x(WO4)3x (PNMWO) with scheelite-type structure, where ▯ denotes cationic vacancies, have been successfully grown by the Czochralski method in air and under 1 MPa. This paper presents the results of structural, optical, magnetic and electrical, as well as the broadband dielectric spectroscopy measurements of PNMWO single crystals. Research has shown that replacing diamagnetic Pb2+ ions with paramagnetic Nd3+ ones, with a content not exceeding 0.01 and possessing a screened 4f-shell, revealed a significant effect of orbital diamagnetism and Van Vleck’s paramagnetism, n-type electrical conductivity with an activation energy of 0.7 eV in the intrinsic area, a strong increase of the power factor above room temperature for a crystal with x = 0.005, constant dielectric value (~30) and loss tangent (~0.01) up to room temperature. The Fermi energy (~0.04 eV) and the Fermi temperature (~500 K) determined from the diffusion component of thermopower showed shallow donor levels.

Our magnetic, electrical, UV-vis diffusion reflection spectroscopy and the broadband dielectric spectroscopy studies of lead tungstate doped with Pr 3+ ions [20] and lead molybdato-tungstates doped with Pr 3+ [22] or Gd 3+ [23,24] ions, have generally shown that they are non-conductive paramagnets or superparamagnets. In particular, microcrystalline samples of Pb 1−3x 1 Pb1-3x xPr2xWO4 x Pr 2x (MoO 4 ) 1−3x (WO 4 ) 3x with 0 < x ≤ 0.2222, have the maximum value of E g = 3.22 eV for x = 0.2, which is even lower than of lead tungstates doped with Pr 3+ [22]. Interesting results were found for lead molybdato-tungstates doped with Gd 3+ ions, i.e., Pb 1−3x Pb1-3x xPr2xWO4 x Gd 2x (MoO 4 ) 1−3x (WO 4 ) 3x materials with x = 0.0455, 0.0839, 0.1154, 0.1430, 0.1667 and 0.1774 and x = 0.0455, 0.0839, 0.1430 synthesized via solid state reaction route [23] and via combustion one [24], respectively. For the ceramics obtained by the solid state reaction method, it was observed a paramagnetic state with characteristic superparamagnetic-like behavior, the faster and slower dipole relaxation processes up to x = 0.1154 and their complete absence above this value [23]. In the materials obtained by combustion route, paramagnetic state with characteristic superparamagnetic-like behavior and the absence of dipole relaxation processes were also observed. This is because the dipole relaxation disappears as the grain size decreases, resulting in a spatial polarization in which the electron or ionic freedom of charge is limited [24].
In the present work, we applied the Czochralski technique to grow scheelite-type Nd 3+doped lead molybdato-tungstate single crystals. The growth processes were carried out in air under 1 MPa, which significantly stopped the evaporation of volatile metal oxides. The purpose of our research was to investigate the structural, optical, magnetic and electrical properties of the as-grown single crystals. The novelty of this work is the study of poorly conductive materials that are strongly magnetically diluted. The studies mentioned above allow to determine the influence of magnetic contributions independent of temperature on magnetic parameters. In addition, the Fermi energy and temperature were estimated from the measurements of the diffusion component of the thermoelectric power.

Methods
Small pieces of the length less than 0.1 mm were cut off from both PNMWO single crystals. The most suitable parts for the single crystal X-ray measurement were chosen under the polarization microscope, and then mounted on a glass capillaries. SuperNova kappa diffractometer, equipped with Mo Kα X-ray tube and Atlas CCD detector (Agilent Technologies), was used for the X-ray diffraction measurements which were performed at 293 (1) K. CrysAlis Pro [25] program was used for collection of the data as well as for determination and refinement of the unit cell parameters from ca. 4000 reflections. Integrations of the collected data were also performed using CrysAlis Pro [25]. SHELXL-97 program [26] was used to refine both structures. The positions of O atoms as well as the anisotropic displacement parameters of all atoms were refined.
Ultraviolet and visible (UV-vis) diffuse reflectance spectroscopy was realized with a JASCO-V670 (Jasco International Co., Tokyo, Japan) spectrophotometer equipped with an integrating sphere. The spectra were recorded in the range from 200 to 1000 nm.
The static (DC) magnetic susceptibility was measured in the temperature range of 5-300 K and recorded both in zero-field-cooled (ZFC) and field-cooled (FC) mode. Magnetization isotherms were measured at 5, 10, 20, 40, 60, and 300 K using a Quantum Design MPMS-XL-7AC SQUID magnetometer (Quantum Design, San Diego, CA, USA) in applied external fields up to 70 kOe. The effective magnetic µeff moment was determined using the equation [27,28]: where k is the Boltzmann constant, NA is the Avogadro number, µB is the Bohr magneton, and C is the molar Curie constant. The effective number of Bohr magnetons peff was calculated from the equation: where p = g J(J + 1) [29] for a Nd 3+ ion (J = 9/2, L = 6, S = 3/2, g = 8/11, basic term 4 I9/2) with 4f 3 electronic configuration. Electrical conductivity σ(T) of the samples under study was measured by the DC method using a KEITHLEY 6517B Electrometer/High Resistance Meter (Keithley Instruments, LLC, Solon, OH, USA) and within the temperature range of 77-400 K. The thermoelectric power S(T), i.e., the Seebeck coefficient was measured within the temperature range of 100-400 K with the help of a Seebeck Effect Measurement System (MMR Technologies, Inc., San Jose, CA, USA). Dielectric measurements were carried out on PNMWO single crystals which were polished as well as sputtered with (∼80 nm) Ag electrodes. The

Methods
Small pieces of the length less than 0.1 mm were cut off from both PNMWO single crystals. The most suitable parts for the single crystal X-ray measurement were chosen under the polarization microscope, and then mounted on a glass capillaries. SuperNova kappa diffractometer, equipped with Mo Kα X-ray tube and Atlas CCD detector (Agilent Technologies), was used for the X-ray diffraction measurements which were performed at 293 (1) K. CrysAlis Pro [25] program was used for collection of the data as well as for determination and refinement of the unit cell parameters from ca. 4000 reflections. Integrations of the collected data were also performed using CrysAlis Pro [25]. SHELXL-97 program [26] was used to refine both structures. The positions of O atoms as well as the anisotropic displacement parameters of all atoms were refined.
Ultraviolet and visible (UV-vis) diffuse reflectance spectroscopy was realized with a JASCO-V670 (Jasco International Co., Tokyo, Japan) spectrophotometer equipped with an integrating sphere. The spectra were recorded in the range from 200 to 1000 nm.
The static (DC) magnetic susceptibility was measured in the temperature range of 5-300 K and recorded both in zero-field-cooled (ZFC) and field-cooled (FC) mode. Magnetization isotherms were measured at 5, 10, 20, 40, 60, and 300 K using a Quantum Design MPMS-XL-7AC SQUID magnetometer (Quantum Design, San Diego, CA, USA) in applied external fields up to 70 kOe. The effective magnetic µ eff moment was determined using the equation [27,28]: where k is the Boltzmann constant, N A is the Avogadro number, µ B is the Bohr magneton, and C is the molar Curie constant. The effective number of Bohr magnetons p eff was calculated from the equation: where p Nd = g J(J + 1) [29] for a Nd 3+ ion (J = 9/2, L = 6, S = 3/2, g = 8/11, basic term 4 I 9/2 ) with 4f 3 electronic configuration. Electrical conductivity σ(T) of the samples under study was measured by the DC method using a KEITHLEY 6517B Electrometer/High Resistance Meter (Keithley Instruments, LLC, Solon, OH, USA) and within the temperature range of 77-400 K. The thermo-electric power S(T), i.e., the Seebeck coefficient was measured within the temperature range of 100-400 K with the help of a Seebeck Effect Measurement System (MMR Technologies, Inc., San Jose, CA, USA). Dielectric measurements were carried out on PNMWO single crystals which were polished as well as sputtered with (~80 nm) Ag electrodes. The studies were carried out in the frequency range of 5 × 10 2 -2 × 10 6 Hz using a LCR HITESTER (HIOKI 3532-50, Nagano, Japan) and within the temperature range of 80-400 K.

Crystal Structure
The X-ray diffraction measurements revealed that both single crystals belong to tetragonal symmetry and crystallize with scheelite-type structure in I4 1 /a space group, analogously as divalent and scheelite-type molybdates and tungstates, i.e., PbMoO 4 and PbWO 4 [17]. The unit cell parameters of PNMWO crystal (x = 0.001) are as follows: a = b = 5.4380 (4) and c = 12.1111 (13) Å. The R-value is equal to 0.0149. In the case of PNMWO single crystal (x = 0.005) the lattice constants are as follows: a = b = 5.4357 (4) and c = 12.1067 (14) Å. The R-value is equal to 0.0164. The most important crystallographic data are collected in Tables S1-S8.

UV-Vis Diffuse Reflectance Spectra and Optical Band Gap
The optical properties of PNMWO single crystals along both crystallographic directions were investigated at room temperature using UV-vis diffuse reflectance spectroscopy method. The theory which makes possible to use diffuse reflectance spectra for solids was proposed by Kubelka and Munk [30]. According to this method, the reflectance spectra are converted into absorption ones using the following equation [30]: where F(R) is the Kubelka-Munk approach, R is the reflectance, α is the absorption coefficient, and S is the scattering factor which is wavelength independent. Optical band energy gap (E g ) is related to the absorbance and photon energy the equation proposed by Tauc and Wood [31,32]: where hν is the photon energy, A is an energy independent constant characteristic of a material, and n is a constant that can take different values depending on the nature of electronic transition. The permitted direct, forbidden direct, permitted indirect and forbidden indirect transitions take place when n = 1/2, 3/2, 2 and 3, respectively [31,32]. According to literature information, PbMoO 4 and PbWO 4 exhibit the optical spectrum governed by the indirect absorption process, i.e., for n = 2 [33,34]. In the high energy region of the absorption edge, (αhν) 1/2 varied linearly with photon energy. Thus, in the low energy region, the absorption spectrum deviated from a straight line plot. This straight line behavior in the high energy region was taken as prime evidence of an indirect optical band gap. The plots of (αhν) 1/2 vs. hν for PNMWO single crystals are depicted in Figure 2. study. In general, these contributions to susceptibility (χ) coming from the orbital (χdia) and Landau (χL) diamagnetism, Pauli (χP) and Van Vleck (χVV) paramagnetism as well as others, modify the Curie-Weiss law to the form [35]: where C is the Curie constant, θ is the Curie-Weiss temperature and χ0 represents all temperature independent susceptibilities. Multiplying Equation (5) on both sides by the temperature T, we obtain a linear relationship of the product χ⋅T as a function of temperature T in the Curie-Weiss region: where b = is the intercept that tends to the Curie constant C as the temperature T tends to infinity, i.e., lim → / = C, and χ0 is the slope. The dependencies of the product χZFC⋅T(T) from the measurement and the asymptotes determined from Equation (6) in the Curie-Weiss region are shown in Figure 3, and the parameters b and χ0 are shown in Table   1

Magnetic Properties
The results of magnetic measurements of PNMWO single crystals are presented in Table 1 and in  Due to the low content of paramagnetic neodymium ions, which did not exceed 0.01, it was necessary to estimate the temperature-independent magnetic contributions, as they affect the magnetic parameters of the single crystals under study. In general, these contributions to susceptibility (χ) coming from the orbital (χ dia ) and Landau (χ L ) diamagnetism, Pauli (χ P ) and Van Vleck (χ VV ) paramagnetism as well as others, modify the Curie-Weiss law to the form [35]: where C is the Curie constant, θ is the Curie-Weiss temperature and χ 0 represents all temperature independent susceptibilities. Multiplying Equation (5) on both sides by the temperature T, we obtain a linear relationship of the product χ·T as a function of temperature T in the Curie-Weiss region: where is the intercept that tends to the Curie constant C as the temperature T tends to infinity, i.e., lim T→∞ C 1−θ/T = C, and χ 0 is the slope. The dependencies of the product χ ZFC ·T(T) from the measurement and the asymptotes determined from Equation (6) in the Curie-Weiss region are shown in Figure 3, and the parameters b and χ 0 are shown in Table 1  contributions, as they affect the magnetic parameters of the studied single crystals. In gen-202 eral, these contributions to susceptibility () coming from the orbital (dia) and Landau (L) 203 diamagnetism, Pauli (P) and Van Vleck (VV) paramagnetism as well as others, modify the 204 Curie-Weiss law to the form [30]: 206 where C is the Curie constant,  is the Curie-Weiss temperature and 0 represents all tem-207 perature independent susceptibilities. Multiplying Equation (5) on both sides by the tem-208 perature T, we obtain a linear relationship of the product T as a function of temperature 209 T in the Curie-Weiss region: ZFCT(T) from the measurement and the asymptotes determined from Equation (6) in the 214 Curie-Weiss region are shown in Figure 3, and the parameters b and 0 are shown in Table 215 1.     tion may be related to the fact that at a state of thermal equilibrium structural defects (n) are always present in the lattice even in the crystal which is ideal in other respects. A necessary condition for free energy minimalization gives: n ≅ Nexp(−EV/kT) for n << N, where N is the number of atoms in the crystal, EV is the energy required to transfer the atom from the bulk of the crystal on its surface and k is the Boltzmann constant [40]. On the other hand, n-type electrical conductivity in the intrinsic region may be related to the presence of molybdenum ions at a lower oxidation state than 6 + , similar to magnetic studies, where electrons on the unfilled 4d subshell may be a reservoir of current carriers. The temperature dependence of thermoelectric power, S(T), presented in Figure 7, requires special consideration. In general, the thermopower in conventional metals consists of two different parts, i.e., a diffusion component (Sdiff), which according to the Mott formula [41] is proportional to temperature and a phonon resistance component (Sph), which is more complex. The Sph contribution results from a transfer of the phonon momentum to the electron gas. It drops both at low temperatures, such as T 3 below θD/10, when the phonons freeze out (where θD is the Debye temperature), and at high tempera-   (6) were used to correct the magnetic susceptibility measured in the ZFC and FC modes (Figure 4). This allowed for the correct determination of magnetic parameters such as the Curie constant (C), Curie-Weiss temperature (θ) and the effective magnetic moment (µ eff ). They are presented in Table 1. It can be seen from Figure 4 that after the χ 0 correction, both single crystals in both directions are paramagnets with a negative value of the paramagnetic Curie-Weiss temperature, θ (Table 1). This means that short-range magnetic interactions are antiferromagnetic (AFM) in nature. Table 1 shows that the values of the effective magnetic moment (µ eff ) are significantly higher than the effective number of Bohr magnetons (p eff ). This may mean that some of the molybdenum ions are in a lower oxidation state than 6 + , contributing to the total paramagnetic moment. This may explain the existence of short-range AFM interactions, which may result from the competition of interactions between paramagnetic neodymium ions and magnetic molybdenum ones.
Weak paramagnetism is also visible on the magnetization isotherms, M(H), displayed in Figure 5. They showed neither saturation magnetization at 5 K nor magnetic hysteresis for both crystallographic directions resulted in no remanence and coercive field and a transition from paramagnetic to diamagnetic state at 40 K for the single crystal with x = 0.001 and at 300 K for the single crystal with x = 0.005.

Electrical Studies
The results of the electrical conductivity measurements, σ(10 3 /T), of the PNMWO single crystals clearly showed two areas: extrinsic in the wide temperature range of 77-300 K, in which the weak thermal activation E a1~0 .007 eV is observed as well as intrinsic in the temperature range of 350-400 K with a stronger thermal activation of E a2~0 .7 eV (Table 2 and Figure 6). Despite stronger activation in the intrinsic area, the electrical conductivity value at 400 K is only 1.3 × 10 −3 S/m. We have low n-type electrical conductivity in the intrinsic area (Figures 6 and 7). This behavior correlates well with values of the energy gap in the range of 2.4-2.8 eV, which slightly depend on the content of Nd 3+ ions in the sample ( Table 2). For comparison, the values of E g~1 .7 eV found for both crystallographic directions of CdMoO 4 :Eu 3+ single crystal [36] are lower than for the single crystals under study, which results in greater electrical conductivity (σ~9.3 × 10 −3 S/m) due to the fact that the width of Eu 3+ -multiplet is comparable to the thermal energy kT. Two distinct areas of electrical conductivity with strong activation in the intrinsic region were also observed in ceramics such as: Cu 2 In 3 VO 9 [37], M 2 FeV 3 O 11 (M = Mg, Zn, Pb, Co, Ni) [38] and Cd 1−3x Gd 2x Pb1-3x xPr2xWO4 x MoO 4 [39]. The residual n-type electrical conductivity in the extrinsic region appears to be related to the anion surplus seen in the chemical formula. Another explanation may be related to the fact that at a state of thermal equilibrium structural defects (n) are always present in the lattice even in the crystal which is ideal in other respects. A necessary condition for free energy minimalization gives: n ∼ = Nexp(−E V /kT) for n << N, where N is the number of atoms in the crystal, E V is the energy required to transfer the atom from the bulk of the crystal on its surface and k is the Boltzmann constant [40]. On the other hand, n-type electrical conductivity in the intrinsic region may be related to the presence of molybdenum ions at a lower oxidation state than 6 + , similar to magnetic studies, where electrons on the unfilled 4d subshell may be a reservoir of current carriers. tures, such as T −1 above approximately θD/2, when the phonon's excess momentum is limited by anharmonic phonon-phonon scattering [42]. The Debye temperature θD [43] has been estimated from the following formula: where h is the Planck constant, N = 24 and V (taken from Tables S1-S8) are the number of ions and the volume of the scheelite unit cell, respectively, and vD = 2692 m/s is the sound speed in PbMoO4 matrix [44]. Debye temperature values θD = 326 K for both crystals and 327 K for the matrix taken from Ref. [44] for comparison. The S(T) minimum observed above 200 K in Figure 7 indicates a transfer of phonon momentum to electron gas. The diffusion contribution Sdiff is a direct application of the Boltzmann transport equation [41], as follows: where e is the elementary charge, EF is the Fermi energy and a is an empirical slope. From Equation (8), the Fermi energy, EF, can be written as follows: Our experimental dependence of Sdiff on temperature T is marked by solid lines in Figure 7. Equation (9) allows us to evaluate the Fermi energy EF and the Fermi temperature TF (defined as EF/k) using the experimental value of the slope of thermopower, a, for each single crystal. The values of EF and TF are summarized in Table 2. Compared to metals, e.g., for pure copper: EF = 7 eV and TF = 8.19 ×⋅10 4 K [40] and to non-metallic conductors, e.g., for Cu1-xGaxCr2Se4 single crystals: EF ∼0.3 eV and TF ∼3 ×⋅10 3 K [45], the values for materials under study are very small. This means that the Fermi level is near the border of the valence band and the shallow donor level is just below the conduction band. The source of the observed low n-type electrical conductivity, which is more thermally activated above room temperature, may be 4d electrons derived from molybdenum ions with an oxidation state lower than 6+.   Figure 8 shows an interesting dependence of the power factor S 2 σ on temperature T. The power factor has a very small value of several dozen fW/(cmK 2 ). However, its value significantly increases with increasing temperature, i.e., in the intrinsic region above 300 K for a sample richer in neodymium ions, regardless of the crystallographic direction. Similar behavior of S 2 σ(T) with only a few fW/(cmK 2 ) was observed in ceramic Gd 3+ and Co 2+ -co-doped calcium molybdato-tungstates [46] as well as in Nd 3+ and Mn 2+ -co-doped calcium molybdato-tungstates [47]. The above mentioned studies show that even in ionbonded materials containing a constant content of 3d transition metal ions, thermoelectric efficiency can be improved by doping them with 4f rare-earth ions.  Figure 9 presents temperature dependence of the relative dielectric permittivity, εr, for various electric field frequencies of PNMWO single crystals with x = 0.001 and 0.005, measured along [001] and [100] crystallographic directions. As can be seen, for each single crystal εr ∼30 remains independent of temperature and frequency up to 300 K and increases rapidly above this temperature as well as at the same time decreases with increasing frequency. In the thermally activated region, the accumulation of electric charge is significantly higher for the sample with x = 0.001 (max. εr ∼200) than for the sample with The temperature dependence of thermoelectric power, S(T), presented in Figure 7, requires special consideration. In general, the thermopower in conventional metals consists of two different parts, i.e., a diffusion component (S diff ), which according to the Mott formula [41] is proportional to temperature and a phonon resistance component (S ph ), which is more complex. The S ph contribution results from a transfer of the phonon momentum to the electron gas. It drops both at low temperatures, such as T 3 below θ D /10, when the phonons freeze out (where θ D is the Debye temperature), and at high temperatures, such as T −1 above approximately θ D /2, when the phonon's excess momentum is limited by anharmonic phonon-phonon scattering [42]. The Debye temperature θ D [43] has been estimated from the following formula:

Dielectric Properties
where h is the Planck constant, N = 24 and V (taken from Tables S1-S8) are the number of ions and the volume of the scheelite unit cell, respectively, and v D = 2692 m/s is the sound speed in PbMoO 4 matrix [44]. Debye temperature values θ D = 326 K for both crystals and 327 K for the matrix taken from Ref. [44] for comparison. The S(T) minimum observed above 200 K in Figure 7 indicates a transfer of phonon momentum to electron gas. The diffusion contribution S diff is a direct application of the Boltzmann transport equation [41], as follows: where e is the elementary charge, E F is the Fermi energy and a is an empirical slope. From Equation (8), the Fermi energy, E F , can be written as follows: Our experimental dependence of S diff on temperature T is marked by solid lines in Figure 7. Equation (9) allows us to evaluate the Fermi energy E F and the Fermi temperature T F (defined as E F /k) using the experimental value of the slope of thermopower, a, for each single crystal. The values of E F and T F are summarized in Table 2. Compared to metals, e.g., for pure copper: E F = 7 eV and T F = 8.19 × 10 4 K [40] and to non-metallic conductors, e.g., for Cu 1−x Ga x Cr 2 Se 4 single crystals: E F~0 .3 eV and T F~3 × 10 3 K [45], the values for materials under study are very small. This means that the Fermi level is near the border of the valence band and the shallow donor level is just below the conduction band. The source of the observed low n-type electrical conductivity, which is more thermally activated above room temperature, may be 4d electrons derived from molybdenum ions with an oxidation state lower than 6+. Figure 8 shows an interesting dependence of the power factor S 2 σ on temperature T. The power factor has a very small value of several dozen fW/(cmK 2 ). However, its value significantly increases with increasing temperature, i.e., in the intrinsic region above 300 K for a sample richer in neodymium ions, regardless of the crystallographic direction. Similar behavior of S 2 σ(T) with only a few fW/(cmK 2 ) was observed in ceramic Gd 3+ and Co 2+ -codoped calcium molybdato-tungstates [46] as well as in Nd 3+ and Mn 2+ -co-doped calcium molybdato-tungstates [47]. The above mentioned studies show that even in ion-bonded materials containing a constant content of 3d transition metal ions, thermoelectric efficiency can be improved by doping them with 4f rare-earth ions.  Figure 8 shows an interesting dependence of the power factor S 2 σ on temperature T. The power factor has a very small value of several dozen fW/(cmK 2 ). However, its value significantly increases with increasing temperature, i.e., in the intrinsic region above 300 K for a sample richer in neodymium ions, regardless of the crystallographic direction. Similar behavior of S 2 σ(T) with only a few fW/(cmK 2 ) was observed in ceramic Gd 3+ and Co 2+ -co-doped calcium molybdato-tungstates [46] as well as in Nd 3+ and Mn 2+ -co-doped calcium molybdato-tungstates [47]. The above mentioned studies show that even in ionbonded materials containing a constant content of 3d transition metal ions, thermoelectric efficiency can be improved by doping them with 4f rare-earth ions.  Figure 9 presents temperature dependence of the relative dielectric permittivity, εr, for various electric field frequencies of PNMWO single crystals with x = 0.001 and 0.005, measured along [001] and [100] crystallographic directions. As can be seen, for each single crystal εr ∼30 remains independent of temperature and frequency up to 300 K and increases rapidly above this temperature as well as at the same time decreases with increasing frequency. In the thermally activated region, the accumulation of electric charge is significantly higher for the sample with x = 0.001 (max. εr ∼200) than for the sample with  Figure 9 presents temperature dependence of the relative dielectric permittivity, ε r , for various electric field frequencies of PNMWO single crystals with x = 0.001 and 0.005, measured along [001] and [100] crystallographic directions. As can be seen, for each single crystal ε r~3 0 remains independent of temperature and frequency up to 300 K and increases rapidly above this temperature as well as at the same time decreases with increasing frequency. In the thermally activated region, the accumulation of electric charge is significantly higher for the sample with x = 0.001 (max. ε r~2 00) than for the sample with x = 0.005 (max. ε r~1 00). The loss tangent, tanδ, shows a similar behavior and its value does not exceed 0.01 below room temperature ( Figure 10) and a strong energy loss above this temperature, i.e., in a highly thermally activated region. Impedance spectroscopy used to analyze the above results, did not reveal the Cole-Cole semicircles (not presented here). This suggests that in single crystals under study no dipole relaxation processes were observed in the temperature range up to 400 K. Therefore, a charge accumulation visible in the spectra may be caused by the polarization of the space charge in the macroscopic region where the charge freedom of the electron or ion is limited. Similar behavior was found in microcrystalline Gd 3+ -doped lead molybdato-tungstates with the chemical formula of Pb 1−3x Pb1-3x xPr2xWO4

Dielectric Properties
x Gd 2x (MoO 4 ) 1−3x (WO 4 ) 3x for x > 0.1154, synthesized via solid state reaction route [23] and in nanoparticles of the same solid solution obtained via combustion route [24]. This effect was there additionally confirmed by the analysis of the fit of the dielectric loss spectra of Gd 3+ -doped samples by the sum of the conductivity and Havriliak-Negami, Cole-Cole and Cole-Davidson functions [24]. the spectra may be caused by the polarization of the space charge in the macroscopic region where the charge freedom of the electron or ion is limited. Similar behavior was found in microcrystalline Gd 3+ -doped lead molybdato-tungstates with the chemical formula of Pb1-3x xGd2x(MoO4)1-3x(WO4)3x for x > 0.1154, synthesized via solid state reaction route [23] and in nanoparticles of the same solid solution obtained via combustion route [24]. This effect was there additionally confirmed by the analysis of the fit of the dielectric loss spectra of Gd 3+ -doped samples by the sum of the conductivity and Havriliak-Negami, Cole-Cole and Cole-Davidson functions [24].

Conclusions
PNMWO single crystals obtained by the Czochralski method in air and under 1 MPa were characterized by structural, magnetic, UV-vis, electrical conductivity, thermoelectric power, power factor and dielectric spectroscopy measurements. They have shown scheelite-type structure, anisotropic character of the temperature-independent paramagnetic

Conclusions
PNMWO single crystals obtained by the Czochralski method in air and under 1 MPa were characterized by structural, magnetic, UV-vis, electrical conductivity, thermoelectric power, power factor and dielectric spectroscopy measurements. They have shown scheelite-type structure, anisotropic character of the temperature-independent paramagnetic contributions, weak n-type conductivity in the extrinsic region (77-300 K) with the activation energy of 0.008 eV and stronger one with the activation energy of 0.7 eV in the intrinsic region (350-400 K), a strong increase of the power factor above room temperature for a crystal with x = 0.005, constant dielectric value (~30) and loss tangent (~0.01) up to room temperature. Calculations of the Fermi energy (~0.04 eV) and the Fermi temperature (~500 K) revealed the existence of shallow donor levels. In turn, the impedance spectroscopy analysis showed no dipole relaxation processes and possible charge accumulation through space charge polarization. The final conclusion is that the source of observed weak n-type electrical conductivity may be 4d electrons derived from molybdenum ions with an oxidation state lower than 6+ and anionic vacancies. Single crystals under study with such properties can be useful in the production of lossless capacitors used in the temperature range up to 300 K.