Electrical and thermal properties of Pr0.6Sr0.4−xAgxMnO3 (x = 0.05 and 0.1) manganite

Monovalent silver-doped Pr0.6Sr0.4−xAgxMnO3 manganite has been chosen for the electrical and thermal transport studies. The electrical measurements confirmed a metal–insulator transition around room temperature. For the analysis of the resistivity data, in the high-temperature paramagnetic region, the adiabatic small polaron hopping model was operative. The magnetoresistance studies, under different external magnetic field, showed that the MR peak is located at the metal–insulator transition and ferromagnetic–paramagnetic transition, which is characteristic for an intrinsic magnetoresistance. The thermal conductivity results exhibit a semicrystalline character with grain boundary scattering as a main mechanism limiting the heat transfer in samples. The electrical contribution to the thermal conductivity is relatively small, around 1%, as in most of the manganites. The transition point around room temperature is also visible. The additionally calculated thermal diffusivity parameter shows values of the order typically found in perovskites.


Introduction
The mixed valence perovskite manganites with general formula T 1-x R x MnO 3 (T = rare earth cation, R = alkaline earth cation) have attracted the attention of researchers and emerged as potential candidates for technological application. Reason behind it was mostly their possible use for magnetic read write heads, magnetic refrigeration and application in electronic devices. The interest in those materials was reinforced due to their specific features such as metal-insulator transition, ferromagnetic-paramagnetic phase transition, colossal magnetoresistance (CMR), charge and orbital ordering and lattice degree of freedom [1][2][3][4][5][6][7]. The transport and magnetic properties of these materials originate mainly from double exchange (DE) mechanism with mobile e g electrons of Mn 3? (t 3 2g e 1 g ) moving to the empty e g orbital of Mn 4? (t 3 2g e 0 g ) via the oxygen p-orbital. This mechanism enhances the ferromagnetic-metallic state (FMM) [8]. However, the paramagnetic-insulator state (PMI) is explained by the strong electron-phonon interaction which is related to the Jahn-Teller (JT) distortion [9]. Several other mechanisms were considered for studying the physical properties of manganites as super exchange (SE), phase separation and charge ordered (CO) [10][11][12]. In order to clarify the physics behind phenomena such as CMR and magnetocaloric effect (MCE), many other factors have been considered. It was reported that physical properties of manganites are very dependent on Mn 3? /Mn 4? ratio, which can be easily changed by simple substitution in the rare earth site or Mn site. Such substitution influences the ferromagnetic-paramagnetic Curie transition temperature (T C ) and metalinsulator transition temperature (T MI ) [13]. In fact each substitution of a divalent element with a monovalent one converts a Mn 3? with the electronic configuration (3d 4 , S = 2) to a Mn 4? with the electronic configuration (3d 3 , S = 3/2). As a result, in the e g band holes are generated, which allows the charge transfer and induces a ferromagnetic coupling between Mn 3? and Mn 4? ions.
In one of our previous studies, we reported that the substitution by a monovalent atom in Pr 0.6 Sr 0.4-x A x-MnO 3 system can play an important role in physical properties. Moreover, the substitution in Sr site with monovalent Na, K or Ag (x = 0.05 to 0.1) induces a second-order phase transition PM-FM around room temperature [14,15]. The electrical transport studies for Pr 0.6 Sr 0.4-x A x MnO 3 (a = Na, K) compounds confirmed a behavior change from the low-temperature metallic-like (dq/dT [ 0) below T q to the insulatorlike (dq/dT \ 0) above T q (where T q is a temperature corresponding to the maximum value of resistivity) [16][17][18]. Moreover, all studied samples do not show a MR peak in vicinity of their Curie temperature around 300 K, and the metal-insulator transition temperature T MI is observed around 200 K, which is about 100 K below Curie temperature T C . Interestingly, there are not many reports on doped manganites that exhibit the coincidence of T C with T MI around room temperature as shown in the case of Pr 0.6 Sr 0.4-x Ag x MnO 3 (x = 0.05 and 0.1). This motivated us to look into electrical and thermal conductivities of monovalent Ag doping in Sr site of Pr 0.6 Sr 0.4 MnO 3 manganite. It is found that T MI is observed around Curie temperature and slightly increasing with an increasing magnetic field from 0 to 3 T. In order to elucidate the conduction mechanisms, the temperature variation of resistivity was compared with two models above the insulator to metal transition temperature, namely the small polaron hopping (SPH) and Mott's variable range hopping (VRH), and at low temperature (in the metallic behavior region): electron-electron and electronmagnon scattering processes. Although the electronic transport has been the focus of studies in these systems systematically, the thermal transport has not yet attracted a proper attention. The relatively high electrical resistivity in various types of manganites entails that the dominant mechanism in a ferromagnetic-metallic phase should be the lattice heat conduction. In fact, thermal conductivity j is a property that reflects scattering of phonons and electrons in a material, which makes it an additional or sometimes also an alternative probe to study the complexity of the CMR phenomena. Survey through the studies on doped manganites shows two types of major behaviors [19,20]. In the paramagnetic phase, j is rather of a low value and exhibits an amorphous-like character of the temperature dependence (dj/dT [ 0). In the ferromagnetic-metallic phase, the observed curves change to the crystalline like (dj/dT \ 0). The transition between the phases and simultaneously alternation of the thermal transport type results in a minimum at T c . Usually, as a reason behind this phenomena the distortion of the MnO 6 octahedra is given.

Materials and methods
Polycrystalline Pr 0.6 Sr 0.4-x Ag x MnO 3 (x = 0.05 and 0.1) manganites were prepared by using the conventional solid-state method. The detailed description of samples can be found in Ref. [21]. The electrical resistivity measurements were carried out on PPMS (physical Property Measurement System) from Quantum Design in applied magnetic fields up to 3 T over temperature range 20-340 K using the four probe method. The thermal conductivity measurements were performed on a specially designed heat bath cryostat using the uniaxial steady-state heat flow method in a temperature range 4.2-300 K. The upper limit of measurement was defined by the restrictions of the experimental setup. The precise description of the technique as well as the used cryostat can be found elsewhere [22].

Results and discussion
Electrical resistivity measurements and conduction models The temperature dependence of electrical resistivity data of Pr 0.6 Sr 0.4-x Ag x MnO 3 (x = 0, 0.05 and 0.1) without and under an applied field up to 3 T is shown in Figs. 1 and 2.
For both investigated samples, resistivity q(T) changes from the low-temperature metallic-like behavior (dq/dT [ 0) below T q to the semiconductorlike (dq/dT \ 0) above T q , where temperature T q corresponds to the temperature point, at which resistivity reaches its maximum value. The metalinsulator transition temperature (T MI ) is observed around room temperature for both samples. For Pr 0.6 Sr 1-x Ag x MnO 3 with Ag x = 0.05, T MI is just a little lower comparing to the more doped sample. Because of the very subtle change, both in stoichiometry and shift of the T MI , the difference is assigned to the sample morphology. With increasing magnetic field (from 0 to 3 T), metal-insulator transition temperature rises up to about 20 K toward high temperatures. The magnitude of the resistivity is observed to decrease with increase in magnetic field for a whole temperature range. In fact, the presence of an external magnetic field reduces electron scattering at grain boundaries and results in a new orientation of magnetic moments toward the applied field, thereby decreasing the magnetic disorder. As a result, local ordering of the electron spins influences the ferromagnetic metallic state and is followed by the suppressing of the paramagnetic insulating regime leading to the observed increase in T MI . The ferromagnetic alignment, which is due to the double exchange mechanism, causes a decrease in resistivity. In comparison with the previously reported results for monovalent doped Pr 0.6-x Bi x Sr 0.4 MnO 3 (x = 0-0.15) [23], the present one shows a smaller resistivity values under lesser applied magnetic field and a higher metal-insulator transition temperature. It is worth to notice that the resistivity values reported for sample x = 0.05 are found to be larger than those reported for x = 0.1 sample. Such difference can be explained by grain sizes of particles for each samples. The preliminary studies claimed that the sample with silver amount equal to x = 0.05 contains smaller grains (which size varies between 1 and 1.3 lm) compared to those of x = 0.1 sample (grain size from 1.3 to 1.8 lm) [24]. The resistivity values were found to be smaller for sample with larger grains. It could be related to the fact that grain boundaries consist more of magnetic disorder and enhance electron scattering. In order to correlate the obtained results with other praseodymium strontium manganites (doped either on the praseodymium or the strontium site), the resistivity values at the metalinsulator transition point at 0 T and 1 T are summarized in Table 1. The included summary manifests also the strong influence of the preparation procedure (sample morphology) and dopants impact on the T MI , changing over 40 K for the pure sample from  184 to 222 K [16,23] and doped ones from 104 [17] to * 300 K in our case of silver-doped manganite.

Low-temperature behavior (T \ T q )
At low temperature (T \ T q ), in ferromagneticmetallic phase, the electrical resistivity data have been numerically approximated with a following polynomial equation (an empirical one): where q 0 is the residual resistivity arising from the temperature-independent processes such as domain wall, grain boundary and vacancies, q 2 T 2 describes the electron-electron scattering, and q 4.5 T 4.5 contributes the combination of electron-electron, electron-magnon and electron-phonon scattering process in FM state [26][27][28]. The obtained values from the best fits of the resistivity data are summarized in Table2.
We have noticed that with an increasing magnetic field from 0 up to 3 T, the parameters are reducing their values. This could be explained by the overall reduction of the spin fluctuation in the presence of an external magnetic field. Moreover, the obtained values indicate that for each particular temperature in the fitted range the term q 2 T 2 is larger than the term q 4.5 T 4.5 which confirms that in the metallic phase the transport mechanism is governed by the electronelectron scattering.

High-temperature behavior (T [ T q )
Above T q , the behavior of electrical resistivity as a function of temperature is explained usually by the adiabatic small polaron (SP) model [28], which is described by the following equation: where E a is the activation energy and B is the residual resistivity coefficient. The E a values are determined from the best fit of plot ln (q/T) versus 1/T (not included in the paper). The parameters resulting from the best fit, summarized in Table3, indicate that E a values are found to be decreasing with increasing magnetic field. This relation could be attributed to a reduction of the charge localization and spin alignment. Following the dopant content, the differences between the activation energies are very subtle, just a bit higher for the x = 0.1 sample, probably stemming from the sample microstructure. A similar effect induced by an external magnetic field was previously reported for H (T) q 0 (X-mm) q 2 (10 -6 X mm/K 2 ) q 4.5 (10 -13 X mm/K 4.5 )  [17,18]. Another example of the suppression of transport energy barriers under the influence of magnetic field has been observed in Pr 0.6 Sr 0.4-x K x MnO 3 [16].

Magnetoresistance
As noted earlier, the application of external magnetic field suppresses the spin fluctuations and consequently leads to a decrease in the electrical resistivity associated with the magnetic disorder. The influence of a magnetic field is described by the magnetoresistance effect (MR), which can be defined as follows: where q(H) and q(0) are the resistivities at magnetic field H of 1, 2 and 3 T and at zero field, respectively. The temperature dependence of magnetoresistance (MR) of both samples is shown in Figs. 3 and 4 at different applied magnetic fields. For both samples, the plots show a peak around room temperature. Their Curie temperatures are 295 K and 289 K for x = 0.05 and x = 0.1, respectively. The observed decrease in T c with increase in silver content is derived indirectly from the microstructure of particular samples. For x = 0.1, grain boundaries (average sample grain size up to 1.8 lm) generate more magnetic disorder and in that way enhance the electron scattering, which in result influence the FM-PM transition temperature and slightly decrease the T c when comparing to x = 0.05 sample (with av. grain size 1-1.3 lm).
One should also note that the maximum negative MR shows a slight decrease when increasing Ag amount from 0.05 to 0.1. This could be explained by a decrease in the resistivity when increasing Ag content. Whereas with increasing magnetic field from 1 to 3 T, the negative MR values observed around room temperature are found to be from 10 to 26% for both samples. In comparison with previous studies on Na-and K-doped manganites [16,17] they reach very high values. The former case we reported showed largest MR values around 25 K followed by a gradual decrease with increasing temperature. The characteristic T MI temperature of those compounds was around 200 K, which is about 100 K bellow the Curie temperature. Venkataiah et al. [26] proposed that the high MR at low temperature can be related to the extrinsic MR effect involving spin-polarized tunneling between grains or spin-dependent scattering of polarized electrons at grain boundaries. Our samples (the silver-doped ones) show a different MR behavior compared to reported previously [16][17][18], which is determined by the substantially bigger grain Table 3 Activation energies E a deduced from electrical resistivity of Pr 0. 6   size of the samples (from 1 lm up to 1.8 lm in Agdoped whereas * 50 nm in K-doped and from 400 to 700 nm in Na-doped ones). Many studies have shown that the microstructure modification strongly influences the extrinsic magnetoresistance [29,30]. The location of the MR peak at metal-insulator temperature transition and ferromagnetic-paramagnetic transition is typical for a different kinds of effectnamely the intrinsic magnetoresistance. The intrinsic MR requires strong magnetic field exceeding 1 T, which in turn suppresses the magnetic disorder and reduces the electron scattering at grain boundaries.

Thermal conductivity
The temperature dependence of thermal conductivity for Pr 0.6 Sr 0.4-x Ag x MnO 3 (x = 0.05 and 0.1) is shown in Fig. 5.
The measured quantities cannot be outright assigned to the amorphous or crystalline type (even though the investigated samples were ceramic pellets). The j value is monotonically increasing with temperature throughout the investigated temperature range-dj/dT [ 0, but with different intensity in particular ranges, what would suggest an amorphous type of behavior. However, the magnitude of j (T) lies in the range 0.4-3.4 W/mK, which is a little higher than typical amorphous material [31]. The observed value of thermal conductivity can be attributed to the presence of JT distortions [19,31]. Below 15 K, the thermal conductivity in both samples is practically equal. For higher temperatures, j (T) of the less doped sample has bigger values. With increasing silver content, thermal conductivity gets smaller to exceed at room temperature j RT = 2.65 W/ mK for Pr 0.6 Sr 0.3 Ag 0.1 MnO 3 and 3.4 W/mK for Pr 0.6-Sr 0.35 Ag 0.05 MnO 3 , respectively. The difference in thermal conductivity coefficient is about 30%, which is substantial considering the relatively small difference in the dopant amount. Lowering of the j value induced by increasing the dopant amount was also observed substituting bismuth in place of praseodymium in Pr 0.6-x Bi x Sr 0.4 MnO 3 studies [23]. The decrease in magnitude of j(T) is connected to the increased phonon scattering from JT distortion as formation of JT polarons may act as scattering centers. Collating our results with studies of Gamzatov et al. [32] for the pure sample, Pr 0.6 Sr 0.4 MnO 3 one notes the same type of unusual behavior of the curve j(T) in a wide temperature range. Likewise, the magnitude of the thermal conductivity parameter is kept at the same level (from * 1.2 W/mK at 80 K up to * 2.6 W/mK just below T c ). Also in the thermal conductivity studies of a different silver-doped lanthanum manganite [33], the same type of dj/dT [ 0 dependences are demonstrated. As mentioned earlier, given the setup restriction and the fact that T c of Ag-doped praseodymium strontium manganite is close to room temperature, thermal conductivity beyond T c in the paramagnetic phase could not be investigated. The only phase for which the measurement was conducted was the ferromagnetic metallic phase.
Because of a high electrical resistivity, one should consider the effect of the electronic contribution to the total thermal conductivity j el . Under the circumstances of investigating solely the ferromagnetic metallic phase, we can omit the considerations of correctness of the Wiedemann-Franz law (WFL) [34] and assume: where L 0 = 2.45Á10 -8 W X/K 2 (the Lorenz number) and q is the resistivity. The results of the calculations from resistivity data are plotted in Fig. 6 (range 20-340 K).
Owing to the extended range (toward high temperatures), one can outright see the minimum connected to the PM-FM transition around room temperature. From exclusively the thermal conductivity results, it was not possible to see the changes in temperature dependence of the j parameter. The slope of the electrical contribution to the thermal conductivity in the paramagnetic phase is roughly the same for both samples. In the ferromagneticmetallic phase, the electrical contribution to the total thermal conductivity is kept around 1% at all temperatures. In our particular case, we will skip the considerations of other contributions to the heat conductions like, e.g., from spin waves. The investigated range (not the calculated electronic contribution) ends exactly at the PM-FM transition point, which makes it impossible to proceed with the data analysis in that vicinity. After subtracting the electronic contribution from the total thermal conductivity, the main heat conducting source remains the lattice conductivity: In the ferromagnetic region, the lattice thermal conductivity of Pr 0.6 Sr 1-x Ag x MnO 3 is dominated by phonons, allowing to analyze the low-temperature data on the basis of the relaxation time method [35]. The phonon thermal conductivity is defined as follows: where d-mass density; M-molecular weight; nnumber of atoms in the chemical formula of the compound; R-gas constant; h D -Debye temperature; x ¼ x D = T -reduced phonon frequency. The phonon relaxation time s ph is given by: where s b corresponds to scattering time due to grain boundaries (s b ¼ l b v ph , l b -average crystalline size, v ph -phonon velocity); K is a phonon scattering rate proportional to x 1 ph , corresponding to scattering by strain fields around dislocation; s-proportional to x 2 ph -is scattering by sheet like faults; p-proportional to x 4 ph -is scattering by point defects. As mentioned above, the magnon contribution is neglected, because the phonon-spin scattering has the largest effect near T c and here the low temperature (away from T c ) is considered. Using the above equation, the fit of the phonon (lattice) thermal conductivity was calculated (for temperatures 20-150 K). The results are shown in Fig. 7. The parameters corresponding to the best fits are summarized in Table 4.
The most striking observation is that independently from the sample type the main mechanism governing and limiting the thermal transport in investigated manganites is the scattering on grain boundaries, which reflect the microstructure of the sample connected to the preparation procedure.

Thermal diffusivity
Thermal diffusivity is a parameter defining the ability of a material to conduct heat. It can be measured directly, e.g., by pyroelectric calorimeter or a laser flash method or can be calculated from the experimental data of thermal conductivity and heat capacity using the formula below: where j-thermal conductivity coefficient, C p -heat capacity and q ¼ 6:44 kg=m 3 -density of a material.
The estimated values based on heat capacity results from our previous paper [21] are presented in Fig. 8. The parameter exhibits a monotonic decrease in the value with increasing temperature due to the reduction in phonon mean free path by phonon-phonon scattering. At the lowest temperatures, the diffusivity drops rapidly and stabilizes around 50 K and furthermore continues to decrease smoothly with a very flat slope mirroring, the behavior noted for the undoped sample [32]. One anomaly is observed at high temperatures, which is connected to the paramagnetic-ferromagnetic transition. The temperature dependence of the thermal diffusivity in the vicinity of the PM-FM is shown in Fig. 9.
Changing the scale allowed to visualize the transition. At room temperature, thermal diffusivity is 1.1 mm 2 /s and 0.91 mm 2 /s for Pr 0.6 Sr 0.4-x Ag x MnO 3 x = 0.05 and x = 0.1, respectively, which lies between the values * 0.8 mm 2 /s (reported for the undoped sample Pr 0.6 Sr 0.4 MnO 3 [32]) and * 1.35 mm 2 /s (reported for PrMnO 3 by Oleaga et al. [36]). The differences in thermal diffusivity might be the result of this property's nature, as it is strongly dependent on the quality of the material (stoichiometrically and crystallographically)-the better the crystal the higher diffusivity value. Considering the observed transition point, it is slightly shifted toward high temperatures when comparing to our previous studies [21] and the diffusivity studies of Gamzatov et al. being just below the room temperature.

Conclusion
The electrical and thermal properties of Pr 0.6 Sr 0.4-x-Ag x MnO 3 (x = 0.05 and 0.1) manganite have been reported. The electrical investigations show that both samples exhibit a metal-insulator transition T MI around room temperature. The application of an external magnetic field up to 3 T leads to a new magnetic moment orientation and reduction of spin fluctuation. Addition of a magnetic field increases T MI about 20 K and decreases the resistivity values in the whole temperature range 20-340 K. The resistivity values reported for sample x = 0.05 are found to be larger than those reported for x = 0.1 sample due  to the grain size of particles. The analysis of resistivity data confirmed that adiabatic small polaron (SP) model is operative above the metal-insulator temperature transition, whereas electron-electron, electron-magnon and electron-phonon scattering processes govern the low-temperature metallic behavior. The temperature dependence of magnetoresistance for both samples shows an intrinsic magnetoresistance behavior with MR peak location at metal-insulator temperature transition and ferromagnetic-paramagnetic which is different to those reported previously [16][17][18]. The thermal transport studies show semicrystalline properties with values common in perovskite manganites group of materials. From the extracted lattice contribution, the main factor limiting the heat transfer was defined to stem from grain boundaries, supporting the conclusion about strong influence of the sample morphology.
The electrical contribution to thermal conductivity exhibits less than 1% of the total thermal conductivity, and the evidence of the PM-FM phase transition is observed around room temperature. The thermal diffusivity parameter decreases with increasing temperature in the whole investigated temperature range (abruptly at low temperatures, above 50 K very smoothly) resembling the values of other perovskite manganites.

Compliance with ethical standards
Conflict of interest The authors declare that they have no conflict of interest.
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