Various fitting parameters for (La/Pr)2/3Ba1/3(Mn1-xSbx)O3 (0≤ x≤ 0.03) systems using equation (Eq. 3).
Magneto-resistance (MR) is generally defined as the relative change in the electrical resistivity of a material upon the application of magnetic field. Mathematically, MR can be defined by the following equation,
where ρH and ρ0 are the electrical resistivities with and without magnetic field respectively. Electrical resistivity can increase or decrease upon the application of magnetic field and accordingly MR is defined as positive or negative respectively. By using the above definition observed MR could be ~106% or even higher, but if we define MR by the following relation,
then maximum MR will be ~100%.
W. Thomson (Lord Kelvin) in 1857, for the first time, discovered magneto-resistance1. All metals exhibit MR due to Lorentz force but the value of MR is only few percent even after the application of higher magnetic field. For example, Cu metal exhibits 1% MR at room temperature under 7 Tesla applied magnetic field. In the case of ferromagnetic metals like Fe and Co, MR is more (~ 15%) as compared to that of nonmagnetic metals such as gold (Au). Semimetal bismuth (Bi) shows about 18% MR in a transverse magnetic field of 0.6T and 250% MR at room temperature under the application of 5 Tesla magnetic field.
In search of higher MR values near room temperatures, the last two decades have witnessed the discovery of an enormous suppression in electrical resistivity upon the application of magnetic field in certain class of materials called manganites. The observed change was so large that a special name “colossal magneto-resistance (CMR)” had to be coined for this phenomenon to distinguish it from the already existing giant magneto-resistance (GMR) in the magnetic multilayers. For example, Chahara et al., R. von Helmolt et al., Jin et al., Xiong et al. have reported ~ 106 % MR under the application of 6T magnetic field. Searle and Wang et al.,  were the first to report MR studies in La1-xPbxMnO3 single crystal manganites. The renewed surge of interest in manganites in the 1990s started with the experimental observation of large magneto-resistance (MR) studies in Nd0.5Pb0.5MnO3 by Kusters et al. and in La2/3Ba1/3MnO3 by R. von Helmolt et al.. MR effect was found to be as high as 60% (using Eq. 2) in thin films at room temperature, and it was exciting to observe that this value was higher than found in artificial magnetic/nonmagnetic multilayers i.e. Giant magneto-resistive materials (GMR), allowing for potential applications in magnetic recording. Thereafter Chahara et al.[ 3] on La3/4Ca1/4MnO3 and Ju et al. on La1-xSrxMnO3 films produced similar results. Jin et al.[ 5] observed 127,000% around 77K using Eq. (1) for defining MR in thin films of La0.67Ca0.33MnO3 and Xiong et al.[ 6] 100,000% in Nd0.7Sr0.3MnO3 film at 60K.
1.1. Crystal structure
Rare-earth manganites possess a perovskite crystal structure (Fig. 1a) with the general formula R1-xAxMnO3, where R is any trivalent rare-earth ion like La+3, Pr+3, Nd+3, Eu+3 etc. and A is divalent alkaline-earth ion (Ca+2, Sr+2, Ba+2 etc.) whereas x represents the amount of doping of such divalent ions at the rare-earth site and equal number of Mn+3-ions are converted into Mn+4- ions. The mixed valency of manganese ions can also be controlled by varying the oxygen content,. In the perovskite structure each manganese (Mn) ion is surrounded by six oxygen ions forming an octahedron (Fig. 1a).
In MnO6 octahedron overlapping of manganese 3d orbitals with the 2p orbital of oxygen splits the five-fold degeneracy of the manganese 3d orbitals due to their different shapes (Fig. 1b). This is called crystal field splitting (CFS). Thus in an MnO6 octahedron three degenerate orbitals (dxy, dyz, dzx) with lower energy (because their lobes are oriented between the O-2 ions) are called t2g levels and two degenerate orbitals (dx2- y2, d3z2- r2) with higher energy (their lobes are towards O-2 ions and hence large Coulomb repulsion) called eg levels.Due to crystal field splitting the energy difference between t2g and eg levels is ~ 1.5 eV. All electrons in these energy levels get aligned parallel to each other due to strong on-site Hund′s coupling, leading to a total spin (S) of 2 for Mn+3 and S = 3/2 for Mn+4 ions respectively. The three electrons of Mn+4 - ion occupy t2g states whereas fourth electron of Mn+3 goes to the eg state. The eg electrons are more itinerant than the t2g electrons and can hop from one Mn-site to the other. However, according to Jahn-Teller (JT) theorem this configuration is not stable and the degeneracy of the eg levels are further removed. The oxygen ions surrounding the Mn+3 -ion slightly readjust their positions, creating an asymmetry in different directions which ultimately breaks the degeneracy. The breaking of degeneracy due to orbital- lattice interaction is called Jahn-Teller splitting (Fig. 2). Only those ions like Mn+3 which have odd number of electrons in the eg levels can undergo Jahn-Teller distortion. Therefore Mn+3 is a Jahn-Teller ion whereas Mn+4 is not. In the case of manganites there are 21 degrees of freedom (modes of vibration) for the movement of oxygen and Mn ion. Out of these only two types of distortion are relevant for the splitting of eg levels i.e. Q2 and Q3 (Fig. 3) . Q2 is a basal plane distortion (defined as Q2 mode) in which one diagonally O pair is displaced inwards whereas the other pair is displaced outwards. On the other hand, Q3 is a tetragonal distortion which results in elongation or distortion of MnO6 octahedron. JT distortion can be static or dynamic.
Perovskite manganites not only exhibit the colossal magnetoresistance (CMR) effect but also other important phenomena like charge ordering, phase separation at nanoscale owing to the subtle balance between charge, spin, lattice and orbital degrees of freedom. As mentioned earlier, electrical resistivity of these manganites can change dramatically in response to an applied magnetic field. The occurrence of magneto-resistance can be explained by Zener’s theory of double exchange along-with the formation of Jahn-Teller polarons. In order to understand magnetoresistance behavior and other peculiar properties
exhibited by these materials, substitution engineering is carried out either at the rare-earth site or at the manganese site. However, out of the two, the last is more appropriate as it directly affects the mechanism happening among different MnO6 octahedra. In this regard, several authors have substituted different transition metal ions like Fe+3, Al+3, Ga+3, Zn+2, Cu+3, Ni+2 at the Mn-site and have shown that Mn-site substitution severely affects the conduction mechanism as well as the magnetic properties-[ 28]. However, fewer results exist for higher valent ion substitution at Mn-site to see its effect on the transport properties-. Substitutions at Mn-sites in manganites, irrespective of their electronic and magnetic nature, lower the ferromagnetic transition temperature but to different extents except in the case of Ru-doped Pr0.5Sr0.5MnO3 where it is found to increase with Ru. In this work, we have attempted to substitute Sb+5 ion on the Mn-site in two different manganite materials viz. La2/3Ba1/3MnO3 (LBMO) and Pr2/3Ba1/3MnO3 (PBMO) -[ 38]. Sb+5 ion has been chosen because its ionic size is also comparable to that of manganese ion in the six-fold co-ordination. Besides, by virtue of its closed shell configuration, Sb+5 ion is not expected to introduce any additional magnetic coupling. It is also not expected to participate explicitly in the mechanism between Mn+3/Mn+4 ions, however, due to its filled shell structure it can hinder the electron transfer. We have carried out structural, morphological, electrical, magnetoresistive and thermal measurements on the aforementioned compositions and the results will be discussed here.
2. Experimental procedure
Bulk polycrystalline manganite samples of La2/3Ba1/3(Mn1−xSbx)O3 and Pr2/3Ba1/3(Mn1−xSbx)O3 (0 ≤ x ≤ 0.03) [referred hereafter as (La, Pr)2/3Ba1/3(Mn1−xSbx)O3] were synthesized following the conventional solid-state reaction method. Powders of La2O3, Pr6O11, BaCO3, Sb2O5 and MnO2 were mixed in nominal stoichiometric ratios, grounded properly and calcined several times between 900-1100 ˚C for 15 h with intermediate grindings. Finally, the pellets were made from the calcined powders and sintered at1260 ˚C for 20 h. X-ray diffraction (XRD) was carried out with Cu Kα radiation (λ = 1.54 Å) between 20° and 80° with a step size of 0.05◦ in 2θ mode to ascertain the phase purity of the synthesized materials. Electrical resistivity measurement in the absence and presence of a magnetic field was carried out using a four-probe technique with the field (0.6 T) applied parallel to the direction of the current flow. Thermoelectric power S(T) and thermal conductivity κ(T) measurements were carried out simultaneously from 350 to 10K in a closed cycle refrigerator by using a direct-heat pulse technique. Specific heat CP(T) was measured from 350 to 77K with a high resolution ac calorimeter, using chopped light as heat source. Further details of the thermal measurements techniques can be found in ref..
3. Results and discussion
3.1. Structural studies 40,
Fig. 4 shows the x-ray diffractograms of La2/3Ba1/3(Mn1−xSbx)O3 and Pr2/3Ba1/3(Mn1−xSbx)O3 (0 ≤ x ≤ 0.03) series. All samples are single phase in nature. It is also clear that Sb+5 ion occupies the Mn-site in LBMO and PBMO. Substitutional criteria of valence, ionic size and the coordination assured the preferential occupation of Mn+4 ion site by Sb+5 ion. The parent compound LBMO possesses the cubic structure [lattice parameter = 3.9094( 0.09%) Å] at room temperature. In refs.-[ 42] the structure of LBMO has been reported cubic. In some reports neutron diffraction study has been carried out as a function of temperature on LBMO perovskite manganite and it has been deduced that it crystallizes in the rhombohedral structure (closer to cubic, space group R3c) at room temperature43,44. However, the final sintering temperature in our case is 1260 ˚C while it is much higher as reported in ref. (e.g.1470 ˚C used by Beznosov et al. and 1400 ˚C by Moutis et al.) and such a high temperature can change the lattice structure from cubic to rhombohedral. With the subsequent doping of Sb+5 ion the lattice parameters increase successively [e.g. 3.9180 ( 0.011%) Å for 3% Sb-doped sample] which indicates the occupation of Mn+4 ion by Sb+5 in LBMO. The increase in the lattice parameter is also evident as the main peak shifts towards lower 2θ values with increasing Sb-content. The lower value of 2θ implies higher d values and consequently higher lattice parameter. The increase in the lattice parameters can also be understood in terms of the increase of the mean ionic radius at Mn site [Mn+3 (0.645 Å)/Sb+5 (0.60 Å)/Mn+4 (0.53 Å), ionic radii are in six- fold coordination] with increase in Sb+5 content.
The lattice parameters were calculated using the powder X software. Similar results were also observed in case of Sb-substituted PBMO samples except that the crystal structure here is orthorhombic.
3.2. Morphological studies
The SEM micrographs of bulk LBMO, 3Sb-LBMO, PBMO, 3Sb-PBMO are shown in Fig. 5(a-d). The SEM micrographs clearly show the grain and grain boundaries. The grains show good connectivity among each other and the grain size is found to increase with doping in both cases. It is assumed that Sb-doping helps in promoting the grain growth.
3.3. Electrical resistivity measurement
Figure 6 shows the electrical resistivity variation with temperature (ρ-T) of La2/3Ba1/3(Mn1-xSbx)O3 and Pr2/3Ba1/3(Mn1-xSbx)O3 (0≤ x≤ 0.03) samples. Undoped samples LBMO and PBMO exhibit two insulator-metal (I-M) transitions. The higher temperature transition (TP1) is sharp and at ~ 340 K and 194K whereas the lower temperature transition (TP2) is broader and at ~ 250K and 160K respectively. In case of LBMO, Ju et al. reported two transitions at the same temperatures TP1 and TP2 but the value of the resistivity at TP2 in their sample was lesser than that at TP1 but in our case the situation is reverse. The reason for this is the grain size difference in two cases. While the average grain size is ~ 5 m reported by Ju et al., it is much smaller (0.5 m) in our case (Fig. 5a). Smaller grain size leads to extra strain at the grain boundary, which eventually leads to the enhancement of the resistivity. However, the same transition temperatures confirm that oxygen content is close to 3.0 in our sample as in the other report Ju et al. have studied the effect of oxygen variation on the electrical and magnetic properties of LBMO and observed that only the samples having oxygen content close to 3.0 show two transitions in the resistivity-temperature behavior.
With Sb-doping at the Mn-site the two transitions, in both the cases, shift to lower temperatures successively with the overall increase in the resistivity. However, TP1 shifts to lower temperatures at a faster rate than TP2 and almost disappear with higher Sb content. TP1 is a result of the competition between double-exchange and the super-exchange (SE) mechanisms generally observed in all perovskite manganites. However, TP2 results out of the grain boundary effects that in turn arise due to the larger ionic size mismatch between the ions present at the rare-earth site in LBMO and PBMO (La+3/Ba+2 and Pr+3/Ba+2 respectively). Due to such ionic size difference the lattice comes under strain but since this is not a situation where the mechanical energy is minimum (which should be the case in equilibrium) and because of the presence of the grain boundaries in the polycrystalline sample, the lattice transfers the extra strain to the grain boundaries to attain a minimum energy configuration. This transferred strain at the grain boundary tilts the MnO6 octahedra of the LBMO/PBMO lattices present there and thus weakens the electron transfer probability t (t = t0cosθ, which depends upon the angle between two neighboring Mn-ions). Therefore the two transitions one from the grain (TP1, where the Mn -ions are more parallel and the electron transfer is easier and hence stronger double exchange mechanism) and the other, TP2, from the grain boundary (weaker double exchange) separate from each other. When Sb+5 ion is doped at Mn+4- site, it does not participate in the exchange mechanism between Mn+3/Mn+4 ions because of its closed shell electronic structure (4d10). However, it does decrease the available number of sites where the electron can hop from the eg orbital of Mn+3, resulting in some sort of localization of the carriers and the two transitions shift to lower temperatures with increasing of Sb content. It is worthwhile to mention here that ionic size mismatch between the ions present at rare-earth site [Pr+3 (1.179Å) and Ba+2 (1.47 Å)] in case of PBMO is larger than in LBMO [La+3 (1.210Å) and Ba+2 (1.47Å)]. Therefore, TP2, is lower in case of PBMO. However, TP1, depends upon the average ionic radius at the rare earth site which is smaller for PBMO that’s why TP1 is also smaller in this case.
3.4. Electrical resistivity at low temperature (< 50K)
At low temperatures, transport mechanisms such as weak localization,, electron-electron interaction,, Kondo effect,, etc. can cause an upturn in the resistivity with decreasing temperature, whereas scattering mechanisms such as electron-electron scattering,, electron-phonon scattering,, electron-magnon scattering,, magnon-magnon scattering increase resistivity with increasing temperature in metals and alloys. Figure 7 shows the temperature dependence of resistivity of Sb-doped LBMO and PBMO systems in the temperature range 4K ≤ T ≤ 50K. It is clear that electrical resistivity exhibits an increasing trend with decreasing temperature reminiscent of semiconducting behavior for all compositions. There is a resistivity minimum which is lowest for the undoped samples and shift to high temperatures with antimony substitution. In order to analyze the electrical resistivity behavior at low temperatures we tried to fit the data using the following equation:
where ρ0=1/a and ρ1= b/a2 are constants. ‘a’ is temperature independent residual conductivity; ‘b’ is the diffusion constant and is due to weak localization effect46. The other two terms viz. ρ2T2 and ρ5T5 arise due to the electron-electron and electron-phonon scattering53. The fitting parameters ρ0, ρ1, ρ2, ρ5 for the two systems are shown in Table 1.
|La2/3Ba1/3(Mn1-xSbx)O3 (0≤ x≤ 0.03)|
|Sample||ρ0 (Ω cm)||ρ1 (Ω cm K-1/2)||ρ2 (Ω cm K-2)||ρ5 (Ω cm K-5)|
|x = 0||0.01436||0.00023||1.8885×10-7||6.89×10-13|
|x = 0.01||0.01723||0.00033||3.3297×10-7||6.9613×10-13|
|x = 0.02||0.02282||0.00093||1.269×10-6||3.184×10-13|
|x = 0.03||0.03529||0.00081||9.8659×10-7||1.8152×10-12|
|Pr2/3Ba1/3(Mn1-xSbx)O3 (0≤ x≤ 0.03)|
|x = 0||0.2175||0.0082||8.9x10-6||4.83x10-11|
|x = 0.01||3.0015||0.1922||1.7x10-4||5.26x10-10|
|x = 0.02||19.044||2.4068||2.53x10-3||7.18x10-10|
|x = 0.03||362.885||61.8983||7.69x10-2||1.09x10-7|
It is observed that the value of fitting parameters ρ0, ρ1, ρ2, ρ5 increases with doping. This indicates that the weak localization, electron-electron and electron-phonon scattering increases with doping and making pristine material more disordered. This is also obvious from the fact that random distribution of ions La+3/Pr+3/Ba+2/Mn+3/Mn+4/Sb+5 leads to random variation in the potential experienced by the electrons so the electrons get trapped due to less kinetic energy at low temperatures. The other two terms i.e. electron-electron and electron-phonon scattering will increase because of the difference in ionic sizes. It is worth mentioning here that in addition to these effects the Coulomb blockade (CB) effect could also contribute to the observed electrical resistivity upturn as the large ionic size mismatch between La+3/Pr+3 and Ba+2 ions leads to the strong disorder at the grain boundaries and eventually increases the Coulomb charging energy EC leading to increase in resistivity. This would get further enhanced for grains with smaller sizes (EC ∝ 1/d). In this case grain size d, however, has increased with Sb-doping (figure 5), which implies that EC should decrease and hence the resistivity upturn should also decrease but here a reverse situation is observed. The CB effect, therefore, cannot account for the resistivity upturn for the Sb-doped samples, even though it might be one of the possible sources of localization in the pristine sample case.
3.5. Transport mechanism in the metallic region
We used the following Eq. to fit the metallic region of the temperature dependent electrical resistivity data
here ρ0 is the temperature independent residual resistivity. ρ2.5T2.5 represents the electrical resistivity due to electron-magnon scattering processes in the ferromagnetic phase. We found that in the metallic regime electrical resistivity data for Sb doped samples best fit the Eq. (4). The quality of these fittings, in general, is evaluated by comparing the square of the linear correlation coefficient (R2) obtained for each equation. The values of R2 were found as high as 99.9% for Eqn. (4) which confirms the applicability of electron-magnon scattering process. The obtained fitted parameters are given in Table 2. It is observed that value of both ρ0 and ρ2.5 increases with doping. This reflects the dominating nature of the electron-magnon scattering mechanism with increasing Sb content. Similar results were observed for the Sb-doped PBMO manganites.
|x = 0||0.11296||8.1315x10-6||0.99994|
|x = 0.01||0.31814||0.00005||0.99905|
|x = 0.02||3.18173||0.00015||0.99962|
|x = 0.03||33.90211||0.00103||0.99952|
3.6. Transport mechanism above TP1
Conduction in manganites at higher temperature (T ≥ TP) is governed either by variable range hopping (VRH) or by small polaron hopping (SPH) depending on the Debye temperature (θD),. If T > θD/2, the conduction mechanism is governed by small polarons and these polaronic models can be either adiabatic or non-adiabatic. Since the Debye temperature of the LBMO system is ~400 K  so the polaronic model can be applied to the insulating region above TP1. The adiabatic small polaron hopping model is given by, :
where ρ0 is the residual electrical resistivity, Eρ is the activation energy and kB is the Boltzmann’s constant. We estimated the activation energy Eρ and it is found to increase with Sb content as shown in Table 3. Similar results were observed for Sb-doped PBMO system.
|x = 0||91.2||21.693||-0.8491||69.507||139.014|
|x = 0.01||98.02||14.016||-0.6444||84.004||168.008|
|x = 0.02||112.92||7.903||-0.457||105.001||210.002|
|x = 0.03||126.15||5.869||-0.3941||120.281||240.562|
3.7. Magnetoresistance studies
Generally, application of the external magnetic field enhances spin ordering, promotes the charge transfer and thus suppresses the electrical resistivity. Alignment of the spins of the neighboring Mn-sites favors the electronic motion. Figure 8 (a) & (b)shows the temperature dependent magnetoresistance behavior of all the samples from 77K to 300K, for an applied magnetic field of 0.6T. For Sb-doped LBMO samples a sharp peak is observed in all the samples near TP1 and below it MR increases continuously reflecting the important role of grain boundaries in producing LFMR (in case of single crystals MR decreases very fast below TP1). With Sb doping the MR is found to increase. Magnetoresistance for 3% Sb-doped sample La2/3Ba1/3Mn0.97Sb0.03O3 is 6% under the application of 0.6 T magnetic field which shows that this material may be useful from the application point of view. In case of Sb-doped PBMO (Fig. 8b), Pr2/3Ba1/3(Mn1-xSbx)O3 series, besides a usual peak near TP1 there is the development of an additional peak with increasing Sb-content. For 3% Sb sample low temperature peak MR is larger than that the high temperature peak. Also, in case of Sb-doped PBMO, MR value at the respective TP1 decreases with Sb which is reverse to that of Sb-LBMO system. The difference of MR below TP1 may be attributed to the varying grain boundary effects in both the cases. To identify this we carried out the MR measurement with magnetic field variation at 77K and the results are shown in figure 9 (a) & (b). MR behavior of Sb-doped LBMO series exhibits the trend of spin polarized tunneling proposed by Hwang et al. with lower applied field MR increases sharply and at higher values of the field it gets saturated. Whereas in case of Sb-doped PBMO, it seems that spin dependent scattering and not the spin polarized tunneling dominates the process.
3.8. Thermoelectric power
Thermoelectric Power (TEP) is especially suited to explore the carrier dynamics because it is expected to be very sensitive to the local moments63 and thus it monitors the ferromagnetic transition and provide new insight into the dynamics of manganite systems. S(T) is less affected by the presence of grain boundaries and hence the grain boundary effects that are observed in the resistivity temperature measurements, can be masked. The thermoelectric power data for the two series is shown in Figure 10. In the case of Sb-doped LBMO series, a crossover of thermopower is observed from positive to negative at temperature T * = 264, 258, 250, 241 and 210 K respectively with increasing Sb-content whereas in Sb-PBMO series only two samples viz. pristine PBMO and 1% Sb-doped exhibit such behavior. Further, in
case of Sb-LBMO, insulator-metal transition TS is very close to TP1 for all the samples whereas for Sb-PBMO, the two transitions are closer for PBMO sample only and as the doping of Sb increases at Mn-site a peak starts developing near the phase transition and separation between TP1 and TS increases. The development of the thermopower peak and separation of TP1 and TS can be related to the increase in magnetic inhomogeneity due to increase in spin entropy by the weakening of double exchange interaction between Mn+3/Mn+4 ions in the sample with Sb-doping that could lead to a phase separation. In the ferromagnetic state, the magnitude of the observed thermoelectric power in the range of a few μV/K seems to be reminiscent of the metallic system. In order to explain the change of sign of thermopower from hole-like behavior (positive) to electron-like behavior (negative) in the metallic ferromagnetic (FMM) state we adopt the model given by Asamitsu et al. that is based on the vanishing of the exchange interaction J. This interaction arises due to the excitation of the electrons from the valence band (VB) t2g to the conduction band (CB) eg. The mobility of electrons in the conduction band is high, leading to a negative thermopower. The degeneracy of the eg band seems to be gradually lifted as the temperature is lowered below T * and the thermopower changes its sign from negative to positive with the increase of spin polarization. Based on thermoelectric data, we have attempted to explore various mechanisms governing the thermoelectric power in different temperature regions. It would be worthwhile mentioning here that the effect of Jahn-Teller distortion in manganites results in strong electron-phonon coupling and hence the formation of polarons. Therefore, charge carriers in the insulating region above TP are not itinerant and transport properties are governed by thermally activated carriers (polarons). We, therefore, fitted the S(T) data above TS (TP1) fig. 10, with the Mott’s polaron hopping relation66:
where e is the electronic charge; kB is the Boltzmann constant, ES is the activation energy required to activate the hopping of the carriers and α is a constant related to the kinetic energy of the polarons. The value of α < 1 suggests the conduction due to small polarons hopping (SPH) whereas α > 2 corresponds to the case of large polaron hopping (LPH)[ 66]. The fitting for two systems are shown in figure 11. The electrical resistivity activation energy Eρ and the thermopower activation energy ES, are shown in Table 3 for Sb-doped LBMO manganites and from there it is clear that Eρ is much larger than ES. Such a large difference in the values of two activation energies is the indication of the applicability of the small polaron-hopping (SPH) model in the insulating region above TP1 which is further corroborated by the value of constant α (less than 1). In the framework of SPH model, Eρ is the sum of the activation energy required for the creation of the carriers and activating the hopping of the carriers and ES is the energy required to activate the hopping of carriers only. Hence ES is much smaller than Eρ. Based on Eρ & ES, both the polaronic energy WH = Eρ - ES and the polaronic formation energy EP = 2WH are also given in Table 3 for Sb substituted LBMO.
Similar to ρ(T) data, several factors, such as impurity, complicated band structure, electron-electron, electron-magnon scattering etc also affect S(T) data in the FM metallic regime. S(T) data in this intermediate temperature FM metallic region has been analyzed by the following relation68,69:
here S0, S3/2, and S4 are fitting parameters. S0 has no physical origin but inserted to account for the low temperature data, S3/2T 3/2 is attributed to single magnon scattering process,. The term S4T 4 dominant in high temperature region near TC, is thought to arise from spin wave fluctuation in the FM phase,. Figure 12 shows the fitting of Eq. (6) in the metallic region of the Sb-doped LBMO samples and the fitting parameters are given in Table 4. From Table 4, it is clear that S3/2 is nearly five orders of magnitude larger than that of S4, implying that the second term i.e. electron-magnon scattering in Eq. (6) dominates the transport mechanism in the FM metallic regime below TP1. The hole-like to electron-like cross over in thermoelectric power arises due to the fact that S4< 0. Then due to higher power of T, the term S4T4 will dominate for large T making thermopower negative. Hence, based on the electrical resistivity and thermopower data fittings we can conclude that insulating region above TP1 is governed by the small polaron hopping (SPH) model whereas electron-magnon scattering is dominant in ferromagnetic metallic region.
|x = 0||4.5365± 0.03756||-0.00036± 0.00002||- 6.3773x10-10 ± 9.951x10-12|
|x = 0.01||4.7905± 0.06958||-0.00009± 0.00004||- 1.0287x10-9± 2.2475x10-11|
|x = 0.02||4.43458± 0.08659||0.00003± 0.00006||- 1.212x10-9± 3.5867x10-11|
|x = 0.03||3.69632± 0.0923||0.00028± 0.00006||- 1.4882x10-9± 3.8002x10-11|
3.9. Thermal conductivity
Figure 13 shows the temperature dependent thermal conductivity (κ) measurements of Sb-doped manganites. The magnitude of κ(T), typically of non-crystalline materials (bad metals), lies in the range of 5-70 mW/cm K. For a crystalline solid, such a low value of thermal conductivity in manganites can be attributed to the disorder due to strong Jahn-Teller effect. Magnitude of κ decreases with decreasing temperature down to Tκ (close to TS and TP1), which is unusual since the high temperature thermal conductivity of the crystalline insulators is mostly a decreasing function of temperature and cannot be attributed to high temperature electron or phonon processes. Also the thermal conductivity decreases with Sb-doping in the whole temperature range. As discussed earlier, number of Mn+3 -ions increases with Sb-doping and since Mn+3 is a Jahn-Teller ion it causes the distortion in Mn+3O6 octahedra which eventually scatters the phonons and causes κ to decrease with Sb-doping.
At high temperatures thermal conductivity of the crystalline solids is expected to follow the temperature dependency according to the formula κ aMCPθD/ γ2T, where a is the lattice constant, M is the mass per atom, CP is the specific heat, θD is the Debye temperature, and γ is the Gruneisen constant with a value ranging from 2-3 for solids. These parameters are considered to be a weak function of temperature at high temperatures. As a result, κ is expected to increase with decreasing temperature. However, in the present case κ decreases monotonically with temperature for all the samples, which is peculiar. Neutron scattering experiments in these manganites, however, have shown that the Gruneisen constant γ is much higher (~180) than usual and decreases remarkably with temperature. Thus, high temperature behaviour of κ in the paramagnetic state could be understood in terms of the local anharmonic lattice distortions associated with small polarons. An anomaly in thermal conductivity below TP1 has been observed for all the studied samples. It may be noticed that this anomaly is closely related to the phase transition at TP1. Below TP1, κ first increases for pure and 1% doped samples and change in slope for the other doped samples which may be attributed to the reduction in phonon-phonon scattering (Umklapp process) as a result of JT distortions which become delocalized alongwith the charge carriers. The small peak observed in thermal conductivity below 35K in all the samples is an indication of the crossover from Umklapp to defect limited scattering,. In general, the total thermal conductivity for ordinary metals and semimetals is sum of the electronic and lattice terms. The electronic thermal conductivity κe can be evaluated using Wiedemann-Franz (W-F) law κe ρ/T=L. Here ρ is the electrical resistivity and the Lorentz number L is 2.45x10-8 WΩ/K2. Therefore, using the above W-F formula electronic thermal conductivity at any particular temperature (say 250K, where the value of electrical resistivity is shown in Table 5), is very small to the total thermal conductivity κ at that temperature. Hence the measured κ is suggested to arise from phonons, the contribution of charge carriers being negligible.
|x = 0||30.48||0.201||0.0917||12.065|
|x = 0.01||45.95||0.1333||0.194||17.45|
|x = 0.02||64.2||0.0954||0.1265||12.71|
|x = 0.03||119.97||0.0511||0.1231||10.116|
3.10. Specific heat
The observed specific heat measurements [CP(T)] carried out from 85 K to 380 K for the Sb-doped manganites is shown in Figure 14. It increases with temperature for all pure as well as doped samples. There is not much effect of Sb doping up to ~ 250K. However all the samples show a peak in its CP(T) plot just below the corresponding paramagnetic-ferromagnetic transition temperature (TC). For clarity, each curve has been offset by 10 J/mole K. The transition temperature, defined as the peak position, being lower than the
corresponding I-M transition temperature TP1 reflects that the specific heat anomaly is related to the magnetic ordering in the sample due to paramagnetic-ferromagnetic transition. This specific heat anomaly shifts to lower temperatures and becomes progressively broader with Sb-doping. However, no such anomaly corresponding to TP2 could be observed in our measurements, which again confirm that thermal measurements are insensitive to the grain boundaries. Considerable broadening in the CP(T) curves with Sb substituted samples implies the increase in local structural disordering or/and magnetic inhomogeneity.
In order to separate the lattice contribution and to estimate the excess specific heat (∆CP) due to magnetic ordering a smooth background line (tangential to both end points and shown in Fig.14(b) for pristine PBMO manganite) was subtracted from the data of every sample and the obtained curves are plotted in Figure 15. Integration of ∆CP/T gives the excess entropy (∆S) under the CP anomaly of the specific heat curve. Considerable reduction in the value of ∆S is observed with the increase in Sb content (Table 5). This confirms that magnetic inhomogeneity increases with Sb. The value of ∆S is also less than the theoretical value Rln2 for a paramagnetic-ferromagnetic transition (where R is the ideal gas constant). This discrepancy can be attributed to the magnetic inhomogeniety or partially canted spins in the ferromagnetic state.
Substitution effect of Sb5+ ion on the structural, morphological, magneto-transport and thermal properties (including thermoelectric power, specific heat and thermal conductivity) of La2/3Ba1/3MnO3 (LBMO) and Pr2/3Ba1/3MnO3 (PBMO) manganites have been carried out. Structural measurements on polycrystalline samples synthesized showed that lattice parameters increase with Sb-doping. The grain size is also found to increase with Sb. Electrical resistivity variation with temperature of these managnites showed two insulator-metal like transitions (TP1 and TP2) which suppressed to low temperatures with an overall increase in electrical resistivity with Sb substitution. Thermal measurements and their analyses show that high temperature insulating region was governed by the hopping of small polarons and the metallic region below TP1 was dominated by electron-magnon scattering process. Intrinsic magneto-resistance (MR due to grain) at TP1 (high temperature insulator-metal transition) was suppressed whereas extrinsic MR (due to grain boundary) got enhanced with Sb. While in the case of Sb-LBMO, MR kept on increasing below a peak near TP1 in all samples whereas in Sb-PBMO system second peak appeared in MR with its value larger than that at the high temperature peak. MR ~7% was observed in 3% Sb-LBMO sample at room temperature under 0.6T magnetic field which indicates the potential application of these materials as low magnetic field sensors.
The authors are thankful to Prof. Y. K. Kuo (National Dong Hwa University Taiwan), Prof. G. L. Bhalla (University of Delhi, India), Prof. Ashok Rao (Manipal University, India) and Prof. D. K. Pandya (I.I.T. Delhi, India) for scientific discussions. One of the authors (SKA) would like to thank the Council of Scientific and Industrial Research (CSIR, India) for providing the financial grants under the Emeritus Scientist Scheme.