Transport and magneto-transport properties

state, thus making these materials a perfect candidate for maximizing spin polarization, including spin-valve magnetoresistance (MR). In the case of single crystals, however, thin film and ceramic CMR materials, magnetic fields of many teslas are naturally necessary to acquire this colossal magnetoresistive response to applied magnetic fields near FM Curie temperature (TC) [6, 7], thus limiting the potentials for applications. Moreover, a question about the technological relevance of the manganites arises. This is due not only to the fact that this large MR related to TC is limited to a narrow temperature range, but also to the fact that the large resistivity near TC would bring about elevated levels of electrical noise in any real field-sensing device. Drawn up the aforementioned features make these materials worthless for real field-sensing device applications. While CMR is associated with the intrinsic system properties, the so-called low-field MR (LFMR) is another contribution that is extrinsic in nature, whose origin lies in the existence of interfaces and grain boundaries [6-9]. In the case of poly and nanocrystalline manganites, a basic observed feature is a large negative MR at very low fields (LFMR) followed by a slower varying MR in a relatively high-field [high-field MR (HFMR)] regime at temperatures far below the FM Curie temperature TC. This LFMR in manganites is governed by the spin-polarized tunneling transport of conduction electrons across grain boundaries [1, 6, 10]. Despite the potential of LFMR for possible sensor applications, all previously reported experimental results revealed that the effect is significant only at low temperatures and drops drastically with the increase in temperature [1, 6-9, 11]. Near room temperature, such effect nearly disappears since the high degree of spin polarization emanating from the half-metallic nature of these materials, remains only in the low temperature FM regime.
It is in this context that the present work lies to systematically examine the influence of particle size on the electronic and magneto-transport behavior of the La0.8K0.2-xxMnO3 (x = 0 and 0.1) nanoparticles and evaluate the underlying mechanisms of these properties in nano-sized manganites.

2. Experimental details:

Nanocrystalline samples La0.8K0.2-xxMnO3 (x = 0 and 0.1) were prepared by the sol-gel route. Indeed, the stoichiometric amounts of the nitrate precursor reagents La(NO3)3 6H2O, Mn(NO3)2 4H2O and KNO3 were dissolved in water and mixed with ethylene glycol and citric acid, forming a stable solution. The molar ratio metal:citric acid was 1:1. The solution was then heated on a thermal plate under constant sintering at 80° C to eliminate the superfluous water and get a viscous gel. The obtained gel was decomposed at 300° C and the resulting precursor powder was heated in air at 500°, 600° and 700° C for 24 h to improve crystallinity. Subsequently, the powder was pelletized and sintered at 700° C for 12 h. The samples were quenched in air by eliminating the furnace.
The crystallinity and phase composition of the powders were checked by X-ray diffraction (XRD) pattern using (CuKα) radiation source. The average particle sizes of the samples were estimated both from the X-ray peak width using Debye-Scherer formula and from transmission electron microscopy (TEM) imaging.
The magnetic measurements were performed with a BS1 and BS2 magnetometer developed at Néel Institute. Electronic transport and magneto-transport properties have been performed by the standard four-probe method in a commercial Physical Property Measurement System (PPMS Quantum Design) under different magnetic applied fields.

3. Results and discussions:

X-ray diffraction measurements at room temperature indicate a single-phase nature of both nanoparticle samples x = 0 and 0.1 (Fig. 1.a).
The obtained results reveal that both samples are crystallized in the rhombohedral structure belonging to the space group. It is noteworthy that the structural and magnetic details were formerly published in our work [12].
The average particle size was estimated from the X-ray peak width by using the Scherer formula:
(1)
where λ is the X-ray wavelength, θ and β are the diffraction angle and the full width for the most intense peak with:
β = – (2)
is the experimental full width at half maximum (FWHM) and is the FWHM of a standard silicon sample.
The D values were found to be 50 and 69 nm, respectively, for x = 0 and 0.1 nanoparticle samples.
The particle size was also checked using TEM. Fig 1. b gives the representative TEM images for La0.8K0.2-xxMnO3 (x = 0 and 0.1) samples with different sizes were found to be similar to the values estimated from the XRD peaks (45 and 65 nm, respectively for x = 0 and 0.1).
Before embarking on the study of electronic transport properties, we evoke our conclusion pertaining to the previously-published magnetic properties [12]. We reported that with the increase in temperature, all samples exhibit a magnetic transition from a paramagnetic (PM) to a ferromagnetic (FM) state. The associated Curie Temperature TC decreased with x from 325 to 300 K for x = 0 and 0.1, respectively.
The temperature (T) dependence of the zero field resistivity  (T) for both nanoparticle samples x = 0 and 0.1 with different grain sizes is shown in Fig. 2.
It is to be noted that the electrical resistivity shows a complex variation, decreasing from low temperature, going through a minimum at around 50 K (Tmin) and a maximum near room temperature, indicating the existence of metal-insulator transition at TMI = 270 and 235K for x = 0 and 0.1, respectively. On the other hand, It is worthwhile that the resistivity  decreases systematically with the increase in grain size over the whole range of temperature. This is not surprising considering that  is gradually influenced by the presence of grain boundaries, which act as regions of improved scattering for the conduction electrons and disorder. As shown by Isaac et al. [13] and Sanchez et al. [14], the spin becomes greatly disordered at the grain boundary because of the strain with the reduction of the grain size, which may result in the growth of the resistivity. Moreover, Das et al. [15] have proposed that the resistivity decreases considerably with the grain growth as the boundaries of the grains comprise more magnetic disorder than the cores. Gupta et al. [16] explain the variation in properties with grain size as the reflection of magnetic disorder induced canting of Mn spins near the surface of the grains. On the other side, many studies have been conducted on the manganite family to explain the minimum resistivity observed at low temperature [1-3]. With the increase of temperature, Tmin clearly moves towards lower temperatures as the particle size increases, which can be seemingly accredited to the drop of the GB effect [17].
We present a detailed study of the effect of constant external magnetic field on the temperature dependence of electrical resistivity of both nanoparticle samples x = 0 and 0.1 on the charge transport in the low temperature region (5 K < T < 70 K), ferromagnetic metallic region (70 K < T < TMI), and paramagnetic insulating region (TMI < T < 300 K) by fitting through three main conduction mechanisms.

3. 1 low temperature region (5 K < T < 70 K).

Generally, the origin of this phenomenon has been ascribed to the competition of two contributions [18]. The first one is the Coulomb blockade effect (CB, an electrostatic blockade of carriers between grains) [1, 3, 19-20] of weak localization and strong electron-electron interaction with a disordered metallic state [21].
Considering the bulk scattering model, which comprises quantum correction to conductivity, Rozenberg et al. claimed that this model is in intense disagreement with the experimental data for ceramic manganites as the resistivity minima is present even in a finite magnetic field [18]. Nevertheless, for strongly field-dependent minima of resistivity at low temperature for granular materials, intergranular spin polarized tunneling model (ISPT) is proposed [22].
According to this model, the depth of the resistivity minima decreases with rise of magnetic field, and at a specific field value, it disappears. The simplified functional form of resistivity at low temperature, considering tunneling through the grain boundary, is given by [23]:

(3)
where r1 and r2 are field-independent parameter and is linked to the degree of polarization of the charge carriers in each granule. In the absence of an external magnetic field, the spin correlation function is represented by the following equation:
(4)

where, is the Langevin function and ‘J’ is the inter grain antiferro-magnetic exchange integral. In the presence of an external magnetic field, Ciftja et al. deduced the analytical expression for spin correlation function, which is given by the following equation [24]:
(5)

where, and S is the atomic ion spins [22].
Similar upturn trend of resistivity is also expected for CB effect in the granular system. Sheng et al. deduced the expression describing the growing nature of resistivity at low temperature, which is given by:
(6)

where ‘A’ is the fitting parameter and is the energy barrier [25]. The presence of CB contribution in the resistivity of manganites has been studied by several authors. For example, Balcells et al. made the experimental estimation of the CB effect in resistivity for La0.7Sr0.3MnO3 having different grain sizes [26]. Furthermore, Dey et al. have proven that for single phase nanocrystalline La0.7Ca0.3MnO3 of particle size 14-27 nm, the low temperature upturn in resistivity can be well described considering the CB effect [2]. Physically, the CB effect cannot describe the extremely field-dependent minima of resistivity at low temperature.
In our case Tmin shift to low temperature under the magnetic field. Hence, it can be concluded that the ISPT model is mainly responsible for the resistivity minimum at low temperatures of strong field- and particle-size dependence of the nanocrystalline manganites (Fig. 3).

3. 2 Ferromagnetic metallic region (70 K T TMI)

In this ferromagnetic metallic region, there is a ferromagnetically coupled interaction of electrons from neighboring Mn3+ to Mn4+ ions through oxygen when their localized spins are parallel [27], which is responsible for the simultaneous occurrence of ferromagnetism and metallic conduction below TMI in these manganites [28].
To understand the conduction mechanism of the materials at this temperature region, the experimental data are found to be in good agreement with the empirical equation of the type , where is the residual resistivity due to domain boundary and other temperature-independent scattering mechanisms [29], where n = 1, 2, 2.5, 4.5, 5 and 7.5.
On the first hand, in the metallic region, the transport mechanism is generally described by one of these equations based on the scattering mechanism:
(7)
(8)
(9)

where, is the electrical resistivity due to electron-magnon scattering process in the ferromagnetic phase [30]. The term is a combination of electron-electron, electron-magnon and electron-phonon scattering processes [31, 32]. The term is ascribed to the electron-phonon interaction [33]. The experimental data were analyzed taking in to consideration the mentioned equations. We have deduced that that the best fit of our experimental results is obtained by the use of Eq. (9), which shows that the transport mechanism at low temperature is governed by the electron-electron and electron-phonon scattering process (Fig. 4).
3. 3. Paramagnetic insulating region (TMI T 400 K)

It is well documented that at high temperature region, especially above the metal insulator transition, the electronic transport is governed through small polaron hopping [34]. The classical expression for the resistivity in this temperature region is given by the expression:

(10)

where A is a pre-exponential coefficient, Ea is the activation energy and KB is the Boltzmann constant.
For our samples, we found that this model is responsible for transport at high temperature region. Fig. 5 confirms the validity of this model through a linear shape of Ln( /T) curves as a function of T-1. Activation energy Ea was calculated from the slope of the fitted line and it was found to be 13.06 and 1.243 eV for x = 0 and 0.1, respectively.

4. 4 Magnetoresistance properties

The coexistence of ferromagnetism and metallic conductivity at low temperatures proves the coexistence of MR. This phenomenon has two different contributions [35], the first which is the intrinsic MR (IMR), emanating from the suppression of spin fluctuations by aligning the spins on the application of magnetic field. This MR has the highest value near the ferromagnetic transition temperature Tc, and it is commonly observed among single-crystalline bulk as well as thin films. There is an additional MR, which is extrinsic in nature (EMR), due to the inter-grain spin polarized tunneling (ISPT) across the grain boundaries (GBs). This MR contribution rises with the decline in temperature and is typically found in nanocrystalline materials.
The temperature dependence of magnetoresistance (MR) [MR = {R(H) – R(0)}/R(0)] at different magnetic fields of nanocrystalline samples La0.8K0.2-xxMnO3 (x = 0 and 0.1) is displayed in Fig. 6. It is worthy to note that the studied samples does not only exhibit high MR at high magnetic fields but also remains high in low temperature regime and then decreases with the increase in temperature. Consequently, both samples can be deduced to exhibit a competition between IMR and EMR by showing the existence of a small peak in MR observed around TMI and the increase of MR on cooling, respectively.
This sharp drop of MR observed at low temperature can be explained by taking into account the intergranular spin polarized tunneling happening through the GBs [1, 3, 36]. Thus, the nature of the grain boundary is the key ingredient in the mechanism of the electrical transport, as it constitutes the barrier through which carriers tunnel. The application of an external magnetic field brings about the movement of the magnetic domain walls through the grain boundaries. This movement is associated with the progressive alignment of magnetic domains, and as a result, a sharp drop of MR at low fields is commonly observed.
We have also studied the evolution of MR as a function of magnetic field of nanocrystalline samples La0.8K0.2-xxMnO3 (x = 0 and 0.1) (Fig. 7). Those curves exhibit distinct large low-field MR (LFMR), characterized by a sharp drop of MR at low fields (H 1 T), followed by a slower varying MR at a comparatively high-field regime (H 1 T ), where MR is almost linear with H. Therefore, it is interesting to separate out the part of the MR originating from SPT (MRSPT) from the part of the MR identified by the suppression of spin fluctuation (MRINT) and chiefly to examine their respective temperature dependencies. To this end, we have used the model as suggested by Raychaudhuri et al. [8], based on SPT transport of conduction electrons at the grain boundaries with a special focus on the magnetic domain wall motion at grain boundaries under the application of a magnetic field. Extending the idea of SPT as suggested by Helman and Abeles [22], this model describes the magnetic field dependence of MR taking into consideration the regular slippage of domain walls across the grain boundaries’ pinning centers in an applied magnetic field. From this model, we obtain the expression for MR as:
(11)
where, J, H and K are field-independent constants, whereas f (K) is defined by the pinning strength of the grain boundaries as pinning centers and is considered as the weighted average of a Gaussian and skewed Gaussian distribution, which is given by the following equation:
(12)

By using the value of the fitting parameters A, B, C, D, J and K (because is absorbed in A and C), one can separate out MRSPT and MRINT parts from total MR as follows:
(13)

(14)

To fit the MR data of the nanostructure compounds, we have followed the same procedure as that considered by Raychaudhuri et al [7, 8]. Differentiating Eq. (11) with respect to H and putting Eq. (12), we get:
(15)

The experimental (MR-H) curves were differentiated and fitted to Eq. (15) to find the best-fit parameters at several temperatures (Fig. 8)
Using these best fitting parameters, we have calculated MR as a function of H from Eq. (11). The variation of MR with an external magnetic field along with the fitted line for x = 0 and 0.1 samples are shown in Fig. 7.
By using the best-fitted parameters at different temperatures, we have calculated the temperature dependence of MRSPT and MRINT for both compounds from Eq (13) and (14), respectively.
The variation of MRSPT and MRINT is plotted in Fig. 9 (a) and (b), respectively.
It is clear that MRSPT decreased with the increase of the particle size. Actually, it is reported that MRSPT is very sensitive to the grain surface effect, which is estimated to be continuously increasing with the decrease in the particle size [1, 2]. The moment surface effect is brought to the fore, showing that it is not the direct SPT of conduction electrons between two neighboring grains can explain this strange phenomena. Again, the direct tunneling model, as previously suggested by Helman and Abeles [22] in granular nickel films, principally pictures a decrease of MR with the increase in temperature. Thus, to illustrate the basic physics behind this unusual temperature dependence of MR, the dominating key factor needs to be given importance is the intermediate state of tunneling involving the grain boundary interface, which makes it sensitive to the magnetization of the surface (MS) [11]. Grain surface magnetization or shell magnetization (MS) will be substantial to be studied under the effect of a magnetic field. The presence of a magnetic field will diminish the antiferromagnetism [37] at the grain surface; at significantly high fields, the surface spins will tend to align parallel to the bulk. As a main result from an application point of view, this type of MR (SPT) occurs at relatively weak fields which is promising for potential application such as magnetic field sensor and spintronics.
To further understand the relevance of MS in this nanodimensional manganites case, we should take into account the nanometric grain size of our samples for which the surface-to-volume ratios of each individual grain are satisfactorily large. Hence, surface-related physical properties are thought to be very much more noticeable than its bulk counterpart. Following this, we may sensibly proclaim that the relevant magnetization controlling the spin-polarized tunneling is that of the surface rather than the bulk. It has been previously reported that in the nanosize regime, with the increase in surface-to-volume ratio, net magnetic behavior is dominated by surface magnetic properties [38-40]. Nevertheless, the microscopic nature of the grain surface region has not been well understood so far. Moreover, there is inconsistency between several reports on the behavior of MS of manganites grains. For example, while Park et al [41] affirms that MS is suppressed compared to the bulk magnetization, Soh et al [42] reported that the TC near the grain boundary is boosted, up to 20 K higher than the grain interior. However, to address this phenomenon, we have adopted the theoretical perspective reported by Lee et al [11], according to which magnetoconductivity ( ) as a function of magnetic field is given by :

(16)
where is the zero-field conductivity, Sb is the spin orientation at the grain boundary, and M is the normalized magnetization of the bulk spin. At high fields, Eq. (16) reduces to:

. (17)
Here the third term yields , since the third term can be written as , where is the angle between Sb and M. The thermal average of the boundary spin is proportional to , where is the spin susceptibility of the boundary spins. Hence, to analyze our data using this model, we have presented in Fig. 10 (a) and (b), a detailed study of magnetoconductivity (MC), calculated as as a function of temperature and magnetic field for La0.8K0.2-xxMnO3 (x = 0 and 0.1) nanocrystalline samples, respectively. Considering the model, the slope (S) of the MC versus H curve at high-field regime can be taken to be the measure of the surface spin susceptibility . Fig. 10 (c) and (d) show the temperature dependence of surface spin susceptibility ‘S’ of La0.8K0.2-xxMnO3 (x = 0 and 0.1) samples. Interestingly, we found that the nature of the S (T) is qualitatively similar to that of MR (T). On the other hand, comparing the magnitude of S at T = 50 K of our samples, we found that the magnitude of S for x = 0 is 23 order larger than that of x = 0.1 sample.
This theoretical analysis indirectly supports our understanding of the role of the MS, which we believe to be the key factor for this unusual temperature-dependent behavior of MR in our nanodimensional manganite system. In the aim of providing a reliable physical explanation of this insensitive temperature behavior of MR, as well as that of to substantially high temperatures, we would like to recall the fact that in the case of nanocrystalline materials, grain boundaries provide defect sites where the anisotropy energy of the surface spin is minimum. So, a strong pinning of surface spins may be expected at the disordered surface of polycrystalline grains. In the present case, due to the nanometric grain size of our manganites samples, the surface-to-volume ratio of each individual grain is sufficiently large, and therefore the following physical effects are most probable to occur in a higher degree. These effects are (a) contamination of the grain surface, (b) breaking of Mn-O-Mn paths at the grain surface, (c) deviation of stoichiometric composition at the grain surface, (d) termination of the crystal structure at the grain surface, and (e) dislocation at the grain boundaries. Drawn together, these effects make the surface of our nanocrystalline manganite grains full of defect sites having strong pinning strength (k) of spin at the grain surface.

4. Conclusion:

In brief, our results indicate that the particle size effect plays a significant role in determining the transport and magneto-transport properties of La0.8K0.2-xxMnO3 (x = 0 and 0.1) synthesized by a sol-gel method. We shed the light on the effect of particle size on the electrical properties of the samples in the low-temperature region (5 T 70 K), ferromagnetic metallic region (70 K T TMI) and paramagnetic-insulating region (TMI T 400 K) based on three electrical conduction models.
The resistivity minimum at low temperatures is well described by spin polarized tunneling model through the GBs. It is concluded that both samples exhibit a competition between IMR and EMR by showing the existence of small peak in MR observed around TMI and the increase of MR on cooling, respectively. The sharp drop of MR observed at low temperature has been explained by taking into consideration the intergranular spin polarized tunneling occurring through the GBs. Most interestingly, the MR as a function of magnetic field measurements show that LFMR as well as HFMR varied slowly with H. We have analyzed our experimental MR data following a phenomenological model to separate out the MR arising from spin-polarized transport (MRSPT), from the intrinsic contribution in our nanosize granular La0.8K0.2-xxMnO3 (x = 0 and 0.1) samples. As a main result from an application point of view, we note that the enhancement of magnetoresistance with particle size also has relevance for the development of new materials and devices in the technological perspectives as magnetic field sensor and spintronics.