Small Polaron Hopping Model Research Articles

Correlation between structural, magnetic and electrical transport properties of barium vacancies in the La0.67Ba0.33−x□xMnO3 (x=0, 0.05, and 0.1) manganite

Abstract We investigate the effects of barium vacancies on the physical properties of the La0.67Ba0.33−x□xMnO3 (x = 0, 0.05, and 0.1) manganite. The X-ray diffraction studies show that all samples crystallize in the rhombohedral structure within the space group R-3c (No. 167). Rietveld refinement shows that the barium vacancies modify the structural parameters such as the volume, the Mn–O bond length and the Mn–O–Mn angles. An increase of the Mn–O bond length with increasing barium deficiencies leads to the decrease of the one-electron bandwidth W, which results in a decrease of the Curie temperature (TC) and of the metal–semiconductor transition temperature (TM-SC). Magnetic measurements showed a paramagnetic to ferromagnetic transition at T = TC. The temperature dependence of the resistivity shows that all samples undergo a sharp metal–semiconductor transition at TM-SC accompanying the ferromagnetic-paramagnetic transition. Metallic resistivity ρ(T) = ρ0 + ρ2T2 + ρ4.5T4.5 is observed below TM-SC. Above TM-SC the electrical conductivity is dominated by adiabatic small polaron hopping model (ASPH), giving the electrical resistivity in the paramagnetic region as ρ = BT exp (Ea/kBT). Based on the idea that the doped manganites consist of ferromagnetic-metallic and paramagnetic-semiconducting regions coexisting in the same specimen, a good fit of ρ(T) with a phenomenological percolation model may be obtained by combining the contributions of the resistivity above and below TM-SC by a single expression in the temperature region between 15 and 390 K. We found that the estimated results are in good agreement with the experimental data. Our results show that the transition to a metallic state occurs if the volume fraction of the ferromagnetic phase f reaches a percolation threshold. We also found that the volume fraction of the ferromagnetic phase f has the same physical meaning as the reduced magnetization M/MS (MS, saturation moment).

High-temperature metal–insulator transition in YxCa1−xMnO3 (0.05⩽x⩽0.12): An electron-spin resonance study

Abstract Electron-spin resonance (ESR) studies have been performed on Y x Ca 1− x MnO 3 (0.05 ⩽ x ⩽ 0.12) compounds in the temperature range from 140 K to 470 K. It is found that with the temperature increasing, the ESR linewidth increases to the maximum at T max (=200 K, 220 K, and 270 K for x = 0.08, 0.10, and 0.12, respectively), and then decreases for all the compounds except that with x = 0.05 which shows a continuous decrease in the whole temperature range. For x ⩾ 0.08, the change of the ESR linewidth can be described very well by the adiabatic small polaron hopping model in the temperature range from 140 K to T max . The ESR intensity decreases with temperature increasing for all the compounds between 140 K and 470 K except 300 K ⩽ T ⩽ 330 K in which it increases with temperature increasing. Meanwhile, the g -factor reaches the minimum at about T = 300 K. The characteristics of the ESR linewidth and intensity indicate the appearance of the short-range magnetic correlations and that the spin–lattice relaxation plays an important role for x ⩾ 0.08. In addition, the electronic transport properties of Y x Ca 1− x MnO 3 compounds reveal a metal–insulator transition at T MI which varies from 254 K to 293 K with Y content increasing. The resistivity versus temperature between 140 K and T MI can be fitted well by the adiabatic small polaron hopping model. It is suggested that the metal–insulator transition in Y x Ca 1− x MnO 3 compounds is correlated with the variation of the magnetism under high temperature.

Thermopower and resistivity studies of Nd-Na-Mn-O manganites

The electrical transport properties of the polycrystalline Nd1−xNaxMnO3 (0.05 ≤ x ≤ 0.25) were investigated. All the samples are found to exhibit insulating behavior down to the lowest measured temperature. However, on application of 4 T magnetic field, metal-insulator transitions along with a low temperature resistivity upturn are observed for the samples with x ≥ 0.15. Thermopower values of samples with x = 0.05, 0.10, and 0.20 are negative in the entire temperature range of investigation, while they changes from negative to positive with decreasing temperature in the case of samples with x = 0.15 and 0.25. The resistivity and thermopower data in the high temperature region are explained within the framework of variable range and small polaron hopping models, while the resistivity minima are explained using the combined effect of electron-electron and electron-phonon scattering is considered.

Electrical and magnetic properties of La0.67Ba0.33Mn1−x (Me) x O3 perovskite manganites: case of manganese substituted by trivalent (Me = Cr) and tetravalent (Me = Ti) elements

The effects of non-magnetic Ti4+ substitution on the structural, electrical and magnetic properties of La0.67Ba0.33Mn1−x Ti x O3 (0≤x≤0.1) are investigated and compared to those existing in La0.67Ba0.33Mn1−x Cr x O3 (magnetic Cr3+). The structural refinement by the Rietveld method revealed that Ti-doped samples crystallize in the cubic lattice with space group $\mathrm{Pm}\bar{3}\mathrm{m}$ , while samples with Cr crystallize in the hexagonal setting of the rhombohedral $\mathrm{R}\bar{3}\mathrm{C}$ space group for identical contents of dopant. The most relevant structural features are an increase of the lattice parameters, of the cell volume and of the inter-ionic distances with increasing Ti doping level. Both series of samples show a decrease of the paramagnetic–ferromagnetic transition temperature when the amount of chromium or titanium increases. Transport measurements show that when increasing the metal doping, the resistivity increases whereas the metallic behavior of the parent compound La0.67Ba0.33MnO3 is destroyed. For a substitution higher than 5 at.% of Ti and 10 at.% of Cr, the samples exhibit a semiconducting behavior in the whole range of temperature, for which the electronic transport can be explained by variable range hopping and/or small polaron hopping models.

Structural characterization and observation of variable range hopping conduction mechanism at high temperature in CdSe quantum dot solids

We have used Rietveld refinement technique to extract the microstructural parameters of thioglycolic acid capped CdSe quantum dots. The quantum dot formation and its efficient capping are further confirmed by HR-TEM, UV-visible and FT-IR spectroscopy. Comparative study of the variation of dc conductivity with temperature (298 K ≤ T ≤ 460 K) is given considering Arrhenius formalism, small polaron hopping and Schnakenberg model. We observe that only Schnakenberg model provides good fit to the non-linear region of the variation of dc conductivity with temperature. Experimental variation of ac conductivity and dielectric parameters with temperature (298 K ≤ T ≤ 460 K) and frequency (80 Hz ≤ f ≤ 2 MHz) are discussed in the light of hopping theory and quantum confinement effect. We have elucidated the observed non-linearity in the I-V curves (measured within ±50 V), at dark and at ambient light, in view of tunneling mechanism. Tunnel exponents and non-linearity weight factors have also been evaluated in this regard.

Adiabatic to non adiabatic change in conduction mechanism of Zn doped La0.67Sr0.33MnO3 perovskite

We reported the results of electrical transport properties of La0.67Sr0.33Mn1−xZnxO3 (x=0.1 and 0.2) bulk samples prepared by solid-state reaction route over a wide temperature range from 5 to 300K in the presence of magnetic fields. Powder X-ray diffraction patterns at room temperature confirmed that both samples were formed in a single phase. Temperature dependent resistivity data were fitted using Mott’s variable-range hopping (VRH) model for a limited range of temperatures (from 235.5 to 300K for 10% Zn doped and from 133 to 300K for 20% Zn doped samples) to calculate the hopping distance (Rh) and the density of states near the Fermi level, [N(EF)]. It was found that all the parameters vary systematically with the increase in Zn concentration. Moreover, the temperature dependent resistivity data were also fitted using the small polaron hopping (SPH) model. The adiabatic SPH conduction is followed for 10% doped sample at all fields while a non-adiabatic SPH conduction is found to be active for 20% doped sample in all fields. This type of change in the conduction mechanism is accompanied by subtle electronically induced structural changes involving Mn–O–Mn and Zn–O–Mn bond angles and bond lengths. Thus, we suggest that the transport properties can be explained according to the additional delocalization of charge carriers induced by Zn doping.

Dielectric and transport properties of bismuth sulfide prepared by solid state reaction method

We report synthesis of bismuth sulfide (Bi2S3) via conventional solid state reaction method at low temperature ∼150 °C and ambient pressure. X-ray diffraction analysis confirmed the orthorhombic phase of prepared material. Transmission electron microscope images revealed the formation of nanorods having diameter ∼20 nm and length ∼100 nm to ∼150 nm. Impedance and modulus plane plots from 20 Hz to 2 MHz show presence of bulk and grain boundary phases in Bi2S3 at each measurement temperature from 310 K to 400 K. An equivalent circuit model comprised of two resistance–R and constant phase element-Q (RQ) loops in series explains the electrical parameters (resistance and capacitance) and relaxation processes coupled with grains and grain boundaries. The conduction in Bi2S3 obeyed adiabatic small polaron hopping model. High and temperature dependent dielectric constant was observed in Bi2S3 suggesting it as an efficient material to be used in capacitive energy storage devices.

Metal-Insulator Phase Transition and Structural Stability in ‘Sb’ Doped CaMnO3 Perovskite

Electron doped Ca1-xSbx MnO3 (X = 0 to 0.4) compound when prepared by high temperature solid state reaction, exhibits orthorhombic distorted perovskite structure. A systematic, continuous doping increases the metal – insulator transition temperature to above the room temperature (≈431 to 469 K); due to the mismatch of ionic radii in A site rising anti - site effect, which consequently changes the bond length. Doping induced metal – insulator transition accompanied by structural transition is reflected through the drastic changes in the parameters like cation size variance factor (), average ionic radius <r>, tolerance factor (t) and To-which is correlated to the band related transport properties. Structural transition from the phase of perovskite to Brownmillerite has been found for the compositions x = 0.3 and 0.4, which is attributed due to the ionic radii mismatch. Doping exerts chemical pressure by modifying compression of A-O bond and relaxation of B-O bond, giving rise to strain similar to external pressure in ABO3 perovskite. The dependence of electrical transport at high temperature has been studied, by employing variable range hopping and small polaron hopping model as an account for the experimental observation due to disorder induced localization.

Change of conduction mechanism in the impedance of grain boundaries in Pr0.4Ca0.6MnO3

Freshly synthesized polycrystalline Pr0.4Ca0.6MnO3 sample has been analyzed by employing X-ray diffraction, magnetization and impedance spectroscopic techniques. Magnetization M(T) showed charge ordering (TCO) around 268K and below this temperature variation of magnetic and electric field effects is discussed. With the decrease of temperature, the change in the size and shape of the impedance plane plot is explored in terms of modulation of different relaxation processes. An equivalent circuit model (RQ) is used to determine the electrical parameters of Pr0.4Ca0.6MnO3 sample at different temperatures. Impedance of grain boundaries derived from the fitting of experimental data using an equivalent circuit model shows a change in conduction mechanism from small polaron hopping (SPH) to the variable range hopping (VRH) model around 148K. Activation energies calculated from the SPH model and relaxation frequencies of imaginary part of impedance are compared and discussed. Average normalized change (ANC) deduced from the impedance data illustrates a change in conduction mechanism around 148K due to the superexchange networks of Mn3+ and Mn4+.

High-temperature thermoelectric characteristics of B-site substituted Yb0.1Ca0.9Mn1−x Nb x O3 system (0≤x≤0.1)

The thermoelectric performance of Yb0.1Ca0.9MnO3 doped with Nb5+ at B-site is investigated in this paper. It is found that there is a phase transition from O-type to O*-type orthorhombic structure with increasing of Nb doping content, which indicates that the structure distortion becomes more seriously. Since the electron–phonon interaction can be enhanced by the structure distortion, the small polaron formation is promoted in Yb0.1Ca0.9Mn1−x Nb x O3 with increasing Nb content. In the whole measured temperature range, the electrical conductivity can be fitted very well by the adiabatic small polaron hopping model. The activated energy E α is ascending with increasing Nb content. The temperature dependence of Seebeck coefficient S of Yb0.1Ca0.9Mn1−x Nb x O3 shows that the S is basically inversive to the charge carrier concentration. S(T) can be fitted well by the Cutler and Mott model, which indicates that the density of state around the Fermi level is strongly affected by Nb-doping at B-site. It is contrary to those of CaMnO3 and RE0.1Ca0.9MnO3, when Nb content x>0.05, the |S| and σ show a same tendency of the temperature dependence.

Electrical and spectroscopic properties of Fe2O3 doped Na2SO4–BaO–P2O5 glass system

Na2SO4–BaO–P2O5 glasses doped with different concentrations of Fe2O3 were prepared. The valence states of iron ions and their coordination in the glass network have been investigated using optical absorption, ESR, IR and Raman spectroscopy. Electrical and dielectric spectral features have been studied over a wide frequency range (10−2–106Hz) and within the temperature range from 303 to 523K. The ac and dc conductivities have exhibited maximal effect, whereas the activation energy for the conductivity demonstrated minimum at 1.5mol% of Fe2O3. The ac conductivity in the low temperature region is explained based on quantum mechanical tunneling (QMT) model. The analysis of the dc conductivity indicated that at T>θD/2, the small polaron hopping model is appropriate. The dispersion of real part of dielectric constant ε′(ω), and loss, tan δ, with temperature have been analyzed quantitatively on the basis of space charge and orientation polarization models.

Surface wettability of titania thin films with increasing Nb content

TiO2 and TiO2/Nb amorphous thin films were grown on glass substrates by a sol-gel technique (spin coating). Films' surface composition, structure, and morphology were derived from x-ray photoelectron spectroscopy, x-ray diffraction, and atomic force microscopy data. The investigated films showed a smooth surface (roughness values below 5 nm). A separate surface wettability investigation showed that by increasing the Nb amount in pristine titania films results in a decrease of contact angle (CA) values from 40° to nearly 0°, thus, indicating a super-hydrophilic conversion under UV illumination. This conversion rate is greatly enhanced by increasing the Nb content, the surface super-hydrophilic behavior occurring after a couple of minutes in the TiO2/Nb samples, but after 4 h in the pristine titania specimen. The current results are discussed in terms of the optical band gap shift towards higher energies, by increasing the Nb content in the films, a process explained based on small polaron hopping model.

Structural and electrical properties of Nd1.7Ba0.3Ni0.9Cr0.1O4+δ compound

The Nd1.7Ba0.3Ni0.9Cr0.1O4+δ polycrystalline sample was synthesized by the sol–gel process and a subsequent annealing at 1523 K in 1 atm of flowing argon. X-ray diffraction (XRD) analysis and electrical transport properties have been investigated as well. The oxygen non-stoichiometry was determined by iodometric titration. The sample shows adoption of the K2NiF4-type structure based on a tolerance factor calculation. Rietveld refinement of the crystal structure from X-ray powder diffraction data confirmed that Nd1.7Ba0.3Ni0.9Cr0.1O4+δ adopts the tetragonal structure (space group I4/mmm, Z = 2). The room temperature unit-cell parameters are determined to be a = 3.82515(2) and c = 12.47528(6) Å. The reliability factors are: RB = 0.043, Rwp = 0.012 and χ2 = 3.00. The Nd1.7Ba0.3Ni0.9Cr0.1O4+δ compound exhibits a semi-conductive behaviour. The electrical transport mechanism has been investigated and it agrees with the adiabatic small polaron hopping model in the temperature range 313 K ≤ T ≤ 708 K.

Structural and electrical properties of La0.5Ca0.5Mn0.95Fe0.05O3+δ perovskite

La0.5Ca0.5Mn0.95Fe0.05O3+δ was synthesized by co-precipitation method. The structure refinement by using the Rietveld method indicates that the sample was single phase with the presence of small impurities (Mn3O4) and crystallizes in an orthorhombic (Pbmn) structure. The room temperature (RT) Mössbauer spectrum shows clear evidence of the local structural distortion of the Mn(Fe)O6 octahedron on the basis of non-zero nuclear quadrupole interactions for high-spin Fe3+ ions. The Jahn–Teller coupling strength (EJT) was estimated from the Mössbauer results. Metal-Semiconductor transition temperature (Tp) is observed at 80K. At high temperature (TP<T<θD/2) conductivity data satisfy the variable range hopping (VRH) model. For T>θD/2 the small polaron hopping model is more appropriate than the VRH model.

Enhanced low-field-magnetoresistance and electro-magnetic behavior of La0.7Sr0.3MnO3/BaTiO3 composites

We report the structural, magentoresistance and electro-magnetic properties of ferromagnet–ferroelectric–type (1−x)La0.7Sr0.3MnO3/xBaTiO3 (with x=0.0%, 3.0%, 6.0%, 12%, 15.0% and 18.0%, in wt%) composites fabricated through a solid-state reaction method combined with a high energy milling method. The insulator–metal transition temperature shifts to a lower temperature and resistivity increases while the feromagnetic–paramagnetic transition temperature remains almost unchanged with the increase of BaTiO3 content. Magnetoresistance of the composites at an applied magnetic field H=3 kOe is enhanced in the wide temperature ranges with the introduction of BaTiO3, which could be explained by the enhanced spin polarized tunneling effect induced by the introduction of BaTiO3. The low-field magnetoresistance of the composite is analyzed in the light of a phenomenological model based on the spin polarized tunneling at the grain boundaries. Furthermore, the temperature dependence of resistivity for this series has been best-fitted by using the adiabatic small polaron and variable range hopping models. These models may be used to explain effect of BTO on the electronic transport properties on high temperature paramagnetic insulating region.

Influence of Ce doping on electrical and thermal properties of La0.7−xCexCa0.3MnO3 (0.0≤x≤0.7) manganites

The effect of Ce-doping on structural, magnetic, electrical and thermal transport properties in hole-doped manganites La0.7−xCexCa0.3MnO3 (0.0≤x≤0.7) is investigated. The structure of the compounds was found to be crystallized into orthorhombically distorted perovskite structure. dc Susceptibility versus temperature curves reveal various magnetic transitions. For x≤0.3, ferromagnetic regions (FM) were identified and the magnetic transition temperature (TC) was found to be decreasing systematically with increasing Ce concentration. The electrical resistivity ρ(T) separates the well-define metal-semiconducting transition (TMS) for low Ce doping concentrations (0.0≤x≤0.3) consistent with magnetic transitions. For the samples with 0.4≤x≤0.7, ρ(T) curves display a semiconducting behavior in both the high temperature paramagnetic (PM) phase and low temperature FM or antiferromagnetic phase. The electron–phonon and electron–electron scattering processes govern the low temperature metallic behavior, whereas small polaron hopping model is found to be operative in PM phases for all samples. These results were broadly corroborated by thermal transport measurements for metallic samples (x≤0.3) in entire temperature range we investigated. The complicated temperature dependence of Seebeck coefficient (S) is an indication of electron–magnon scattering in the low temperature magnetically ordered regime. Specific heat measurements depict a broadened hump in the vicinity of TC, indicating the existence of magnetic ordering and magnetic inhomogeneity in the samples. The observation of a significant difference between ρ(T) and S(T) activation energies and a positive slope in thermal conductivity κ(T) implying that the conduction of charge carriers were dominated by small polaron in PM state of these manganites.

Structure and electrical conductivity relaxation studies of Nb2O5-doped B2O3–Bi2O3–LiF glasses

Glasses with composition (70 − x) B2O3·15Bi2O3·15LiF·xNb2O5 with x = 0–1.0 mol% were prepared by conventional glass-melting technique. The molar volume Vm values decrease and the glass transition temperatures Tg increase with increase of Nb2O5 content up to 0.2 mol%, which indicates that Nb5+ ions act as a glass former. Beyond 0.2 mol% Nb2O5 the Vm increases and the Tg decreases, which suggests that Nb5+ ions act as a glass modifier. The FTIR spectra suggest that Nb5+ ions are incorporated into the glass network as NbO6 octahedra, substituting BO4 groups. The temperature dependence of the dc conductivity follows the Greaves variable range hopping model below 454 K, and follows the small polaron hopping model at temperatures >454 K. σdc, σac conductivity and dielectric constant (e) decrease and activation energy for dc conduction ΔEdc which increases with increasing Nb2O5 content up to 0.2 mol%, whereas σdc, σac and (e) increase and ΔEdc decreases with increasing Nb2O5 content beyond 0.2 mol%. The impedance spectroscopy shows a single semicircle or arcs which indicate only the ionic conduction mechanism. The electric modulus formalism indicates that the conductivity relaxation is occurring at different frequencies exhibit temperature-independent dynamical process. The (FWHM) of the normalized modulus increases with increase in Nb2O5 content suggesting that the distribution of relaxation times is associated with the charge carriers Li+ or F− ions in the glass network.

Effects of pH and sintering temperature on the synthesis and electrical properties of the bilayered LaSr2Mn2O7 manganite prepared by the sol–gel process

The bilayered LaSr2Mn2O7 manganite was synthesized by the sol–gel process at different pH values (3.5, 7, and 9.5) and different sintering temperatures (1553, 1623, and 1723 K) to investigate the effects of growth conditions upon the structural and electrical properties of the samples under investigation. X-Ray diffraction and FT-IR spectroscopy techniques confirm the phase formation for all samples. However, samples sintered at 1553, 1623, and 1723 K, and formed at pH = 7 are single phased having a tetragonal structure. Study of these single-phased samples indicates that with increase in the sintering temperature from 1553 to 1723 K, the average grain size increases from ~200 to ~1000 nm. To investigate the influence of grain size on the conduction mechanism, resistivity of the samples was measured as a function of temperature. The data obtained was analyzed by the adiabatic small polaron hopping model. These analyses show the influence of grain size on the parameters obtained by fitting the data by the above models.

Impact of the sintering temperature on the structural, magnetic and electrical transport properties of doped La0,67Ba0,33Mn0,9Cr0,1O3 manganite

A systematic investigation of the La0,67Ba0,33Mn0,9Cr0,1O3 perovskite has been undertaken, mainly to understand the impact of the sintering temperature on the structural, microstructural, magnetic and electrical transport properties in these materials. The La0,67Ba0,33Mn0,9Cr0,1O3 manganite was sintered by a solid-state route at 1000°C, 1200°C and 1400°C. The X-ray diffraction studies show that all samples crystallize with the rombohedral symmetry within the space group R3¯C, regardless of the sintering temperatures employed in this work. The MnOMn bond angle decreases and the MnO bond length increases with the increase of the grain size. All samples undergo a paramagnetic (PM)–ferromagnetic (FM) phase transition at T=TC. Both the magnetization and the Curie temperature TC decrease with increasing grain size mainly due to the increase of the MnO bond length dMnO. The electrical resistivity (ρ) increases with decreasing grain size because of the enhancement of the grain boundary effect. Low temperature resistivity data below TC was fitted by the relation ρ=ρ0+ρ2T2+ρ4.5T4.5, indicating the importance of the grain/domain boundary, the electron–electron scattering effects and, to a lesser extent, the electron–(magnon,phonon) scattering effects in the mechanism of conduction. On the other hand, the high temperature resistivity above the metal–insulator (M–I) transition Tp for the sample sintered at 1000°C was explained using variable range hopping (VRH) and small polaron hopping (SPH) models. IR studies revealed that the vibration mode at 411cm−1, associated with the internal bending of MnO6 octahedra, becomes softer, indicating an increase of the distortion.

Structural studies and magnetic and transport properties of Cr-substituted La0.67Ba0.33Mn1−xCrxO3 (0 ≤ x ≤ 0.15) perovskites

We have investigated the structural, magnetic and electrical transport properties of a series of ABO3-type perovskite compounds, La0.67Ba0.33Mn1−xCrxO3 (0≤x≤0.15), which strongly depend on the doping level x. The slight difference between the ionic radii of Cr3+ and Mn3+ causes no change in the structure when x≤0.1, remaining rhombohedral (space group R-3C), while for x=0.15 the structure becomes cubic (space group Pm-3m). Energy dispersive X-ray analysis (EDAX) confirms the expected stoichiometry of all samples. Upon Cr doping on the Mn site, the lattice parameters, the unit cell volume and the BOB bond angle are reduced. All samples present a single magnetic transition from ferromagnetic to paramagnetic phase, showing a decrease of the Curie temperature Tc and the magnetization M when x increases (x≤0.15). However, Cr doping makes the saturation magnetization at 5K to decrease, which indicates that the Cr3+ moments tend to be antiparallel to the Mn3+ moments at low temperature.The Cr-doped manganites exhibit a large variation in resistivity values. The increase of Cr doping (x≤0.15) leads to an increase of the electrical resistivity. Below 10at.% of Cr3+, the electrical resistivity shows a metallic behavior, which is well fitted by the relation ρ=ρ0+ρ2T2+ρ4.5T4.5, indicating the importance of the grain/domain boundary, the electron–electron scattering effects and, to a lesser extent, the electron–(magnon, phonon) scattering effects in the mechanism of conduction. On the other hand, the 15at.% of Cr3+ doping makes the material to exhibit a semiconductor behavior, for which the electronic transport can be explained by a variable range hopping (VRH) and small polaron hopping (SPH) models. Results are consistent with a reduction of the number of available hopping sites for the Mn eg (↑) electron due to the substitution of Mn3+ by Cr3+, which suppresses the double exchange (DE) interactions.