altering the electrical and magnetic properties of the material. On the other hand, controlled doping in the B site with magnetic ion, as Cr, appears interesting. The Cr3+ion is iden-tical in electronic conguration to Mn4+. As the Cr3+ionic radius (0.62 "A) is much closer to that of Mn3+high spin (0.64 "A) than Mn4+radius (0.53 "A), low substitutions of Cr3+result in changes in the Mn3+density without large distortions of the crystal cell.11 Therefore, the number of Mn3+/Mn4+pairs is reduced, which is an essential ingredient for the DE interaction.
The sol–gel process for the synthesis of manganite has many advantages over conventional ceramic processing, including high purity, good homogeneity, and low processing tempera-ture.6,12,13However, nanocrystalline materials have attracted the attention of the scientic community because of the rich physics involved as well as their potential use in device appli-cations.14 The physical properties of bulk polycrystalline manganites can be modied by reducing their individual particle sizes to the nanometer scale.15 17However, compounds with small grain sizes oen show large differences between TC and metal–semiconductor transition TM–SC.18,19The rst aim of this study was to experimentally investigate the structural, magnetic and magneto-transport properties related to the substitution effect of Mn by Cr ions, up to 17%, in La0.67 -Ba0.33Mn1!xCrxO3series, which has been prepared by the sol– gel method at low temperatures, resulting in small grain sizes. The second is to study on the effects of chromium inducing disorder effects of second-order phase transition of the system. For this purpose, the Bean–Rodbell model was applied to the magnetization data of the samples for x ¼ 0.10 and x ¼ 0.15.
II. Experimental details
Polycrystalline samples in bulk form with the compositional formula La0.67Ba0.33Mn1!xCrxO3 denoted as LBMCrx (x ¼ 0 (LBMO), 0.05, 0.08, 0.1, 0.12, 0.15 and 0.17) were prepared by the Pechini sol–gel method20using highly pure metal nitrates as starting materials (>99.99% purity): La(NO3)3$6H2O, Ba(NO3)2, Mn(NO3)2$4H2O and Cr(NO3)3$9H2O. The initial solution was prepared by mixing distilled water and the nitrates (properly weighed according to the specic composition), citric acid (CA) (99.5% purity) and ethylene glycol (EG) (99.5% purity) in the following molar proportion 1 : 5 : 4 : 3. The resulting solution was heated by constant stirring at temperatures of 80#C. Aer
the evaporation of water at 80–100 #C, the viscosity of the
solution increased and further heating led to the formation of polymeric resin. The resin was pre-calcined (673 K for 3 h) to eliminate the organic material, ground and calcined again (1073 K for 3 h) to eliminate the residual organic material. The obtained black powder was cold-pressed into pellets with a diameter of 13 mm and thickness of about 2–3 mm under a pressure of 5 tons per cm2. Subsequently, the powder was sintered at 1423 K for 12 hours in air. The morphological properties of the samples were investigated by scanning elec-tron microscopy (SEM) on a JSM-6400 apparatus working at 20 kV. Structural characterization was carried out by X-ray diffraction (XRD) using a “Panalytical X pert Pro” diffractom-eter with Cu Ka radiation (l ¼ 1.5406 "A). The data for Rietveld
renement were collected in the range of 2q from 10#to 120#
with a step size of 0.017#and a counting time of 18 s per step.
The D.C. magnetization data were measured using a SQUID (Quantum Design, MPMS-5XL model), over the temperature range 4.2–400 K, with magnetic elds from 0 to 5 T. The elec-trical transport measurements in magnetic elds of up to 3.0 T were performed using the DC resistivity option in a Quantum Design physical property measurement system (PPMS).
III. Results and discussion
A. Structural and morphological properties
The XRD data of the LBMCrx(x ¼ 0 (LBMO), 0.05, 0.1 and 0.17) compositions were obtained at room temperature and the structural parameters were determined by performing the Rietveld renement using the FULLPROF program.21 The results of X-ray diffraction indicate that all the studied samples had a single-phase perovskite structure with a R3c space group (no. 167), in which the (La, Ba) atoms are at the 6a (0, 0, 1/4) positions, Mn at 6b (0, 0, 0) and O at 18e (x, 0, 1/4). The struc-tural parameters were determined by Rietveld renement method. The data were rst analyzed with a “whole pattern tting” algorithm to determine accurately the prole shape function, background and the cell parameters. As a representa-tive of the series, the XRD pattern of x ¼ 0.05 composition is depicted in Fig. 1 along with its renement data. Detailed results of the structural renements are grouped in Table 1, where a and c are the hexagonal cell parameters, V is the unit cell volume, Bisois the isotropic thermal parameter and xOis the oxygen position. The residuals for the weighted patterns, Rwp, the pattern, Rp, the structure factor, RF, and the goodness of t, c2, are also reported in this table. The rhombohedral unit cell volume decreased gradually with increasing chromium content from 0 to 0.17, which can be explained by the replacement of Mn3+
ions (r ¼ 0.64 "A) by smaller Cr3+
ions (r ¼ 0.62 "A).22This suggests that the doped Cr3+ does not obviously change the crystalline structure of pure LBMO. In addition, with increasing chromium concentration, the lattice parameters change in a continuous manner, indicating perfect solid solubility of Cr at Mn site. This is consistent with previous reports of similar materials.23 25
The average crystallite size (CS), determined from a Rietveld renement,26 was estimated to be 106 nm ($2 nm) for the nanosized LBMCr0.17 (see Table 1). The average particle sizes (PS) estimated by eld emission scanning electron microscopy (FE-SEM) were approximately 100 nm ($10 nm). A comparison with the average CS deduced from Rietveld renement showed good agreement with the PS provided by FE-SEM. As a repre-sentation, the SEM images for x ¼ 0, 0.10, and 0.15 are dis-played in Fig. 2. For quantitative analysis of the samples, EDX analysis was carried out for several spectra on the surface and the samples contained all the expected chemical elements with no foreign elements. The average cationic composition for each sample was coincident in all cases with the expected one, within experimental error ($1%). As an example, experimental atomic percentages for the x ¼ 0.05 composition was as follows: 47.67%
La, 21.14% Ba, 0.93% Cr, and 30.26% Mn (theoretical 46.28% La, 22.50% Ba, 1.56% Cr, and 29.66% Mn).
B. Magnetic properties
Fig. 3 shows the temperature dependent zero eld cooled (ZFC) and eld cooled (FC) magnetization of LBMCrx(x ¼ 0, 0.15 and 0.17) samples measured at 0.01 T in the temperature range of 2–400 K. The measurements were taken during the heating run, aer the sample was cooled to the lowest temperature. Para-magnetic (PM) to ferroPara-magnetic (FM) phase transition at the Curie temperature, TC(dened as the one corresponding to the peak of dM/dT in the M vs. T curve), was observed. From Fig. 3, the ZFC and FC curves bifurcate below the Curie temperature, TC, for all samples. The ZFC curves lie somewhat lower than the FC curves. This was attributed to the more random frozen magnetic conguration than that achieved in the FC cases,27 which is usually observed easily in nano-sized materials due to the increased boundary/surface effects. With increasing chro-mium content x the transitions become broader and show prominent divergence between the ZFC and FC curves (see Fig. 3). Furthermore, it was proposed that the canted anti-ferromagnetic (AFM) state arises due to the random distribu-tion of Cr3+ ions with random oriented spin27 in Cr doped systems. The substitution of Cr3+ for Mn3+ ions not only changes the Mn–O bond length dMn–Oand the qMn–O–Mnbond angles (see Table 1), but could also lead to the additional presence of AFM super-exchange (SE) interactions associated with the pairs of Cr3+–O–Mn4+and Cr3+–O–Cr3+in addition to
the pre-existing AFM pairs of Mn3+–O–Mn3+and Mn4+–O–Mn4+. With increasing Cr doping, these AFM interactions become more prominent than the DE-based FM interactions of Mn3+–O– Mn4+. As shown Fig. 4, the introduction of Cr substituting for Mn ions affects the measured TC values, lowering them continuously, about 62 K for the x ¼ 0.17 composition, con-rming the weakening of the FM DE interactions.
C. Bean–Rodbeel model and magnetovolume coupling To examine the magnetic properties and gain insight into the nature of the magnetic transition, the isothermal magnetization M(H) data for nanocrystalline LBMCr0.10 and LBMCr0.15 were analyzed using the Bean and Rodbell model.28As shown previ-ously,29 31this model is applicable to interpreting second- and rst-order phase transition manganite materials. The phenomenological model considers, in particular, the magne-tovolume interactions,28assuming a linear dependence (with a proportionality factor b) of the Curie temperature (TC) of the system with the relative volume (n) change in the way as follows:
TC¼ T0[1 + bu], (1)
where u ¼ ðnnn0Þ
0 is the cell deformation, n is the volume and
n0 is the equilibrium volume obtained in the absence of magnetic interaction. T0 is the Curie temperature of the incompressible system. The parameter b represents the slope of Fig. 1 Rietveld refinement profile for the LBMCr0 05sample performed using FULLPROF. The open circles correspond to the experimental data and the lines are the fits. The vertical bars are the Bragg reflections for the space group R3!c. The difference pattern between the observed data and fits is shown at the bottom. Inset (a) shows a zoom in the 2q region between 21#and 44#. Inset (b) represents the crystal structure of LBMCr0 05at room temperature in space group R3!c.
the dependence of the Curie temperature (TC) on the cell deformation.
Considering a material with compressibility K, spin J and spin density N, one denes the h parameter as follows:
h¼ 5 2NkBKT0b 2 " 4JðJ þ 1Þ2 ð2J þ 1Þ4 1 # ; (2)
where (kB) is the Boltzmann constant. For h < 1, the transition is of second order, whereas for h > 1, the transition is of rst order,28with the coupled volume and magnetization disconti-nuities at the specic eld and temperature values. In this study, K and b are controlled by the adjustment of h manually. The model is a modied form of the Bean–Rodbell model extended to include spin clustering by treating J as an adjust-able parameter. The experimental data can only be described Table 1 Refined structural parameters of the LBMCrx(0 # x # 0.17) samples at room temperature. Space group R!3c. V is the cell volume; Bisois the overall isotropic thermal parameter, CS is the crystallite size evaluated from Rietveld refinements, W is the bandwidth, Rwp, Rpand RFare the agreement factors for the weighted profiles, the profiles and the structure factors; c2is the goodness of fit. The numbers in parentheses are the estimated standard deviations to the last significant digit
Sample 0 0.05 0.10 0.17
Structure type Rhombohedral Rhombohedral Rhombohedral Rhombohedral
Space group R!3c R!3c R!3c R!3c Lattice parameter a ("A) 5.5304 (3) 5.5343 (2) 5.5338 (1) 5.5356 (2) c ("A) 13.5553 (3) 13.5277 (7) 13.5143 (1) 13.4884 (2) V ("A3) 359.06 (3) 358.82 (2) 358.40 (1) 357.94 (9) d(Mn, Cr)–O("A) 1.9531 (1) 1.9543 (4) 1.9563 (2) 1.9602 (9) q(Mn, Cr–O–Mn, Cr)(#) 176.50 (4) 173.74 (2) 172.65 (8) 171.90 (4) W 0.0960 0.0957 0.0953 0.0946 La/Ba x 0.000 0.000 0.000 0.000 y 0.000 0.000 0.000 0.000 z 0.25 0.25 0.25 0.25 Biso("A2) 0.84 (0) 0.90 (1) 0.45 (3) 0.59 (3) Mn/Cr x 0.000 0.000 0.000 0.000 y 0.000 0.000 0.000 0.000 z 0.000 0.000 0.000 0.000 Biso("A2) 0.99 (3) 0.68 (2) 0.40 (4) 0.24 (4) O x 0.480 (6) 0.472 (7) 0.461 (4) 0.452 (1) y 0.000 0.000 0.000 0.000 z 0.25 0.25 0.25 0.25 Biso("A2) 2.6 (1) 1.38 (9) 1.53 (1) 1.15 (2) CS (nm) 123 100 112 106 Discrepancy factors (%) Rwp(%) 8.71 7.83 8.58 9.55 Rp(%) 5.87 6.02 6.28 7.34 RF(%) 4.85 2.70 6.53 5.92 c2(%) 3.59 2.32 3.47 3.48
well if a Gaussian distribution of values with a variable full width at half maximum (FWHM), accounting for the sample inhomogeneity, is incorporated into the model. The parame-ters, h, J, T0, and its FWMH, are tuned to provide a best t to experimental curves such as M vs. H, M vs. T, and H/M vs. M2.31 As can be observed in Fig. 5, approximate agreement, especially at high eld, and high magnetization exists between the theory and experimental data. As the model assumes a homogeneous and isotropic system, effects, such as magnetic domains,
anisotropy, and demagnetization, are not taken into account, justifying the higher deviation between experimental data and simulations at lower elds.32Table 2 lists the parameters ob-tained from these simulations.
The second-order transition of LBMCr0.10and LBMCr0.15was conrmed by their h parameter (h < 1).28 Furthermore, Cr3+ substitution induces more disorder in the system, as can be observed from the evolution of the disorder parameter in Table 2.
D. Magneto-transport properties
The temperature dependencies of resistivity, r, for LBMCrx(x ¼ 0 (LBMO), 0.1, 0.12 and 0.17) compounds were measured in magnetic elds up to 3.0 T using a four-probe technique, as indicated by the symbols shown in Fig. 6. As expected, the measurements revealed an overall increase in resistivity with increasing chromium content x. For x ¼ 0 and x ¼ 0.1 compounds the maximum in r(T) curve, usually regarded as the metal–semiconductor (M–SC) transition temperature (TM–SC), appears at about TC and an additional broad peak grows up before it. Under an applied magnetic eld, the resistivity is suppressed drastically for both peaks and while the original peak near TCshis to a higher temperature, the additional peak appears to be independent of the eld. Double-peaked r(T) curves similar to that shown in Fig. 6 were oen observed in polycrystalline manganite samples.32 34 In all cases, this behavior was quite reasonably attributed to the inuence of the grain boundaries. On the contrary, for x ¼ 0.12 and x ¼ 0.17 compounds, only a single maximum in r(T) curves occur much below their TC. The TM–SCvalues determined from these curves are listed in Table 3. Compared to LBMO, TM–SCdecreases with Cr doping, which can be attributed to the weakening of the DE interaction between the Mn3+ and Mn4+ via the intervening oxygen. From Fig. 6, all the samples exhibit metallic behavior (dr/dT < 0) at low temperatures (T < TM–SC) and semiconductor-like features above TM–SC.
In the presence of an external magnetic eld (H ¼ 3.0 T), the resistivity decreases signicantly and TM–SC shis slightly to higher temperatures (see Table 3). Cr substitution may favor the charge carrier delocalization induced by the magnetic eld, which suppresses the resistivity and consequently leads to the local ordering of the electron spins. Owing to this ordering, the ferromagnetic metallic state might have suppressed the para-magnetic semiconductor regime, resulting in the observed increase in TM–SCwith the application of a magnetic eld. In fact, a similar explanation was given earlier.35Furthermore, the percentage of MR of all the materials of the present investiga-tion was calculated in the vicinity of room temperature (300 K) using the well-known relation shown as follows:
MR%¼ ! r0 rH r0 " ( 100; (3)
where r0¼ resistivity without a magnetic eld, and rH¼ resis-tivity in a eld. The calculated MR values are listed in Table 3.
To elucidate the transport mechanism in the whole measured temperature, we attempted to t the r(T, H) curves according to the phenomenological model based on the phase Fig. 3 Temperature dependence of the magnetization for LBMCrx(x
0, x 0.15 and x 0.17) measured in both the zero field cooling (ZFC) and field cooling (FC) modes at an applied magnetic field of H 100 Oe.
Fig. 4 Variation of the Curie temperature, TC, as a function of the Cr content x.
segregation mechanism proposed by Li et al.36 This model assumes the materials to be composed of ferromagnetic and paramagnetic regions and semiconductor-like transport prop-erties are exhibited in the paramagnetic region, whereas metallic transport always show up in the ferromagnetic region. Following this mechanism, the electrical resistivity at any temperature is determined by the change in the volume frac-tions of both regions. Suppose f and f0represent the volume
fractions of PM-semiconductor and FM-metallic regions in the system, respectively, one apparently has the relation, f + f0¼ 1.
Physically, it is acceptable and reasonable to assume that there is an energy difference (per unit cell) DU between the FM state PM state. As a result, the volume fractions obey a simple two energy-level Boltzmann distribution shown as follows:
f ¼ 1 1þ exp # DU kBT $ ; (4) and f0¼ 1 f ¼ exp # DU kBT $ 1þ exp # DU kBT $ ; (5) where DU z U0 1 T Tmod C ! ; (6)
Fig. 5 LBMCrx(x 0.10 and x 0.15) experimental (black lines) and simulated (red dots) curves showing ((a) and (c)) magnetization as a function of the applied magnetic field, at the indicated temperature values and ((b) and (d)) corresponding H/M vs. M2Arrott plots.
Table 2 Parameters extracted from Bean Rodbeel based analysis for LBMCr0 10and LBMCr0 15
Composition La0.67Ba0.33Mn0.90Cr0.10O3 La0.67Ba0.33Mn0.85Cr0.15O3
Mean eld and Bean Rodbell analysis
MSat 78 78.50
TC(K) 325 288
h 0.84 0.55
Magnetic spin clustering (no. ions) 4.60 4.68
where Tmod
C means a temperature in the vicinity of what the resistivity has a maximum value.36Moreover, the total resistivity of the system can be considered to be the sum of the resistivity of the phase separated FM and PM regions and thus the whole resistivity r of the system can be written as follows:
r(T)¼ rFMf + rPMf0 (7)
In the metallic conducting temperature region well below TM–SC, the metallic resistivity can be ascribed to the resistivity due to grain/domain boundaries and point defects scattering r0,37electron–magnon scattering contribution r2 (ref. 38) and a combination of electron–electron, electron–magnon and electron phonon scattering processes T4.5,39,40namely, r
FM(T) ¼ r0+ r2T2+ r4.5T4.5. In contrast, in the semiconductor-like con-ducting temperature region well above TM–SC, the resistivity can Fig. 6 Temperature dependence of the resistivity r at different applied magnetic fields for LBMCrxcompounds with x 0, 0.1, 0.12 and 0.17. Red solid line corresponds to fit by eqn (8).
Table 3 Best fit parameters of the electrical resistivity r(T, H) for LBMCrx(x 0, 0.1, 0.12 and 0.17) using (eqn (8)). Metal semiconductor transition temperature TM–SC, activation energy Eaand correlation factors R2
r(T) (r0+ AT2+ BT4.5)f + DT exp(Ea/kBT)(1 f) x H (T) TM–SC(K) r0(U cm) A (U cm K 2) B (U cm K 4.5) Ea(meV) MR% 300 K R2 0 0 340 0.018 1.189 ( 10 6 3.79 ( 10 13 109.83 0.998 1 350 0.013 1.179 ( 10 6 3.64 ( 10 13 106.22 11 0.998 2 355 0.013 1.089 ( 10 6 3.32 ( 10 13 103.52 16 0.999 3 361 0.013 9.982 ( 10 7 3.03 ( 10 13 101.34 24 0.999 0.10 0 325 0.019 8.427 ( 10 7 2.34 ( 10 13 111.46 0.998 1 335 0.014 8.331 ( 10 7 2.25 ( 10 13 107.72 15 0.999 2 345 0.013 8.086 ( 10 7 2.24 ( 10 13 105.60 21 0.999 3 350 0.013 7.656 ( 10 7 2.15 ( 10 13 102.03 26 0.999 0.12 0 185 2.307 7 ( 10 5 1.03 ( 10 10 116.73 0.996 1 195 1.935 6 ( 10 5 4.71 ( 10 11 113.16 7 0.999 2 197 1.825 5 ( 10 5 4.06 ( 10 11 110.38 15 0.999 3 199 1.722 4 ( 10 5 3.53 ( 10 11 105.65 22 0.999 0.17 0 145 171.20 3.720 ( 10 5 6.67 ( 10 9 135.48 0.999 1 154 120.14 5.4 ( 10 3 1.09 ( 10 8 120.74 10 0.999 2 158 113.34 4.69 ( 10 3 9.64 ( 10 9 116.06 15 0.999 3 160 107.14 4.11 ( 10 3 8.58 ( 10 9 110.67 19 0.999
be almost described by a formula as rPM(T) ¼ BT exp(Ea/kBT) in terms of a magnetic polaron picture.41Therefore, the complete expression describing the temperature dependence of the electrical resistivity in the whole temperature range can be written in the form as follows:
r¼%r0þ r2T 2 þ r4:5T 4:5& 1 1þ exp U0 1 T Tmod C ! kBT 0 B B B B @ 1 C C C C A þ BT expðEa=kBTÞ exp U0 1 T Tmod C ! kBT 0 B B B B @ 1 C C C C A 1þ exp U0 1 T Tmod C ! kBT 0 B B B B @ 1 C C C C A (8)
Eqn (8) was tted to our experimental data in the whole measured temperature, with only two adjustable parameters, i.e., TmodC and U0. All other parameters, viz., r0, r2, r4.5, and Eaare maintained xed to their respective values obtained indepen-dently for the metallic-ferromagnetic (T < TM–SC) and semiconductor-paramagnetic (T > TM–SC) regions (see Table 3). The solid lines in Fig. 6 show the tting results. The results calculated from eqn (8) agree well with the experimental data. As listed in Table 3, the values of the parameters, r0, r2, r4.5, which increase as the amount of Cr increases. However, for all the LBMCrx(x ¼ 0, 0.1, 0.12 and 0.17) samples, the domain/ grain boundary (GB) contribution is high. It was further observed that the activation energy Eain the transport process of the carriers increases with increasing Cr doping. With further increases in Cr concentration, the number of eg electrons of Mn3+become more localized (discussed above), which increases the activation energy.22,35
Note that the external magnetic eld suppresses the forma-tion of polarons and spin-disorder scattering, leading to a monotonous decrease in Ea(see Table 3). This is because the ability of the polarons to trap electrons is weakened as the spins in the polarons attempt to align along the magnetic eld.
IV. Conclusion
We studied, in detail, the crystal structure and physical prop-erties of single phase Cr doped La0.67Ba0.33MnO3 rare-earth nanocrystalline manganites, which were synthesized using the Pechini method. The Rietveld renement of the X-ray data, along with the magnetic and resistivity measurements support the fact that Cr3+ (t3
2g e0g) ions substitute for Mn3+ (t32g e1g). In addition, substitution by the magnetic trivalent element Cr3+up to x ¼ 0.17, whereas it does not change the rhombohedral symmetry of the pristine sample LBMO and cause only very
small compression of the unit cell volume (z0.31%), it sup-pressed locally the double exchange interaction causing a decrease of TCand TM–SC. Although Cr3+is isoelectronic with Mn4+, the resistivity of La
0.67Ba0.33CrxMn1!xO3 manganites increase with increasing metal doping concentration, resulting in an increase of activation energy. Moreover, the behavior of r(T, H) of these samples over a wide range of temperatures and magnetic elds can be explained using the phenomenological model based on the phase segregation mechanism, wherein the metal–semiconductor phase transition is considered as a percolation transition. On the other hand, the Bean and Rodbell model was used successfully to simulate the magneti-zation data of the samples with x ¼ 0.10 and x ¼ 0.15. The second order phase transition of both samples is conrmed by the value of the h parameter (h < 1). The random replacement of Mn3+by Cr3+is shown to induce more disorder in the system, which is reected in the increase in the tted disorder param-eter and spin value uctuations.
Acknowledgements
This study is a framework of collaboration between Tunisia, Spain and Portugal. Dr Marw`ene Oumezzine acknowledges the Tunisian National Ministry of Higher Education, Scientic Research for a Grant.
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