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Electrical transport properties and transport–entropy correlations in La0.57Nd0.1Sr0.33MnO3 manganite
Journal of Magnetism and Magnetic Materials 384 (2015) 219–223
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Electrical transport properties and transport–entropy correlations in La0.57Nd0.1Sr0.33MnO3 manganite S. Mnefgui a,n, N. Zaidi a, N. Dhahri a, J. Dhahri a, E.K. Hlil b a b
Laboratoire de la matière condensée et des nanosciences, Université de Monastir, 5019, Tunisia Institut Néel, CNRS et Université Joseph Fourier, B.P. 166, 38042 Grenoble, France
art ic l e i nf o
a b s t r a c t
Article history: Received 3 December 2014 Received in revised form 17 February 2015 Accepted 22 February 2015 Available online 23 February 2015
An investigation of the electrical and magnetoresistance behavior of La0.57Nd0.1Sr0.33MnO3 is presented. The temperature dependence of electrical resistivity shows a metal–semiconductor transition, which occurs at TM–SC ¼336 K and shifts to higher temperatures under applied magnetic fields. It shows a large
Keywords: Manganite Resistivity Magnetoresistance Magnetic entropy change
giving the electrical resistivity in the paramagnetic region as ρPM (T ) = CT exp ( K
magnetoresisance (MR) effect ( 30% at 5 T field). Metallic resistivity ρ (T ) = ρ0 + ρ1T
2
is observed below
TM–SC. Above TM–SC, the electrical conductivity is dominated by adiabatic small polaron hopping model, Ea ). T B
The percolation
theory is introduced to understand the transport mechanism in the whole temperature range. Hence, we found that the estimated values of the resistivity are in good agreement with experimental data. A relation between the resistivity ρ and magnetic entropy change ΔSM is also presented by using an equation H of the form ΔSMρ (T , H) = − α ∫ ⎡⎣ ∂∂LnTρ ⎤⎦ dH , which relates magnetic order to transport behavior of the 0 H compounds. & 2015 Elsevier B.V. All rights reserved.
1. Introduction The discovery of giant magnetoresistance effect in certain magnetic metallic superlattices [1] has renewed interest in studying magneto-transport in a family of perovskite like oxides of the form La1 xMxMnO3 where M¼Ba, Ca, and Sr, etc. [2–5]. In fact, these oxides have become an interesting field of research due to the complex systems showing dramatic electric transport, magnetic properties, charge ordering and colossal magnetoresistance (CMR), etc. [6,7]. The close relation between transport and magnetism in these materials has been explained by the double exchange (DE) interaction [8], polaronic effects [9] and phase separation [10]. Recent studies have shown that the double exchange (DE) interaction, between Mn3 þ and Mn4 þ ions, cannot explain alone the behaviors observed in these systems. These studies suggest that other effects play a crucial role for further explanation, such as the average A-site cationic radius ‹rA› [11], the oxygen deficiency [12] and the annealing temperature [13]. Generally, manganese oxides exhibit a metal–semiconductor (M–SC) transition accompanied by a ferromagnetic–paramagnetic (FM–PM) transition near the Curie temperature TC. Some models are used to n
Corresponding author. E-mail address: [email protected] (S. Mnefgui).
http://dx.doi.org/10.1016/j.jmmm.2015.02.049 0304-8853/& 2015 Elsevier B.V. All rights reserved.
explain the electronic transport mechanism in manganite materials: the electron scattering process and electron–phonon interaction usually used to describe the metallic behavior [14] but in the semi-conductor state, the carriers are localized as small polarons due to the strong Jahn Teller distortion. In this state, the electrical conduction is governed by small polaron hopping mechanism [15–17]. However, most of these models are applied to fit the prominent change of the ρ − T curves in a limited temperature region (paramagnetic or ferromagnetic). In order to explain the transport mechanism in the whole temperature range, a phenomenological percolation model based on phase segregation was proposed by Li et al. [18,19]. The electrical resistivity at any temperature is determined by the change of the volume fractions of both regions (above and below TC). According to the double exchange theory, electrons tend to hop between Mn ions of different valences while keeping their spins unchanged. Therefore, when the arrangement of the spins of the Mn ions is modified by external field, resistivity changes simultaneously. In this picture, the colossal magnetoresistance (MR) in the manganites can be qualitatively understood [20,21]. This explanation actually suggests a magnetic-resistive interplay in the manganites. The colossal magnetoresistance and magnetocaloric effects are usually observed in the vicinity of the magnetic phase transition temperature, and, obviously, there is interesting
220
S. Mnefgui et al. / Journal of Magnetism and Magnetic Materials 384 (2015) 219–223
correlations between the transport properties such as resistivity and the change of the magnetic entropy. This relation was described by Xiong et al. who proposed a new method for evaluating the change of the magnetic entropy from data on the temperature and field dependences of the electrical resistivity of manganites [22]. They suggested that the relation between ΔSM and resistivity H ρ in manganites is ΔSMρ (T , H) = − α ∫0 ⎡⎣ ∂∂LnTρ ⎤⎦ dH , where the paraH meter α determines the magnetic properties of the sample. The electrical and magnetic properties and the magnetocaloric effect in manganites are studied quite a lot [23–26]. We noted that most of the previous studies concentrated on the relation between magnetization and resistivity. In fact, magnetic entropy is also a parameter often used to characterize magnetic order. In contrast, the relation between magnetic entropy and transport behavior has been raised in few previous studies [27,28]. Considering the fact that magnetic disorder has a strong effect on the resistive behavior of the manganites, we expect a definite relation between these two quantities. Finding out this relation and giving it a quantitative description is one of the aims of this study in addition to the study of electronic transport mechanism in the whole temperature range using the percolation model.
2. Experimental Polycrystalline sample of La0.57Nd0.1Sr0.33MnO3 was prepared by conventional solid-state reaction method with a similar heat treatment as reported in our previous work [29], where the structural and magnetic properties were also investigated. Electrical resistivity as a function of temperature was measured by a conventional four-probe method. In order to analyze the resistivity data of high temperature region, T 4TM–SC, we have used the adiabatic small polaron-hopping model (SPH) where the resistivity follows: ρPM (T ) = CT exp (Ea/k B T ). The T < TM − SC experimental data were fitted by ρ (T ) = ρ0 + ρ2 T 2 . The percolation model, based on phase segregation has been used successfully in whole measured temperature where resistivity can be written in the following way: ρ (T ) = ρFM f + ρPM (1 − f ) .
3. Results and discussion 3.1. Transport mechanisms analysis The resistivity measurement was carried out in both magnetic and without magnetic field using the conventional four-probe method. Fig. 1 illustrates the temperature dependence of resistivity of La0.57Nd0.1Sr0.33MnO3 sample under different magnetic fields. Taking the sign of the temperature derivative of the resistivity (dρ /dT ) as a criterion, we found that the sample exhibit a metallic behavior (dρ /dT > 0)at low temperature (T < TM − SC ) and become semiconductor-like (dρ /dT < 0) above the temperature TM − SC , where TM − SC is the temperature of the maximum value of resistivity ρmax. We noted a decrease of resistivity when the magnetic field increases which may be due to the fact that the applied magnetic field induces the delocalization of charge carriers. As a result, the ferromagnetic-metallic state may suppress the paramagnetic-semiconductor regime. In fact, randomly oriented moments of particles can be aligned by an external field. This causes a significant increase in tunnel conductance, thereby reducing resistivity of the granular system. In order to study the transport mechanisms in our material we will use theoretical models, which describe it.
Fig. 1. Electrical resistivity ρ as a function of temperature (T) of La0.57Nd0.1Sr0.33MnO3 under applied magnetic field of 0, 2, and 5 T. The red solid line represents the best fit of experimental data with percolation using Eq. (4).
First, for the low-temperature range (T oTM–SC), the electrical conduction mechanism is approximated by an expression that includes several scattering mechanisms according to the following formula:
ρ (T ) = ρ 0 + ρ2 T 2
(1)
where ρ0 is the residual resistivity due to grain or domain boundaries [30]. ρ2T2 is ascribed to the electrical resistivity due to the electron–electron scattering process [31]. Then, for the high temperature range (T 4TM–SC), the electrical conduction mechanism is governed by the adiabatic small polaron hopping mechanism (SPH) [15,32] that is described by the formula:
⎛ Ea ⎞ ρ PM (T ) = CT exp ⎜ ⎟ ⎝ kB T ⎠
(2)
where C is a pre-exponential coefficient, Ea is the activation energy and kB is the Boltzmann constant. Moreover, to understand the mechanism of electrical transport in the whole temperature range and by taking into account that the metal–semiconductor transition (M–SC) has a percolation character and assuming that a competition between ferromagnetic and paramagnetic (FM–PM) regions is of great importance in the formation of CMR effect, the expression for resistivity can be written in the following way [19]:
ρ (T ) = ρ FM f + ρ PM (1 − f )
(3)
where f is the volume concentration of ferromagnetic (FM) phase and (1 f) is the volume concentrations of the (PM) phase. The function f can be determined by a simple mathematical combination as f =
ρ (T ) − ρ PM ρ FM − ρ PM
. In another way, the volume con-
centration of FM and PM phases satisfy the Boltzman distribution:
f=
1 , 1 + exp (ΔU / K B T )
where ΔU≈U0 (1 − TCmod ) implies an energy dif-
ference between FM and PM states. TCmod is the temperature of the maximum resistivity used in this model and is nearly equal to TC. U0 is taken as the energy difference for temperatures well below
TCmod [19]. Thus, a complete expression describing the temperature dependence of resistivity is of the form:
S. Mnefgui et al. / Journal of Magnetism and Magnetic Materials 384 (2015) 219–223
221
Table 1 Parameters obtained corresponding to the best fit of the experimental data of La0.57Nd0.1Sr0.33MnO3 compound using Eq. (4). H (T) ρ0 (Ω cm) ρ2 10 7
C 10 6 (Ω cm)
2 Ea/k B (k) ΔU /k B (K) TCmod (K ) R
2.01 3.28 4.21
2646.47 1650.58 1085.62
(Ω cm/K 2 ) 0 2 5
0.121 0.183 0. 239
7.19 7.00 6.08
⎛ Ea ⎞ ρ (T ) = (ρ 0 + ρ2 T 2) f + CT exp ⎜ ⎟ (1 − f ) ⎝ KB T ⎠
3737 3486 3041
317 320 325
0.998 0.999 0.999
(4)
The simulated curves (solid line) obtained under 0 T, 2 T and 5 T for La0.57Nd0.1Sr0.33MnO3 are shown in Fig. 1. It is clear that the calculated results from Eq. (4) are in good agreement with the experimental data. The best-fit parameters are given in Table 1. It can be seen that the activation energy Ea decreases when increasing the applied magnetic field. Thus, due to the spins' attempt to align along the magnetic field, which favors the conduction and decreases the ability of charge localization, the electrons jumping requires less energy. Consequently, the estimate values of Ea seem reasonable. Fig. 2 shows the variation of the volume fraction of the ferromagnetic phase (f) and of the paramagnetic phase (1 f) as a function of the temperature for La0.57Nd0.1Sr0.33MnO3 under 0, 2 and 5 T. It is clear that f (T) remains equal to 1 below the metal– semiconductor transition temperature, which confirms the strong dominance of the FM fraction in this range. Then the FM volume fraction begins to decrease to 0 from the ferromagnetic metallic state to a paramagnetic-semiconductor state confirming the validity of the percolation approach which assumes a conversation of ferromagnetic to paramagnetic regions. 3.2. Magnetoresistance studies The magnetoresistance (MR) dependence of the temperature of La0.57Nd0.1Sr0.33MnO3 is shown in Fig. 3 under two magnetic fields of 2 and 5 T. The MR is a fundamental property of manganites, which is related to the reduction of the electrical resistivity of the material by applying a magnetic field. It is defined as
Fig. 2. The temperature dependence of ferromagnetic phase volume fraction f and of the paramagnetic phase (1 f) for La0.57Nd0.1Sr0.33MnO3 under applied magnetic field of 5 T.
Fig. 3. Variation of MR vs. T curves for La0.57Nd0.1Sr0.33MnO3 under applied magnetic field of 2 and 5 T.
MR(%) = [ρ (0, T ) − ρ (H , T )]/ρ (0, T ) × 100%
(5)
where ρ (0,T) and ρ (H, T) are the resistivity values for zero and applied fields (2 T and 5 T) respectively. It is clear from the plot (Fig. 3) that the MR was decreasing with the increase in temperature. This decrease is almost linear with a small peak around TC. The MR is the largest (32% and 20% for 5 T and 2 T, respectively) and then gradually decreases with increasing temperature. Venkataiah et al. suggested that the reason for the higher MR at low temperature can be related to the extrinsic MR effect involving spin polarized tunneling between grains or spin dependent scattering of polarized electrons at grain boundaries [33]. While at TC, the high MR is attributed to Zener double-exchange [34]. In fact in the double exchange mechanism, the hopping of electron from Mn3 þ to Mn4 þ upon the spin alignment of Mn ions. The application of a magnetic field aligns the spin of the incomplete d orbital of the adjacent Mn ions, which results in the increase of the electrons' hopping rate and therefore an increase in electrical conductivity occurs [35]. In the present case, a high magnetic field has been found to affect MR at TC.
Fig. 4. Magnetization vs. applied magnetic field H, measured at different temperatures, for the La0.57Nd0.1Sr0.33MnO3.
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S. Mnefgui et al. / Journal of Magnetism and Magnetic Materials 384 (2015) 219–223
and from the experimental M (T, μ0H) curves are shown in Fig. 5, where the resistivity results agree quite well with the fitting parameter α ¼7.78 emu/g in the intermediate temperature range. The calculated ( ΔSM ) values from the temperature dependence of the resistivity were found to present a similar maximum of the magnetic entropy change deduced from the experimental M (T, μ0H) curves, around the Curie temperature TC. These results reveal a close relation between the temperature derivative of resistivity and magnetic entropy. It can be seen also that deviation of the magnetic results from the resistivity measurements occurs in the temperature range below 320 K, where the system is well inside the ferromagnetic state and distant from the critical transition region, and above 380 K, where the paramagnetic state prevails (Fig. 5). This result implies that the resistivity measurements are in agreement with the magnetic data mainly in the intermediate temperature range, i.e., during the establishment of perfect ferromagnetic order.
Fig. 5. Comparison of the magnetic entropy-temperature ΔS–T relations calculated from magnetic data and the resistive data.
3.3. Transport–entropy correlation Fig. 4 shows the typical results of isothermal field scans. The steep increase of magnetization with applied field in the low temperature region reveals the soft magnetic character of La0.57Nd0.1Sr0.33MnO3. With the increase of temperature, the growth of magnetization with field becomes more and more gradual, and the M–H dependence experiences a significant variation in the vicinity of Curie temperature. Based on the thermodynamic theory, the magnetic entropy change (ΔSM ), which characterized the magnetocaloric effect (MCE) in manganites and which results from the spin ordering, depends on the temperature gradient of the magnetization and attains a maximum value around the Curie temperature, at which the magnetization decays most rapidly. The temperature dependence of the magnetic entropy change (ΔSM ), for La0.57Nd0.1Sr0.33MnO3 sample is computed from Eq. (5) [36,37]:
T1 + T2 1 )= −ΔS M ( 2 T2 − T1 ⎡ ⎢ ⎣
∫0
μ0 H
μ 0 dH ′ −
M (T2, μ 0 H)
∫0
μ0 H
⎤ M (T1, μ 0 H) μ 0 dH ′⎥ ⎦
(6)
In manganites, the effect of CMR and MCE are usually observed near the magnetic phase transition temperature and it is obvious that there is some relation between the change in magnetic entropy and resistivity. Such a relation is presented in Ref. [38] by Perring et al. and then developed by Xiong et al. [22], where the authors proposed a method, which can evaluate the change in magnetic entropy from the data on the temperature and field dependence of resistivity in manganites. The relationship between ΔS and ρ is as follows:
ΔS Mρ (T , μ 0 H) = − α
∫0
μ0 H
⎡ ∂Lnρ ⎤ ⎢⎣ ⎥ dμ 0 H ∂T ⎦H
(7)
where α ¼7.78 emu/g, is determined from the fitting of ρ vs. M curve around the transition temperature TC with the equation ρ = α exp ( − M /T )[22]. According to Eqs. (6) and (7), the entropy changes of La0.57Nd0.1Sr0.33MnO3 determined by the resistivity measurement
4. Conclusions A descriptive report on detailed investigation of electrical resistivity and magnetoresistive (MR) properties of the sample La0.57Nd0.1Sr0.33MnO3 has been presented. Temperature dependence of resistivity revealed the presence of a metal–semiconductor transition at TM–SC. The conduction mechanisms were explained by a small polaron hopping in the semi-conductor region and by electron scattering mechanisms in the metallic region. Then, to understand the transport mechanism in the whole temperature range, we have used the phenomenological percolation model, which is based on the phase segregation of ferromagnetic and paramagnetic-semiconductor regions. The magnetoresistance studies reveal that a high magnetic field has been found to affect MR at TC. The relation between magnetic entropy change and resistivity has been also studied. It is noted that there is a strong correlation between ΔSM and ρ in La0.57Nd0.1Sr0.33MnO3 manganite in the vicinity of the phase transition temperature.
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Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Electrical transport properties and transport–entropy correlations in La0.57Nd0.1Sr0.33MnO3 manganite S. Mnefgui a,n, N. Zaidi a, N. Dhahri a, J. Dhahri a, E.K. Hlil b a b
Laboratoire de la matière condensée et des nanosciences, Université de Monastir, 5019, Tunisia Institut Néel, CNRS et Université Joseph Fourier, B.P. 166, 38042 Grenoble, France
art ic l e i nf o
a b s t r a c t
Article history: Received 3 December 2014 Received in revised form 17 February 2015 Accepted 22 February 2015 Available online 23 February 2015
An investigation of the electrical and magnetoresistance behavior of La0.57Nd0.1Sr0.33MnO3 is presented. The temperature dependence of electrical resistivity shows a metal–semiconductor transition, which occurs at TM–SC ¼336 K and shifts to higher temperatures under applied magnetic fields. It shows a large
Keywords: Manganite Resistivity Magnetoresistance Magnetic entropy change
giving the electrical resistivity in the paramagnetic region as ρPM (T ) = CT exp ( K
magnetoresisance (MR) effect ( 30% at 5 T field). Metallic resistivity ρ (T ) = ρ0 + ρ1T
2
is observed below
TM–SC. Above TM–SC, the electrical conductivity is dominated by adiabatic small polaron hopping model, Ea ). T B
The percolation
theory is introduced to understand the transport mechanism in the whole temperature range. Hence, we found that the estimated values of the resistivity are in good agreement with experimental data. A relation between the resistivity ρ and magnetic entropy change ΔSM is also presented by using an equation H of the form ΔSMρ (T , H) = − α ∫ ⎡⎣ ∂∂LnTρ ⎤⎦ dH , which relates magnetic order to transport behavior of the 0 H compounds. & 2015 Elsevier B.V. All rights reserved.
1. Introduction The discovery of giant magnetoresistance effect in certain magnetic metallic superlattices [1] has renewed interest in studying magneto-transport in a family of perovskite like oxides of the form La1 xMxMnO3 where M¼Ba, Ca, and Sr, etc. [2–5]. In fact, these oxides have become an interesting field of research due to the complex systems showing dramatic electric transport, magnetic properties, charge ordering and colossal magnetoresistance (CMR), etc. [6,7]. The close relation between transport and magnetism in these materials has been explained by the double exchange (DE) interaction [8], polaronic effects [9] and phase separation [10]. Recent studies have shown that the double exchange (DE) interaction, between Mn3 þ and Mn4 þ ions, cannot explain alone the behaviors observed in these systems. These studies suggest that other effects play a crucial role for further explanation, such as the average A-site cationic radius ‹rA› [11], the oxygen deficiency [12] and the annealing temperature [13]. Generally, manganese oxides exhibit a metal–semiconductor (M–SC) transition accompanied by a ferromagnetic–paramagnetic (FM–PM) transition near the Curie temperature TC. Some models are used to n
Corresponding author. E-mail address: [email protected] (S. Mnefgui).
http://dx.doi.org/10.1016/j.jmmm.2015.02.049 0304-8853/& 2015 Elsevier B.V. All rights reserved.
explain the electronic transport mechanism in manganite materials: the electron scattering process and electron–phonon interaction usually used to describe the metallic behavior [14] but in the semi-conductor state, the carriers are localized as small polarons due to the strong Jahn Teller distortion. In this state, the electrical conduction is governed by small polaron hopping mechanism [15–17]. However, most of these models are applied to fit the prominent change of the ρ − T curves in a limited temperature region (paramagnetic or ferromagnetic). In order to explain the transport mechanism in the whole temperature range, a phenomenological percolation model based on phase segregation was proposed by Li et al. [18,19]. The electrical resistivity at any temperature is determined by the change of the volume fractions of both regions (above and below TC). According to the double exchange theory, electrons tend to hop between Mn ions of different valences while keeping their spins unchanged. Therefore, when the arrangement of the spins of the Mn ions is modified by external field, resistivity changes simultaneously. In this picture, the colossal magnetoresistance (MR) in the manganites can be qualitatively understood [20,21]. This explanation actually suggests a magnetic-resistive interplay in the manganites. The colossal magnetoresistance and magnetocaloric effects are usually observed in the vicinity of the magnetic phase transition temperature, and, obviously, there is interesting
220
S. Mnefgui et al. / Journal of Magnetism and Magnetic Materials 384 (2015) 219–223
correlations between the transport properties such as resistivity and the change of the magnetic entropy. This relation was described by Xiong et al. who proposed a new method for evaluating the change of the magnetic entropy from data on the temperature and field dependences of the electrical resistivity of manganites [22]. They suggested that the relation between ΔSM and resistivity H ρ in manganites is ΔSMρ (T , H) = − α ∫0 ⎡⎣ ∂∂LnTρ ⎤⎦ dH , where the paraH meter α determines the magnetic properties of the sample. The electrical and magnetic properties and the magnetocaloric effect in manganites are studied quite a lot [23–26]. We noted that most of the previous studies concentrated on the relation between magnetization and resistivity. In fact, magnetic entropy is also a parameter often used to characterize magnetic order. In contrast, the relation between magnetic entropy and transport behavior has been raised in few previous studies [27,28]. Considering the fact that magnetic disorder has a strong effect on the resistive behavior of the manganites, we expect a definite relation between these two quantities. Finding out this relation and giving it a quantitative description is one of the aims of this study in addition to the study of electronic transport mechanism in the whole temperature range using the percolation model.
2. Experimental Polycrystalline sample of La0.57Nd0.1Sr0.33MnO3 was prepared by conventional solid-state reaction method with a similar heat treatment as reported in our previous work [29], where the structural and magnetic properties were also investigated. Electrical resistivity as a function of temperature was measured by a conventional four-probe method. In order to analyze the resistivity data of high temperature region, T 4TM–SC, we have used the adiabatic small polaron-hopping model (SPH) where the resistivity follows: ρPM (T ) = CT exp (Ea/k B T ). The T < TM − SC experimental data were fitted by ρ (T ) = ρ0 + ρ2 T 2 . The percolation model, based on phase segregation has been used successfully in whole measured temperature where resistivity can be written in the following way: ρ (T ) = ρFM f + ρPM (1 − f ) .
3. Results and discussion 3.1. Transport mechanisms analysis The resistivity measurement was carried out in both magnetic and without magnetic field using the conventional four-probe method. Fig. 1 illustrates the temperature dependence of resistivity of La0.57Nd0.1Sr0.33MnO3 sample under different magnetic fields. Taking the sign of the temperature derivative of the resistivity (dρ /dT ) as a criterion, we found that the sample exhibit a metallic behavior (dρ /dT > 0)at low temperature (T < TM − SC ) and become semiconductor-like (dρ /dT < 0) above the temperature TM − SC , where TM − SC is the temperature of the maximum value of resistivity ρmax. We noted a decrease of resistivity when the magnetic field increases which may be due to the fact that the applied magnetic field induces the delocalization of charge carriers. As a result, the ferromagnetic-metallic state may suppress the paramagnetic-semiconductor regime. In fact, randomly oriented moments of particles can be aligned by an external field. This causes a significant increase in tunnel conductance, thereby reducing resistivity of the granular system. In order to study the transport mechanisms in our material we will use theoretical models, which describe it.
Fig. 1. Electrical resistivity ρ as a function of temperature (T) of La0.57Nd0.1Sr0.33MnO3 under applied magnetic field of 0, 2, and 5 T. The red solid line represents the best fit of experimental data with percolation using Eq. (4).
First, for the low-temperature range (T oTM–SC), the electrical conduction mechanism is approximated by an expression that includes several scattering mechanisms according to the following formula:
ρ (T ) = ρ 0 + ρ2 T 2
(1)
where ρ0 is the residual resistivity due to grain or domain boundaries [30]. ρ2T2 is ascribed to the electrical resistivity due to the electron–electron scattering process [31]. Then, for the high temperature range (T 4TM–SC), the electrical conduction mechanism is governed by the adiabatic small polaron hopping mechanism (SPH) [15,32] that is described by the formula:
⎛ Ea ⎞ ρ PM (T ) = CT exp ⎜ ⎟ ⎝ kB T ⎠
(2)
where C is a pre-exponential coefficient, Ea is the activation energy and kB is the Boltzmann constant. Moreover, to understand the mechanism of electrical transport in the whole temperature range and by taking into account that the metal–semiconductor transition (M–SC) has a percolation character and assuming that a competition between ferromagnetic and paramagnetic (FM–PM) regions is of great importance in the formation of CMR effect, the expression for resistivity can be written in the following way [19]:
ρ (T ) = ρ FM f + ρ PM (1 − f )
(3)
where f is the volume concentration of ferromagnetic (FM) phase and (1 f) is the volume concentrations of the (PM) phase. The function f can be determined by a simple mathematical combination as f =
ρ (T ) − ρ PM ρ FM − ρ PM
. In another way, the volume con-
centration of FM and PM phases satisfy the Boltzman distribution:
f=
1 , 1 + exp (ΔU / K B T )
where ΔU≈U0 (1 − TCmod ) implies an energy dif-
ference between FM and PM states. TCmod is the temperature of the maximum resistivity used in this model and is nearly equal to TC. U0 is taken as the energy difference for temperatures well below
TCmod [19]. Thus, a complete expression describing the temperature dependence of resistivity is of the form:
S. Mnefgui et al. / Journal of Magnetism and Magnetic Materials 384 (2015) 219–223
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Table 1 Parameters obtained corresponding to the best fit of the experimental data of La0.57Nd0.1Sr0.33MnO3 compound using Eq. (4). H (T) ρ0 (Ω cm) ρ2 10 7
C 10 6 (Ω cm)
2 Ea/k B (k) ΔU /k B (K) TCmod (K ) R
2.01 3.28 4.21
2646.47 1650.58 1085.62
(Ω cm/K 2 ) 0 2 5
0.121 0.183 0. 239
7.19 7.00 6.08
⎛ Ea ⎞ ρ (T ) = (ρ 0 + ρ2 T 2) f + CT exp ⎜ ⎟ (1 − f ) ⎝ KB T ⎠
3737 3486 3041
317 320 325
0.998 0.999 0.999
(4)
The simulated curves (solid line) obtained under 0 T, 2 T and 5 T for La0.57Nd0.1Sr0.33MnO3 are shown in Fig. 1. It is clear that the calculated results from Eq. (4) are in good agreement with the experimental data. The best-fit parameters are given in Table 1. It can be seen that the activation energy Ea decreases when increasing the applied magnetic field. Thus, due to the spins' attempt to align along the magnetic field, which favors the conduction and decreases the ability of charge localization, the electrons jumping requires less energy. Consequently, the estimate values of Ea seem reasonable. Fig. 2 shows the variation of the volume fraction of the ferromagnetic phase (f) and of the paramagnetic phase (1 f) as a function of the temperature for La0.57Nd0.1Sr0.33MnO3 under 0, 2 and 5 T. It is clear that f (T) remains equal to 1 below the metal– semiconductor transition temperature, which confirms the strong dominance of the FM fraction in this range. Then the FM volume fraction begins to decrease to 0 from the ferromagnetic metallic state to a paramagnetic-semiconductor state confirming the validity of the percolation approach which assumes a conversation of ferromagnetic to paramagnetic regions. 3.2. Magnetoresistance studies The magnetoresistance (MR) dependence of the temperature of La0.57Nd0.1Sr0.33MnO3 is shown in Fig. 3 under two magnetic fields of 2 and 5 T. The MR is a fundamental property of manganites, which is related to the reduction of the electrical resistivity of the material by applying a magnetic field. It is defined as
Fig. 2. The temperature dependence of ferromagnetic phase volume fraction f and of the paramagnetic phase (1 f) for La0.57Nd0.1Sr0.33MnO3 under applied magnetic field of 5 T.
Fig. 3. Variation of MR vs. T curves for La0.57Nd0.1Sr0.33MnO3 under applied magnetic field of 2 and 5 T.
MR(%) = [ρ (0, T ) − ρ (H , T )]/ρ (0, T ) × 100%
(5)
where ρ (0,T) and ρ (H, T) are the resistivity values for zero and applied fields (2 T and 5 T) respectively. It is clear from the plot (Fig. 3) that the MR was decreasing with the increase in temperature. This decrease is almost linear with a small peak around TC. The MR is the largest (32% and 20% for 5 T and 2 T, respectively) and then gradually decreases with increasing temperature. Venkataiah et al. suggested that the reason for the higher MR at low temperature can be related to the extrinsic MR effect involving spin polarized tunneling between grains or spin dependent scattering of polarized electrons at grain boundaries [33]. While at TC, the high MR is attributed to Zener double-exchange [34]. In fact in the double exchange mechanism, the hopping of electron from Mn3 þ to Mn4 þ upon the spin alignment of Mn ions. The application of a magnetic field aligns the spin of the incomplete d orbital of the adjacent Mn ions, which results in the increase of the electrons' hopping rate and therefore an increase in electrical conductivity occurs [35]. In the present case, a high magnetic field has been found to affect MR at TC.
Fig. 4. Magnetization vs. applied magnetic field H, measured at different temperatures, for the La0.57Nd0.1Sr0.33MnO3.
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and from the experimental M (T, μ0H) curves are shown in Fig. 5, where the resistivity results agree quite well with the fitting parameter α ¼7.78 emu/g in the intermediate temperature range. The calculated ( ΔSM ) values from the temperature dependence of the resistivity were found to present a similar maximum of the magnetic entropy change deduced from the experimental M (T, μ0H) curves, around the Curie temperature TC. These results reveal a close relation between the temperature derivative of resistivity and magnetic entropy. It can be seen also that deviation of the magnetic results from the resistivity measurements occurs in the temperature range below 320 K, where the system is well inside the ferromagnetic state and distant from the critical transition region, and above 380 K, where the paramagnetic state prevails (Fig. 5). This result implies that the resistivity measurements are in agreement with the magnetic data mainly in the intermediate temperature range, i.e., during the establishment of perfect ferromagnetic order.
Fig. 5. Comparison of the magnetic entropy-temperature ΔS–T relations calculated from magnetic data and the resistive data.
3.3. Transport–entropy correlation Fig. 4 shows the typical results of isothermal field scans. The steep increase of magnetization with applied field in the low temperature region reveals the soft magnetic character of La0.57Nd0.1Sr0.33MnO3. With the increase of temperature, the growth of magnetization with field becomes more and more gradual, and the M–H dependence experiences a significant variation in the vicinity of Curie temperature. Based on the thermodynamic theory, the magnetic entropy change (ΔSM ), which characterized the magnetocaloric effect (MCE) in manganites and which results from the spin ordering, depends on the temperature gradient of the magnetization and attains a maximum value around the Curie temperature, at which the magnetization decays most rapidly. The temperature dependence of the magnetic entropy change (ΔSM ), for La0.57Nd0.1Sr0.33MnO3 sample is computed from Eq. (5) [36,37]:
T1 + T2 1 )= −ΔS M ( 2 T2 − T1 ⎡ ⎢ ⎣
∫0
μ0 H
μ 0 dH ′ −
M (T2, μ 0 H)
∫0
μ0 H
⎤ M (T1, μ 0 H) μ 0 dH ′⎥ ⎦
(6)
In manganites, the effect of CMR and MCE are usually observed near the magnetic phase transition temperature and it is obvious that there is some relation between the change in magnetic entropy and resistivity. Such a relation is presented in Ref. [38] by Perring et al. and then developed by Xiong et al. [22], where the authors proposed a method, which can evaluate the change in magnetic entropy from the data on the temperature and field dependence of resistivity in manganites. The relationship between ΔS and ρ is as follows:
ΔS Mρ (T , μ 0 H) = − α
∫0
μ0 H
⎡ ∂Lnρ ⎤ ⎢⎣ ⎥ dμ 0 H ∂T ⎦H
(7)
where α ¼7.78 emu/g, is determined from the fitting of ρ vs. M curve around the transition temperature TC with the equation ρ = α exp ( − M /T )[22]. According to Eqs. (6) and (7), the entropy changes of La0.57Nd0.1Sr0.33MnO3 determined by the resistivity measurement
4. Conclusions A descriptive report on detailed investigation of electrical resistivity and magnetoresistive (MR) properties of the sample La0.57Nd0.1Sr0.33MnO3 has been presented. Temperature dependence of resistivity revealed the presence of a metal–semiconductor transition at TM–SC. The conduction mechanisms were explained by a small polaron hopping in the semi-conductor region and by electron scattering mechanisms in the metallic region. Then, to understand the transport mechanism in the whole temperature range, we have used the phenomenological percolation model, which is based on the phase segregation of ferromagnetic and paramagnetic-semiconductor regions. The magnetoresistance studies reveal that a high magnetic field has been found to affect MR at TC. The relation between magnetic entropy change and resistivity has been also studied. It is noted that there is a strong correlation between ΔSM and ρ in La0.57Nd0.1Sr0.33MnO3 manganite in the vicinity of the phase transition temperature.
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