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Critical properties in La0.7Ca0.2Sr0.1MnO3 manganite: A comparison between sol-gel and solid state process
Journal of Alloys and Compounds 693 (2017) 658e666
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Critical properties in La0.7Ca0.2Sr0.1MnO3 manganite: A comparison between sol-gel and solid state process A. Ezaami a, b, *, I. Sfifir a, b, W. Cheikhrouhou-Koubaa a, b, M. Koubaa a, A. Cheikhrouhou a a b
Material Physics Laboratory, Faculty of Sciences of Sfax, B. P. 1171, Sfax University, 3000 Sfax, Tunisia Digital Research Center, Sfax Technopark, BP 275, 3021 Sakiet-ezzit, Tunisia
a r t i c l e i n f o
a b s t r a c t
Article history: Received 22 June 2016 Received in revised form 6 September 2016 Accepted 20 September 2016 Available online 22 September 2016
The critical properties of La0.7Ca0.2Sr0.1MnO3 manganite elaborated using two different methods have been investigated around the ferromagnetic-paramagnetic phase transition. Our sample was successfully synthesized by solid-state reaction (S1) and sol-gel route (S2). The X-ray diffraction characterizations show that (S1) crystallized in orthorhombic structure with Pnma space group without any detectable impurity. Though, (S2) crystallized in rhombohedra structure with R-3C space group. Various techniques such as modified Arrott plots, Kouvel-Fisher method and critical isotherm analysis were used to determine the values of the Curie temperature TC, as well as the critical exponents b (corresponding to the spontaneous magnetization), g (corresponding to the initial susceptibility) and d (corresponding to the critical magnetization isotherm). The estimated results are close to those expected by the mean-field model for sample S2; while for sample S1, the exponents values are close to those expected using the tricritical model. The obtained values from critical isotherm M (TC, m0H) are close to those determined using the Widom scaling relation, and also there are found to follow scaling equation with the magnetization data scaled into two different curves below and above TC, which implies the reliability and accuracy of the exponents. The change of the universality class can be explained by the reduction of the grain size. These results show that the critical behavior of our sample depend havely on the synthesis technique. © 2016 Elsevier B.V. All rights reserved.
Keywords: Critical behavior Perovskite manganite Magnetic phase transition Magnetization
1. Introduction Perovskite type manganites Ln1-xAxMnO3 (Ln is a trivalent rareearth and A is a divalent alkaline-earth) have attracted great attention because of their wonderful magnetic and electronic properties as well as their technological potential applications [1e7]. These materials exhibit a rich variety of physical properties. The most accepted interpretations for the cause of these properties are the double exchange model [8] and JahneTeller effect [9,10]. On one hand, these properties can be controlled by doping with suitable elements in the A-site and/or B-site to change the structural parameters and/or the Mn3þ/Mn4þ ratio. On the other hand, these properties depend strongly on the experimental conditions. Moreover, several studies in literature which emphasizes on the rare-earth manganite perovskites found that some of the basic
* Corresponding author. Material Physics Laboratory, Faculty of Sciences of Sfax, B. P. 1171, Sfax University, 3000 Sfax, Tunisia. E-mail address: [email protected] (A. Ezaami). http://dx.doi.org/10.1016/j.jallcom.2016.09.223 0925-8388/© 2016 Elsevier B.V. All rights reserved.
physical properties depend strongly on the synthesis method, such as the effective morphology, the chemical composition, the grain size distribution and their correlation with magnetic and magnetocaloric properties [11e13]. Such studies deeply affect the physical and chemical properties of the materials prepared by the various elaborating routes and they never resort to the study of this effect on critical properties. For this reason, it is necessary to investigate in details the correlation between the synthesis conditions and critical exponents around the paramagnetic-ferromagnetic transition. The critical behavior analysis for these materials can provide important information about the thermodynamic observations above and below TC; especially that recent theoretical calculations have predicted that the critical exponents in manganites could not be included in a universality class [14e17]. Four different theoretical models such as mean field (b ¼ 0.5, g ¼ 1.0 and d ¼ 3.0), threedimensional (3D) Heisenberg (b ¼ 0.365, g ¼ 1.336 and d ¼ 4.8), three-dimensional (3D) Ising (b ¼ 0.325, g ¼ 1.24 and d ¼ 4.82) and tricritical mean field (b ¼ 0.25, g ¼ 1.0 and d ¼ 5.0) were used to discuss the critical properties in manganites. Consequently, it is substantial to understand how elaborating methods affect various
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aspects of the physical properties of manganites. One of the most studied compounds in the last few years is the La0.7Ca0.3-xSrxMnO3 system. Depending on the variation of both dopant concentration and sintering temperature, this system undergoes a structural transition between the orthorhombic and the rhombohedral structure at a threshold concentration of x ¼ 0.1. From this reason, an essay has been made to comprehend the effect of elaborating method on the critical properties in La0.7Ca0.2Sr0.1MnO3 manganite prepared differently, characterized in the fact with a TC around room temperature together with a first order-second order magnetic transition [18], where the critical exponents b, g, and d have been estimated reliably using different analytical methods such as the modified arrott-plot, the Kouvel-Fisher method and the critical isotherm analysis. In addition, we demonstrate that the process of elaboration presents an intensive impact on the critical properties. 2. Experimental details La0.7Ca0.2Sr0.1MnO3 powder sample was synthesized using both solid state route and sol-gel reaction (denoted S1 and S2 respectively). Starting with La2O3, CaCO3, SrCO3 and MnO2 precursors with high purity (up to 99.9%) according to the reaction: 0.35 La2O3 þ 0.2 CaCO3 þ 0.1 SrCO3 þ MnO2 / La0.7Ca0.2Sr0.1MnO3 þ dO2 þ d0 CO2
2.1. Solid-state reaction: (S1) The starting precursors were mixed in stoichiometric proportions in an agate mortar and the obtained mixture was calcinated at 900 C in air for 24 h. It was then pressed into pellets of 12 mm diameter and 1 mm thickness under an axial pressure of 4 tons for 2 min and sintering at 1200 C for 48 h after regrinding and repelling processes to ensure a better crystallization. 2.2. Sol-gel route: (S2) The stoichiometric amounts of precursors were dissolved in dilute nitric acid at 70 C and then a suitable amount of citric acid and ethylene glycol as coordinate agents were added. The resulting gel was decomposed at 300 C to insure the propagation of a combustion which transforms the gel into a fine powder. Then, the sample was calcined at 600 C. The obtained powder was then pressed into pellets (of about 1 mm thickness under an axial pressure of 4 tons for 2 min) and sintered at 1200 C for 24 h to improve crystallinity. The structure and phase purity were checked by powder X-ray diffraction (XRD) using CuKa radiation (l ¼ 1.54059 Å) at room temperature. The pattern was recorded in the 10 2q 70 angular range with a step of 0.02 . The morphology of the samples was observed with a scanning electron microscope (SEM). The magnetic measurements were carried out using a vibrating sample magnetometer (VSM). In order to accurately extract the critical exponents of our sample, magnetization isotherms were measured in the range of 0e5 T with a temperature interval of 2 K in the vicinity of the Curie temperature (TC). 3. Scaling analysis
the critical region, both below and above Curie temperature. From the temperature dependence of MS we have found the critical exponentb, given by:
MS ðTÞ ¼ M0 ðεÞb
(1)
where M0 is critical amplitudes, and ε¼(T TC)/TC is the reduced temperature. Also, the critical exponent g has been established from the temperature dependence of the inverse of susceptibility c1 0 , which is given by
c1 0 ðTÞ ¼
h0 g ε M0
(2)
where h0 is the corresponding critical amplitude. Again, from the magnetic applied field, the dependence of magnetization M at TC given by:
M ¼ DðHÞ1=d
(3)
we have found d, where D is the critical amplitude. We have also shown that the exponents b, g and d follow the static scaling relationship:
d ¼ 1 þ g= b
(4)
The magnetic equation of state is a relationship among the variables M (m0H,ε), m0H and T. Using scaling hypothesis this can be expressed as:
. Mðm0 H; εÞ ¼ εb f ± H εbþg
(5)
where fþ for T > TC and f for T < TC, respectively are regular functions. This last Eq. (5) implies that for true scaling relations and right choice of b, g and d values, the scaled M/jεjb plotted as a function of the scaled m0H/jεjbþg will fall on two universal curves, one above TC and the other below TC. This is an important criterion of critical regime.
4. Results and discussions The phase identification and the structural analysis of La0.7Ca0.2Sr0.1MnO3 manganite sample was carried out using the Xray diffraction patterns recorded at room temperature. A typical XRay diffraction pattern of both samples is shown in Fig. 1. The two samples are single phase without any detectable impurity. We have refined the structure by the Rietveld method [20] using the Fullprof program [21]. The refinement shows that (S1) crystallized in orthorhombic structure with Pnma space group and (S2) crystallized in rhombohedra structure with R-3C space group. These results are in agreement with those elaborated by the hydrothermal synthesis process [22] and the single crystal elaborated by floatingzone [23]. The measured manganite density (D) is found to be 6.20 and 6.19 (g/cm3) for (S1) and (S2) respectively. The XRD density (DXRD) was also calculated according to the following formula [24]:
DXRD ¼ ZM=AV It is noted that the values of critical exponents b, g and d of La0.7Ca0.2Sr0.1MnO3 manganite sample are obtained, from magnetization measurements through below asymptotic relations [19]. For this intention, careful measurements were made of the magnetization at several magnetic fields at various temperatures in
659
(6)
Where: Z: the number of manganite molecules per unit cell; M: molecular mass;
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Fig. 1. Observed (the point symbols) and calculated (the solid lines) X-ray diffraction pattern for both samples. Positions for the Bragg reflection are marked by vertical bars. Differences between the observed and the calculated intensities are shown at the bottom of the diagram.
A: Avogadro number; V: the unit cell volume. The result was 6.22 and 6.20 (g/cm3) for (S1) and (S2), respectively. These values are in a range typical for manganites [24,25]. A comparison of the measured density (D) with the XRD density (DXRD) reveals the relatively low porosity (P) defined as [24]:
P ¼ 1 ðD=DXRD Þ
(7)
The obtained values are 0.003 and 0.002 for (S1) and (S2), respectively. Such a low porosity gives evidence of the high quality of the well compacted manganite [24]. The morphology and grain size of our samples have been studied by scanning electron microscopy (SEM). The SEM micrographs indicated excellent crystallinity with average particle sizes varying between 169 nm for (S1) and 80 nm for (S2) as shown in Fig. 2. In fact a grain is composed of several crystallites, probably due to the internal stress or defects in the structure [26,27]. Magnetization measurements as a function of temperature at 0.05 T show that our samples exhibit a paramagnetic to
ferromagnetic transition with decreasing temperature. Although not shown here, the paramagneticeferromagnetic phase-transition temperature TC obtained from the minimum of the dM/dT versus T curve decreases from 308 K for S1 (sintered at 1200 C) to 260 K for S2 (sintered at the same temperature 1200 C). It was remarked that the increase of TC has the same trend of the increase of crystallite size [26]. Fig. 3 shows the isothermal magnetization M (m0H) curves for both samples with dT ¼ 2 K. For S1 and in the FM region, the magnetization increases rapidly for m0 H less than 0.5 T and then saturates for fields above 1 T, which confirms the ferromagnetic behavior of our compounds at low temperatures. However, for S2, the saturation in the FM region is not fully reached. Almost the same behavior is observed in La0.7Ca0.25Ba0.05MnO3 manganite sample elaborated by the combination of solid-state reaction and mechanical milling [28], and this can be due to the presence of a magnetic disorder, magnetic inhomogeneity, and/or antiferromagnetic clusters in the samples. Moreover, this behavior is characteristic of the samples without true long range order ferromagnetism. These isotherms are then performed as M1/b vs. (m0H/M)1/g
Fig. 2. Scanning electron micrograph for both samples.
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Fig. 3. Isothermal magnetization around TC of both samples.
known as the standard Arrott plots [29] and plotted in Fig. 4 where b and g are given by their mean field values (0.5 and 1 respectively). We have analyzed these isotherms using Banerjee criterion [29]. According to this model, a positive slope of the Arrott plots can be observed, which indicates second order phase transition for both samples. This is good candidate to investigate the critical properties. Thus, the method of preparation does not affect the order of the transition. But, it could be indicated that the first order magnetic transition in La0.7Ca0.3MnO3 was rounded effectively by strontium dopants [30,31]. In addition, in the same figure, and according to the mean field theory [31] one can clearly see that such curves are not linear for S1 and show curvature downward even in the high field region, implying that the mean field theory is not valid for this sample. However, this curvature completely disappears for S2 and the Arrott plots curves in the vicinity of Curie temperature are parallel straight lines. The straight line TC passes through the origin, suggesting that the mean-field theory can describe the critical behavior of this sample. Therefore, this fact implies that the FM short range order exists in our sample, thus a modified Arrott plot should be employed to obtain correct critical parameters. Hence, the modified Arrott plots (MAP) are based on the so-called Arrott-Noakes equation [32]:
1=g H a½T TC þ bM1=b ¼ M T
(8)
where a and b are considered to be constants, b and g are the critical exponents. Fig. 5 shows the modified Arrots plots (M1/b versus (H/M)1/g) at several temperatures for S1 by using models of critical exponents: Fig. 5(a) Tricritical mean-Field model (b ¼ 0.25 and g ¼ 1). Fig. 5(b) 3D-Ising model (b ¼ 0.325 and g ¼ 1.24) and Fig. 5(c) 3D-Heisenberg model (b ¼ 0.365 and g ¼ 1.336). It was found that in the high field region, these four models give quasi straight lines, so it is difficult to determine which one is the best for critical exponent determination. Thus, to confirm the better model to fit our experimental data, their relative slopes (RS) were calculated at the critical point, defined as:
RS ¼ SðTÞ=SðTC Þ
(9)
where S(T) and S(TC) are the slopes deduced from MAP around and at TC respectively. The RS vs T plots for the four models are shown in Fig. 5(d). The RS of the most satisfactory model should be close to 1 (unity) [33]. Given the demonstration mentioned above, we have chosen initial
Fig. 4. The standard Arrott plot M2 vs. m0 H/M for both samples.
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Fig. 5. Modified Arrott plots: isotherms of M1/b vs (H/M)1/g with (a) the tricritical mean-field model, (b) the 3D-Ising model (c) 3D-Heisenberg model and (d) the relative slope (RS) as a function of temperature defined as RS ¼ S (T)/S (TC) for S1.
values of the critical exponents of the Tricritical mean-Field model (b ¼ 0.25 and g ¼ 1) for S1 and the critical exponents of the meanfield model (b ¼ 0.5 and g ¼ 1) for S2. According to the modified Arrott plots, the spontaneous magnetization MS (T) and the inverse of magnetic susceptibility c1 0 (T) were determined from the intersections of the linear extrapolation with the (M)1/b and the (H/M)1/g axis respectively. MS (T) and c1 0 (T) vs. T are shown in Fig. 6(a) for S1. These curves denote the power low fitting of MS (T) vs. T and c1 0 (T) vs. T according to Eqs. (1) and (2) respectively. Thus, new values of the critical exponents and the Curie temperatures associated are also mentioned in the same figure and reported in Table 1 for both samples. Alternately, the critical exponents b, g and TC can be also determined by the Kouvel-Fisher (KF) method [34]:
MS ½T TC ¼ dMS =dT b
"
(10)
#
c1 ½T TC 0 ¼ 1 g dc0 dT
(11)
According to this later equation, the plots of MS (dMS/dT)1 and 1 (d c1 versus temperature should yield straight lines 0 /dT) with slopes 1/b and 1/g, respectively and the intercepts on T axes are equal to Curie temperature (TC). These plots are shown in Fig. 6(b) for S1. It is outstanding that the values of the critical exponents obtained by the modified Arrott plots method and the Kouvel-Fisher method are in good agreement. The estimated critical exponents and TC for both samples are also listed in Table 1. In regards to the value of d, it can be determined directly from
c1 0
the critical isotherm of M (TC, m0H) (see in Fig. 6(c)). The inset of Fig. 6(c) shows the plot of Ln-Ln scale. According to Eq. (3), Ln(M) vs Ln(m0H) plot would give a straight line with slope 1/d of S1. From the linear fitting, we have got d ¼ 4.164 and 3.612 for S1 and S2 respectively. Furthermore, exponent d has also been calculated from Widom scaling relation according to which critical exponents b, g, and d are related in following way [35]:
d ¼ 1 þ g=b
(12)
As a result, the obtained value of d from the above values of b and g is found to be 4.164 for S1 and 3.305 for S2. When b and g are obtained from the modified Arrott plot d is found to be 4.577 for S1 and 3.143 for S2 and when b and g are obtained from the KF method d is found to be 4.028 for S1 and 3.160 for S2. It is clearly seen a small difference between the values obtained from critical isotherms M (TC, m0H) and those determined from the Widom scaling. This difference can be explained by the experiments errors. The values of the critical exponents for our samples derived from various methods and some of other manganites, besides the theoretical values based on various models [36e39], are summarized in Table 1. As a further test the reliability of the critical exponents and Curie temperature values, three different constructions have been used in this work, both based on the scaling equation of state. The magnetic equation of state is a relationship among the variables M (m0H,ε), m0H and T. Using scaling hypothesis this can be expressed as:
Mðm0 H; εÞ ¼ εb f ± H= εbþg
(13)
where fþ for T > TC and f for T < TC, respectively are regular functions. Eq. (13) implies that for true scaling relations and right
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663
Fig. 6. (a) The spontaneous magnetization MS (T,0) (left) and the inverse initial susceptibility. c1 0 (right) as a function of temperature of S1. (b) Kouvel-Fisher plot for the spontaneous magnetization MS (T) (left) and the inverse initial susceptibility c1 0 (right) of S1 (Solid lines are fits to the model). (c) Isothermal M vs m0H plot of S1 at TC ¼ 308 K; the inset shows the same plot in log-log scale and the solid line is the linear fit following Eq. (3).
Table 1 Comparison of critical exponents of our compounds with earlier reports, and with the various theoretical models. Sample
Technique
b
g
d
Ref.
S1
MAP KF CI MAP KF CI Theory Theory Theory Theory TC 363 360 248 260
0.276 0.315
0.966/ 0.954/
This work
0.484 0.469
1.037 1.013
0.5 0.365 0.325 0.25
1 1.336 1.24 1
4.500 4.028 4.164 3.143 3.160 3.612 3.0 4.80 4.82 5
0.323 0.387 0.36 0.212
1.083 1.166 1.2 e
4.353 4.01 4.33 e
[36] [37] [38] [39]
S2
Mean Field model 3D-Heisenberg model 3D-Ising model Tricritical mean-field model La0.7Sr0.3MnO3 La0.7Sr0.3MnO3 La0.7Ca0$3MnO3 La0.7Ca0.3MnO3
M’~ M (m0H, ε)εb and h~(m0H) ε-(bþg) [23]. Such plot observed in Fig. 7(b) showed two separate curves, above and below TC. This behavior clearly confirms that the critical exponents values are unambiguous. Also, the reliability of b, d and TC can be ascertained by checking the scaling of the magnetization curves. In fact, the scaling equation takes the form:
ε ¼ f Md M 1=b
m0 H [15] [15] [15] [15]
choice of b, g and d values, the scaled Mjεjb plotted as a function of the scaled m0H/jεjbþg will fall on two universal curves, one above TC and the other below TC. This is an essential criterion of critical regime. Using the values of b and g obtained from the KF method, the scaled data for our considered sample are plotted in Fig. 7(a). The performance of M/jεjb and m0H/jεjbþg reveals that the magnetic isotherms in the vicinity of TC fall on two individual branches; for T < TC and for T > TC. This shows that the critical parameters determined are in good agreement with the scaling hypothesis, which further corroborates the reliability of the obtained critical exponents. The inset of Fig. 7(a) shows the same plots in log-log scale. It is found that the scaling is particularly good at higher fields. Moreover, the reliability of the obtained exponents and TC can also be ensured with the analysis by plotting M0 2 vs h/M0 , where,
(14)
where f is a scaling function which characterizes the magnetizations behavior along the coexistence (m0H ¼ 0, ε < 0) and the critical isotherm (ε ¼ 0), respectively. Thus, according to Eq. (14) and using the appropriate values for the critical exponents and the Curie M ε temperature, the plot of 1=D (D ¼ b þ g), should 1=d vs: ðm0 HÞ
ðm0 HÞ
correspond to a universal curve onto which all experimental data points collapse [40]. Using the values of b, g, and TC obtained from the K-F method, the scaled data are plotted in Fig. 7(c) for S1. The excellent overlap of the experimental data points clearly indicates that the obtained values of b, g, and TC for this compound is in agreement with the scaling hypothesis near magnetic transition. Moreover, the influence of disorder on the critical behavior of magnetic systems whose undergoes a second order phase transition is predicted by the criterion of Harris [41]. In this context, Harris asserts that if the critical exponent apure > 0, the disorder modifies the critical exponents. While, if apure is negative, the disorder is irrelevant. Using the scaling relation defined as:
apure þ 2b þ g ¼ 2
(15)
The exponent apure is found to be positive for S1 which implies that the disorder is relevant.
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Fig. 7. (a) Scaling plots indicating two universal curves below and above TC for S1. Inset shows the same plots on a log-log scale. (b) Scaling plot of M0 2 versus h/m for S1 at temperature T < TC and T > TC. (C) Normalized isotherms of S1 below and above the Curie temperature using the values of b and D determined by the K-F method.
In addition, there is another important tool in understanding the critical behavior, which is the study of the field dependence of the magnetic entropy change. The field dependence of the magnetic entropy change of materials with second order magnetic transition can be expressed as a power law given by Ref. [42]: n DSmax M zaðm0 HÞ
(16)
where: a is a constant and the local exponent n resulting from both temperature and magnetic field variation. It depends on the magnetic state of the sample. A fit of the power law was done on the results of the magnetic entropy change DSmax M for our samples, and allows the prediction of the variation of the maximum entropy for each applied magnetic field [43], as shown in Fig. 8. It can be expressed as a power law by taking account of the field dependence of entropy change DSmax M
Fig. 8. Field dependence of entropy change. Lines indicate non-linear curve fitting of the data.
A. Ezaami et al. / Journal of Alloys and Compounds 693 (2017) 658e666
and reference temperature into consideration. At TC, the exponent n becomes field independent and is expressed as:
n¼1þ
b1 bþ g
(17)
where b and g are the critical exponents. Apparently, the n values obtained from the power-law fitting of theDSmax vs. m0H curve are higher than those calculated from Eq. M (17). The difference is due to the presence of local inhomogeneities around the Curie temperature.
[11]
[12]
[13]
[14]
5. Conclusion
[15]
In the present work, we have studied the effect of synthesis route on the critical behavior of La0.7Ca0.2Sr0.1MnO3 manganite sample in the vicinity of the Curie temperature from magnetization measurements. On one hand, we have successfully elaborated our sample using both methods: the solid state and the sol-gel. On the other hand, the values of critical exponents for both samples were extracted using the modified Arrott plots method, Kouvel-Fisher method and critical isotherm analysis. The validity of the obtained critical exponents using various methods has been confirmed by the scaling equation of state. These critical exponents are found to pursue scaling equation with the magnetization data scaled into two different curves below and above TC. This confirms that the critical exponents and TC are reasonably accurate. For S1, the obtained exponents value are close to those expected for tricritical mean field model and the value of critical exponents g decreased and approached the mean field model. Interestingly, the reduction of the grain size, due to changing the elaborating method, is the main cause of change in the universality class. These results indicate that the critical properties of our sample depend strongly on the synthesis conditions.
[16]
[17] [18]
[19] [20] [21] [22] [23]
[24]
[25]
[26]
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Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom
Critical properties in La0.7Ca0.2Sr0.1MnO3 manganite: A comparison between sol-gel and solid state process A. Ezaami a, b, *, I. Sfifir a, b, W. Cheikhrouhou-Koubaa a, b, M. Koubaa a, A. Cheikhrouhou a a b
Material Physics Laboratory, Faculty of Sciences of Sfax, B. P. 1171, Sfax University, 3000 Sfax, Tunisia Digital Research Center, Sfax Technopark, BP 275, 3021 Sakiet-ezzit, Tunisia
a r t i c l e i n f o
a b s t r a c t
Article history: Received 22 June 2016 Received in revised form 6 September 2016 Accepted 20 September 2016 Available online 22 September 2016
The critical properties of La0.7Ca0.2Sr0.1MnO3 manganite elaborated using two different methods have been investigated around the ferromagnetic-paramagnetic phase transition. Our sample was successfully synthesized by solid-state reaction (S1) and sol-gel route (S2). The X-ray diffraction characterizations show that (S1) crystallized in orthorhombic structure with Pnma space group without any detectable impurity. Though, (S2) crystallized in rhombohedra structure with R-3C space group. Various techniques such as modified Arrott plots, Kouvel-Fisher method and critical isotherm analysis were used to determine the values of the Curie temperature TC, as well as the critical exponents b (corresponding to the spontaneous magnetization), g (corresponding to the initial susceptibility) and d (corresponding to the critical magnetization isotherm). The estimated results are close to those expected by the mean-field model for sample S2; while for sample S1, the exponents values are close to those expected using the tricritical model. The obtained values from critical isotherm M (TC, m0H) are close to those determined using the Widom scaling relation, and also there are found to follow scaling equation with the magnetization data scaled into two different curves below and above TC, which implies the reliability and accuracy of the exponents. The change of the universality class can be explained by the reduction of the grain size. These results show that the critical behavior of our sample depend havely on the synthesis technique. © 2016 Elsevier B.V. All rights reserved.
Keywords: Critical behavior Perovskite manganite Magnetic phase transition Magnetization
1. Introduction Perovskite type manganites Ln1-xAxMnO3 (Ln is a trivalent rareearth and A is a divalent alkaline-earth) have attracted great attention because of their wonderful magnetic and electronic properties as well as their technological potential applications [1e7]. These materials exhibit a rich variety of physical properties. The most accepted interpretations for the cause of these properties are the double exchange model [8] and JahneTeller effect [9,10]. On one hand, these properties can be controlled by doping with suitable elements in the A-site and/or B-site to change the structural parameters and/or the Mn3þ/Mn4þ ratio. On the other hand, these properties depend strongly on the experimental conditions. Moreover, several studies in literature which emphasizes on the rare-earth manganite perovskites found that some of the basic
* Corresponding author. Material Physics Laboratory, Faculty of Sciences of Sfax, B. P. 1171, Sfax University, 3000 Sfax, Tunisia. E-mail address: [email protected] (A. Ezaami). http://dx.doi.org/10.1016/j.jallcom.2016.09.223 0925-8388/© 2016 Elsevier B.V. All rights reserved.
physical properties depend strongly on the synthesis method, such as the effective morphology, the chemical composition, the grain size distribution and their correlation with magnetic and magnetocaloric properties [11e13]. Such studies deeply affect the physical and chemical properties of the materials prepared by the various elaborating routes and they never resort to the study of this effect on critical properties. For this reason, it is necessary to investigate in details the correlation between the synthesis conditions and critical exponents around the paramagnetic-ferromagnetic transition. The critical behavior analysis for these materials can provide important information about the thermodynamic observations above and below TC; especially that recent theoretical calculations have predicted that the critical exponents in manganites could not be included in a universality class [14e17]. Four different theoretical models such as mean field (b ¼ 0.5, g ¼ 1.0 and d ¼ 3.0), threedimensional (3D) Heisenberg (b ¼ 0.365, g ¼ 1.336 and d ¼ 4.8), three-dimensional (3D) Ising (b ¼ 0.325, g ¼ 1.24 and d ¼ 4.82) and tricritical mean field (b ¼ 0.25, g ¼ 1.0 and d ¼ 5.0) were used to discuss the critical properties in manganites. Consequently, it is substantial to understand how elaborating methods affect various
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aspects of the physical properties of manganites. One of the most studied compounds in the last few years is the La0.7Ca0.3-xSrxMnO3 system. Depending on the variation of both dopant concentration and sintering temperature, this system undergoes a structural transition between the orthorhombic and the rhombohedral structure at a threshold concentration of x ¼ 0.1. From this reason, an essay has been made to comprehend the effect of elaborating method on the critical properties in La0.7Ca0.2Sr0.1MnO3 manganite prepared differently, characterized in the fact with a TC around room temperature together with a first order-second order magnetic transition [18], where the critical exponents b, g, and d have been estimated reliably using different analytical methods such as the modified arrott-plot, the Kouvel-Fisher method and the critical isotherm analysis. In addition, we demonstrate that the process of elaboration presents an intensive impact on the critical properties. 2. Experimental details La0.7Ca0.2Sr0.1MnO3 powder sample was synthesized using both solid state route and sol-gel reaction (denoted S1 and S2 respectively). Starting with La2O3, CaCO3, SrCO3 and MnO2 precursors with high purity (up to 99.9%) according to the reaction: 0.35 La2O3 þ 0.2 CaCO3 þ 0.1 SrCO3 þ MnO2 / La0.7Ca0.2Sr0.1MnO3 þ dO2 þ d0 CO2
2.1. Solid-state reaction: (S1) The starting precursors were mixed in stoichiometric proportions in an agate mortar and the obtained mixture was calcinated at 900 C in air for 24 h. It was then pressed into pellets of 12 mm diameter and 1 mm thickness under an axial pressure of 4 tons for 2 min and sintering at 1200 C for 48 h after regrinding and repelling processes to ensure a better crystallization. 2.2. Sol-gel route: (S2) The stoichiometric amounts of precursors were dissolved in dilute nitric acid at 70 C and then a suitable amount of citric acid and ethylene glycol as coordinate agents were added. The resulting gel was decomposed at 300 C to insure the propagation of a combustion which transforms the gel into a fine powder. Then, the sample was calcined at 600 C. The obtained powder was then pressed into pellets (of about 1 mm thickness under an axial pressure of 4 tons for 2 min) and sintered at 1200 C for 24 h to improve crystallinity. The structure and phase purity were checked by powder X-ray diffraction (XRD) using CuKa radiation (l ¼ 1.54059 Å) at room temperature. The pattern was recorded in the 10 2q 70 angular range with a step of 0.02 . The morphology of the samples was observed with a scanning electron microscope (SEM). The magnetic measurements were carried out using a vibrating sample magnetometer (VSM). In order to accurately extract the critical exponents of our sample, magnetization isotherms were measured in the range of 0e5 T with a temperature interval of 2 K in the vicinity of the Curie temperature (TC). 3. Scaling analysis
the critical region, both below and above Curie temperature. From the temperature dependence of MS we have found the critical exponentb, given by:
MS ðTÞ ¼ M0 ðεÞb
(1)
where M0 is critical amplitudes, and ε¼(T TC)/TC is the reduced temperature. Also, the critical exponent g has been established from the temperature dependence of the inverse of susceptibility c1 0 , which is given by
c1 0 ðTÞ ¼
h0 g ε M0
(2)
where h0 is the corresponding critical amplitude. Again, from the magnetic applied field, the dependence of magnetization M at TC given by:
M ¼ DðHÞ1=d
(3)
we have found d, where D is the critical amplitude. We have also shown that the exponents b, g and d follow the static scaling relationship:
d ¼ 1 þ g= b
(4)
The magnetic equation of state is a relationship among the variables M (m0H,ε), m0H and T. Using scaling hypothesis this can be expressed as:
. Mðm0 H; εÞ ¼ εb f ± H εbþg
(5)
where fþ for T > TC and f for T < TC, respectively are regular functions. This last Eq. (5) implies that for true scaling relations and right choice of b, g and d values, the scaled M/jεjb plotted as a function of the scaled m0H/jεjbþg will fall on two universal curves, one above TC and the other below TC. This is an important criterion of critical regime.
4. Results and discussions The phase identification and the structural analysis of La0.7Ca0.2Sr0.1MnO3 manganite sample was carried out using the Xray diffraction patterns recorded at room temperature. A typical XRay diffraction pattern of both samples is shown in Fig. 1. The two samples are single phase without any detectable impurity. We have refined the structure by the Rietveld method [20] using the Fullprof program [21]. The refinement shows that (S1) crystallized in orthorhombic structure with Pnma space group and (S2) crystallized in rhombohedra structure with R-3C space group. These results are in agreement with those elaborated by the hydrothermal synthesis process [22] and the single crystal elaborated by floatingzone [23]. The measured manganite density (D) is found to be 6.20 and 6.19 (g/cm3) for (S1) and (S2) respectively. The XRD density (DXRD) was also calculated according to the following formula [24]:
DXRD ¼ ZM=AV It is noted that the values of critical exponents b, g and d of La0.7Ca0.2Sr0.1MnO3 manganite sample are obtained, from magnetization measurements through below asymptotic relations [19]. For this intention, careful measurements were made of the magnetization at several magnetic fields at various temperatures in
659
(6)
Where: Z: the number of manganite molecules per unit cell; M: molecular mass;
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Fig. 1. Observed (the point symbols) and calculated (the solid lines) X-ray diffraction pattern for both samples. Positions for the Bragg reflection are marked by vertical bars. Differences between the observed and the calculated intensities are shown at the bottom of the diagram.
A: Avogadro number; V: the unit cell volume. The result was 6.22 and 6.20 (g/cm3) for (S1) and (S2), respectively. These values are in a range typical for manganites [24,25]. A comparison of the measured density (D) with the XRD density (DXRD) reveals the relatively low porosity (P) defined as [24]:
P ¼ 1 ðD=DXRD Þ
(7)
The obtained values are 0.003 and 0.002 for (S1) and (S2), respectively. Such a low porosity gives evidence of the high quality of the well compacted manganite [24]. The morphology and grain size of our samples have been studied by scanning electron microscopy (SEM). The SEM micrographs indicated excellent crystallinity with average particle sizes varying between 169 nm for (S1) and 80 nm for (S2) as shown in Fig. 2. In fact a grain is composed of several crystallites, probably due to the internal stress or defects in the structure [26,27]. Magnetization measurements as a function of temperature at 0.05 T show that our samples exhibit a paramagnetic to
ferromagnetic transition with decreasing temperature. Although not shown here, the paramagneticeferromagnetic phase-transition temperature TC obtained from the minimum of the dM/dT versus T curve decreases from 308 K for S1 (sintered at 1200 C) to 260 K for S2 (sintered at the same temperature 1200 C). It was remarked that the increase of TC has the same trend of the increase of crystallite size [26]. Fig. 3 shows the isothermal magnetization M (m0H) curves for both samples with dT ¼ 2 K. For S1 and in the FM region, the magnetization increases rapidly for m0 H less than 0.5 T and then saturates for fields above 1 T, which confirms the ferromagnetic behavior of our compounds at low temperatures. However, for S2, the saturation in the FM region is not fully reached. Almost the same behavior is observed in La0.7Ca0.25Ba0.05MnO3 manganite sample elaborated by the combination of solid-state reaction and mechanical milling [28], and this can be due to the presence of a magnetic disorder, magnetic inhomogeneity, and/or antiferromagnetic clusters in the samples. Moreover, this behavior is characteristic of the samples without true long range order ferromagnetism. These isotherms are then performed as M1/b vs. (m0H/M)1/g
Fig. 2. Scanning electron micrograph for both samples.
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Fig. 3. Isothermal magnetization around TC of both samples.
known as the standard Arrott plots [29] and plotted in Fig. 4 where b and g are given by their mean field values (0.5 and 1 respectively). We have analyzed these isotherms using Banerjee criterion [29]. According to this model, a positive slope of the Arrott plots can be observed, which indicates second order phase transition for both samples. This is good candidate to investigate the critical properties. Thus, the method of preparation does not affect the order of the transition. But, it could be indicated that the first order magnetic transition in La0.7Ca0.3MnO3 was rounded effectively by strontium dopants [30,31]. In addition, in the same figure, and according to the mean field theory [31] one can clearly see that such curves are not linear for S1 and show curvature downward even in the high field region, implying that the mean field theory is not valid for this sample. However, this curvature completely disappears for S2 and the Arrott plots curves in the vicinity of Curie temperature are parallel straight lines. The straight line TC passes through the origin, suggesting that the mean-field theory can describe the critical behavior of this sample. Therefore, this fact implies that the FM short range order exists in our sample, thus a modified Arrott plot should be employed to obtain correct critical parameters. Hence, the modified Arrott plots (MAP) are based on the so-called Arrott-Noakes equation [32]:
1=g H a½T TC þ bM1=b ¼ M T
(8)
where a and b are considered to be constants, b and g are the critical exponents. Fig. 5 shows the modified Arrots plots (M1/b versus (H/M)1/g) at several temperatures for S1 by using models of critical exponents: Fig. 5(a) Tricritical mean-Field model (b ¼ 0.25 and g ¼ 1). Fig. 5(b) 3D-Ising model (b ¼ 0.325 and g ¼ 1.24) and Fig. 5(c) 3D-Heisenberg model (b ¼ 0.365 and g ¼ 1.336). It was found that in the high field region, these four models give quasi straight lines, so it is difficult to determine which one is the best for critical exponent determination. Thus, to confirm the better model to fit our experimental data, their relative slopes (RS) were calculated at the critical point, defined as:
RS ¼ SðTÞ=SðTC Þ
(9)
where S(T) and S(TC) are the slopes deduced from MAP around and at TC respectively. The RS vs T plots for the four models are shown in Fig. 5(d). The RS of the most satisfactory model should be close to 1 (unity) [33]. Given the demonstration mentioned above, we have chosen initial
Fig. 4. The standard Arrott plot M2 vs. m0 H/M for both samples.
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Fig. 5. Modified Arrott plots: isotherms of M1/b vs (H/M)1/g with (a) the tricritical mean-field model, (b) the 3D-Ising model (c) 3D-Heisenberg model and (d) the relative slope (RS) as a function of temperature defined as RS ¼ S (T)/S (TC) for S1.
values of the critical exponents of the Tricritical mean-Field model (b ¼ 0.25 and g ¼ 1) for S1 and the critical exponents of the meanfield model (b ¼ 0.5 and g ¼ 1) for S2. According to the modified Arrott plots, the spontaneous magnetization MS (T) and the inverse of magnetic susceptibility c1 0 (T) were determined from the intersections of the linear extrapolation with the (M)1/b and the (H/M)1/g axis respectively. MS (T) and c1 0 (T) vs. T are shown in Fig. 6(a) for S1. These curves denote the power low fitting of MS (T) vs. T and c1 0 (T) vs. T according to Eqs. (1) and (2) respectively. Thus, new values of the critical exponents and the Curie temperatures associated are also mentioned in the same figure and reported in Table 1 for both samples. Alternately, the critical exponents b, g and TC can be also determined by the Kouvel-Fisher (KF) method [34]:
MS ½T TC ¼ dMS =dT b
"
(10)
#
c1 ½T TC 0 ¼ 1 g dc0 dT
(11)
According to this later equation, the plots of MS (dMS/dT)1 and 1 (d c1 versus temperature should yield straight lines 0 /dT) with slopes 1/b and 1/g, respectively and the intercepts on T axes are equal to Curie temperature (TC). These plots are shown in Fig. 6(b) for S1. It is outstanding that the values of the critical exponents obtained by the modified Arrott plots method and the Kouvel-Fisher method are in good agreement. The estimated critical exponents and TC for both samples are also listed in Table 1. In regards to the value of d, it can be determined directly from
c1 0
the critical isotherm of M (TC, m0H) (see in Fig. 6(c)). The inset of Fig. 6(c) shows the plot of Ln-Ln scale. According to Eq. (3), Ln(M) vs Ln(m0H) plot would give a straight line with slope 1/d of S1. From the linear fitting, we have got d ¼ 4.164 and 3.612 for S1 and S2 respectively. Furthermore, exponent d has also been calculated from Widom scaling relation according to which critical exponents b, g, and d are related in following way [35]:
d ¼ 1 þ g=b
(12)
As a result, the obtained value of d from the above values of b and g is found to be 4.164 for S1 and 3.305 for S2. When b and g are obtained from the modified Arrott plot d is found to be 4.577 for S1 and 3.143 for S2 and when b and g are obtained from the KF method d is found to be 4.028 for S1 and 3.160 for S2. It is clearly seen a small difference between the values obtained from critical isotherms M (TC, m0H) and those determined from the Widom scaling. This difference can be explained by the experiments errors. The values of the critical exponents for our samples derived from various methods and some of other manganites, besides the theoretical values based on various models [36e39], are summarized in Table 1. As a further test the reliability of the critical exponents and Curie temperature values, three different constructions have been used in this work, both based on the scaling equation of state. The magnetic equation of state is a relationship among the variables M (m0H,ε), m0H and T. Using scaling hypothesis this can be expressed as:
Mðm0 H; εÞ ¼ εb f ± H= εbþg
(13)
where fþ for T > TC and f for T < TC, respectively are regular functions. Eq. (13) implies that for true scaling relations and right
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Fig. 6. (a) The spontaneous magnetization MS (T,0) (left) and the inverse initial susceptibility. c1 0 (right) as a function of temperature of S1. (b) Kouvel-Fisher plot for the spontaneous magnetization MS (T) (left) and the inverse initial susceptibility c1 0 (right) of S1 (Solid lines are fits to the model). (c) Isothermal M vs m0H plot of S1 at TC ¼ 308 K; the inset shows the same plot in log-log scale and the solid line is the linear fit following Eq. (3).
Table 1 Comparison of critical exponents of our compounds with earlier reports, and with the various theoretical models. Sample
Technique
b
g
d
Ref.
S1
MAP KF CI MAP KF CI Theory Theory Theory Theory TC 363 360 248 260
0.276 0.315
0.966/ 0.954/
This work
0.484 0.469
1.037 1.013
0.5 0.365 0.325 0.25
1 1.336 1.24 1
4.500 4.028 4.164 3.143 3.160 3.612 3.0 4.80 4.82 5
0.323 0.387 0.36 0.212
1.083 1.166 1.2 e
4.353 4.01 4.33 e
[36] [37] [38] [39]
S2
Mean Field model 3D-Heisenberg model 3D-Ising model Tricritical mean-field model La0.7Sr0.3MnO3 La0.7Sr0.3MnO3 La0.7Ca0$3MnO3 La0.7Ca0.3MnO3
M’~ M (m0H, ε)εb and h~(m0H) ε-(bþg) [23]. Such plot observed in Fig. 7(b) showed two separate curves, above and below TC. This behavior clearly confirms that the critical exponents values are unambiguous. Also, the reliability of b, d and TC can be ascertained by checking the scaling of the magnetization curves. In fact, the scaling equation takes the form:
ε ¼ f Md M 1=b
m0 H [15] [15] [15] [15]
choice of b, g and d values, the scaled Mjεjb plotted as a function of the scaled m0H/jεjbþg will fall on two universal curves, one above TC and the other below TC. This is an essential criterion of critical regime. Using the values of b and g obtained from the KF method, the scaled data for our considered sample are plotted in Fig. 7(a). The performance of M/jεjb and m0H/jεjbþg reveals that the magnetic isotherms in the vicinity of TC fall on two individual branches; for T < TC and for T > TC. This shows that the critical parameters determined are in good agreement with the scaling hypothesis, which further corroborates the reliability of the obtained critical exponents. The inset of Fig. 7(a) shows the same plots in log-log scale. It is found that the scaling is particularly good at higher fields. Moreover, the reliability of the obtained exponents and TC can also be ensured with the analysis by plotting M0 2 vs h/M0 , where,
(14)
where f is a scaling function which characterizes the magnetizations behavior along the coexistence (m0H ¼ 0, ε < 0) and the critical isotherm (ε ¼ 0), respectively. Thus, according to Eq. (14) and using the appropriate values for the critical exponents and the Curie M ε temperature, the plot of 1=D (D ¼ b þ g), should 1=d vs: ðm0 HÞ
ðm0 HÞ
correspond to a universal curve onto which all experimental data points collapse [40]. Using the values of b, g, and TC obtained from the K-F method, the scaled data are plotted in Fig. 7(c) for S1. The excellent overlap of the experimental data points clearly indicates that the obtained values of b, g, and TC for this compound is in agreement with the scaling hypothesis near magnetic transition. Moreover, the influence of disorder on the critical behavior of magnetic systems whose undergoes a second order phase transition is predicted by the criterion of Harris [41]. In this context, Harris asserts that if the critical exponent apure > 0, the disorder modifies the critical exponents. While, if apure is negative, the disorder is irrelevant. Using the scaling relation defined as:
apure þ 2b þ g ¼ 2
(15)
The exponent apure is found to be positive for S1 which implies that the disorder is relevant.
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Fig. 7. (a) Scaling plots indicating two universal curves below and above TC for S1. Inset shows the same plots on a log-log scale. (b) Scaling plot of M0 2 versus h/m for S1 at temperature T < TC and T > TC. (C) Normalized isotherms of S1 below and above the Curie temperature using the values of b and D determined by the K-F method.
In addition, there is another important tool in understanding the critical behavior, which is the study of the field dependence of the magnetic entropy change. The field dependence of the magnetic entropy change of materials with second order magnetic transition can be expressed as a power law given by Ref. [42]: n DSmax M zaðm0 HÞ
(16)
where: a is a constant and the local exponent n resulting from both temperature and magnetic field variation. It depends on the magnetic state of the sample. A fit of the power law was done on the results of the magnetic entropy change DSmax M for our samples, and allows the prediction of the variation of the maximum entropy for each applied magnetic field [43], as shown in Fig. 8. It can be expressed as a power law by taking account of the field dependence of entropy change DSmax M
Fig. 8. Field dependence of entropy change. Lines indicate non-linear curve fitting of the data.
A. Ezaami et al. / Journal of Alloys and Compounds 693 (2017) 658e666
and reference temperature into consideration. At TC, the exponent n becomes field independent and is expressed as:
n¼1þ
b1 bþ g
(17)
where b and g are the critical exponents. Apparently, the n values obtained from the power-law fitting of theDSmax vs. m0H curve are higher than those calculated from Eq. M (17). The difference is due to the presence of local inhomogeneities around the Curie temperature.
[11]
[12]
[13]
[14]
5. Conclusion
[15]
In the present work, we have studied the effect of synthesis route on the critical behavior of La0.7Ca0.2Sr0.1MnO3 manganite sample in the vicinity of the Curie temperature from magnetization measurements. On one hand, we have successfully elaborated our sample using both methods: the solid state and the sol-gel. On the other hand, the values of critical exponents for both samples were extracted using the modified Arrott plots method, Kouvel-Fisher method and critical isotherm analysis. The validity of the obtained critical exponents using various methods has been confirmed by the scaling equation of state. These critical exponents are found to pursue scaling equation with the magnetization data scaled into two different curves below and above TC. This confirms that the critical exponents and TC are reasonably accurate. For S1, the obtained exponents value are close to those expected for tricritical mean field model and the value of critical exponents g decreased and approached the mean field model. Interestingly, the reduction of the grain size, due to changing the elaborating method, is the main cause of change in the universality class. These results indicate that the critical properties of our sample depend strongly on the synthesis conditions.
[16]
[17] [18]
[19] [20] [21] [22] [23]
[24]
[25]
[26]
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