Int. J. Nanotechnology, Vol. 10, Nos. 3/4, 2013
Superparamagnetic behaviour and deviation from Bloch T3/2 law of La0.7Ca0.3MnO3 nanoparticles Do Hung Manh*, Tran Dang Thanh, Nguyen Van Chien, Vu Dinh Lam, Le Van Hong and Nguyen Xuan Phuc Institute of Materials Science, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet Road, Cau Giay Distr., Hanoi, Vietnam Email:
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Pham Thanh Phong Nha Trang Pedagogic College, 01 Nguyen Chanh Street, Nha Trang City, Khanh Hoa Province, Vietnam Email:
[email protected] Abstract: In this study, we investigated superparamagnetism behaviour and saturation magnetisation of single-phase, nanocrystalline, granular La0.7Ca0.3MnO3 (LCMO) samples synthesised by reactive milling method. The superparamagnetic behaviour of as-milled samples with various milling times was studied in the temperature range from 200 K to 300 K. The saturation magnetisation of the samples increased from 14.7 to 36.8 emu/g with higher values corresponding to shorter milling time. The observed un-overlapping of the scaled M(Hext, T)/MS versus Hext/T plots and the Curie-Weiss like behaviour of the dc-susceptibility at high temperatures provide evidence that the nanoparticles are interacting superparamagnetic ensembles. The magnetisation curves of interacting nanoparticles were well described by the argumentcorrected Langevin function. The saturation magnetisation versus temperature showed a Tε dependence with ε deviated from 3/2 (value for the Bloch law), which increased with decreasing of the milling time. Keywords: perovskite; reactive milling; particle size; nanoparticles; CurieWeiss like behaviour. Reference to this paper should be made as follows: Manh, D.H., Thanh, T.D., Chien, N.V., Lam, V.D., Hong, L.V., Phuc, N.X. and Phong, P.T. (2013) ‘Superparamagnetic behaviour and deviation from Bloch T3/2 law of La0.7Ca0.3MnO3 nanoparticles’, Int. J. Nanotechnology, Vol. 10, Nos. 3/4, pp.197–205. Copyright © 2013 Inderscience Enterprises Ltd.
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D.H. Manh et al. Biographical notes: Do Hung Manh received his Bachelor’s Degree in Solid State Physics from the University of Hanoi in 1984. From 1985 to 1989, he was a researcher at the Institute of Physics, Vietnam Academy of Science. He received his Masters in Nanomaterials and Nanodevices in 2008 at the University of Engineering and Technology, Vietnam National University of Hanoi. He defended PhD thesis at the Institute of Materials Science (IMS) in July 2011. He is the author/co-author of about 30 internationally reviewed scientific papers. His current research interests are nanostructure magnetic materials and nanobiomaterials. Tran Dang Thanh received his diploma in Physics at the Hanoi University of Education (HUE) in 1998 and his masters on Solid State Physics in 2001 at the HUE. Since 2002, he has been working at the Laboratory of X-Ray Diffraction, IMS, VAST. In December 2009, he received his PhD in Materials Science at IMS, VAST having completed his thesis titled ‘'Fabrication and study the properties of the colossal dielectric constant material La2-xSrxNiO4+δ’ under Professors L.V. Hong and P.V. Phuc’s supervision. His studies focus on the preparation, structure and characterisations of multiferroic materials. Nguyen Van Chien received diploma in physics at the University of Engineering and Technology in 2009. His undergraduate thesis focuses on the fabrication and characterisation of the multiferroic multilayers. Since 2009, he has been working at the Laboratory of Magnetism and Superconductivity, IMS, VAST. His current studies focus on the electro-magnetic properties of manganites. Vu Dinh Lam received his Diploma in Physics at the Hanoi University of Education in 1995 and Masters on Materials Science in 1997 at the International Training Institute for Materials Science and then he became the researcher of IMS from 1999. In 2005, I got PhD degree in Materials Science at IMS, VAST. He spent 3 years (2006–2009) in Hanyang University for postdoc position. He is the author/co-author of about 40 internationally reviewed scientific papers. His current fields of interest are magnetic materials, metamaterials and renewable energy materials. Currently, he is DeputyDirector of IMS. Le Van Hong studied at the Crakow University of Poland. He received his Diploma in Solid State Physics in 1973. He received his PhD in Physics from the Institute of Physics, Polish Academy of Science, in 1985. He currently works as a Professor and Senior Researcher at the IMS. Most of his work is related to the properties of electromagnetic materials, dealing with both theoretical and experimental aspects of this topic. He is the author/co-author of over 100 scientific papers and the recipient of the 2005 National Prize for Science and Technology. He is also the Supervisor of eight defended PhD theses in Physics and Materials Science. Nguyen Xuan Phuc received his diploma in Solid State Physics in 1973 and his PhD in Condensed Matter Physics in 1977 from the Jagiellonian University in Cracow Poland. In 1996, he received the title of Professor in Physics. He is the author/co-author of more than 100 internationally reviewed scientific papers and the supervisor of 14 defended PhD theses in Physics and Materials Science. His current fields of interest are magnetic materials, nanomaterials and nanotechnology, biomedical materials. Pham Thanh Phong received his Bachelor’s degree in Physics Science from Quy Nhon University, Quy Nhon City, Vietnam in 1992. He received his MSc from the Institute of Physics, VAST in 2003 and his PhD in Materials Science
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from the IMS in 2010. His studies focused on the electro-magnetic properties of manganites. At present, he is a permanent teacher at the Nha Trang College, Khanh Hoa, Vietnam. This paper is a revised and expanded version of a paper entitled ‘Superparamagnetic behaviour and deviation from Bloch T3/2 law of La0.7Ca0.3MnO3 nanoparticles prepared by reactive milling method’ presented at the ‘3rd International Workshop on Nanotechnology and Application (IWNA’2011)’, Vung Tau, Vietnam, 10–12 November 2011.
1
Introduction
Magnetic nanoparticles have been the subject of intensive research not only for their fundamental scientific interest but also for their potential applications in magnetic storage media, sensor devices as well as medical applications [1]. In 1949, Néel [2] noted that the thermal fluctuation prevents the existence of stable magnetisation on nano-scale magnetism, resulting in a superparamagnetic (SPM) state. Recently, Dey et al. [3] have observed that the granular manganite with calcium hole doping of La0.7Ca0.3MnO3 composition (grain size from 17 nm to 27 nm) exhibited superparamagnetism behaviour beside the typical low field magnetoresistance. In a previous report [4] we showed that for La0.7Sr0.3MnO3 nanoparticles the observed behaviour of magnetisation versus field and temperature is not a pure Neel state (non-interacting system), and it could be well described by using the mean-field approximation with a field correction to the argument of the non-interacting SPM Langevin function L ⎡⎣( H ext +α M ) / k BT ⎤⎦ . In this report, we present systematic investigation of magnetic characteristics for La0.7Ca0.3MnO3 samples synthesised by reactive milling method. Furthermore, the interparticle interaction was well described by using the mean-field approximation correction to the argument of Langevin function [5].
2
Experimental section
La0.7Ca0.3MnO3 nanoparticles (NPs) were synthesised by reactive milling method 0. In this paper the NPs samples obtained after 8 h, 12 h, and 16 h of milling were denoted as S1, S2, and S3, respectively. The structure of the LCMO nanoparticles was checked by powder X-ray diffraction (XRD) performed on a SIEMENS D5000 diffractometer. Thermomagnetic measurements were carried out in a commercial apparatus (PPMS6000, Quantum Design) in the temperature range of 5–300 K and under the applied field of 10 Oe. Besides, isothermal magnetisation curves were carried out with applied fields up to 50 kOe at several temperatures in the range above.
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Results and discussion
Figure 1 shows the magnetisation curves, M(H), measured at 200 K for the samples with various milling times. As seen, the anhysteresic property is observed for all the samples.
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The similar behaviour is also observed from M(H) curves measured at other temperatures in the range of 200 K to 300 K. This shows that all samples are superparamagnetic in this temperature range. Another special point was shown in the inset of Figure 1 for the sample S1, in which the scaled plots of M/MS vs. Hext/T do not overlap into a universal magnetisation curve as desired for non-interacting SPM systems. The terminology ‘interacting superparamagnetism’ was used to indicate interacting behaviour of SPM particles arising from the strong dipolar interaction between nanoparticles in the SPM systems [7]. Figure 1
Anhysteresic curves for NPs with various milling time measured at T = 200 K. Inset: M/MS vs. Hext/T curves measured at different temperatures for the sample S1 (see online version for colours)
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M (emu/g)
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As shown in Figure 2, the dc susceptibility deduced from MZFC(T) in applied field of 10 Oe (the inset of Figure 2) obeys the Curie-Weiss law, χ = CS/(T-T0), where CS is a Curie-like constant and T0 is a characteristic temperature related with the strength of ferromagnetic interaction. For our samples, T0 decreases from 182.9 K to 138.5 K, correspondingly for the samples from S1 to S3. In order to understand the nature of field dependence of magnetisation in the superparamagnetic behaviour, the isothermal field dependence of magnetisation has been analysed in terms of the so-called ‘law of approach to saturation’ (LAS) [8]:
M ( H ) = M S ⎡⎣1 − a / H − b / H 2 ⎤⎦ + χ d H
(1)
where MS is the saturation magnetisation and χd is the high-field susceptibility. The best fit of the magnetisation curves using equation (1) are shown in Figure 3 for the sample S1 by considering a, b and χd as free parameters (similar behaviour is observed for the samples S2 and S3).
Superparamagnetic behaviour and deviation Figure 2
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Inverse dc susceptibility vs. temperature measured at 10 Oe for the sample S1. Inset: The temperature dependence of magnetisation of the sample S1 under FC and ZFC mode at H = 10 Oe (see online version for colours)
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Figure 3
χ
1 M (emu/g)
χ (Oe.g/emu)
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ZFC FC
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Magnetisation curves for the sample S1 measured at several temperatures from 5 K to 240 K. The solid line through the M(H) data correspond to the fits using equation (1) in the text (see online version for colours)
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As indicated in Table 1, MS found from fitting of the magnetisation curve measured at 5 K decreases as milling time increases, namely it decreases from 36.8 emu/g to 14.7 emu/g for the milling time varied from 8 h to 16 h, correspondingly. Thus, the values of magnetisation at 5 K and 50 kOe for all the cases are much smaller than the saturation magnetisation (97.5 emu/g) of bulk sample.
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Table 1
Fitting parameters: B, ε and MS of the samples
Sample name
B × 10–5 (K–ε)
ε
S1
11.40
1.69
37.3
36.8
182.9
S2
9.44
1.73
19.2
19.0
165.4
S3
7.83
1.76
14.8
14.7
138.5
MS (emu/g) at 0 K MS (emu/g) at 5 K
T0 (K)
To investigate the magnetisation curves, we used the mean-field approximation by addition a mean field term Hdip = αM to the external field Hext, which was described more detail in [6]. The magnetisation M, therefore, can be expressed by an argument-corrected Langevin function ⎛ M PS m ⎡⎣ H ext + α M ( H , T ) ) ⎤⎦ ⎞ M ( H , T ) = M PS L ⎜ ⎟ ⎜ ⎟ k BT ⎝ ⎠
(2)
where L(x) is the Langevin function of x, m is the average particle mass (in g/m3) and
M Ps was determined by fitting the value of the magnetisation measured at 5 K from equation (1). The value of α was determined by using the experimental data for the initial susceptibility χ at low field. From equation (3), χ is expressed as initial slope of the universal curve. ⎧ M Ps 2 m ⎪χ = 3k B (T − T0 ) ⎪ ⎪⎪ 1 1 1 T −α (T − T0 ) = ⎨ = CS ⎪ χ CS ⎪ M s2m ⎪CS = P 3k B ⎪⎩
(3)
The value of α can be determined by extrapolating the 1/χ vs. T curves as shown in Figure 2. Two parameters α and MS are used to plot the scaled curves of M/MS vs. (Hext + α M)/T at different temperatures for all the samples. As expected, the scaled curves overlap into a universal curve for each sample. The universal scaling magnetisation curves of all the samples are shown in Figure 4. We inserted m in equation (3) and M Ps into the argument-corrected Langevin function in equation (1) and fit the function with the data of corresponding universal magnetisation curves (in Figure 4) for each sample. The best fit for the sample S1 is shown in Figure 5. As mentioned in a lot of recent papers [6, 9, 10], in case of a continuous distribution of spin-wave states as in the bulk, the temperature dependence of magnetisation is given by the expression [10] M S (T ) = M S (0) ⎡⎣1 − BT ε ⎤⎦
(4)
where MS(0) is the spontaneous magnetisation at 0 K and B is a constant, which is closely related to the exchange integral, J (B ∼ 1/ J ε). Equation (4) is known as the Bloch T3/2 law for ε = 3/2 which has been verified experimentally for most of the bulk materials 0. However, for nanoparticles, the thermal dependence of the magnetisation deviates from
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the expected Bloch law as the magnons with wavelength larger than the particle diameter cannot be excited and a threshold of thermal energy is required to generate spin waves [10]. Figure 4
Scaled magnetisation curves M/MS vs. (Hext + αM)/T for all the samples at 200 K, 250 K and 300 K (see online version for colours)
0.8
S3
0.7
S1
0.6 0.5 M/MS
S2
0.4 0.3
200 K 250 K 300 K
0.2 0.1 0 0
Figure 5
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400 600 800 1000 1200 (Hext +αM)/T (Oe/K)
Scaled magnetisation curves for the sample S1. Solid line: the argument-corrected Langevin function fitting to the scaled data (see online version for colours)
0.5
M/M
S
0.4 0.3
200 K 250 K 300 K Langevin fit
0.2 0.1 0 0
100 200 300 400 500 600 700 (H+αM)/T (Oe/K)
We have also performed isothermal magnetisation measurements as a function of magnetic field at different temperatures (see Figure 3). Figure 6 shows the behaviour
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of the saturation magnetisation MS vs. temperature for all samples, with MS values obtained via fitting the magnetisation curves by equation (1). Figure 6
Saturation magnetisation as a function of temperature for LCMO nanoparticle samples. Solid curves: fitted curves to the data points by using equation (4) (see online version for colours)
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M (emu/g)
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A fit to the saturation magnetisation data by equation (4) is shown in Figure 6 (solid curve). The values of MS(0), B, and ε were reported in Table 1. As seen in this table, when decreasing milling time the values of MS(0) and B increase, while the value of ε decreases but still quite large compared with the value 3/2 of bulk sample [7].
4
Conclusion
In summary, the magnetisations versus field and temperature have been characterised and analysed thoroughly for La0.7Ca0.3MnO3 nanoparticles fabricated by reactive milling method. Magnetic measurements showed the existence of strong magnetic interaction between particles in nanoparticles assembly resulting in non-overlapping of the scaled magnetisation curves into a universal curve. A mean field approximation can be used to describe well magnetic behaviour of the nanoparticles. The values of the spontaneous magnetisation of the samples decrease sharply from 36.8 emu/g to 14.7 emu/g as milling time increase from 8 h to 16 h. The temperature dependence of saturation magnetisation
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follows a Tε law with ε increases from 1.69 to 1.76 as milling time increases from 8 h to 16 h.
Acknowledgements This work was completed with financial support from the National Foundation for Science and Technology Development (NAFOSTED), grant coded 103.02-2011.31 and the State Key Laboratory (IMS – GC 11-03). The second author is thankful to Nha Trang Pedagogic College.
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