Applied Surface Science 258 (2012) 7556–7561
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Enhanced microwave absorption of BaTiO3 -based ferroelectric/ferromagnetic nanocomposite Zhi Ma, Chentao Cao, Jing Yuan, Qingfang Liu, Jianbo Wang ∗ Key Laboratory for Magnetism and Magnetic Materials of Ministry of Education, Lanzhou University, Lanzhou 730000, People’s Republic of China
a r t i c l e
i n f o
Article history: Received 17 January 2011 Received in revised form 13 April 2012 Accepted 13 April 2012 Available online 20 April 2012 Keywords: Nanoparticles Polarization Microwave absorption
a b s t r a c t Morphology, crystal structure, magnetic and microwave absorption properties of BaTiO3 -based ferromagnetic/ferroelectric composites were investigated in this research. It was evident that Ni Co P/BaTiO3 composite was a narrowband absorber, whereas carbonyl iron/BaTiO3 composite samples showed broadband absorption characteristics. For the carbonyl iron/BaTiO3 composite, a reflection loss exceeding −20 dB was obtained in the frequency range of 3.8–5.8 GHz with an absorber thickness of 2.3–3.3 mm. An optimal RL of −46 dB was found at 4.7 GHz for an absorber thickness of 2.8 mm. The effective absorption bandwidth with RL < −10 dB was extended and reached 16 GHz (2–18 GHz). Moreover, the intrinsic reasons for microwave absorption of the composites, the dielectric loss and magnetic loss mechanics were also investigated. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Recently, the demand on the high-frequency circuit devices, high performance of wireless mobile communication equipment and wideband radar defense systems has increased the use of microwave absorption materials (MAMs) [1,2]. Ideal electromagnetic (EM) wave absorbing materials are thin layers, low density, broad absorbing band and strong absorption [3,4]. Many kinds of MAMs have been studied in the past few years, mainly including magnetic materials and dielectric materials. However, the strong microwave absorption can only be obtained in a higher frequency range under a thick layer for MAMs [3], the absorption in low frequency range (2–8 GHz) with thin thickness is still the most challenging part for absorbing materials. The microwave absorption performances are associated with the complex permittivity, the complex permeability, the EM impedance match and the microstructure of the absorber [5]. The materials used as microwave absorbers can have high magnetic and dielectric loss due to interaction between the magnetization and electric polarization [6]. The fabrication of composite materials with both dielectric and magnetic phases is a promising way to enhance the microwave absorbing of MAMs. The composite, in which magnetic phase act as a magnet that increases the permeability, dielectric phase act as centers of polarization that increase the dielectric loss. As a result, both the electric and magnetic loss of MAMs contributes to the microwave absorbing.
∗ Corresponding author. Tel.: +86 931 8914171; fax: +86 931 8914160. E-mail address:
[email protected] (J. Wang). 0169-4332/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.apsusc.2012.04.086
It is well known that Barium titanate BaTiO3 (BTO) is an excellent ferroelectric material and widely applied in the electronic industries. It is often used as multilayer ceramic capacitor (MLCC), positive temperature coefficient (PTC) thermistors, sensors and electro-optic devices due to its remarkable ferroelectric and piezoelectric properties [7–10]. But the high-frequency permeability of BTO is very low, which limits its microwave absorbing characteristics. Therefore, in order to optimize the microwave absorption performances, it is necessary to modify the microwave magnetic properties of BTO. In this work, BTO were coated with a thin Ni Co P layer or mixed with carbonyl iron to improve its permeability, magnetic loss and microwave absorption performance. Carbonyl iron–BTO composite and Ni Co P/BTO core–shell composite with BTO core have been prepared and studied. The reflection loss (RL) mapping was proposed for comparison and clarification of the main differences of reflection loss between samples. The microwave EM absorption mechanics were investigated in detail.
2. Experimental procedure 2.1. Preparation of BTO powders Barium titanate (BTO) was prepared from analytical grade chemical BaCl2 and TiCl4 . First, TiCl4 was added to the HCl solution (5 wt.%) under continuous magnetic stirring. Then the TiCl4 solution was mixed with oxalic acid and BaCl2 solution, the white precipitation was obtained. Finally, the precipitation was filtered and then heated at 750 ◦ C for 4 h to obtain BTO powders.
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Table 1 Operation conditions of the electroless Ni Co P bath (pH = 9 and temperature 85 ◦ C). Bath constituents
Formula
Quantity
Nickel sulfate, hexahydrate Cobalt sulfate, heptahydrate Sodium citrate Ammonium sulfate Sodium hypophosphite, monohydrate
NiSO4 ·6H2 O CoSO4 ·7H2 O Na3 C6 H5 O7 ·2H2 O (NH4 )2 SO4 NaH2 PO2 ·H2 O
0.2 mol/L 0.4 mol/L 20 g/L 20 g/L 0.1 mol/L
2.2. Preparation of carbonyl iron/BTO composite Raw commercial carbonyl iron powder and as prepared BTO powders were mixed (the weight ratio was 1:1) and milled on a QM-3A vibration ball mill for 6 h to obtain the composite of carbonyl iron and BTO, and no process control agent was used in the milling procedure. The ball milling vial was filled with Ar gas to prevent the oxidation of powder, and the ball-to-powder weight ratio was 20:1. The resultant powder was dried in a vacuum drying oven at 60 ◦ C. 2.3. Preparation of BTO powders coated by Ni Co P Operation conditions of electroless plating Ni–Co–P ternary alloy on BTO are listed in Table 1. The BTO powders were sensitized by immersion in SnCl2 solution and activated by immersion in PdCl2 solution. Then it was rinsed in distilled water after each step as mentioned above. The proportion of pre-treated BTO particles that added to the plating bath was 10 g/L, and with continuous stirring, the particles were put into the electroless plating solution when the temperature reached 85 ◦ C. The plating time was 60 min. After electroless plating, the solution was washed and dried. 2.4. Measurements Size-distribution, morphology and surface composition of powders were characterized by scanning electron microscopy (SEM) on a Hitachi S-4800, which is equipped with an energy-dispersive X-ray spectrometer (EDS). The crystalline phases of samples were examined by X-ray diffraction (XRD) with Panalytical X’pert Pro model using Cu K␣ ( = 0.154056 nm) radiation. Magnetic properties were studied by vibrating sample magnetometer (VSM, Lakeshore 7304, USA) with a maximum magnetic field of 1.2 T. Scattering parameters were recorded on an Agilent E8363B vector network analyzer in the range of 0.1–18 GHz. Relative complex permittivity and permeability were extracted from the measured scattering parameters. Sample containing 75 wt.% magnetic particles in the powder–paraffin composites were made into toroidal-shaped samples with an outer diameter of 7.00 mm and an inner diameter of 3.04 mm for the microwave measurement. 3. Results and discussion 3.1. Crystal structure and morphology of samples BaTiO3 is a typical ABO3 perovskite-type material. Depending on the transition temperature, BaTiO3 has five kinds of crystal systems, that is, hexagonal, cubic, tetragonal, orthorhombic and rhombohedra, and the tetragonal phase is stable at room temperature among them. Some work had demonstrated that BTO particles over 100 nm showed tetragonal phase [11,12]. XRD patterns of pure BTO and its composites with different components are shown in Fig. 1. The XRD spectrum of pure BTO shows P4mm symmetry and all the peaks can be indexed as tetragonal BTO with the lattice constant ˚ which is in good agreement with JCPDS, a = 3.996 A˚ and c = 4.0164 A, No. 80-0601. No diffraction peaks other than those from BTO were
Fig. 1. XRD patterns of BTO, carbonyl iron, carbonyl iron/BTO and Ni Co P/BTO composite.
obtained, indicating high purity of the as-synthesized products. The XRD pattern of BTO in the composite has no obvious differences in contrast to the XRD spectrum of pure BTO. This indicates that the crystal structure of BTO is still stable in the composites. The intensity of deposited Ni Co P diffraction peaks is much weaker than that of BTO and it means that the Ni Co P is amorphous and microcrystalline phases, which have also been observed before [13]. The surface morphology of the pure BTO, carbonyl iron, carbonyl iron/BTO and Ni Co P/BTO are shown in Fig. 2. The particle size of BTO is approximately 40 nm with a narrow particles size distribution. The carbonyl iron particles have much bigger particle size, about 3 m. After mechanical alloying, the surface of sphere-shaped carbonyl iron and BTO particles became irregular and the particle size was from several tens nanometers to several micrometers. The Ni Co P/BTO particles have a uniform size distribution, about 100 nm. The elemental composition has been verified through EDS analysis, which is in good agreement with the nominal composition. 3.2. Magnetic properties of carbonyl iron/BTO and Ni Co P/BTO composites The magnetic hysteresis loops of carbonyl iron, carbonyl iron/BTO and Ni Co P/BTO shown in Fig. 3 were measured at room temperature. The saturation magnetization and coercivity of carbonyl iron are 193 emu/g and 23 Oe, while those of carbonyl iron/BTO are 84 emu/g and 318 Oe and Ni Co P/BTO are 5.2 emu/g and 80 Oe, respectively. The saturation magnetization value of carbonyl iron/BTO lower than that of pure carbonyl iron, this is due to that the nonmagnetic BTO powder causes the decrease of saturation magnetization of carbonyl iron/BTO. On the other hand, the magnetic Ni Co P shell causes the increase of saturation magnetization of BaTiO3 . In addition, it is worth noting that the coercivity of Ni Co P/BTO is much larger than that of carbonyl iron, which should be attributed to the larger magneto-crystalline anisotropy in Ni Co P particles compared with that of carbonyl iron. The coercivity of carbonyl iron/BTO is found to be larger than carbonyl iron after mechanical alloying. The increase in coercivity should originate from the residual stress, impurities and defects, which are introduced during mechanical alloying. According to the nucleation field theory [14], the effective anisotropy field influences the value of coercivity, and the anisotropy field is a function of microstrain and increasing the microstrain increases the anisotropy field. The introduced residual strain will lead to magneto-striction effective anisotropy, and resulting in the increase of coercivity
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Fig. 2. SEM images of (a) prepared pure BaTiO3 . (b) Carbonyl iron. (c) Carbonyl iron/BaTiO3 and (d) Ni Co P/BaTiO3 .
[15]. The impurities or nonmagnetic inclusions will also increase the coercivity through the pinning of the magnetic domain walls [16]. A large density of defects like dislocation which can react with domain walls and will increase the coercivity as well [15]. 3.3. Dynamic magnetic properties and microwave absorptive properties of BTO/carbonyl iron and Ni Co P/BTO composite The real part and the imaginary part of the relative permeability are plotted in Fig. 4 as a function of frequency in the range 0.1–18 GHz. It can be seen that the values of the complex dielectric constant increase with increasing frequency. For the complex permittivity of Ni Co P/BTO, the ε spectrum exhibits a resonance peak near 11.4 GHz (Fig. 4(a)). The ε curves of carbonyl iron/BTO present three broad peaks at around 7.4, 10.4 and 15.8 GHz, respectively (Fig. 4(c)). According to the free-electron
theory [17], ε = 1/2ε0 f ( is the resistivity), the lower ε values Ni Co P/BTO indicate higher electrical resistivity than those of carbonyl iron/BTO, which is favorable for improving the microwave-absorption properties. The higher resistivity is ascribed to the effective dispersion of metal-based particles in the insulated paraffin matrix. In general, the resonance behaviors of the permittivity can be explained by space-charge polarization, dipole polarization, ionic polarization and electronic polarization in the composite [18–20]. The permittivity dispersion was described by the Debye law [21], Cole–Cole law [22], Drude law [23], Lorentzian dispersion law [24], Jonscher’s power law [25], etc. However, in the metal-based composites, the dipole polarization is dominant at higher frequency other than the space charge polarization [26]. Since the ionic polarization and electronic polarization work at THz and PHz, these two types of polarization can be precluded. Thus, the resonance of permittivity in the composite–paraffin mixture should arise from the dipole polarization. Based on this analysis, the permittivity spectrum will be fitted by the Lorentzian dispersion law [24]: ε(f ) = ε∞ +
Fig. 3. Magnetic hysteresis loops of carbonyl iron, carbonyl iron/BaTiO3 and Ni Co P/BaTiO3 composite. The inset is the local magnification image of the loops.
ε0 − ε∞ 1 − i(f/fd ) − (f/fr )
2
(1)
where ε0 is the static permittivity, ε∞ is the permittivity at extremely high frequency. fd and fr are the Debye relaxation frequency and natural relaxation frequency respectively. The solid lines in Fig. 4(a) represent the best fit for the experimental data and the fitted resonance frequency is 11.4 GHz. Consequently, the permittivity spectrum of carbonyl iron/BTO should be a linear overlap of three resonance bands. As shown in Fig. 4(b), for the complex permeability of Ni Co P/BaTiO3 , the and values decrease slightly with frequency ranging from 0.1 to 18 GHz and the curve shows distinct peaks at 4.8 and 11.8 GHz, which implies that magnetic loss should arise from the natural resonance and exchange resonance other than the domain-wall resonance or the eddy current loss [27]. It can be speculated that the high frequency resonance peak (above 10 GHz) is a consequence of the small size of the particles, the
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Fig. 4. Complex permittivity and complex permeability of Ni Co P/BaTiO3 (a, b), carbonyl iron/BaTiO3 (c, d). The open symbols are experimental results, the lines are fitting results.
surface effect, and spin wave excitations, defined as “exchange mode” resonance [28,29]. However, for carbonyl iron/BTO composite (Fig. 4(d)), the values show distinct multi-resonance broad peaks at 4–14 GHz, which implies that the spectrum should be an overlap of nature resonance and exchange resonance. The natural resonance frequency can be calculated according to the kittel equation [30]: fr = (0 /2) × Ha , where 0 is the gyromagnetic ratio, about 28 GHz/T [31], Ha = 2|K1 |/(0 Ms ) is the anisotropy field, the anisotropy coefficient K1 for bulk ␣-Fe which is about 4.81 × 104 J/m3 , the natural-resonance frequency fr should be about 650 MHz, which is much lower than the measured resonance frequency at 4–14 GHz. The enhanced resonance frequency is due to the enhancement of the anisotropy energy. As it is well known that the anisotropy energy of nanometer scale particles may be remarkably increased due to the surface anisotropic field affected by the size effect [32]. And also, for the milling ferromagnetic samples, the internal demagnetizing fields contribute to the resonance broadening [33], and the resonance will extend up to higher frequency: fr = (0 /2) × (Ha + 4Ms ). Here, one gets fr = 4.35 GHz, which is consistent with the resonance frequency observed in the frequency range of 4–14 GHz. The exchange resonance frequency for spherical particles with a cylindrical symmetry can be calculated by [28,34]: fex =
0 2
4 2K1 Ckn 2 + H0 − Ms + 3 Ms R2 Ms
(2)
where C = 2A is the exchange constant (for an iron sphere, C = 2A = 4 × 10−6 erg/cm), H0 is the external applied field, R is
the radius of the sphere and kn is the eigenvalue of the derivative of spherical Bessel function. The five first kn roots are 11 = 2.08; 12 = 3.34; 13 = 4.51; 14 = 5.65; 21 = 5.94. Since carbonyl iron/BTO and Ni Co P/BTO composite particles were obtained in a wide size range, several shoulders are observed on the broad resonance band (Fig. 4(d)), the dynamic permeability presents several peaks (Fig. 4(b)). For these particles, the broadening of the peaks allows them to reach high permeability levels. Such a multi-resonance behavior is also observed in Co80 Ni20 and Fe14 Co43 Ni43 powders [34]. Nevertheless, from the equation above, the exchange resonance frequencies are related to kn and R, so, it is reasonable that the resonance peaks appear in higher frequency range due to the exchange effect for our composite sample. The strong and broad multi-resonance peaks affects the EM properties through homogeneously dispersed magnetic particles in the dielectric BTO matrix, reducing the magnetic coupling effect and realizing EM matching, which is important for their use as EM-wave absorption materials in the higher-frequency region. Moreover, it is believed that the coexistence of natural resonance and exchange resonance and high permeability are beneficial to large bandwidth as a microwave absorber. The reflection loss curves are evaluated from the relative complex permeability (r = + j ) and permittivity (εr = ε + jε ) for a given frequency f and a given absorber thickness d, according to the transmission line theory [35,36]:
Zin − 1 Z +1
RL (dB) = 20 · log10
in
(3)
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Fig. 5. Reflection loss map of (a) carbonyl iron, (b) BaTiO3 , (c) carbonyl iron/BaTiO3 and (d) Ni Co P/BaTiO3 .
Zin =
r · th εr
√ j2fd r εr c
(4)
where Zin is the normalized input impedance, c is the velocity of EM waves in free apace. Therefore, microwave propagation in EM media is largely determined by the complex relative permittivity εr and the permeability r of the absorbing materials, as well as the EM impedance match. Here, EM impedance match is the condition that an EM wave is completely absorbed according to the transmission line theory could be described as:
r · th(d) = 1 εr
(5)
where is a propagation factor, d is the thickness of the ideal homogeneous medium. This is a complex equation, it can be rewrite as a real function as [37]: sh(2˛d) · sin(2ˇd) 1 + tan2 ıe = · 2 tan ı − tan ı ε m e [ch(2˛d) − cos(2ˇd)]
(6)
where ˛ and ˇ are the real and imaginary parts of the propagation factor (), respectively. tan ıe = ε /ε and tan ım = / are the dielectric and magnetic dissipation factors. The microwave absorbing comes from magnetic and dielectric loss could be analyzed by the input impedance. Dielectric and magnetic loss were due to the polarization and magnetization in the materials. Composite with various surfaces or interfaces could directly affect the polarized and magnetized process and thus affect their input impedance of absorbers. A delta method was provided to quantitative analyze EM impedance matching degree for designing microwave absorbing materials with better performance in a broad frequency range [38]. From that we can see, the microwave absorption is really a type of ‘surface effect’. Only electro-magnetic wave could transmit the surface of absorbers, and then which will be effectively absorbed. Fig. 5 shows the reflection loss mapping of carbonyl iron, BaTiO3 , carbonyl iron/BaTiO3 and Ni Co P/BaTiO3 at different thicknesses in 0.1–18 GHz. The region enclosed by each reflection loss curve directly represents the microwave absorption in that frequency range. The low frequency (2–8 GHz) absorption is the most
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challenging part for absorbing materials. As can be seen from Fig. 5, the ideal absorption RL exceeding −10 dB can be found, but in different ranges of thickness and frequency. For carbonyl iron sample (Fig. 5(a)), the RL exceeding −10 dB is obtained in the frequency range of 3.5–18 GHz. Below 3.5 GHz, even increase thickness of absorbers to 8 mm, there is no regions where the RL exceeding −10 dB. For the BTO powders (Fig. 5(b)), only some small ‘island’ can be found with RL exceeding −10 dB. For carbonyl iron/BTO (Fig. 5(c)), the optimal RL is −46 dB at 4.7 GHz with a matching thickness of 2.8 mm and RL values exceeding −10 dB are obtained in the 1.5–18 GHz range for absorber thicknesses of 1.0–8.0 mm. The absorbing frequency range of RL < −10 dB is much extended when compared with the pure carbonyl iron samples especially in the low frequency range of 1.5–3.5 GHz. The white dashed line in Fig. 5(a) and (c) plots the thickness of 2 mm and the frequency of 3.5 GHz. The microwave absorption of ferroelectric/ferromagnetic nanocomposite in 2–8 GHz has been enhanced. 4. Conclusion Carbonyl iron/BTO and Ni Co P coated BTO were prepared by means of the ball milling technique and electroless plating method to investigate their application in microwave absorption. For the carbonyl iron/BTO composite, strong microwave absorption could be obtained in a wide frequency range and the reflection loss (RL) was enhanced since the ferroelectric nano BaTiO3 had been introduced. In addition, the absorbing frequency range of RL < −10 dB had been extended to 2–8 GHz and the effective absorbing bandwidth reached 16 GHz. The excellent microwaveabsorption properties mainly resulted from proper EM matching, the strong natural/exchange resonance, as well as the dipolepolarization of the different phase interfaces. Acknowledgements This work is supported by the National Basic Research Program of China (2012CB933101), National Science Fund of China (11074101, 51171075), and the Fundamental Research Funds for the Central Universities (Lzujbky-2012-k29). References [1] J.R. Liu, M. Itoh, K. Machida, Applied Physics Letters 83 (2003) 4017. [2] J.R. Liu, M. Itoh, T. Horikawa, K. Machida, S. Sugimoto, T. Maeda, Journal of Applied Physics 98 (2005) 054305.
7561
[3] Z.H. Wang, X. He, X. Wang, Z. Han, D.Y. Geng, Y.L. Zhu, Z.D. Zhang, Journal of Physics D: Applied Physics 43 (2010) 495404. [4] X.F. Zhang, X.L. Dong, H. Huang, Y.Y. Liu, W.N. Wang, X.G. Zhu, B. Lv, J.P. Lei, C.G. Lee, Applied Physics Letters 89 (2006) 053115. [5] R.C. Che, C.Y. Zhi, C.Y. Liang, X.G. Zhou, Applied Physics Letters 88 (2006) 033105. [6] A. Verma, A.K. Saxena, D.C. Dube, Journal of Magnetism and Magnetic Materials 263 (2003) 228. [7] L. Affleck, C. Leach, Journal of the European Ceramic Society 25 (2005) 3017. [8] K. Park, D.J. Seo, Materials Chemistry and Physics 85 (2004) 47. [9] J. Wang, Q.H. Lin, R.Q. Zhou, B.K. Xu, Sensors Actuators B: Chemical 81 (2002) 248. [10] M. Mori, T. Kineri, K. Kadono, T. Sakaguchi, M. Miya, H. Wakabayashi, T. Tsuchiya, Journal of the American Ceramic Society 78 (2005) 2391. [11] T.K. Mandal, Materials Letters 61 (2007) 850. [12] M. Yashima, T. Hoshina, D. Ishimura, S. Kobayashi, W. Nakamura, T. Tsurumi, S. Wada, Journal of Applied Physics 98 (2005) 014313. [13] Z. Ma, J.B. Wang, Q.F. Liu, J. Yuan, Applied Surface Science 255 (2009) 6629. [14] G. Herzer, W. Fernengel, E. Adler, Journal of Magnetism and Magnetic Materials 58 (1986) 48. [15] Q. Zeng, I. Baker, V. McCreary, Z.C. Yan, Journal of Magnetism and Magnetic Materials 318 (2007) 28. [16] A.H. Taghvaei, A. Ebrahimi, M. Ghaffari, K. Janghorban, Journal of Magnetism and Magnetic Materials 323 (2011) 150. [17] X.G. Liu, D.Y. Geng, H. Meng, P.J. Shang, Z.D. Zhang, Applied Physics Letters 92 (2008) 173117. [18] G. Panzmer, B. Egert, Surface Science 144 (1984) 651. [19] S.S. Kim, S.T. Kim, J.M. Ahn, K.H. Kim, Journal of Magnetism and Magnetic Materials 271 (2004) 39. [20] P.C.P. Watts, W.K. Hsu, A. Barnes, B. Chambers, Advanced Materials 15 (2003) 600. [21] X.L. Dong, X.F. Zhang, H. Huang, F. Zuo, Applied Physics Letters 92 (2008) 013127. [22] K.S. Cole, R.H. Cole, The Journal of Chemical Physics 9 (1941) 341. [23] D. Dragoman, M. Dragoman, Journal of Applied Physics 99 (2006) 076106. [24] A.N. Lagarkov, S.M. Matytsin, K.N. Rozanov, A.K. Sarychev, Journal of Applied Physics 84 (1998) 3806. [25] A.K. Jonscher, Nature 267 (1977) 673. [26] R. Ravindran, K. Gangopadhyay, S. Gangopadhyay, N. Mehta, N. Biswas, Applied Physics Letters 89 (2006) 263511. [27] J. Ma, J.G. Li, X. Ni, X.D. Zhang, J.J. Huang, Applied Physics Letters 95 (2009) 102505. [28] A. Aharoni, Journal of Applied Physics 81 (1997) 830. [29] D. Mercier, J.C.S. Levy, G. Viau, F. Fievet-Vincent, F. Fievet, P. Toneguzzo, O. Acher, Physical Review B 62 (2000) 532. [30] C. Kittel, Physical Review 73 (1948) 155. [31] X. Liu, M.M. Steiner, R. Sooryakumar, G.A. Prinz, R.F.C. Farrow, G. Harp, Physical Review B 53 (1996) 12166. [32] D.L. Leslie-Pelecky, R.D. Rieke, Chemistry of Materials 8 (1996) 1770. [33] D. Polder, J. Smit, Reviews of Modern Physics 25 (1953) 89. [34] G. Viau, F. Fievet-Vincent, F. Fievet, P. Toneguzzo, F. Ravel, O. Acher, Journal of Applied Physics 81 (1997) 2749. [35] S.S. Kim, S.B. Jo, K.I. Gueon, K.K. Choi, J.M. Kim, K.S. Churn, IEEE Transactions on Magnetics 27 (1991) 5462. [36] H.M. Musal Jr., H.T. Hahn, IEEE Transactions on Magnetics 25 (1989) 3851. [37] Y.Q. Huang, J. Yuan, W.L. Song, B. Wen, X.Y. Fang, M.S. Cao, Chinese Physics Letters 27 (2010) 027702. [38] Z. Ma, C.T. Cao, Q.F. Liu, J.B. Wang, Chinese Physics Letters 29 (2012) 038401.