Synthesis and magnetic characterization of nickel ferrite nanoparticles prepared by co-precipitation route

Synthesis and magnetic characterization of nickel ferrite nanoparticles prepared by co-precipitation route

ARTICLE IN PRESS Journal of Magnetism and Magnetic Materials 321 (2009) 1838–1842 Contents lists available at ScienceDirect Journal of Magnetism and...

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ARTICLE IN PRESS Journal of Magnetism and Magnetic Materials 321 (2009) 1838–1842

Contents lists available at ScienceDirect

Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm

Synthesis and magnetic characterization of nickel ferrite nanoparticles prepared by co-precipitation route K. Maaz a,b,, S. Karim a, A. Mumtaz b, S.K. Hasanain b, J. Liu c, J.L. Duan c a b c

PINSTECH, Post Office Nilore, Islamabad, Pakistan Department of Physics, Quaid-i-Azam University, Islamabad, Pakistan Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou, PR China

a r t i c l e in f o

a b s t r a c t

Article history: Received 22 September 2008 Received in revised form 26 November 2008 Available online 7 December 2008

Magnetic nanoparticles of nickel ferrite (NiFe2O4) have been synthesized by co-precipitation route using stable ferric and nickel salts with sodium hydroxide as the precipitating agent and oleic acid as the surfactant. X-ray diffraction (XRD) and transmission electron microscope (TEM) analyses confirmed the formation of single-phase nickel ferrite nanoparticles in the range 8–28 nm depending upon the annealing temperature of the samples during the synthesis. The size of the particles (d) was observed to be increasing linearly with annealing temperature of the sample while the coercivity with particle size goes through a maximum, peaking at 11 nm and then decreases for larger particles. Typical blocking effects were observed below 225 K for all the prepared samples. The superparamagnetic blocking temperature (TB) was found to be increasing with increasing particle size that has been attributed to the increased effective anisotropy energy of the nanoparticles. The saturation moment of all the samples was found much below the bulk value of nickel ferrite that has been attributed to the disordered surface spins or dead/inert layer in these nanoparticles. & 2008 Elsevier B.V. All rights reserved.

PACS: 73.63–b 75.50Gg 75.50Tt 75.70Rf Keywords: Magnetic properties Ferrite nanoparticles Surface anisotropy Magnetic materials

1. Introduction In the recent years much attention has been paid to the understanding of nanostructured materials (such as multi-layers, nanowires, nanoparticles, as well as composite materials), that exhibit interesting optical, electrical, chemical and magnetic properties [1–4]. These properties along with their great chemical and physical stability, that appear them different from their bulk counterparts, make these materials of great scientific and technological interests [5–9]. The magnetic character of the nanoparticles used in medical, electronic and recording industries depends crucially on the size, shape, purity and magnetic stability (e.g. blocked, unblocked state at particular operating temperature) of these nanoparticles. These particles should be in single-domain state, of pure phase, having high coercivity (HC) and moderate magnetization. From the application point of view, the superparamagnetic blocking temperature (TB) of the nanoparticles used for recording devices should be well above the room temperature in order to have a stable data recording in

 Corresponding author at: Department of Physics, Quaid-i-Azam University, Islamabad, Pakistan. Tel.: +92 321 5029820; fax: +92 51 9290275. E-mail addresses: [email protected], [email protected] (K. Maaz).

0304-8853/$ - see front matter & 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2008.11.098

these devices. In biomedical applications the magnetic nanoparticles are used as drug carriers inside the body where conventional drug delivery systems may not work. The nanoparticles used for this purpose should be magnetically in the superparamagnetic unblocked state with relatively low blocking temperature. The most significant properties of magnetic nanoparticles (ferrites), namely magnetic saturation, coercivity, magnetization and loss, etc. change drastically as the particle size reduces to the nanometric range [10–12]. Among various ferrites, which form a major constituent of the magnetic ceramic materials, nano-sized nickel ferrite possesses attractive properties for the application as soft magnets and low loss materials at high frequencies [13]. Conventional techniques for preparation of nanoparticles and nanowires include sol–gel processing, evaporation condensation, microemulsion technique, combustion method, spray pyrolysis, hydrothermal process and template-assisted electrochemical synthesis [14–20]. Generally in most of these methods the precise control over the size and its distribution is quite difficult [1]. In order to overcome these difficulties, co-precipitation method has been used for synthesis of these nanoparticles. In this method the nanometer-sized reactors for the formation of homogeneous nanoparticles of nickel ferrite have been used. To protect the oxidation of these nanoparticles in the presence atmospheric

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2. Synthesis procedure 3 M solution of sodium hydroxide (as the precipitating agent) was slowly mixed with salt solutions of 0.4 M ferric chloride (FeCl3  6H2O) and 0.2 M nickel chloride (NiCl2  6H2O). The pH of the solution was constantly monitored as the NaOH solution was added dropwise. The reactants were constantly stirred using a magnetic stirrer until a pH level of 412 was achieved. A specified amount of oleic acid (2–3 drops for total reacting solution of 75 ml) was added to the solution as the surfactant [23,24]. The liquid precipitate was then brought to a reaction temperature of 80 1C and stirred for 40 min. The product was cooled to room temperature and then washed twice with distilled water and ethanol to remove unwanted impurities and the excess surfactant from the prepared sample. The sample was centrifuged for 15 min at 2000 rpm and then dried overnight at above 80 1C. The acquired substance was then grinded into a fine powder and then annealed for 10 h at 600 1C. The final product obtained as confirmed by the X-ray diffraction and SAED was found to be magnetic nanoparticles of nickel ferrite (NiFe2O4) with inverse spinel structure.

(311)

8500 8000

~28 nm NiFe2O4

7500 7000

5000

(511) (422)

5500

(400)

6000

(440)

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Intensity (a.u)

oxygen and also to stop their agglomeration, the particles are usually coated with some surfactant like sodium dodecyl sulfate (NaDS) or the oleic acid [21,22] and then dispersed in some carrier liquid like ethanol, methanol, ammonia, etc. depending upon the nature of the materials (nanoparticles) to be dispersed. The advantage of this method over the others is that the production rate of ferrite nanoparticles, its size and size distribution is relatively easy and there is no need of extra mechanical or microwave heat treatments. In this work, nickel ferrite nanoparticles (NiFe2O4) have been prepared by coprecipitation technique and then they were heat treated (annealed) at different temperatures (from 600 to 1000 1C) to synthesize magnetic nanoparticles with different grain sizes. Various magnetic properties of nickel ferrite nanoparticles have been explored as a function of particle size and temperature. Debey Scherrer formula was used for size determination using the strongest peak in the XRD pattern. The size variation in this study was carried out from 8 to 28 nm with a distribution of 73 nm. The physical characterization was performed by X-ray diffractometer (Model: X’Pert Philips, Holland, with Cu-Ka l ¼ 0.154056 nm) and high-resolution transmission electron microscope (HRTEM, 300 keV) (Model: JEM-3010, JEOL) while the magnetic characterization was done by vibrating sample magnetometer (VSM, Model 7300 Lake Shore, USA) with an applied field of 710 kOe. In this article we have reported three new results that have not been reported previously, to the best of our knowledge. Firstly, we have studied the superparamagnetic blocking effects in detail for the given size (8–28 nm) of NiFe2O4 nanoparticles that has not been reported so far, at least for this size range. Secondly, we have used a theoretical model for calculating the ratio of critical single-domain radii for bulk Ni- and Co-ferrite. This ratio has been used to calculate the single-domain limit for Ni-ferrite nanoparticles using the previously reported values for Co-ferrite nanoparticles, that comes out to be 10.7 nm (the detail is given in Section 3). Comparison of the results shows that our reported value for the single-domain limit (11 nm) is in good agreement with calculated (theoretical) value for Ni-ferrite nanoparticles. The third and important point that makes this work different from the previous reports is that we have presented a single-domain limit of around 11 nm for NiFe2O4 nanoparticles that has not been reported previously (the detail is given in Section 3).

1839

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50 2θ (degree)

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Fig. 1. X-ray diffraction pattern of NiFe2O4 nanoparticles prepared by coprecipitation method annealed at 1000 1C for 10 h with average grain size of 28 m.

Fig. 2. TEM micrograph of NiFe2O4 nanoparticles prepared by co-precipitation route annealed at 1000 1C for 10 h.

3. Results and discussion The X-diffraction pattern (Fig. 1) of the sample annealed at 1000 1C prepared by co-precipitation technique shows that the final product is cubic NiFe2O4 with average crystallite size of 28 nm (the XRD peaks were compared to the standard PDF card number 742081 for inverse cubic nickel ferrite). The average sizes of the particles annealed at 600, 700, 800, 900 and 1000 1C for 10 h were found to be 8, 11, 18, 24 and 2873 nm. Fig. 2 shows the highresolution TEM images of the same sample annealed at 1000 1C for 10 h. In the TEM image most of the particles appear spherical in shape, however, some elongated particles are also present in the images. Some moderately agglomerated particles as well as separated particles are also present in the sample. The inset of Fig. 2 shows the selected area electron diffraction (SAED) analysis of the sample indicating that the nanoparticles prepared are crystalline. The same has also been confirmed from the XRD peaks

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50

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indicating the ploycrystalline nature of the prepared sample. Fig. 3 shows the dependence of size of the particles on annealing temperature (Tann). The size of the particles was observed to be increasing linearly with annealing temperature. It has been reported earlier that annealing process generally decreases the lattice defects and strains; however, it can also cause coalescence of smaller grains that results in increasing the average grain size of the nanoparticles [25]. The observed increase in particle size with annealing temperature is most likely due to the fact that higher annealing temperature and time enhances the coalescence process resulting in an increase in the grain size. Thus it appears that particle size may be controlled either by varying the annealing temperature of the sample or the annealing time during the synthesis process. Magnetic characterization of the particles was performed by vibrating sample magnetometer (VSM) between the room temperature (300 K) and 77 K with maximum applied field upto 10 kOe. Fig. 4 shows the M(H) loops of 28 nm sample both at room temperature (300 K) and 77 K. The insets of the figure show the expanded regions around the origin with different field ranges (7400 and 71000 Oe) in order to make the coercivities more visible at these temperatures. For the 28 nm size particles the coercivity at room temperature as derived from the M(H) loops was 89 Oe, while at 77 K it has increased to 175 Oe. The saturation magnetization (MS) obtained at room temperature was found to be 40.5 emu/g smaller than the bulk value of 56 emu/g for nickel ferrite, while at 77 K this value has increased to 45 emu/g. The relatively large coercivity and saturation magnetization at 77 K are consistent with the pronounced growth of magnetic anisotropy inhibiting the alignment of the moment along the applied field direction [24,26]. The coercivity of nanoparticles was also studied as a function of particle size at room temperature (300 K) as shown in Fig. 5. The figure shows that for smaller sizes (8–11 nm) the coercivity increases with size rapidly, attaining a maximum value of 175 Oe at 11 nm and then decreases with size of the particles, for larger particles (12–28 nm). A ratio of the critical single-domain radii for Ni-ferrite (dSD)Ni and Co-ferrite (dSD)Co has been calculated using the relation for critical single-domain radius dSD ¼ 36klex; where k is the magnetic hardness parameter defined by k ¼ (K1/moMS2)1/2 [27]. For very hard magnetic materials kb1,

2500 5000 7500 10000

Fig. 4. Hysteresis loops for 28 nm NiFe2O4 nanoparticles at room temperature (300 K) and 77 K at maximum applied field of 10 kOe. The two insets of the figure show the expanded field region around the origin for clear visibility of the readers.

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Fig. 3. Particle size as a function of annealing temperature for NiFe2O4 nanoparticles. Samples were annealed at 600, 700, 800, 900 and 1000 1C with average sizes of 8, 11, 18, 24 and 2873 nm, respectively.

0 H (Oe)

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Fig. 5. The coercivity (HC) as a function of average particle diameter at room temperature. The peak of HC at 11 nm is evident in the figure.

while for very soft magnetic materials k51. The exchange length (lex) is defined by lex ¼ (A/moMS2)1/2 representing the length below which the atomic exchange interactions dominate the typical magnetostatic fields. For a typical permanent magnet the value of exchange length (lex) is of the order of 3 nm and A is the called the exchange constant or the exchange stiffness parameter. The value of k was calculated by taking the values of K1 and MS for bulk materials from Skomsky [27], while the value of lex was calculated by estimating the exchange constant (A) directly proportional to the respective Tc’s of Co- and Ni-ferrite (790 and 865 K for Co- and Ni-ferrite). The ratio [(dSD)Ni]/[(dSD)Co] was found to be 0.38. For a single-domain limit of 28 nm for CoFe2O4 as reported in one of our previous papers [24], this suggests the value of single-domain limit (dSD) for Ni-ferrite as 10.7 nm. We observed a maximum in HC-d curve (Fig. 5) for NiFe2O4 at 11 nm. This value is smaller than the previously reported value of 14 nm for single-domain limit of NiFe2O4 nanoparticles [12]. We noticed in Fig. 5 that the

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coercivity of nickel ferrite shows a non-monotonic behavior with particle size, i.e. for small sizes the coercivity first increases, goes through peaks (at around 11 nm) and afterwards it decreases for larger particles (12–28 nm), above the peak. The initial increase of coercivity for smaller particles, below the peak, with increasing size may be assigned to the departure from the superparamagnetic state i.e., from unblocked to blocked state. This occurs for small particles when the thermal energy dominates the volume-dependent anisotropy energy (EA ¼ KeffV). Hence in the lower d region (8–11 nm) the coercivity may increase with increasing sizes as the larger-sized particles would tend to show a blocked moment. The decline in HC with increasing d, above the peak, can occur due to the two different mechanisms. Firstly, it may occur as the particle sizes become large enough to sustain a domain wall. In this situation the magnetization reversal would occur via domain wall motion and consequently a lower coercivity would be observed. In NiFe2O4, however, this crossover is expected at much higher than 11 nm where we observed the peak in our samples. Secondly, it may be due to the varying role of the surface and the observed bulk anisotropies as the size is diminished. Starting from larger sizes, with decreasing size of particles (from 28 nm), the role of the surface and its associated anisotropy energy is increased. It has been shown by Bodker et al. [28] that the effective anisotropy constant increases with decreasing particle sizes according to phenomenological expression (Keff ¼ KV+(6/d)KS) for the effective anisotropy of spherical particles. Several other works including simulation and experimental have also supported this expression [29]. If we assume similar behavior in NiFe2O4 nanoparticles i.e. an increase in the effective anisotropy constant with reducing particle sizes (from 28 nm), this would tend to increase the coercivity of the nanoparticles within the Stoner–Wohlfarth picture (HC ¼ 2K/MS) consistent with the behavior of HC above the peak (28–11 nm) as shown in Fig. 5. This increase will, however, not continue indefinitely and as the particle size decreases to a small enough value (dSD), the thermal effects will take over. For particles below the critical size (say dSD11 nm) the thermal energy becomes sufficient to overcome the overall anisotropy energy enabling the easier reversal of the moments leading to the lower critical fields for these small sizes [30]. This leads to the lowering of coercivity in the small size regime (8–11 nm).

Fig. 6 shows the blocking temperature (Tb) as a function of particle size, derived from the M(T) curves of the samples. The inset of the figure shows a typical zero-field cooled (ZFC) M(T) curve for one of the representative samples (with average size of 28 nm). For a single particle, at finite temperature, the ferromagnetically aligned magnetic moments fluctuate between their two energetically degenerate ground states on a time scale given by the relation [31]

t ¼ to exp

  K eff V p kB T

where t is the relaxation time and Keff VP the effective anisotropy energy (EA) of the particles. The blocking temperature Tb of a particle is the temperature at which t ¼ tm, the measurement time of the instrument. For a finite temperature T4Tb the particle behaves like a superparamagnet (unblocked state). On the other hand, for ToTb the particle is said to be in the blocked state, i.e. behaves like a ferromagnet. Referring back to our data of (Tb–d) curve for nickel ferrite (Fig. 6), we see that there is a clear increase in the blocking temperature with size of the particles. The larger particles seem to be blocked at high temperatures as compared to the smaller particles. For larger particles, the larger volume causes increased anisotropy energy, which decreases the probability of a jump across the anisotropy barrier and hence the blocking is shifted to higher temperatures. Fig. 7 shows the dependence of saturation magnetization on particle size. The MS values obtained for our samples varied between 9 and 40.5 emu/g for the sizes from 8 to 28 nm. The saturation magnetization increases consistently with size of the nanoparticles. A similar trend has also been reported for NiFe2O4 nanoparticles earlier [32,33]. The decrease in MS at smaller sizes is attributed to the pronounced surface effects in these nanoparticles. The surface of the nanoparticles is considered to be composed of some canted or disordered spins that prevent the core spins to align along the field direction resultantly decreasing the saturation magnetization of the nanoparticles for smaller sizes [34–36]. The surface may also behaves like a dead or inert layer that has negligible magnetization [24,37,38]. This effect becomes more pronounced for smaller particles; due to the increased number of surface to volume atoms that resultantly decreasing the saturation magnetization for the smaller-sized NiFe2O4 nanoparticles.

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Fig. 6. The dependence of superparamagnetic blocking temperature (TB) on particle size for NiFe2O4 nanoparticles. The inset of the figure shows the temperature dependence of zero-field cooled (ZFC) magnetization.

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Particle Size (nm) Fig. 7. Saturation magnetization (MS) as function of particle size for NiFe2O4 nanoparticles. The observed values of MS lie much below the bulk value of 56 emu/g for NiFe2O4.

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4. Conclusion In this article we have presented synthesis of NiFe2O4 nanoparticles by co-precipitation route in the range 8–28 nm. The size of the particles was measured both by XRD and TEM and was found in good agreement with each other. The size of the particles appeared to increase linearly with annealing temperature most probably due to the coalescence that increases with increasing temperature of annealing. The relatively large coercivity and saturation magnetization at 77 K in comparison with room temperature appeared to be due to the pronounced growth of magnetic anisotropy at low temperatures. The coercivity showed a peak with particle size at a value smaller than the previously reported value of single-domain limit for NiFe2O4 that has been attributed to the enhanced role of the surface anisotropy as compared to the bulk for small sizes. The superparamagnetic blocking temperature was found to increase linearly with increasing particle sizes. This was assigned to the increasing volume of the larger particles that resultantly increasing the effective anisotropy energy and hence the blocking temperature of nanoparticles. The smaller value of MS for smaller particles was attributed to the greater fraction of surface spins in these nanoparticles that tend to be in a canted, spin glass like or dead layer like state with a smaller net moment.

Acknowledgments K. Maaz acknowledges the PCSIR of Pakistan for providing 6 months fellowship titled ‘‘Establishment of Nano-Tech Lab at PCSIR’’ and some financial support from the Material Science Group-II, Institute of Modern Physics, Chinese Academy of Sciences P.R. China. J. Liu and J.L. Duan acknowledge the National Natural Science Foundation of China (No.10775161, 10775162, 10805062) and the West Light Foundation of Chinese Academy of Sciences for their financial support to enable this work. References [1] M. Dariel, L.H. Bennett, D.S. Lashmore, P. Lubitz, M. Rubinstein, W.L. Lechter, M.Z. Harford, J. Appl. Phys. 61 (1987) 4067.

[2] W.D. Williams, N. Giordano, Phys. Rev. B 33 (1986) 8146. [3] T.M. Whitney, J.S. Jiang, P.C. Searson, C.L. Chien, Science 261 (1993) 1316. [4] L. Piraux, J.M. George, J.F. Despres, C. Leroy, E. Ferain, R. Legras, K. Ounadjela, A. Fert, Appl. Phys. Lett. 65 (1994) 2484. [5] C.J. Brumlik, C.R. Martin, Anal. Chem. 59 (1992) 2625. [6] Z. Cai, C.R. Martin, J. Am. Chem. Soc. 111 (1989) 4138. [7] S.K. Chakarvarti, J. Vetter, Nucl. Instruments Methods. B 62 (1991) 109. [8] S.K. Chakarvarti, J. Vetter, J. Microm. Microeng. 3 (1993) 57. [9] S.K. Chakarvarti, J. Vetter, Radiat. Measur. 29 (2) (1998) 149. [10] I.M.L. Billas, A. Chatelain, W.A. de Heer, Science 265 (1994) 1682. [11] D.D. Awschalom, D.P.D. Vincenzo, Phys. Today 43 (1995). [12] M. George, A.M. John, S.S. Nair, P.A. Joy, M.R. Anantharaman, J. Magn. Magn. Mater. 302 (2006) 190. [13] S. Son, M. Taheri, E. Carpenter, V.G. Harris, M.E. McHenry, J. Appl. Phys. 91 (10) (2002) 7589. [14] D.H. Chen, Y.Y. Chen, J. Colloid Interface Sci. 9 (2001) 235. [15] J.J. Kingsley, K. Suresh, K.C. Patil, J. Mater. Sci. 25 (1990) 1305. [16] D.H. Chen, X.R. He, Bull. Mater. Res. 36 (2001) 1369. [17] S.Z. Zhang, G.L. Messing, J. Am. Ceram. Soc. 73 (1990) 61. [18] D.H. Chen, Y.Y. Chen, J. Colloid Interface Sci. 41 (2001) 236. [19] J.L. Duan, J. Liu, H.J. Yao, Dan Mo, M.D. Hou, Y.M. Sun, Y.F. Chen, L. Zhang, Mater. Sci. Eng. B 147 (2008) 57. [20] D. Mo, J. Liu, H.J. Yao, J.L. Duan, M.D. Hou, Y.M. Sun, Y.F. Chen, Z.H. Xue, L. Zhang, J. Cryst. Growth 310 (2008) 612. [21] T. Feried, G. Shemer, G. Markovich, Adv. Mater. 13 (15) (2001) 1158. [22] C. Liu, A.J. Rondinone, Z.J. Zhang, Pure Appl. Chem. 72 (1–2) (2000) 37. [23] V. Pallai, D.O. Shah, J. Magn. Magn. Mater. 163 (1996) 243. [24] K. Maaz, A. Mumtaz, S.K. Hasanain, A. Ceylan, J. Magn. Magn. Mater. 308 (2007) 289. [25] T.P. Raming, A.J.A. Winnubst, C.M. van Kats, P. Philipse, J. Colloid Interface Sci. 249 (2002) 346. [26] A. Mumtaz, K. Maaz, B. Janjua, S.K. Hasanain, M.F. Bertino, J. Magn. Magn. Mater. 313 (2007) 266. [27] R. Skomski, J.D.M. Coey, Permanent Magnetism, Institute of Physics Publishing Ltd., UK, 1999. [28] F. Bodker, S. Morup, S. Linderoth, Phy. Rev. Lett. 72 (1994) 282. [29] B.R. Pujada, E.H.C.P. Sinnecker, A.M. Rossi, A.P. Guimaraes, J. Appl. Phys. 93 (2003) 7217. [30] H. Pfeiffer, Phys. Status Solidi (a) 118 (1990) 295; Christy R. Vestal, Z. John Zhang, Nano-Letters 3 (1) (2003) 1739. [31] A. Aharoni, Introduction to the Theory of Ferromagnetism, vol. 94, Clarendon Press, Oxford, 1996. [32] N. Hann, O.K. Quy, N.P. Thuy, L.D. Tung, L. Spinu, Physca B 327 (2003) 382. [33] Y. Shi, J. Ding, H. Yin, J. Alloys Compd. 308 (2000) 290. [34] A.E. Berkowitz, J.A. Lahut, I.S. Jacobs, L.M. Levinson, D.W. Forester, Phys. Rev. Lett. 34 (1975) 594. [35] A.E. Berkowitz, J.A. Lahut, C.E. Van Buren, IEEE Trans. Magn. MAG-16 (1980) 184. [36] J.M.D. Coey, Phys. Rev. Lett. 27 (1971) 1140. [37] J. Nogues, I.K. Schuller, J. Magn. Magn. Mater. 192 (1999) 203. [38] J. Nogues, J. Sort, V. Langlias, et al., Phys. Rep.-Rev. Sect. Phys. Lett. 422 (3) (2005) 65.