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Thickness and temperature dependence of the dynamic magnetic behavior in disordered FePt films
ARTICLE IN PRESS Journal of Magnetism and Magnetic Materials 321 (2009) 2941–2945
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Thickness and temperature dependence of the dynamic magnetic behavior in disordered FePt films M. Va´squez Mansilla a, J. Go´mez a, E. Sallica Leva a, F. Castillo Gamarra a, A. Asenjo Barahona b, A. Butera a, a b
´mico Bariloche (CNEA) and Instituto Balseiro (U.N. Cuyo), 8400 Bariloche, Rı´o Negro, Argentina Centro Ato Instituto de Ciencia de Materiales de Madrid-CSIC, Cantoblanco-Madrid 28049, Spain
a r t i c l e in fo
abstract
Article history: Received 27 November 2008 Received in revised form 6 April 2009 Available online 24 April 2009
We present in this work an investigation of the magnetic behavior of FePt films as a function of film thickness and thermal treatment. The films have been sputter-deposited on oxidized Si (1 0 0) crystals and are ferromagnetic at room temperature. Using ferromagnetic resonance techniques at 9.5 GHz we have studied a series of four films with a thickness in the range 10 nmptp100 nm. The resonance spectra of these films were measured at and also above room temperature. The high temperature measurements produce irreversible changes in the samples which depend on the maximum temperature reached during the experiment. For relatively low measuring temperatures (Tt200 C) the magnetic properties are generally improved, probably due to the release of stress formed during film fabrication. For larger temperatures (T4200 C) the absorption linewidth gradually broadens and the line could be hardly observed at room temperature if the measuring temperature exceeded 300 C. This behavior is due to the partial transformation of the metastable FCC phase to the ordered L10 high anisotropy phase. These data are consistent with the results found in samples annealed outside the resonant cavity. & 2009 Elsevier B.V. All rights reserved.
PACS: 75.70.Ak 76.50.þg 75.30.Gw 75.50.Bb Keywords: FePt film Ferromagnetic resonance Magnetocrystalline anisotropy Order–disorder transformation
1. Introduction The alloys of Fe or Co with Pt or Pd present a great technological interest because of their unique magnetic properties, particularly the very large magnetocrystalline anisotropy and the high coercivity that can reach values of several kOe [1–5]. These properties make the alloy a potential candidate for ultrahigh density magnetic recording media, and considerable effort has been devoted to study FePt in the form of thin films and nanoparticles [1,6–10]. The singular magnetic properties are observed when the intermetallic alloy is close to the equiatomic composition and the Fe and Pt atoms are ordered in the crystal cell. This ordered phase is known as L10 and has a face centered tetragonal symmetry. Although the ordered FCT phase is of thermodynamic equilibrium, thin films grow in a metastable chemically disordered FCC phase (generally called A1 phase), which has a similar value of the saturation magnetization, but a much smaller anisotropy and coercive field. Atomic order can be established by annealing the films at high temperatures [2,5], and
Corresponding author. Tel: +54 2944 445158; fax: +54 2944 445299.
E-mail address: [email protected] (A. Butera). 0304-8853/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2009.04.045
the degree of atomic order is usually described by an order parameter S that ranges between 0 (for a fully disordered system) and 1 (in the case of a completely ordered FCT structure). It has been experimentally observed that the value of the first order uniaxial magnetocrystalline anisotropy has an almost linear dependence with the degree of atomic order [11] reaching values larger than 7 107 emu=cm3 for S ¼ 1 and decreasing to less than 1 106 emu=cm3 for S ¼ 0 [6,12]. Most of the published work has been focused on the ordered FCT phase due to the possibility of technological applications, while less attention was paid to the asdeposited disordered films. We have recently published a research on the correlation between the static and dynamic magnetic properties of as deposited FePt films [6]. We have shown that the coercivity increases with the film thickness (HC 15220 Oe for tp30 nm and HC 120 Oe for tX60 nm) and that there is a notorious change in the shape of the loops for films thicker than 30 nm, in coincidence with the appearance of stripe-like magnetic domains. The change in the magnetic microstructure is due to the competition between exchange, anisotropy and demagnetization energies [13]. These films are characterized by the presence of a small uniaxial out of plane anisotropy which, above a critical film thickness tc , favors the formation of magnetic regions with the shape of stripes. In these stripes the magnetization lies essentially in the film plane but has a small out of plane component that
ARTICLE IN PRESS ´squez Mansilla et al. / Journal of Magnetism and Magnetic Materials 321 (2009) 2941–2945 M. Va
2. Sample preparation The films used in this study are the same samples that we have used in Ref. [6]. The samples have been fabricated by DC magnetron sputtering on oxidized Si (1 0 0) substrates with the following thicknesses: 10, 30, 60, and 100 nm. X-ray diffraction analysis in as-made samples confirmed the absence of atomic order and showed a moderate degree of texture along the [111] direction. EDX studies gave an atomic ratio Fe/Pt of 45/55 indicating a small excess of Pt in the samples. Using MFM techniques we have obtained magnetic images of the domain structure in the four films. We have observed that the two thicker films present a stripe-like structure with a stripe period ls 115 nm (for t ¼ 60 nm) and ls 160 nm (for t ¼ 100 nm). The half period of the stripe structure for t ¼ 60 nm is almost equal to the film thickness indicating that the critical thickness for stripe formation is t cr o60 nm [17]. For t ¼ 30 nm and below the magnetization is essentially parallel to the film plane and no stripe structure could be observed. The Curie temperature of FePt alloys is dependent on the concentration of the elements. According to Ref. [18] the Curie temperature of ordered L10 FePt alloy films is maximum (T C 450 C) for an Fe atomic content slightly below 55%, and decreases steeply for other Fe concentrations (more than 10 C for each atomic% of Fe). For a film with a composition Fe47:5 Pt52:5 the Curie temperature of the A1 phase is approximately 290 C, well below the order–disorder transition temperature (T OD 447 C). The films studied in this work have a composition Fe45 Pt55 so that even a smaller T C could be expected in these samples. Ferromagnetic resonance spectra have been acquired with a commercial Bruker ESP 300 spectrometer at a frequency of 9.5 GHz (X-Band). The samples were placed at the center of a resonant cavity where the derivative of the absorbed power was measured using a standard field modulation technique. The film plane was in most cases parallel to the excitation microwave field, except in the case of in-plane angular variations that were measured to test for the presence of magnetic anisotropy. In this configuration the microwave field was perpendicular to the film plane. The maximum available DC field was 21 kOe. Measurements above RT were made in a Bruker ER 4114HT cavity that can reach temperatures of 1000 K with a flow of a hot N2 =H2 (90/10) gas.
resonance line was always observed for the in-plane configuration while one or two (and sometimes more than two) absorptions could be observed when the field H was applied normal to the film plane, depending on the film thickness. Apart from the out of plane anisotropy that is dominated by the planar shape of the samples, we have also noticed that some films present an in-plane easy axis. Although the magnitude of the in-plane anisotropy field is much smaller that the effective out of plane field (which is around 9 kOe as already reported in Ref. [6]), it is still larger than the coercive field in the thinner samples and produces different hysteresis loops when measuring at different in-plane angles. In Fig. 1 we show the variation of the resonance field and the linewidth as a function of the in-plane angle for samples of different thickness. Due to the relatively small in-plane anisotropy compared with the field where the resonance occurs, the resonance field can be very well described assuming that the magnetization vector is always in the film plane and parallel to the external field [19]. In this situation the resonance field can be expressed as 1 þ 3 cosð2fH Þ . (1) Hr ðfH Þ Hrk Heff U 4 In the above formula fH is the angle between the external field and the in-plane easy axis, Heff U is the in-plane effective uniaxial anisotropy, and Hrk is the resonance field parallel to the film plane in the absence of in-plane anisotropy, that can be directly obtained from the well-known Kittel [6,20] formula sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 o (2) : Hrk ¼ 2pMeff þ ð2pM eff Þ2 þ
g
In the above expression o is the microwave excitation frequency and g is the gyromagnetic ratio defined by the relation g ¼ 2pg mb =h (g is the electron g-factor which is close to 2.09 in FePt [6], mb is the Bohr magneton, and h is the Planck constant). It is observed in the figure that a very good fit of the experimental data is obtained with this simple model. The values of Heff U are maximum for the thinnest sample (Heff U ¼ 82 Oe) and decrease
1.15
Hr (kOe)
changes from the ‘‘up’’ to the ‘‘down’’ direction in contiguous stripes [12,13]. In coincidence with the changes in the static magnetic behavior, we have observed that the ferromagnetic resonance (FMR) spectra for thicker films presented additional absorption lines that were not observed for tp30 nm. These additional lines have been related to standing spin waves or domain mode FMR [6,14–16]. In this paper we present results of ferromagnetic resonance measurements in a set of films with different thickness as a function of temperature. We have focused our attention in the principal resonance mode corresponding to the uniform precession of the magnetization vector. In all cases measurements above room temperature (RT) produced irreversible changes in the magnetic properties of the samples, that could lead to the disappearance of the resonance if sufficiently high temperatures were reached.
1.10
1.05
1.00 220 200
Δ Hr (Oe)
2942
t=10 nm t=30 nm t=60 nm t=100 nm
180 160 140 120
3. Room temperature FMR In Ref. [6] we have reported the resonance spectra for the cases in which the external field was applied either parallel or perpendicular to the film plane. We have found that a single
0
45
90
135 180 225 270
φH (deg.)
Fig. 1. In-plane angular variation for different film thicknesses of (a) the resonance field and (b) the linewidth. The continuous lines in panel (a) are fits obtained from Eq. (1).
ARTICLE IN PRESS ´squez Mansilla et al. / Journal of Magnetism and Magnetic Materials 321 (2009) 2941–2945 M. Va
Q-band experiments for the thicker films. This behavior may be indicating that the in-plane anisotropy does not disappear in thicker films, but is more randomly distributed. The random distribution of easy axes would produce an inhomogeneous broadening in the in-plane linewidth of the thicker samples but would not affect the perpendicular linewidth.
4. FMR in annealed samples In order to study the influence of temperature on the magnetic properties of FePt films, we have investigated the behavior of the resonance spectra at and above RT. We have performed two kinds of experiments in samples treated by different methods. After deposition, a first set of samples (which we will call ES) was ex situ annealed during 1 h in a closed tubular furnace with a flowing N2 =H2 (90/10) atmosphere at temperatures in the range 2002700 C in steps of 100 C. The FMR spectra of the samples were then measured at RT with the external field applied parallel to the film plane. The FMR spectra of a second set of samples (called IS) were measured as a function of temperature directly inside the resonant cavity in the same geometry as for the ES samples. After reaching the highest temperature where the absorption could still be observed, the samples were then measured cooling down to RT. An estimation of the degree of atomic order in ES samples can be made by measuring the M vs. H loops of the 100 nm samples. The coercive field of these films annealed at different temperatures is presented in Fig. 2. It is observed that annealing at temperatures as low as 300 C already produces an increase in HC indicating that the transformation to the L10 has already started. We show in the same figure HC data reported by other authors, which are comparable but smaller than our values. This is indicating that for the same annealing temperature the fraction of the ordered phase in our samples is probably larger than the values reported by other authors. Note, however, that a very small fraction of the low coercivity FCC phase still persists in the sample annealed at 700 C (as evidenced by the sudden decrease of magnetization close to zero field in the inset of Fig. 2). The X-ray diffraction pattern of another sample with a larger area, treated in similar annealing conditions, showed two different [111] peaks
20 18 16 14
Hc (kOe)
as the film thickness is increased (Heff U ¼ 61 Oe for t ¼ 30 nm, eff Heff U ¼ 35 Oe for t ¼ 60 nm, and H U o10 Oe for t ¼ 100 nm). The resonance field for the 100 nm film is almost isotropic and no clear uniaxial anisotropy could be determined. The linewidth is weakly dependent on the in-plane angle (see Fig. 1(b)) and the most notable feature is a difference by almost a factor of two between the values measured in thinner films (DH130 Oe, for t ¼ 10 and 30 nm) compared to those observed in thicker films (DH210 Oe, for t ¼ 60 and 100 nm). In a general FMR experiment the linewidth tends to be an increasing function of the anisotropy, at least in systems in which the fluctuations in the mean value of the anisotropy and the distribution of easy axis orientations are not negligible [21]. In our case the films with larger in-plane anisotropy have a smaller linewidth and a larger variation of Hrk which is an indication that in these films the anisotropy is less random distributed than in the thicker films. From the peak to peak linewidth of the 100 nm film, which has an almost isotropic resonance field and linewidth, it is possible to estimate a value for the anisotropy through the relation DHpp 3=2Heff U (valid in the limit in which the anisotropy field is larger than the intrinsic relaxation, and the exchange length is smaller than the typical grain size) [22], which yields Heff U ¼ 120 Oe. This value is of the order of the anisotropy field estimated from the angular variation of the resonance field of the 10 nm film, suggesting that the absolute value of the in-plane anisotropy field is similar in all samples but the average value goes to zero as the thickness increases. The behavior of the samples as a function of film thickness is then suggesting that thinner films tend to grow with an in-plane easy axis parallel to one direction which becomes more random as the film thickness increases. Note that a [111] texture perpendicular to the film plane should give an almost isotropic in-plane behavior for the magnetocrystalline anisotropy and could not explain the observed anisotropy. To elucidate this point we have performed room temperature X-ray diffraction experiments and measured the lattice parameter of 100 nm films deposited at RT and at 250 C from the [111] diffraction peak. We have found that the lattice parameter of the film deposited at RT (a ¼ 0:3851 nm) is larger that the corresponding bulk value (a ¼ 0:3816 nm [23]), and is reduced in the film treated at 250 C (a ¼ 0:3825 nm). This variation of the lattice parameter is indicating that as-made films are under tensile stress, which tends to relax with temperature. We also did FMR measurements of the in-plane angular variation of the resonance field in 10 nm samples annealed at 200 and 300 C. We observed that the in-plane uniaxial anisotropy is quickly reduced in the annealed samples (Heff U ¼ 63 Oe for the ¼ 17 Oe for the film treated at sample annealed at 200 C and Heff U 300 C) indicating that even a relatively low temperature annealing is enough to reduce this anisotropy. These two measurements are consistent with a stress induced anisotropy that tends to disappear after a relatively low temperature annealing. There is a recent work [24] on disordered FePd thin films (which have the same crystalline structure) that shows a positive in-plane magnetostriction constant of disordered films deposited at 150 and 300 C. As the stress induced anisotropy is proportional to the product of the magnetostriction and the stress, the observation of a small in-plane anisotropy in our films is consistent with the presence of some degree of tensile stress. Regarding the thickness dependence of the anisotropy, the experimental data seems to indicate that the in-plane anisotropy is still present in the thicker films, but more randomly distributed. Out of plane measurements and frequency dependent FMR of these samples have been already reported in Ref. [6] for the asdeposited films. In Fig. 5 of that paper it is shown that the perpendicular linewidth varies weakly with film thickness, while the parallel linewidth increases considerably in both X- and
2943
12 10 8 6 FePt ES t=100 nm
4 2 0 0
100
200
300 400 Tann (°C)
500
600
700
Fig. 2. Coercive field of a 100 nm film ex situ annealed at different temperatures (circles). Additional symbols correspond to coercive field data reported in Refs. [2–4,25]. We show in the inset the M vs. H loop for the sample annealed at 700 C.
ARTICLE IN PRESS ´squez Mansilla et al. / Journal of Magnetism and Magnetic Materials 321 (2009) 2941–2945 M. Va
2944
related to the two crystalline phases, with areas that scale reasonably well with the contribution to the total magnetization of the soft and hard phases. The total fraction of the ordered phase in the sample annealed at 700 C can then be estimated to be around 90%. A typical evolution of the resonance spectra in ES samples is shown in Fig. 3. In this figure we present selected curves (t ¼ 30 nm) measured at room temperature of films that have been annealed at different temperatures. When compared with the as-deposited sample it is observed that the FMR line moves to lower resonance fields and narrows for the lowest annealing temperature (T ann ¼ 200 C), while it rapidly broadens for T ann X300 C. The line intensity decreases by more than 3 orders of magnitude for T ann ¼ 400 C and is almost completely lost for T ann 4500 C. The abrupt decrease in line intensity is accompanied by a shift of Hr to fields closer to the field corresponding to g ¼ 2 and by a considerable line broadening. Data for all samples are presented in Fig. 4. Note that even the annealing at relatively low temperatures (T ann ¼ 200 C) produces irreversible changes in the magnetic properties of the films, although the total intensity does
no anneal Tann = 200 °C FMR signal (arb. units)
Tann = 300 °C Tann = 400 °C
0.0
0.5
1.0 H (kOe)
1.5
2.0
Fig. 3. Room temperature in-plane resonance spectra for ES FePt films of 30 nm annealed at different temperatures.
not change significantly in this case. When treated at higher temperatures the films start to transform partially to the high anisotropy L10 phase which in general could not be observed in a standard FMR experiment due to small exchange length caused by the extremely large value of HU [21,8,9]. The estimated exchange length for the L10 phase is around 1 nm (considering an exchange stiffness constant A ¼ 106 erg=cm [1] and a magnetocrystalline anisotropy of 7 107 emu=cm3 [11]) while that of the A1 phase is close to 10 nm which is similar to the average grain size that we have observed by TEM in as-made samples. In samples in which both phases coexist the intensity of the absorption corresponding to the A1 phase decreases much faster than the corresponding volume fraction. As already mentioned the line is hardly observed for samples annealed at T ann X400 C in which the fraction of the ordered phase becomes to be significant. This behavior could be due to the strong interaction between both phases which produces drastic changes in the FMR spectra. Additional studies and modeling are necessary to support this assumption and will be the issue of a separate publication. To get a further insight in the evolution of the magnetic behavior with the thermal treatment, we measured the resonance spectra of the second set of samples as a function of temperature. In this case we started the measurement at RT and slowly increased T while taking spectra with the external field applied parallel to the film plane. In Fig. 5 we show the resonance field, the linewidth and the integrated intensity as a function of temperature for the four samples. We have chosen to present the four measurements simultaneously in order to show the overall temperature behavior, although some of the fine details could not be clearly resolved. The resonance field shifts to higher fields as T increases indicating that the effective magnetization decreases (see Eq. (2)). The lines can be observed up to an average temperature T C 200 C. This is an estimation for the Curie temperature of the alloy which, as mentioned in Section 2, should be considerably below 290 C for the composition of our films. The values of T C are dependent on the film thickness. For
t=10 nm t=30 nm t=60 nm t=100 nm
2.5 Hr (kOe)
t=10nm t=30nm t=60nm t=100nm
2.0
0.5 2.0
400 200 0
1.5
Intensity (arb. units)
ΔHr in-plane (kOe)
1.5
600
1.0
1.0 0.5 0.0
2.0
1.0
1.5
ΔHr (Oe)
Hr in-plane (kOe)
2.5
0
100
200 300 T anneal (°C)
400
500
Fig. 4. Room temperature in-plane resonance field (a) and linewidth (b) for ES FePt films annealed at different temperatures. The absorption intensity decreases rapidly for T ann X300 C, and resonance spectra could hardly be measured for T ann X400 C. Continuous lines are guides to the eye.
1.0
0.5
0.0
0
50
100 150 T (°C)
200
Fig. 5. In-plane resonance field (a), linewidth (b) and integrated intensity (c) for different FePt films as a function of temperature. Each curve contains the heating (full symbols) and cooling (open symbols) cycles. The intensity was normalized to the value measured at room temperature.
ARTICLE IN PRESS ´squez Mansilla et al. / Journal of Magnetism and Magnetic Materials 321 (2009) 2941–2945 M. Va
Hr ΔHr
2.0
t = 30 nm 400
1.5 300 1.0
ΔHr (Oe)
Hr (kOe)
5. Conclusions
500
2.5
200 0.5 100 0.0
0
50
100 T (°C)
150
2945
200
Fig. 6. Resonance field (squares) and linewidth (circles) as a function of temperature, measured with the applied field parallel to the film plane. The arrows indicate the heating (full symbols) and cooling (open symbols) portions of each curve, respectively.
the thinnest film (t ¼ 10 nm) T C 190 C, while for t ¼ 30 nm T C 200 C, and T C 210 C for t ¼ 60 and 100 nm. A considerable broadening of the linewidth is observed as the temperature is increased as shown in Fig. 5(b). This is again a consequence of the temperature dependence of M eff : The rapid variation of DHr close to the Curie temperature is coincident with the region where the variation of M eff (and consequently Hr ) is larger. The intensity of the absorption decreases when the temperature approaches T C . This behavior is due to the proportionality between the intensity and the magnetization [26] and is representative of the temperature variation of the film magnetization. The irreversibility of the magnetic properties after heating the samples can be better seen in Fig. 6. For clarity we present data for only one sample (t ¼ 30 nm), but the overall behavior is similar for all other films as already discussed. The as-made film was heated at a speed of 2 C/min and kept for 10 min at the first temperature where the resonance was no longer observed (T ¼ 200 C in this case), it was then cooled down at approximately the same rate until RT was reached. It can be observed that both the resonance field and the linewidth decrease after the temperature cycle was completed. In this case the relative amount of change is almost the same for Hr and DHr ð18%Þ. In other samples the decrease is always between 10% and 20%. For one particular sample (t ¼ 100 nm) we have made a second measurement cycle to check if further changes occurred after a new annealing. In this case we have found that the room temperature resonance field remained almost unchanged and the linewidth started to increase, indicating that the additional annealing does not improve the magnetic properties. The sample of t ¼ 10 nm was heated up to T300 C and then cooled down to RT. After this treatment, the line was no longer detected at RT indicating that the transformation to the ordered phase had already started and was large enough to prevent the observation of the FMR absorption. The observed variations in Hr and DHr are generally in accordance with the results found in ES films annealed at low temperatures, as shown in Fig. 4.
We have found that the magnetic properties of chemically disordered FePt films depend considerably on the thermal history of the samples. For low annealing temperatures (Tp200 C) the samples tend to improve the magnetic properties, increasing the effective magnetization (reflected in a decrease of the in-plane resonance field) and decreasing the effective in-plane anisotropy (which produces a narrowing of the absorption line). In this region of annealing temperatures the alloy is still chemically disordered, but the thermal energy is high enough to favor the release of stress produced during the fabrication process. Annealing at larger temperatures promotes the transformation to the L10 phase which, due to its very large anisotropy, produces drastic changes in the FMR spectrum of the resonance lines associated to the A1 phase.
Acknowledgments This was supported in part by Conicet under Grant PIP5250, ANPCyT Grant PICT 03-13297, and U.N. Cuyo Grant 06/C235, all from Argentina. We would like to acknowledge very fruitful discussions with Dr. Carlos A. Ramos. References [1] S. Okamoto, N. Kikuchi, O. Kitakami, T. Miyazaki, Y. Shimada, K. Fukamichi, Phys. Rev. B 66 (2002) 024413. [2] K.R. Coffey, M.A. Parker, J.K. Howard, IEEE Trans. Magn. 31 (1995) 2737. [3] R.A. Ristau, K. Barmak, L.H. Lewis, K.R. Coffey, J.K. Howard, J. Appl. Phys. 86 (1999) 4527. [4] S. Jeong, Y-H. Hsu, D.E. Laughlin, M.E. McHenry, IEEE Trans. Magn. 37 (2001) 1299. [5] R.F.C. Farrow, D. Weller, R.F. Marks, M.F. Toney, S. Hom, G.R. Harp, A. Cebollada, Appl. Phys. Lett. 69 (1996) 1166. [6] M. Va´squez Mansilla, J. Go´mez, A. Butera, IEEE Trans. Magn. 44 (2008) 2883. [7] S. Sun, C.B. Murray, D. Weller, L. Folks, A. Moser, Science 287 (2000) 1989. [8] J.M. Vargas, R.D. Zysler, A. Butera, Appl. Surf. Sci. 254 (2007) 274. [9] A. Butera, S.S. Kang, D.E. Nikles, J.W. Harrell, Physica B 354 (2004) 108. [10] J.M. Vargas, R.D. Zysler, L.M. Socolovsky, M. Knobel, D. Zanchet, J. Appl. Phys. 101 (2007) 023903. [11] H. Kanazawa, G. Lauhoff, T. Suzuki, J. Appl. Phys. 87 (2000) 6143–6145. [12] V. Gehanno, R. Hoffmann, Y. Samson, A. Marty, S. Auffret, Eur. Phys. J. B 10 (1999) 457. [13] A.L. Sukstanskii, K.I. Primak, J. Magn. Magn. Mater. 169 (1997) 31. [14] J. BenYoussef, H. Le Gall, N. Vukadinovic, V. Gehanno, A. Marty, Y. Samson, B. Gilles, J. Magn. Magn. Mater. 202 (1999) 277. [15] N. Vukadinovic, H. Le Gall, J. BenYoussef, V. Gehanno, A. Marty, Y. Samson, B. Gilles, Eur. Phys. J. B 13 (2000) 445. [16] A. Martins, S.C. Trippe, A.D. Santos, F. Pelegrini, J. Magn. Magn. Mater. 308 (2007) 120. [17] A. Hubert, R. Scha¨fer, in: Magnetic Domains, Springer, Berlin, 1998, pp. 301–302. [18] K. Barmak, J. Kim, D.C. Berry, W.N. Hanani, K. Wierman, E.B. Svedberg, J.K. Howard, J. Appl. Phys. 97 (2005) 024902. [19] Due to the formation of a stripe domain structure this assumption is not strictly true for the thicker samples, especially for the 100 nm film which has a saturation field of 1500 Oe. [20] C. Kittel, Phys. Rev. 73 (1948) 155. [21] A. Butera, Eur. Phys. J. B 52 (2006) 297. [22] E. de Biasi, C.A. Ramos, R.D. Zysler, J. Magn. Magn. Mater. 262 (2003) 235. [23] JCPDS, International Centre for Diffraction Data, 1995, 29-0718. Cited in Ref. [25]. [24] W. Wunderlich, K. Takahashi, D. Kubo, Y. Matsumara, Y. Nishi, J. Alloys Compd. 475 (2009) 339. [25] A. Martins, M.C.A. Fantini, A.D. Santos, J. Magn. Magn. Mater. 265 (2003) 13. [26] C. Wilts, S. Prasad, IEEE Trans. Magn. 17 (1981) 2405.
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Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Thickness and temperature dependence of the dynamic magnetic behavior in disordered FePt films M. Va´squez Mansilla a, J. Go´mez a, E. Sallica Leva a, F. Castillo Gamarra a, A. Asenjo Barahona b, A. Butera a, a b
´mico Bariloche (CNEA) and Instituto Balseiro (U.N. Cuyo), 8400 Bariloche, Rı´o Negro, Argentina Centro Ato Instituto de Ciencia de Materiales de Madrid-CSIC, Cantoblanco-Madrid 28049, Spain
a r t i c l e in fo
abstract
Article history: Received 27 November 2008 Received in revised form 6 April 2009 Available online 24 April 2009
We present in this work an investigation of the magnetic behavior of FePt films as a function of film thickness and thermal treatment. The films have been sputter-deposited on oxidized Si (1 0 0) crystals and are ferromagnetic at room temperature. Using ferromagnetic resonance techniques at 9.5 GHz we have studied a series of four films with a thickness in the range 10 nmptp100 nm. The resonance spectra of these films were measured at and also above room temperature. The high temperature measurements produce irreversible changes in the samples which depend on the maximum temperature reached during the experiment. For relatively low measuring temperatures (Tt200 C) the magnetic properties are generally improved, probably due to the release of stress formed during film fabrication. For larger temperatures (T4200 C) the absorption linewidth gradually broadens and the line could be hardly observed at room temperature if the measuring temperature exceeded 300 C. This behavior is due to the partial transformation of the metastable FCC phase to the ordered L10 high anisotropy phase. These data are consistent with the results found in samples annealed outside the resonant cavity. & 2009 Elsevier B.V. All rights reserved.
PACS: 75.70.Ak 76.50.þg 75.30.Gw 75.50.Bb Keywords: FePt film Ferromagnetic resonance Magnetocrystalline anisotropy Order–disorder transformation
1. Introduction The alloys of Fe or Co with Pt or Pd present a great technological interest because of their unique magnetic properties, particularly the very large magnetocrystalline anisotropy and the high coercivity that can reach values of several kOe [1–5]. These properties make the alloy a potential candidate for ultrahigh density magnetic recording media, and considerable effort has been devoted to study FePt in the form of thin films and nanoparticles [1,6–10]. The singular magnetic properties are observed when the intermetallic alloy is close to the equiatomic composition and the Fe and Pt atoms are ordered in the crystal cell. This ordered phase is known as L10 and has a face centered tetragonal symmetry. Although the ordered FCT phase is of thermodynamic equilibrium, thin films grow in a metastable chemically disordered FCC phase (generally called A1 phase), which has a similar value of the saturation magnetization, but a much smaller anisotropy and coercive field. Atomic order can be established by annealing the films at high temperatures [2,5], and
Corresponding author. Tel: +54 2944 445158; fax: +54 2944 445299.
E-mail address: [email protected] (A. Butera). 0304-8853/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2009.04.045
the degree of atomic order is usually described by an order parameter S that ranges between 0 (for a fully disordered system) and 1 (in the case of a completely ordered FCT structure). It has been experimentally observed that the value of the first order uniaxial magnetocrystalline anisotropy has an almost linear dependence with the degree of atomic order [11] reaching values larger than 7 107 emu=cm3 for S ¼ 1 and decreasing to less than 1 106 emu=cm3 for S ¼ 0 [6,12]. Most of the published work has been focused on the ordered FCT phase due to the possibility of technological applications, while less attention was paid to the asdeposited disordered films. We have recently published a research on the correlation between the static and dynamic magnetic properties of as deposited FePt films [6]. We have shown that the coercivity increases with the film thickness (HC 15220 Oe for tp30 nm and HC 120 Oe for tX60 nm) and that there is a notorious change in the shape of the loops for films thicker than 30 nm, in coincidence with the appearance of stripe-like magnetic domains. The change in the magnetic microstructure is due to the competition between exchange, anisotropy and demagnetization energies [13]. These films are characterized by the presence of a small uniaxial out of plane anisotropy which, above a critical film thickness tc , favors the formation of magnetic regions with the shape of stripes. In these stripes the magnetization lies essentially in the film plane but has a small out of plane component that
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2. Sample preparation The films used in this study are the same samples that we have used in Ref. [6]. The samples have been fabricated by DC magnetron sputtering on oxidized Si (1 0 0) substrates with the following thicknesses: 10, 30, 60, and 100 nm. X-ray diffraction analysis in as-made samples confirmed the absence of atomic order and showed a moderate degree of texture along the [111] direction. EDX studies gave an atomic ratio Fe/Pt of 45/55 indicating a small excess of Pt in the samples. Using MFM techniques we have obtained magnetic images of the domain structure in the four films. We have observed that the two thicker films present a stripe-like structure with a stripe period ls 115 nm (for t ¼ 60 nm) and ls 160 nm (for t ¼ 100 nm). The half period of the stripe structure for t ¼ 60 nm is almost equal to the film thickness indicating that the critical thickness for stripe formation is t cr o60 nm [17]. For t ¼ 30 nm and below the magnetization is essentially parallel to the film plane and no stripe structure could be observed. The Curie temperature of FePt alloys is dependent on the concentration of the elements. According to Ref. [18] the Curie temperature of ordered L10 FePt alloy films is maximum (T C 450 C) for an Fe atomic content slightly below 55%, and decreases steeply for other Fe concentrations (more than 10 C for each atomic% of Fe). For a film with a composition Fe47:5 Pt52:5 the Curie temperature of the A1 phase is approximately 290 C, well below the order–disorder transition temperature (T OD 447 C). The films studied in this work have a composition Fe45 Pt55 so that even a smaller T C could be expected in these samples. Ferromagnetic resonance spectra have been acquired with a commercial Bruker ESP 300 spectrometer at a frequency of 9.5 GHz (X-Band). The samples were placed at the center of a resonant cavity where the derivative of the absorbed power was measured using a standard field modulation technique. The film plane was in most cases parallel to the excitation microwave field, except in the case of in-plane angular variations that were measured to test for the presence of magnetic anisotropy. In this configuration the microwave field was perpendicular to the film plane. The maximum available DC field was 21 kOe. Measurements above RT were made in a Bruker ER 4114HT cavity that can reach temperatures of 1000 K with a flow of a hot N2 =H2 (90/10) gas.
resonance line was always observed for the in-plane configuration while one or two (and sometimes more than two) absorptions could be observed when the field H was applied normal to the film plane, depending on the film thickness. Apart from the out of plane anisotropy that is dominated by the planar shape of the samples, we have also noticed that some films present an in-plane easy axis. Although the magnitude of the in-plane anisotropy field is much smaller that the effective out of plane field (which is around 9 kOe as already reported in Ref. [6]), it is still larger than the coercive field in the thinner samples and produces different hysteresis loops when measuring at different in-plane angles. In Fig. 1 we show the variation of the resonance field and the linewidth as a function of the in-plane angle for samples of different thickness. Due to the relatively small in-plane anisotropy compared with the field where the resonance occurs, the resonance field can be very well described assuming that the magnetization vector is always in the film plane and parallel to the external field [19]. In this situation the resonance field can be expressed as 1 þ 3 cosð2fH Þ . (1) Hr ðfH Þ Hrk Heff U 4 In the above formula fH is the angle between the external field and the in-plane easy axis, Heff U is the in-plane effective uniaxial anisotropy, and Hrk is the resonance field parallel to the film plane in the absence of in-plane anisotropy, that can be directly obtained from the well-known Kittel [6,20] formula sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 o (2) : Hrk ¼ 2pMeff þ ð2pM eff Þ2 þ
g
In the above expression o is the microwave excitation frequency and g is the gyromagnetic ratio defined by the relation g ¼ 2pg mb =h (g is the electron g-factor which is close to 2.09 in FePt [6], mb is the Bohr magneton, and h is the Planck constant). It is observed in the figure that a very good fit of the experimental data is obtained with this simple model. The values of Heff U are maximum for the thinnest sample (Heff U ¼ 82 Oe) and decrease
1.15
Hr (kOe)
changes from the ‘‘up’’ to the ‘‘down’’ direction in contiguous stripes [12,13]. In coincidence with the changes in the static magnetic behavior, we have observed that the ferromagnetic resonance (FMR) spectra for thicker films presented additional absorption lines that were not observed for tp30 nm. These additional lines have been related to standing spin waves or domain mode FMR [6,14–16]. In this paper we present results of ferromagnetic resonance measurements in a set of films with different thickness as a function of temperature. We have focused our attention in the principal resonance mode corresponding to the uniform precession of the magnetization vector. In all cases measurements above room temperature (RT) produced irreversible changes in the magnetic properties of the samples, that could lead to the disappearance of the resonance if sufficiently high temperatures were reached.
1.10
1.05
1.00 220 200
Δ Hr (Oe)
2942
t=10 nm t=30 nm t=60 nm t=100 nm
180 160 140 120
3. Room temperature FMR In Ref. [6] we have reported the resonance spectra for the cases in which the external field was applied either parallel or perpendicular to the film plane. We have found that a single
0
45
90
135 180 225 270
φH (deg.)
Fig. 1. In-plane angular variation for different film thicknesses of (a) the resonance field and (b) the linewidth. The continuous lines in panel (a) are fits obtained from Eq. (1).
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Q-band experiments for the thicker films. This behavior may be indicating that the in-plane anisotropy does not disappear in thicker films, but is more randomly distributed. The random distribution of easy axes would produce an inhomogeneous broadening in the in-plane linewidth of the thicker samples but would not affect the perpendicular linewidth.
4. FMR in annealed samples In order to study the influence of temperature on the magnetic properties of FePt films, we have investigated the behavior of the resonance spectra at and above RT. We have performed two kinds of experiments in samples treated by different methods. After deposition, a first set of samples (which we will call ES) was ex situ annealed during 1 h in a closed tubular furnace with a flowing N2 =H2 (90/10) atmosphere at temperatures in the range 2002700 C in steps of 100 C. The FMR spectra of the samples were then measured at RT with the external field applied parallel to the film plane. The FMR spectra of a second set of samples (called IS) were measured as a function of temperature directly inside the resonant cavity in the same geometry as for the ES samples. After reaching the highest temperature where the absorption could still be observed, the samples were then measured cooling down to RT. An estimation of the degree of atomic order in ES samples can be made by measuring the M vs. H loops of the 100 nm samples. The coercive field of these films annealed at different temperatures is presented in Fig. 2. It is observed that annealing at temperatures as low as 300 C already produces an increase in HC indicating that the transformation to the L10 has already started. We show in the same figure HC data reported by other authors, which are comparable but smaller than our values. This is indicating that for the same annealing temperature the fraction of the ordered phase in our samples is probably larger than the values reported by other authors. Note, however, that a very small fraction of the low coercivity FCC phase still persists in the sample annealed at 700 C (as evidenced by the sudden decrease of magnetization close to zero field in the inset of Fig. 2). The X-ray diffraction pattern of another sample with a larger area, treated in similar annealing conditions, showed two different [111] peaks
20 18 16 14
Hc (kOe)
as the film thickness is increased (Heff U ¼ 61 Oe for t ¼ 30 nm, eff Heff U ¼ 35 Oe for t ¼ 60 nm, and H U o10 Oe for t ¼ 100 nm). The resonance field for the 100 nm film is almost isotropic and no clear uniaxial anisotropy could be determined. The linewidth is weakly dependent on the in-plane angle (see Fig. 1(b)) and the most notable feature is a difference by almost a factor of two between the values measured in thinner films (DH130 Oe, for t ¼ 10 and 30 nm) compared to those observed in thicker films (DH210 Oe, for t ¼ 60 and 100 nm). In a general FMR experiment the linewidth tends to be an increasing function of the anisotropy, at least in systems in which the fluctuations in the mean value of the anisotropy and the distribution of easy axis orientations are not negligible [21]. In our case the films with larger in-plane anisotropy have a smaller linewidth and a larger variation of Hrk which is an indication that in these films the anisotropy is less random distributed than in the thicker films. From the peak to peak linewidth of the 100 nm film, which has an almost isotropic resonance field and linewidth, it is possible to estimate a value for the anisotropy through the relation DHpp 3=2Heff U (valid in the limit in which the anisotropy field is larger than the intrinsic relaxation, and the exchange length is smaller than the typical grain size) [22], which yields Heff U ¼ 120 Oe. This value is of the order of the anisotropy field estimated from the angular variation of the resonance field of the 10 nm film, suggesting that the absolute value of the in-plane anisotropy field is similar in all samples but the average value goes to zero as the thickness increases. The behavior of the samples as a function of film thickness is then suggesting that thinner films tend to grow with an in-plane easy axis parallel to one direction which becomes more random as the film thickness increases. Note that a [111] texture perpendicular to the film plane should give an almost isotropic in-plane behavior for the magnetocrystalline anisotropy and could not explain the observed anisotropy. To elucidate this point we have performed room temperature X-ray diffraction experiments and measured the lattice parameter of 100 nm films deposited at RT and at 250 C from the [111] diffraction peak. We have found that the lattice parameter of the film deposited at RT (a ¼ 0:3851 nm) is larger that the corresponding bulk value (a ¼ 0:3816 nm [23]), and is reduced in the film treated at 250 C (a ¼ 0:3825 nm). This variation of the lattice parameter is indicating that as-made films are under tensile stress, which tends to relax with temperature. We also did FMR measurements of the in-plane angular variation of the resonance field in 10 nm samples annealed at 200 and 300 C. We observed that the in-plane uniaxial anisotropy is quickly reduced in the annealed samples (Heff U ¼ 63 Oe for the ¼ 17 Oe for the film treated at sample annealed at 200 C and Heff U 300 C) indicating that even a relatively low temperature annealing is enough to reduce this anisotropy. These two measurements are consistent with a stress induced anisotropy that tends to disappear after a relatively low temperature annealing. There is a recent work [24] on disordered FePd thin films (which have the same crystalline structure) that shows a positive in-plane magnetostriction constant of disordered films deposited at 150 and 300 C. As the stress induced anisotropy is proportional to the product of the magnetostriction and the stress, the observation of a small in-plane anisotropy in our films is consistent with the presence of some degree of tensile stress. Regarding the thickness dependence of the anisotropy, the experimental data seems to indicate that the in-plane anisotropy is still present in the thicker films, but more randomly distributed. Out of plane measurements and frequency dependent FMR of these samples have been already reported in Ref. [6] for the asdeposited films. In Fig. 5 of that paper it is shown that the perpendicular linewidth varies weakly with film thickness, while the parallel linewidth increases considerably in both X- and
2943
12 10 8 6 FePt ES t=100 nm
4 2 0 0
100
200
300 400 Tann (°C)
500
600
700
Fig. 2. Coercive field of a 100 nm film ex situ annealed at different temperatures (circles). Additional symbols correspond to coercive field data reported in Refs. [2–4,25]. We show in the inset the M vs. H loop for the sample annealed at 700 C.
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2944
related to the two crystalline phases, with areas that scale reasonably well with the contribution to the total magnetization of the soft and hard phases. The total fraction of the ordered phase in the sample annealed at 700 C can then be estimated to be around 90%. A typical evolution of the resonance spectra in ES samples is shown in Fig. 3. In this figure we present selected curves (t ¼ 30 nm) measured at room temperature of films that have been annealed at different temperatures. When compared with the as-deposited sample it is observed that the FMR line moves to lower resonance fields and narrows for the lowest annealing temperature (T ann ¼ 200 C), while it rapidly broadens for T ann X300 C. The line intensity decreases by more than 3 orders of magnitude for T ann ¼ 400 C and is almost completely lost for T ann 4500 C. The abrupt decrease in line intensity is accompanied by a shift of Hr to fields closer to the field corresponding to g ¼ 2 and by a considerable line broadening. Data for all samples are presented in Fig. 4. Note that even the annealing at relatively low temperatures (T ann ¼ 200 C) produces irreversible changes in the magnetic properties of the films, although the total intensity does
no anneal Tann = 200 °C FMR signal (arb. units)
Tann = 300 °C Tann = 400 °C
0.0
0.5
1.0 H (kOe)
1.5
2.0
Fig. 3. Room temperature in-plane resonance spectra for ES FePt films of 30 nm annealed at different temperatures.
not change significantly in this case. When treated at higher temperatures the films start to transform partially to the high anisotropy L10 phase which in general could not be observed in a standard FMR experiment due to small exchange length caused by the extremely large value of HU [21,8,9]. The estimated exchange length for the L10 phase is around 1 nm (considering an exchange stiffness constant A ¼ 106 erg=cm [1] and a magnetocrystalline anisotropy of 7 107 emu=cm3 [11]) while that of the A1 phase is close to 10 nm which is similar to the average grain size that we have observed by TEM in as-made samples. In samples in which both phases coexist the intensity of the absorption corresponding to the A1 phase decreases much faster than the corresponding volume fraction. As already mentioned the line is hardly observed for samples annealed at T ann X400 C in which the fraction of the ordered phase becomes to be significant. This behavior could be due to the strong interaction between both phases which produces drastic changes in the FMR spectra. Additional studies and modeling are necessary to support this assumption and will be the issue of a separate publication. To get a further insight in the evolution of the magnetic behavior with the thermal treatment, we measured the resonance spectra of the second set of samples as a function of temperature. In this case we started the measurement at RT and slowly increased T while taking spectra with the external field applied parallel to the film plane. In Fig. 5 we show the resonance field, the linewidth and the integrated intensity as a function of temperature for the four samples. We have chosen to present the four measurements simultaneously in order to show the overall temperature behavior, although some of the fine details could not be clearly resolved. The resonance field shifts to higher fields as T increases indicating that the effective magnetization decreases (see Eq. (2)). The lines can be observed up to an average temperature T C 200 C. This is an estimation for the Curie temperature of the alloy which, as mentioned in Section 2, should be considerably below 290 C for the composition of our films. The values of T C are dependent on the film thickness. For
t=10 nm t=30 nm t=60 nm t=100 nm
2.5 Hr (kOe)
t=10nm t=30nm t=60nm t=100nm
2.0
0.5 2.0
400 200 0
1.5
Intensity (arb. units)
ΔHr in-plane (kOe)
1.5
600
1.0
1.0 0.5 0.0
2.0
1.0
1.5
ΔHr (Oe)
Hr in-plane (kOe)
2.5
0
100
200 300 T anneal (°C)
400
500
Fig. 4. Room temperature in-plane resonance field (a) and linewidth (b) for ES FePt films annealed at different temperatures. The absorption intensity decreases rapidly for T ann X300 C, and resonance spectra could hardly be measured for T ann X400 C. Continuous lines are guides to the eye.
1.0
0.5
0.0
0
50
100 150 T (°C)
200
Fig. 5. In-plane resonance field (a), linewidth (b) and integrated intensity (c) for different FePt films as a function of temperature. Each curve contains the heating (full symbols) and cooling (open symbols) cycles. The intensity was normalized to the value measured at room temperature.
ARTICLE IN PRESS ´squez Mansilla et al. / Journal of Magnetism and Magnetic Materials 321 (2009) 2941–2945 M. Va
Hr ΔHr
2.0
t = 30 nm 400
1.5 300 1.0
ΔHr (Oe)
Hr (kOe)
5. Conclusions
500
2.5
200 0.5 100 0.0
0
50
100 T (°C)
150
2945
200
Fig. 6. Resonance field (squares) and linewidth (circles) as a function of temperature, measured with the applied field parallel to the film plane. The arrows indicate the heating (full symbols) and cooling (open symbols) portions of each curve, respectively.
the thinnest film (t ¼ 10 nm) T C 190 C, while for t ¼ 30 nm T C 200 C, and T C 210 C for t ¼ 60 and 100 nm. A considerable broadening of the linewidth is observed as the temperature is increased as shown in Fig. 5(b). This is again a consequence of the temperature dependence of M eff : The rapid variation of DHr close to the Curie temperature is coincident with the region where the variation of M eff (and consequently Hr ) is larger. The intensity of the absorption decreases when the temperature approaches T C . This behavior is due to the proportionality between the intensity and the magnetization [26] and is representative of the temperature variation of the film magnetization. The irreversibility of the magnetic properties after heating the samples can be better seen in Fig. 6. For clarity we present data for only one sample (t ¼ 30 nm), but the overall behavior is similar for all other films as already discussed. The as-made film was heated at a speed of 2 C/min and kept for 10 min at the first temperature where the resonance was no longer observed (T ¼ 200 C in this case), it was then cooled down at approximately the same rate until RT was reached. It can be observed that both the resonance field and the linewidth decrease after the temperature cycle was completed. In this case the relative amount of change is almost the same for Hr and DHr ð18%Þ. In other samples the decrease is always between 10% and 20%. For one particular sample (t ¼ 100 nm) we have made a second measurement cycle to check if further changes occurred after a new annealing. In this case we have found that the room temperature resonance field remained almost unchanged and the linewidth started to increase, indicating that the additional annealing does not improve the magnetic properties. The sample of t ¼ 10 nm was heated up to T300 C and then cooled down to RT. After this treatment, the line was no longer detected at RT indicating that the transformation to the ordered phase had already started and was large enough to prevent the observation of the FMR absorption. The observed variations in Hr and DHr are generally in accordance with the results found in ES films annealed at low temperatures, as shown in Fig. 4.
We have found that the magnetic properties of chemically disordered FePt films depend considerably on the thermal history of the samples. For low annealing temperatures (Tp200 C) the samples tend to improve the magnetic properties, increasing the effective magnetization (reflected in a decrease of the in-plane resonance field) and decreasing the effective in-plane anisotropy (which produces a narrowing of the absorption line). In this region of annealing temperatures the alloy is still chemically disordered, but the thermal energy is high enough to favor the release of stress produced during the fabrication process. Annealing at larger temperatures promotes the transformation to the L10 phase which, due to its very large anisotropy, produces drastic changes in the FMR spectrum of the resonance lines associated to the A1 phase.
Acknowledgments This was supported in part by Conicet under Grant PIP5250, ANPCyT Grant PICT 03-13297, and U.N. Cuyo Grant 06/C235, all from Argentina. We would like to acknowledge very fruitful discussions with Dr. Carlos A. Ramos. References [1] S. Okamoto, N. Kikuchi, O. Kitakami, T. Miyazaki, Y. Shimada, K. Fukamichi, Phys. Rev. B 66 (2002) 024413. [2] K.R. Coffey, M.A. Parker, J.K. Howard, IEEE Trans. Magn. 31 (1995) 2737. [3] R.A. Ristau, K. Barmak, L.H. Lewis, K.R. Coffey, J.K. Howard, J. Appl. Phys. 86 (1999) 4527. [4] S. Jeong, Y-H. Hsu, D.E. Laughlin, M.E. McHenry, IEEE Trans. Magn. 37 (2001) 1299. [5] R.F.C. Farrow, D. Weller, R.F. Marks, M.F. Toney, S. Hom, G.R. Harp, A. Cebollada, Appl. Phys. Lett. 69 (1996) 1166. [6] M. Va´squez Mansilla, J. Go´mez, A. Butera, IEEE Trans. Magn. 44 (2008) 2883. [7] S. Sun, C.B. Murray, D. Weller, L. Folks, A. Moser, Science 287 (2000) 1989. [8] J.M. Vargas, R.D. Zysler, A. Butera, Appl. Surf. Sci. 254 (2007) 274. [9] A. Butera, S.S. Kang, D.E. Nikles, J.W. Harrell, Physica B 354 (2004) 108. [10] J.M. Vargas, R.D. Zysler, L.M. Socolovsky, M. Knobel, D. Zanchet, J. Appl. Phys. 101 (2007) 023903. [11] H. Kanazawa, G. Lauhoff, T. Suzuki, J. Appl. Phys. 87 (2000) 6143–6145. [12] V. Gehanno, R. Hoffmann, Y. Samson, A. Marty, S. Auffret, Eur. Phys. J. B 10 (1999) 457. [13] A.L. Sukstanskii, K.I. Primak, J. Magn. Magn. Mater. 169 (1997) 31. [14] J. BenYoussef, H. Le Gall, N. Vukadinovic, V. Gehanno, A. Marty, Y. Samson, B. Gilles, J. Magn. Magn. Mater. 202 (1999) 277. [15] N. Vukadinovic, H. Le Gall, J. BenYoussef, V. Gehanno, A. Marty, Y. Samson, B. Gilles, Eur. Phys. J. B 13 (2000) 445. [16] A. Martins, S.C. Trippe, A.D. Santos, F. Pelegrini, J. Magn. Magn. Mater. 308 (2007) 120. [17] A. Hubert, R. Scha¨fer, in: Magnetic Domains, Springer, Berlin, 1998, pp. 301–302. [18] K. Barmak, J. Kim, D.C. Berry, W.N. Hanani, K. Wierman, E.B. Svedberg, J.K. Howard, J. Appl. Phys. 97 (2005) 024902. [19] Due to the formation of a stripe domain structure this assumption is not strictly true for the thicker samples, especially for the 100 nm film which has a saturation field of 1500 Oe. [20] C. Kittel, Phys. Rev. 73 (1948) 155. [21] A. Butera, Eur. Phys. J. B 52 (2006) 297. [22] E. de Biasi, C.A. Ramos, R.D. Zysler, J. Magn. Magn. Mater. 262 (2003) 235. [23] JCPDS, International Centre for Diffraction Data, 1995, 29-0718. Cited in Ref. [25]. [24] W. Wunderlich, K. Takahashi, D. Kubo, Y. Matsumara, Y. Nishi, J. Alloys Compd. 475 (2009) 339. [25] A. Martins, M.C.A. Fantini, A.D. Santos, J. Magn. Magn. Mater. 265 (2003) 13. [26] C. Wilts, S. Prasad, IEEE Trans. Magn. 17 (1981) 2405.