Self Assembled Arrays Of High Ani Sot Ropy Feptau Nano Particles
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ARTICLE IN PRESS
Physica B 354 (2004) 108–112 www.elsevier.com/locate/physb
Self-assembled arrays of high anisotropy FePt–Au nanoparticles A. Buteraa,,1, S.S. Kangb, D.E. Niklesb, J.W. Harrellb a
Centro Ato´mico Bariloche and Comisio´n Nacional de Energı´a Ato´mica, 8400 San Carlos de Bariloche, Rı´o Negro, Argentina b MINT Center, The University of Alabama, Tuscaloosa, AL 35487-0209 USA
Abstract We have studied the ferromagnetic resonance response of as-made and annealed Fe46 Pt46 Au8 self-ordered nanoparticles forming a film. As-made particles, which crystallize in a low magnetic anisotropy FCC phase, show a single isotropic resonance line close to g ¼ 2:1: Particles annealed at 450 C for 30 min are composed of a mixture of the FCC and the high anisotropy L10 phases. In this sample the resonant spectra are anisotropic when the external applied field is rotated from the in-plane to the out-of-plane direction. This absorption also seems to be related to the minority FCC particles which have a better degree of surface order due to the surrounding ferromagnetic environment. From the line width angular dependence we obtained a large dispersion in the anisotropy constant, probably arising from the different degree of atomic ordering of particles in the L10 phase. r 2004 Elsevier B.V. All rights reserved. PACS: 75.75.þa; 76.50.þg; 81.16.Dn; 75.30.Gw Keywords: Self-assembled FePt nanoparticles; High anisotropy L10 phase; Ferromagnetic resonance
Interest in ordered arrays of high anisotropy magnetic nanoparticles has increased considerably in the last few years due to their potential use as media for ultrahigh density magnetic recording. The chemical synthesis of very small ( 4 nm) and almost monodispersed FePt nanoparticles was Corresponding author. Fax: 54 2944 445299.
E-mail address: [email protected] (A. Butera). Also at Consejo Nacional de Investigaciones Cientı´ ficas y Te´cnicas, Argentina. 1
reported by Sun et al. [1]. These particles can be slowly deposited on a flat substrate to obtain selfordered arrays with nearly perfect hexagonal symmetry. Due to the organic coating, particle size and geometry is well preserved even after thermal treatments at high temperatures. As-made particles crystallize in a disordered FCC phase with a relatively small anisotropy. The order–disorder transformation can be obtained by thermal annealing. In stoichiometric FePt complete order of the high anisotropy L10 tetragonal phase can be
0921-4526/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2004.09.029
ARTICLE IN PRESS A. Butera et al. / Physica B 354 (2004) 108–112
cavity where the derivative of the absorbed power was measured using a standard field modulation technique (100 kHz frequency, 20 Oe amplitude). The X-band resonator was a rectangular cavity operating in the TE102 mode. The film plane was always parallel to the excitation microwave field and the DC external field changed from the inplane to the out-of-plane direction. The maximum available DC field was 19 kOe. Measurements as a function of temperature and angular variations below room temperature were made using a dewar with a flow of cold nitrogen gas. A Lake Shore VSM model 7300 was used for the DC magnetic measurements. In Fig. 1 we show the hysteresis loop of the AN sample with the external field applied parallel and perpendicular to the film plane. AM samples (not shown) are superparamagnetic at room temperature. From the figure it is observed that the coercivity fields are in the range of 5 kOe. For comparison (FePt)92 Ag8 treated at a higher temperature (500 C) has a coercivity of 7 kOe. The perpendicular hysteresis loop also has a very large coercivity, but the remanence and squareness are smaller than those of the parallel loop. These measurements suggest that although the individual easy axis of the FePt–Au particles may be
0.6
FePt-Au H || film H ⊥ film
0.4 0.2
M (memu)
only achieved with a temperature annealing at 650 C for 30 min [2]. The transition temperature can be strongly reduced ( 150 C) by the addition of small amounts of Ag or Au, which leave the structure after the thermal treatment [3]. Annealing at lower temperatures reduces particle sintering and aggregation and preserves the geometrical order of the array. The magnetic properties of these nanoparticle arrays have been extensively studied both experimentally and theoretically [2–4]. It was shown than in general there are large fluctuations in the values of the anisotropy constant K because the order–disorder transition is not complete. Magnetic interactions of magnetostatic type dominate the behavior of samples annealed at low temperatures, while exchange interactions are responsible for the characteristic features observed in highly ordered samples. As most of the magnetic measurements already made involved DC techniques, we have decided to measure the dynamic response of as-made and thermally treated Fe46 Pt46 Au8 ordered arrays of particles using ferromagnetic resonance (FMR) techniques. Fe46 Pt46 Au8 nanoparticles were prepared by chemical synthesis using the technique described in detail in Ref. [3]. The average size of the asmade particles is 3:5 nm plus an organic coating of a thickness of 2 nm. The particles selfassemble in an hexagonal array with an approximate packing fraction of 0.2. For the present study we used a reference as-made (AM) sample and a sample annealed (AN) at 450 C for 30 min. Annealing at this temperature is not enough to produce a complete transformation to the L10 phase. However, based on previous experiments on the FePt–Au system, we expect a significant amount of order to be developed at this relatively low annealing temperature. (See for example Fig. 4 (a) in the last paper of Ref. [3].) It is also observed that the particle size and the degree of geometrical order do not change considerably after the annealing [3]. FMR measurements have been done with a commercial Bruker ESP 300 spectrometer at a frequency of 9.5 GHz (X-band). Measurements at 35 GHz (Q-band) were not possible because of the very small signal intensity. The samples were placed at the center of a resonant
109
0.0 -0.2 -0.4 Hc||=5246 Oe Mr/Ms||=.77 Hc⊥ =4083 Oe Mr/Ms⊥ =.47
-0.6 -20
-10
0
10
20
H (kOe) Fig. 1. Hysteresis loop for the FePt–Au sample annealed at 450 C:
ARTICLE IN PRESS A. Butera et al. / Physica B 354 (2004) 108–112
110
randomly oriented, there are interparticle interactions that produce an effective easy plane anisotropy. From the value of the magnetization at the highest fields we have estimated the number of layers that compose the film. We have assumed a packing fraction x ¼ 0:2 and the reduced magnetic moment of small particles [5] (850 emu/ cm3 ) to obtain a total film thickness of 330 nm, which corresponds to approximately 40–50 layers. The FMR spectra of the AM and AN samples are shown in Fig. 2. Measurements with the magnetic field applied parallel and perpendicular to the film plane revealed that the as-made sample is isotropic. The resonance field is at a g value of 2.10 coincident with the g value of ferromagnetic Fe [6]. As no L10 phase is present in this sample we have associated the observed absorption to the resonance of the low anisotropy disordered FCC phase. The annealed sample, on the other hand, shows some degree of anisotropy in both the resonance field and the line width, but the line shape and width are not very different than what it is observed in the AM sample. The integrated
dχ"/dH (arb. units)
FePt-Au X-band
H ⊥ film plane H || film plane
as-made
0
1
2
3
4
5
6
7
8
H ⊥ film plane
intensity of this line is a factor 4 larger than the intensity of the AM sample. This fact could be taken as an indication that the main contribution to the intensity comes from the L10 phase and not from the FCC phase, which is a small fraction of the sample volume in the AN sample. Unfortunately, we did not have a sample with 100% L10 phase to corroborate or discard this hypothesis. Numerical simulations [7] of the FMR behavior of particles with anisotropies of 107 emu/cm3 predict a totally different behavior for the resonance field and the line width in the cases of 3D randomly distributed easy axis or with some degree of preferential alignment, even if a large dispersion in the magnitude of the anisotropy is considered. We then believe that in the AN sample we are observing the signal of the low anisotropy FCC phase. The larger intensity may be due to the ordering of moments located at the particle surface (which are a considerable fraction in such a small particles) induced by the ferromagnetic ordered L10 phase. This hypothesis is supported by measurements of line intensity as a function of temperature in the AM sample that show an abrupt increase at 200 K, characteristic of particle surface ordering [8]. The change of intensity in the AN sample is much smaller an monotonous, suggesting that the surface of the resonating particles is already ordered at room temperature. In Fig. 3 we present the angular variation of the resonance field and the line width for both samples. For the AM sample it is observed that the resonance field (H r ) and the line width (DH r ) have the following average values: H r ¼ 3220 Oe, DH r ¼ 750 Oe. To explain the angular dependence of the AN sample we propose the following free energy: F ¼ M H þ K eff ðcos jÞ2 :
H || film plane
annealed
0
1
2
3
4 5 H (kOe)
6
7
8
Fig. 2. Ferromagnetic resonance spectra for the as-made and the annealed samples measured with the DC field applied parallel and perpendicular to the film plane.
(1)
The first term is the Zeeman energy and the second term represents an effective anisotropy energy that tends to align the magnetization parallel to the film plane. This anisotropy term depends on the magnetization and anisotropy of the ferromagnetic phase. We have assumed that the film is placed in the y–z plane so that a positive sign of K eff describes an easy plane perpendicular to the
ARTICLE IN PRESS A. Butera et al. / Physica B 354 (2004) 108–112
4000 Resonance Field
as-made: annealed:
3600
Field (Oe)
3200 2800 1600 Linewidth 1200 800 -90
-45
0
45
90
135
180
α (deg.) Fig. 3. Angular variation of the resonance field and line width for the as-made and the annealed samples. Full and open symbols correspond to the experimental data and the continuous line to the numerically calculated best fit.
^ x-axis. Using the Smit and Beljers [9] formula, 2 2 2 o 1 q Fq F q2 F ¼ 2 2 ; g M sin y qy2 qj2 qyqj it is possible to arrive to the following expression for the evaluation of the resonance field: 2 o ¼ ðH cosðj aÞ H eff cosð2jÞÞ g ð2Þ H cosðj aÞ H eff cos2 j : ^ Here a is the angle formed between the x-axis and the external applied field and H eff ¼ 2K eff =M: The resonance field as a function of a can be obtained by evaluating Eq. (2) at the equilibrium angle jeq ; which results from the minimization of the free energy, qF =qj ¼ 0: The numerical fit of the angular variation of the resonance field permits to obtain a value for the anisotropy field, H eff 720 Oe. This field originates mostly from the L10 ordered phase and can be described as a demagnetizing term, due to the planar shape of the film, and a contribution due to stress, magnetocrystalline and surface effects. We could then write [6] H eff ¼ 4pxM þ 2K=ðxMÞ with x the volume faction of the L10 phase. If we set K ¼ 0 we obtain
111
x ¼ 0:07 which is not unreasonable considering the coexistence of phases. If we use the value estimated from TEM images (x 0:2) we can deduce an upper limit for the effective anisotropy K 1:2 105 erg/cm3 : The negative sign in K implies that the anisotropy tends to orient the magnetization of the particles in the out of plane x^ direction. The line width was analyzed considering the following expression [10]: o ; j; H eff ¼ DH 0 þ DH 1 þ DH 2 þ DH 3 DH g qH o ¼ DH 0 þ o D q g g H¼H r qH þ Dj qj H¼H r qH þ DH eff : ð3Þ qH eff H¼H r The terms represent a frequency independent contribution (DH 0 ), the intrinsic contribution or Suhl’s term (DH 1 ), a term related to the change in the magnetization angle, Dj; when the magnetic field is swept during the measurement (DH 2 ), and a last term that considers possible variations in the magnitude of the effective anisotropy field. In this case the second and third terms are irrelevant because of the low value of H eff : The last term can be written as qo=g DH eff qH eff 1 H eff cos2 j cos 2j ¼ o=g H cosðj aÞð1 þ 3 cos 2jÞ DH eff : 4
DH 3 ¼
ð4Þ
This contribution is maximum for a ¼ 0 minimum for a 50 (DH 3? DH eff ), (DH 3 0), and has a relative maximum for a ¼ p=2 of magnitude DH 3jj H jj = 2o=g DH eff : The experimental angular variation of the line width has been numerically fitted using the value of H eff obtained from the fit of the resonance field and the damping factor of pure Fe [6] (G 6 107 s1 ). We have found that the values that best reproduce
ARTICLE IN PRESS 112
A. Butera et al. / Physica B 354 (2004) 108–112
the measured data are DH 0 ¼ 890 Oe and DH eff ¼ 670 Oe. Note that the frequency independent term (DH 0 ) is slightly larger than the value found in the AM sample supporting our assumption that the observed absorption in both samples is due to the low anisotropy phase. The dispersion in the effective field values is considerably large, indicating a large fluctuation in the anisotropy of the ferromagnetic particles in coincidence with the results obtained by DC magnetic measurements in FePt–Ag particles [3]. In summary, the FMR measurements in FePt–Au arrays of nanoparticles seem to indicate that the observed resonant absorption arises in the low crystalline anisotropy FCC magnetic phase. This signal was used as a probe in the annealed sample to estimate a value for the effective anisotropy. Analyzing the angular dependence of the line width we arrived to the conclusion that there is a broad range of anisotropy values, probably due to particles having a different degree of atomic order. We wish to acknowledge the support of ANPCyT, Argentina, through Grant PICT 36340, and Conicet, Argentina through Grant PIP 2626. Very helpful discussions with C.A. Ramos and E. De Biasi are greatly acknowledged.
References [1] S. Sun, C.B. Murray, D. Weller, L. Folks, A. Moser, Science 287 (2000) 1989. [2] T.J. Klemmer, N. Shukla, C. Liu, X.W. Wu, E.B. Svedberg, O. Mryasov, R. Chantrell, D. Weller, M. Tanase, D.E. Laughlin, Appl. Phys. Lett. 81 (2002) 2220; X.W. Wu, K.Y. Guslienko, R.W. Chantrell, D. Weller, Appl. Phys. Lett. 82 (2003) 3475. [3] S. Kang, J.W. Harrell, D.E. Nickles, Nano Lett. 2 (2002) 1033; S.S. Kang, D.E. Nickles, J.W. Harrell, J. Appl. Phys. 93 (2003) 7178; S. Kang, Z. Jia, D.E. Nickles, J.W. Harrell, IEEE Trans. Magn. 39 (2003) 2753. [4] S. Wang, S.S. Kang, J.W. Harrell, X.W. Wu, R.W. Chantrell, Phys. Rev. B 68 (2003) 104413; S. Wang, S.S. Kang, D.E. Nickles, J.W. Harrell, X.W. Wu, J. Magn. Magn. Mater. 266 (2003) 49; G.A. Held, Hao Zeng, S. Sun, J. Appl. Phys. 95 (2004) 1481. [5] X.W. Wu, C. Liu, L. Li, P. Jones, R.W. Chantrell, D. Weller, J. Appl. Phys. 95 (2004) 6810. [6] A. Butera, J.N. Zhou, J.A. Barnard, Phys. Rev. B 60 (1999) 12270. [7] A. Butera, unpublished. [8] E. De Biasi, C.A. Ramos, R.D. Zysler, H. Romero, Phys. Rev. B 65 (2002) 144416. [9] J. Smit, H.G. Beljers, Philips Res. Rep. 10 (1955) 113. [10] A. Butera, J.L. Weston, J.A. Barnard, J. Magn. Magn. Mater., in press. doi:10.1016/j.jmmm.2004.06.015.
Physica B 354 (2004) 108–112 www.elsevier.com/locate/physb
Self-assembled arrays of high anisotropy FePt–Au nanoparticles A. Buteraa,,1, S.S. Kangb, D.E. Niklesb, J.W. Harrellb a
Centro Ato´mico Bariloche and Comisio´n Nacional de Energı´a Ato´mica, 8400 San Carlos de Bariloche, Rı´o Negro, Argentina b MINT Center, The University of Alabama, Tuscaloosa, AL 35487-0209 USA
Abstract We have studied the ferromagnetic resonance response of as-made and annealed Fe46 Pt46 Au8 self-ordered nanoparticles forming a film. As-made particles, which crystallize in a low magnetic anisotropy FCC phase, show a single isotropic resonance line close to g ¼ 2:1: Particles annealed at 450 C for 30 min are composed of a mixture of the FCC and the high anisotropy L10 phases. In this sample the resonant spectra are anisotropic when the external applied field is rotated from the in-plane to the out-of-plane direction. This absorption also seems to be related to the minority FCC particles which have a better degree of surface order due to the surrounding ferromagnetic environment. From the line width angular dependence we obtained a large dispersion in the anisotropy constant, probably arising from the different degree of atomic ordering of particles in the L10 phase. r 2004 Elsevier B.V. All rights reserved. PACS: 75.75.þa; 76.50.þg; 81.16.Dn; 75.30.Gw Keywords: Self-assembled FePt nanoparticles; High anisotropy L10 phase; Ferromagnetic resonance
Interest in ordered arrays of high anisotropy magnetic nanoparticles has increased considerably in the last few years due to their potential use as media for ultrahigh density magnetic recording. The chemical synthesis of very small ( 4 nm) and almost monodispersed FePt nanoparticles was Corresponding author. Fax: 54 2944 445299.
E-mail address: [email protected] (A. Butera). Also at Consejo Nacional de Investigaciones Cientı´ ficas y Te´cnicas, Argentina. 1
reported by Sun et al. [1]. These particles can be slowly deposited on a flat substrate to obtain selfordered arrays with nearly perfect hexagonal symmetry. Due to the organic coating, particle size and geometry is well preserved even after thermal treatments at high temperatures. As-made particles crystallize in a disordered FCC phase with a relatively small anisotropy. The order–disorder transformation can be obtained by thermal annealing. In stoichiometric FePt complete order of the high anisotropy L10 tetragonal phase can be
0921-4526/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2004.09.029
ARTICLE IN PRESS A. Butera et al. / Physica B 354 (2004) 108–112
cavity where the derivative of the absorbed power was measured using a standard field modulation technique (100 kHz frequency, 20 Oe amplitude). The X-band resonator was a rectangular cavity operating in the TE102 mode. The film plane was always parallel to the excitation microwave field and the DC external field changed from the inplane to the out-of-plane direction. The maximum available DC field was 19 kOe. Measurements as a function of temperature and angular variations below room temperature were made using a dewar with a flow of cold nitrogen gas. A Lake Shore VSM model 7300 was used for the DC magnetic measurements. In Fig. 1 we show the hysteresis loop of the AN sample with the external field applied parallel and perpendicular to the film plane. AM samples (not shown) are superparamagnetic at room temperature. From the figure it is observed that the coercivity fields are in the range of 5 kOe. For comparison (FePt)92 Ag8 treated at a higher temperature (500 C) has a coercivity of 7 kOe. The perpendicular hysteresis loop also has a very large coercivity, but the remanence and squareness are smaller than those of the parallel loop. These measurements suggest that although the individual easy axis of the FePt–Au particles may be
0.6
FePt-Au H || film H ⊥ film
0.4 0.2
M (memu)
only achieved with a temperature annealing at 650 C for 30 min [2]. The transition temperature can be strongly reduced ( 150 C) by the addition of small amounts of Ag or Au, which leave the structure after the thermal treatment [3]. Annealing at lower temperatures reduces particle sintering and aggregation and preserves the geometrical order of the array. The magnetic properties of these nanoparticle arrays have been extensively studied both experimentally and theoretically [2–4]. It was shown than in general there are large fluctuations in the values of the anisotropy constant K because the order–disorder transition is not complete. Magnetic interactions of magnetostatic type dominate the behavior of samples annealed at low temperatures, while exchange interactions are responsible for the characteristic features observed in highly ordered samples. As most of the magnetic measurements already made involved DC techniques, we have decided to measure the dynamic response of as-made and thermally treated Fe46 Pt46 Au8 ordered arrays of particles using ferromagnetic resonance (FMR) techniques. Fe46 Pt46 Au8 nanoparticles were prepared by chemical synthesis using the technique described in detail in Ref. [3]. The average size of the asmade particles is 3:5 nm plus an organic coating of a thickness of 2 nm. The particles selfassemble in an hexagonal array with an approximate packing fraction of 0.2. For the present study we used a reference as-made (AM) sample and a sample annealed (AN) at 450 C for 30 min. Annealing at this temperature is not enough to produce a complete transformation to the L10 phase. However, based on previous experiments on the FePt–Au system, we expect a significant amount of order to be developed at this relatively low annealing temperature. (See for example Fig. 4 (a) in the last paper of Ref. [3].) It is also observed that the particle size and the degree of geometrical order do not change considerably after the annealing [3]. FMR measurements have been done with a commercial Bruker ESP 300 spectrometer at a frequency of 9.5 GHz (X-band). Measurements at 35 GHz (Q-band) were not possible because of the very small signal intensity. The samples were placed at the center of a resonant
109
0.0 -0.2 -0.4 Hc||=5246 Oe Mr/Ms||=.77 Hc⊥ =4083 Oe Mr/Ms⊥ =.47
-0.6 -20
-10
0
10
20
H (kOe) Fig. 1. Hysteresis loop for the FePt–Au sample annealed at 450 C:
ARTICLE IN PRESS A. Butera et al. / Physica B 354 (2004) 108–112
110
randomly oriented, there are interparticle interactions that produce an effective easy plane anisotropy. From the value of the magnetization at the highest fields we have estimated the number of layers that compose the film. We have assumed a packing fraction x ¼ 0:2 and the reduced magnetic moment of small particles [5] (850 emu/ cm3 ) to obtain a total film thickness of 330 nm, which corresponds to approximately 40–50 layers. The FMR spectra of the AM and AN samples are shown in Fig. 2. Measurements with the magnetic field applied parallel and perpendicular to the film plane revealed that the as-made sample is isotropic. The resonance field is at a g value of 2.10 coincident with the g value of ferromagnetic Fe [6]. As no L10 phase is present in this sample we have associated the observed absorption to the resonance of the low anisotropy disordered FCC phase. The annealed sample, on the other hand, shows some degree of anisotropy in both the resonance field and the line width, but the line shape and width are not very different than what it is observed in the AM sample. The integrated
dχ"/dH (arb. units)
FePt-Au X-band
H ⊥ film plane H || film plane
as-made
0
1
2
3
4
5
6
7
8
H ⊥ film plane
intensity of this line is a factor 4 larger than the intensity of the AM sample. This fact could be taken as an indication that the main contribution to the intensity comes from the L10 phase and not from the FCC phase, which is a small fraction of the sample volume in the AN sample. Unfortunately, we did not have a sample with 100% L10 phase to corroborate or discard this hypothesis. Numerical simulations [7] of the FMR behavior of particles with anisotropies of 107 emu/cm3 predict a totally different behavior for the resonance field and the line width in the cases of 3D randomly distributed easy axis or with some degree of preferential alignment, even if a large dispersion in the magnitude of the anisotropy is considered. We then believe that in the AN sample we are observing the signal of the low anisotropy FCC phase. The larger intensity may be due to the ordering of moments located at the particle surface (which are a considerable fraction in such a small particles) induced by the ferromagnetic ordered L10 phase. This hypothesis is supported by measurements of line intensity as a function of temperature in the AM sample that show an abrupt increase at 200 K, characteristic of particle surface ordering [8]. The change of intensity in the AN sample is much smaller an monotonous, suggesting that the surface of the resonating particles is already ordered at room temperature. In Fig. 3 we present the angular variation of the resonance field and the line width for both samples. For the AM sample it is observed that the resonance field (H r ) and the line width (DH r ) have the following average values: H r ¼ 3220 Oe, DH r ¼ 750 Oe. To explain the angular dependence of the AN sample we propose the following free energy: F ¼ M H þ K eff ðcos jÞ2 :
H || film plane
annealed
0
1
2
3
4 5 H (kOe)
6
7
8
Fig. 2. Ferromagnetic resonance spectra for the as-made and the annealed samples measured with the DC field applied parallel and perpendicular to the film plane.
(1)
The first term is the Zeeman energy and the second term represents an effective anisotropy energy that tends to align the magnetization parallel to the film plane. This anisotropy term depends on the magnetization and anisotropy of the ferromagnetic phase. We have assumed that the film is placed in the y–z plane so that a positive sign of K eff describes an easy plane perpendicular to the
ARTICLE IN PRESS A. Butera et al. / Physica B 354 (2004) 108–112
4000 Resonance Field
as-made: annealed:
3600
Field (Oe)
3200 2800 1600 Linewidth 1200 800 -90
-45
0
45
90
135
180
α (deg.) Fig. 3. Angular variation of the resonance field and line width for the as-made and the annealed samples. Full and open symbols correspond to the experimental data and the continuous line to the numerically calculated best fit.
^ x-axis. Using the Smit and Beljers [9] formula, 2 2 2 o 1 q Fq F q2 F ¼ 2 2 ; g M sin y qy2 qj2 qyqj it is possible to arrive to the following expression for the evaluation of the resonance field: 2 o ¼ ðH cosðj aÞ H eff cosð2jÞÞ g ð2Þ H cosðj aÞ H eff cos2 j : ^ Here a is the angle formed between the x-axis and the external applied field and H eff ¼ 2K eff =M: The resonance field as a function of a can be obtained by evaluating Eq. (2) at the equilibrium angle jeq ; which results from the minimization of the free energy, qF =qj ¼ 0: The numerical fit of the angular variation of the resonance field permits to obtain a value for the anisotropy field, H eff 720 Oe. This field originates mostly from the L10 ordered phase and can be described as a demagnetizing term, due to the planar shape of the film, and a contribution due to stress, magnetocrystalline and surface effects. We could then write [6] H eff ¼ 4pxM þ 2K=ðxMÞ with x the volume faction of the L10 phase. If we set K ¼ 0 we obtain
111
x ¼ 0:07 which is not unreasonable considering the coexistence of phases. If we use the value estimated from TEM images (x 0:2) we can deduce an upper limit for the effective anisotropy K 1:2 105 erg/cm3 : The negative sign in K implies that the anisotropy tends to orient the magnetization of the particles in the out of plane x^ direction. The line width was analyzed considering the following expression [10]: o ; j; H eff ¼ DH 0 þ DH 1 þ DH 2 þ DH 3 DH g qH o ¼ DH 0 þ o D q g g H¼H r qH þ Dj qj H¼H r qH þ DH eff : ð3Þ qH eff H¼H r The terms represent a frequency independent contribution (DH 0 ), the intrinsic contribution or Suhl’s term (DH 1 ), a term related to the change in the magnetization angle, Dj; when the magnetic field is swept during the measurement (DH 2 ), and a last term that considers possible variations in the magnitude of the effective anisotropy field. In this case the second and third terms are irrelevant because of the low value of H eff : The last term can be written as qo=g DH eff qH eff 1 H eff cos2 j cos 2j ¼ o=g H cosðj aÞð1 þ 3 cos 2jÞ DH eff : 4
DH 3 ¼
ð4Þ
This contribution is maximum for a ¼ 0 minimum for a 50 (DH 3? DH eff ), (DH 3 0), and has a relative maximum for a ¼ p=2 of magnitude DH 3jj H jj = 2o=g DH eff : The experimental angular variation of the line width has been numerically fitted using the value of H eff obtained from the fit of the resonance field and the damping factor of pure Fe [6] (G 6 107 s1 ). We have found that the values that best reproduce
ARTICLE IN PRESS 112
A. Butera et al. / Physica B 354 (2004) 108–112
the measured data are DH 0 ¼ 890 Oe and DH eff ¼ 670 Oe. Note that the frequency independent term (DH 0 ) is slightly larger than the value found in the AM sample supporting our assumption that the observed absorption in both samples is due to the low anisotropy phase. The dispersion in the effective field values is considerably large, indicating a large fluctuation in the anisotropy of the ferromagnetic particles in coincidence with the results obtained by DC magnetic measurements in FePt–Ag particles [3]. In summary, the FMR measurements in FePt–Au arrays of nanoparticles seem to indicate that the observed resonant absorption arises in the low crystalline anisotropy FCC magnetic phase. This signal was used as a probe in the annealed sample to estimate a value for the effective anisotropy. Analyzing the angular dependence of the line width we arrived to the conclusion that there is a broad range of anisotropy values, probably due to particles having a different degree of atomic order. We wish to acknowledge the support of ANPCyT, Argentina, through Grant PICT 36340, and Conicet, Argentina through Grant PIP 2626. Very helpful discussions with C.A. Ramos and E. De Biasi are greatly acknowledged.
References [1] S. Sun, C.B. Murray, D. Weller, L. Folks, A. Moser, Science 287 (2000) 1989. [2] T.J. Klemmer, N. Shukla, C. Liu, X.W. Wu, E.B. Svedberg, O. Mryasov, R. Chantrell, D. Weller, M. Tanase, D.E. Laughlin, Appl. Phys. Lett. 81 (2002) 2220; X.W. Wu, K.Y. Guslienko, R.W. Chantrell, D. Weller, Appl. Phys. Lett. 82 (2003) 3475. [3] S. Kang, J.W. Harrell, D.E. Nickles, Nano Lett. 2 (2002) 1033; S.S. Kang, D.E. Nickles, J.W. Harrell, J. Appl. Phys. 93 (2003) 7178; S. Kang, Z. Jia, D.E. Nickles, J.W. Harrell, IEEE Trans. Magn. 39 (2003) 2753. [4] S. Wang, S.S. Kang, J.W. Harrell, X.W. Wu, R.W. Chantrell, Phys. Rev. B 68 (2003) 104413; S. Wang, S.S. Kang, D.E. Nickles, J.W. Harrell, X.W. Wu, J. Magn. Magn. Mater. 266 (2003) 49; G.A. Held, Hao Zeng, S. Sun, J. Appl. Phys. 95 (2004) 1481. [5] X.W. Wu, C. Liu, L. Li, P. Jones, R.W. Chantrell, D. Weller, J. Appl. Phys. 95 (2004) 6810. [6] A. Butera, J.N. Zhou, J.A. Barnard, Phys. Rev. B 60 (1999) 12270. [7] A. Butera, unpublished. [8] E. De Biasi, C.A. Ramos, R.D. Zysler, H. Romero, Phys. Rev. B 65 (2002) 144416. [9] J. Smit, H.G. Beljers, Philips Res. Rep. 10 (1955) 113. [10] A. Butera, J.L. Weston, J.A. Barnard, J. Magn. Magn. Mater., in press. doi:10.1016/j.jmmm.2004.06.015.
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