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Ferromagnetic resonance line width in Co(x)–SiO2(1−x) granular films
ARTICLE IN PRESS
Physica B 354 (2004) 145–148 www.elsevier.com/locate/physb
Ferromagnetic resonance line width in Co(x)–SiO2(1x) granular films J. Go´mez, A. Butera Centro Ato´mico Bariloche, Comisio´n Nacional de Energı´a Ato´mica, 8400 San Carlos de Bariloche, Rı´o Negro, Argentina
Abstract Using ferromagnetic resonance at X-band (v ¼ 9:4 GHz) and Q-band (v ¼ 34 GHz) we have studied the magnetic behavior of heterogeneous Co–SiO2 granular films as a function of the Co volume concentration, x, and the temperature, T. We have observed a main absorption signal associated to the uniform precession of the magnetic moments in the entire x-range studied. We have also observed an additional absorption above a critical concentration (xc ¼ 0:37) that could be associated to a surface resonance mode. We have found that annealing the films at moderate temperatures produce irreversible changes in the film microstructure. Based on the surface inhomogeneity model we propose that the two surfaces are affected in a different way during the annealing process. Measurements of the line width as a function of x and T could be explained within the framework of an array of randomly distributed anisotropic particles with increasing exchange interactions for larger x. r 2004 Elsevier B.V. All rights reserved. PACS: 81.05.Rm; 75.70.Cn; 76.50.+g; 76.60.Es; 81.07.b Keywords: Granular magnetic films; Ferromagnetic resonance; Resonance line width
Granular magnetic films consist of ferromagnetic grains embedded in an immiscible and often insulating matrix [1]. We have made Co–SiO2 granular films using RF sputtering techniques with a Co volume concentration, x, in the range 0.18–0.62. The film’s thickness was about 100 nm and the average size of the Co grains was 5 nm. Samples with low x have an isolated particle-like Corresponding author. Fax: +54 2944 445299.
E-mail address: [email protected] (A. Butera).
behavior, whereas for large x the strong exchange interaction among grains is predominant [1]. We have focused our attention to study the transition between these limits. Ferromagnetic resonance (FMR) measurements were used to characterize the magnetic behavior of the films. FMR spectra were acquired with a Bruker ESP300 spectrometer operating either at X- or Q-band. In all the samples studied we have observed a main absorption associated to the uniform
0921-4526/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2004.09.037
ARTICLE IN PRESS J. Go´mez, A. Butera / Physica B 354 (2004) 145–148
precession of the magnetization around the internal magnetic field, from which we were able to calculate an effective magnetic field. Above the critical x value (xc ¼ 0:37), corresponding to the percolation concentration, we have observed the presence of an additional resonance line with a resonance field larger than that of the uniform resonance mode. The presence of this additional mode is associated to surface effects which are more important when the exchange interaction among grains becomes dominant. The behavior of this mode could be well explained using the surface inhomogeneity model (SI) [2], under the assumption that it corresponds to a surface resonance mode. From this mode, we estimated the surface anisotropy constant as a function of x. The obtained values are similar to those found from the effective magnetic field [3]. We have chosen a sample with x ¼ 0:48 (x4xc) and measured the resonance spectra while heating from 300 to 500 K. We found that the film is not seriously affected, although some irreversible changes occurred. A second temperature run was done on the same sample from 300 to 800 K, and we observed important changes on the FMR signal, particularly when the applied field is normal to the film surface, as shown in Fig. 1. Note the appearance of a second surface mode and the large increase in the resonance field of the original surface mode. The SI model predicts that
DH ¼
qH qH Do þ Dj þ DH 0 : qo qj
4900
x = 0.48 277 K
4200
527 K
3500
654 K 709 K (x2)
(1)
The first term is usually known as the intrinsic contribution [4] and it is proportional to the excitation frequency o/g the damping constant l: qH=qo Do ¼ l=ðgM 0 Þðo=gÞ=½cosðj aÞ; g ¼ gmb =h is the gyromagnetic ratio and l1.5 108 for bulk Co [5]. This term contributes with a small value (o60 Oe) to DH and is weakly dependent on a. The second term comes from the variation of the magnetization orientation while the magnetic field is swept during the measurement. This term has
α = 0; t = 100 nm
EPR signal [u.a.]
Surface mode Uniform mode
the separation between the surface and the uniform modes depends on the surface anisotropy value. If the conditions at the two surfaces are different we expect to have two surface modes [3]. We have then interpreted the changes on the FMR signal mentioned above as caused by an increase of the surface anisotropy. It is worth mentioning that the effects of the annealing treatment are irreversible, probably due to changes in the film microstructure. The appearance of a second surface mode indicates that each film surface is affected in a different way by the temperature treatment. We have also measured the line width (DH) in a sample with x ¼ 0:52 at X-band. The dependence as a function of the angle between the applied field and the film normal, a; (measured at room temperature) is shown in Fig. 2. Data were fit considering the following contributions to DH:
∆H (Oe)
146
experiment model Heff = 7680 Oe x = 0.52 X-band
2800 2100 1400
817 K (x4) 700
8
10
12 14 H (kOe)
16
Fig. 1. X-band FMR spectra for different temperatures. Co concentration x ¼ 0:48; a ¼ 0:
0
15
30
45
60
75
90
α (deg.)
Fig. 2. Angular dependence of the line width in a sample with x ¼ 0:52; T ¼ 300 K; at X-band.
ARTICLE IN PRESS J. Go´mez, A. Butera / Physica B 354 (2004) 145–148
1000 Uniform mode Surface mode ∆H⊥ (Oe)
800
600
400
200 300
350
400 T (K)
450
500
Fig. 3. Temperature dependence of the perpendicular line width for the uniform and surface modes in a sample with x ¼ 0:48:
2500
X-Band Q-Band Surface mode X-band
2000 ∆H⊥ (Oe)
similar angular dependence as the experimental data, but vanishes when the applied field is normal or parallel to the film plane. For that reason an additional constant term (DH0) is introduced. The calculated contribution of the three terms in Eq. (1) is plotted in Fig. 2 as a continuous line. We have found DH0900 Oe, and a maximum value for Dj 141. We have measured the temperature dependence of DH? (DH for a ¼ 0) in a sample with x ¼ 0:48: For this orientation, the second term in Eq. (1) should be zero. We have observed a decreasing DH value for the uniform mode and a relatively constant DH value for the surface mode (see Fig. 3). We have found in the literature that the damping constant l is weakly temperature dependent [6], indicating that the temperature behavior of DH is dominated by DH0. The decrease in the line width is coincident with the change in the saturation magnetization when the temperature increases, as usually seen in these systems [1]. We want to emphasize that although the line width of the uniform mode varies with temperature, DH of the surface mode stays relatively constant suggesting a different relaxation mechanism. The dependence of DH? as a function of x for X- and Q-bands is shown in Fig. 4. The line narrowing for larger x is caused by an increasing exchange interaction among the Co grains. The interaction forces the magnetic moment precession
147
1500 1000 500 0
20
30
40
50
60
Co concentration (vol %) Fig. 4. Dependence of DH? with the Co concentration x for the uniform and surface modes. Measurements have been done at room temperature for X- and Q-bands.
to occur at similar values of the external magnetic field and with a smaller dispersion. For low x, on the other hand, the system behaves as an array of weakly interacting grains with their anisotropy axes randomly distributed, thus explaining the larger values of DH for lower concentrations. For high concentrations, DH approaches the values found in continuous films where DH00, indicating that DH0 is associated to the intricate film microstructure. In Fig. 4 we can also see that there is very little dependence of DH with the excitation frequency, at least for x40.35. For samples above this concentration, we can then discard the possibility of having a damping constant larger than lCo due to finite size effect of the grains. The concentration dependence of DH for the surface modes is also shown in Fig. 4 for X-band. It is observed that the line width has a relatively constant value for all the concentrations where this mode is detected, indicating that the relaxation mechanism depends weakly on the film microstructure. As expected, it is observed that the line intensity is higher for larger x due to the increasing contribution of the ferromagnetic component. In summary, we have characterized a series of Co–SiO2 heterogeneous films. Using FMR measurements, we have found that annealing at high temperatures produces irreversible changes on the film microstructure. From the behavior of the line width as a function of Co concentration,
ARTICLE IN PRESS 148
J. Go´mez, A. Butera / Physica B 354 (2004) 145–148
temperature, external field angle and excitation frequency, we were able to characterize the transition from an isolated particle-like behavior to a continuous film-like behavior. We have found that the surface mode line width is almost independent of Co concentration and temperature. References [1] A. Butera, J. Zhou, J. Barnard, Phys. Rev. B 60 (1999) 12270.
[2] H. Puszkarski, Prog. Surf. Sci. 9 (1979) 191. [3] J. Go´mez, A. Butera, J.A. Barnard, Phys. Rev. B 70 (2004) 054428. [4] A. Butera, J.L. Weston, J.A. Barnard, J. Magn. Magn. Mat., in press. doi:10.1016/j.jmmm.2004.06.015. [5] F. Schreiber, J. Pflaum, Z. Frait, Th. Mu¨he, J. Pelzl, Solid State Comm. 93 (1995) 965. [6] J.M. Rudd, K. Myrtle, J.F. Cochran, B. Heinrich, J. Appl. Phys. 57 (1985) 3693.
Physica B 354 (2004) 145–148 www.elsevier.com/locate/physb
Ferromagnetic resonance line width in Co(x)–SiO2(1x) granular films J. Go´mez, A. Butera Centro Ato´mico Bariloche, Comisio´n Nacional de Energı´a Ato´mica, 8400 San Carlos de Bariloche, Rı´o Negro, Argentina
Abstract Using ferromagnetic resonance at X-band (v ¼ 9:4 GHz) and Q-band (v ¼ 34 GHz) we have studied the magnetic behavior of heterogeneous Co–SiO2 granular films as a function of the Co volume concentration, x, and the temperature, T. We have observed a main absorption signal associated to the uniform precession of the magnetic moments in the entire x-range studied. We have also observed an additional absorption above a critical concentration (xc ¼ 0:37) that could be associated to a surface resonance mode. We have found that annealing the films at moderate temperatures produce irreversible changes in the film microstructure. Based on the surface inhomogeneity model we propose that the two surfaces are affected in a different way during the annealing process. Measurements of the line width as a function of x and T could be explained within the framework of an array of randomly distributed anisotropic particles with increasing exchange interactions for larger x. r 2004 Elsevier B.V. All rights reserved. PACS: 81.05.Rm; 75.70.Cn; 76.50.+g; 76.60.Es; 81.07.b Keywords: Granular magnetic films; Ferromagnetic resonance; Resonance line width
Granular magnetic films consist of ferromagnetic grains embedded in an immiscible and often insulating matrix [1]. We have made Co–SiO2 granular films using RF sputtering techniques with a Co volume concentration, x, in the range 0.18–0.62. The film’s thickness was about 100 nm and the average size of the Co grains was 5 nm. Samples with low x have an isolated particle-like Corresponding author. Fax: +54 2944 445299.
E-mail address: [email protected] (A. Butera).
behavior, whereas for large x the strong exchange interaction among grains is predominant [1]. We have focused our attention to study the transition between these limits. Ferromagnetic resonance (FMR) measurements were used to characterize the magnetic behavior of the films. FMR spectra were acquired with a Bruker ESP300 spectrometer operating either at X- or Q-band. In all the samples studied we have observed a main absorption associated to the uniform
0921-4526/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2004.09.037
ARTICLE IN PRESS J. Go´mez, A. Butera / Physica B 354 (2004) 145–148
precession of the magnetization around the internal magnetic field, from which we were able to calculate an effective magnetic field. Above the critical x value (xc ¼ 0:37), corresponding to the percolation concentration, we have observed the presence of an additional resonance line with a resonance field larger than that of the uniform resonance mode. The presence of this additional mode is associated to surface effects which are more important when the exchange interaction among grains becomes dominant. The behavior of this mode could be well explained using the surface inhomogeneity model (SI) [2], under the assumption that it corresponds to a surface resonance mode. From this mode, we estimated the surface anisotropy constant as a function of x. The obtained values are similar to those found from the effective magnetic field [3]. We have chosen a sample with x ¼ 0:48 (x4xc) and measured the resonance spectra while heating from 300 to 500 K. We found that the film is not seriously affected, although some irreversible changes occurred. A second temperature run was done on the same sample from 300 to 800 K, and we observed important changes on the FMR signal, particularly when the applied field is normal to the film surface, as shown in Fig. 1. Note the appearance of a second surface mode and the large increase in the resonance field of the original surface mode. The SI model predicts that
DH ¼
qH qH Do þ Dj þ DH 0 : qo qj
4900
x = 0.48 277 K
4200
527 K
3500
654 K 709 K (x2)
(1)
The first term is usually known as the intrinsic contribution [4] and it is proportional to the excitation frequency o/g the damping constant l: qH=qo Do ¼ l=ðgM 0 Þðo=gÞ=½cosðj aÞ; g ¼ gmb =h is the gyromagnetic ratio and l1.5 108 for bulk Co [5]. This term contributes with a small value (o60 Oe) to DH and is weakly dependent on a. The second term comes from the variation of the magnetization orientation while the magnetic field is swept during the measurement. This term has
α = 0; t = 100 nm
EPR signal [u.a.]
Surface mode Uniform mode
the separation between the surface and the uniform modes depends on the surface anisotropy value. If the conditions at the two surfaces are different we expect to have two surface modes [3]. We have then interpreted the changes on the FMR signal mentioned above as caused by an increase of the surface anisotropy. It is worth mentioning that the effects of the annealing treatment are irreversible, probably due to changes in the film microstructure. The appearance of a second surface mode indicates that each film surface is affected in a different way by the temperature treatment. We have also measured the line width (DH) in a sample with x ¼ 0:52 at X-band. The dependence as a function of the angle between the applied field and the film normal, a; (measured at room temperature) is shown in Fig. 2. Data were fit considering the following contributions to DH:
∆H (Oe)
146
experiment model Heff = 7680 Oe x = 0.52 X-band
2800 2100 1400
817 K (x4) 700
8
10
12 14 H (kOe)
16
Fig. 1. X-band FMR spectra for different temperatures. Co concentration x ¼ 0:48; a ¼ 0:
0
15
30
45
60
75
90
α (deg.)
Fig. 2. Angular dependence of the line width in a sample with x ¼ 0:52; T ¼ 300 K; at X-band.
ARTICLE IN PRESS J. Go´mez, A. Butera / Physica B 354 (2004) 145–148
1000 Uniform mode Surface mode ∆H⊥ (Oe)
800
600
400
200 300
350
400 T (K)
450
500
Fig. 3. Temperature dependence of the perpendicular line width for the uniform and surface modes in a sample with x ¼ 0:48:
2500
X-Band Q-Band Surface mode X-band
2000 ∆H⊥ (Oe)
similar angular dependence as the experimental data, but vanishes when the applied field is normal or parallel to the film plane. For that reason an additional constant term (DH0) is introduced. The calculated contribution of the three terms in Eq. (1) is plotted in Fig. 2 as a continuous line. We have found DH0900 Oe, and a maximum value for Dj 141. We have measured the temperature dependence of DH? (DH for a ¼ 0) in a sample with x ¼ 0:48: For this orientation, the second term in Eq. (1) should be zero. We have observed a decreasing DH value for the uniform mode and a relatively constant DH value for the surface mode (see Fig. 3). We have found in the literature that the damping constant l is weakly temperature dependent [6], indicating that the temperature behavior of DH is dominated by DH0. The decrease in the line width is coincident with the change in the saturation magnetization when the temperature increases, as usually seen in these systems [1]. We want to emphasize that although the line width of the uniform mode varies with temperature, DH of the surface mode stays relatively constant suggesting a different relaxation mechanism. The dependence of DH? as a function of x for X- and Q-bands is shown in Fig. 4. The line narrowing for larger x is caused by an increasing exchange interaction among the Co grains. The interaction forces the magnetic moment precession
147
1500 1000 500 0
20
30
40
50
60
Co concentration (vol %) Fig. 4. Dependence of DH? with the Co concentration x for the uniform and surface modes. Measurements have been done at room temperature for X- and Q-bands.
to occur at similar values of the external magnetic field and with a smaller dispersion. For low x, on the other hand, the system behaves as an array of weakly interacting grains with their anisotropy axes randomly distributed, thus explaining the larger values of DH for lower concentrations. For high concentrations, DH approaches the values found in continuous films where DH00, indicating that DH0 is associated to the intricate film microstructure. In Fig. 4 we can also see that there is very little dependence of DH with the excitation frequency, at least for x40.35. For samples above this concentration, we can then discard the possibility of having a damping constant larger than lCo due to finite size effect of the grains. The concentration dependence of DH for the surface modes is also shown in Fig. 4 for X-band. It is observed that the line width has a relatively constant value for all the concentrations where this mode is detected, indicating that the relaxation mechanism depends weakly on the film microstructure. As expected, it is observed that the line intensity is higher for larger x due to the increasing contribution of the ferromagnetic component. In summary, we have characterized a series of Co–SiO2 heterogeneous films. Using FMR measurements, we have found that annealing at high temperatures produces irreversible changes on the film microstructure. From the behavior of the line width as a function of Co concentration,
ARTICLE IN PRESS 148
J. Go´mez, A. Butera / Physica B 354 (2004) 145–148
temperature, external field angle and excitation frequency, we were able to characterize the transition from an isolated particle-like behavior to a continuous film-like behavior. We have found that the surface mode line width is almost independent of Co concentration and temperature. References [1] A. Butera, J. Zhou, J. Barnard, Phys. Rev. B 60 (1999) 12270.
[2] H. Puszkarski, Prog. Surf. Sci. 9 (1979) 191. [3] J. Go´mez, A. Butera, J.A. Barnard, Phys. Rev. B 70 (2004) 054428. [4] A. Butera, J.L. Weston, J.A. Barnard, J. Magn. Magn. Mat., in press. doi:10.1016/j.jmmm.2004.06.015. [5] F. Schreiber, J. Pflaum, Z. Frait, Th. Mu¨he, J. Pelzl, Solid State Comm. 93 (1995) 965. [6] J.M. Rudd, K. Myrtle, J.F. Cochran, B. Heinrich, J. Appl. Phys. 57 (1985) 3693.