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Temperature-dependent FMR investigations on epitaxial Fe (001) films with different thicknesses
Journal of Magnetism and Magnetic Materials 148 (1995) 139-140
Journal of magnetism and magnetic materials
ELSEVIER
Temperature-dependent FMR investigations on epitaxial Fe (001) films with different thicknesses R. Meckenstock *, K. Harms, O. yon Geisau, J. Pelzl Institut fiir Experimentalphysil¢, AG Festki~rperspektroskopie, Ruhr-Universitiit, D-44780 Bochum, Germany
Abstract The temperature dependence of ferromagnetic resonance (FMR) spectra o f single epitaxial (001) Fe films of different thicknesses ( d = 1.0, 2.0, 4.0, 20.0 nm) were examined in the range from 4 to 570 K. Two resonance lines were observed. The change in line position is essentially governed by the strong temperature dependence of the crystalline 8nisotropy constant K 1 which was found to be close to the value o f bulk Fe. The linewidth of the observed resonances decreases roughly with the inverse power of temperature. The narrowing is attributed to the decrease of the crystalline anisotropy and of the magnetostriction.
1. Experiment The experiments were carried out on samples with the following principal structure: (001) (~aAs substrate, 1 nm ((301) Fe seed layer, 150 nm Ag layer, principal Fe film, 2 nm Ag and 50 nm ZnS [1]. Conventional ferromagnetic resonance (FMR) investigations at 9.2 GHz were performed with a commercial EPR spectrometer covering a temperature range from 4 to 570 K. At room temperature, the angular dependence of the FMR spectra was recorded as a function of the orientation of the external magnetic field Bext for three configurations: (a) Bex t in the fihn plane and (b), (c) Bext out-of-plane starting in-plane in the [100] and [110] crystallographic orientations, respectively. From these measurements the magnetization M, the crystalline anisotropy constants K 1 and K 2, the surface anisotropy K s and an additional uniaxial anisotropy K u were deduced self-consistently [2]. These angular dependent measurements were used to determine the exact orientations of the samples for the temperature-dependent measurements treated in this paper.
FMR dispersion relation expressed in terms of the partial derivatives of the free energy density F [3]:
1 [02F 02F ~2t (-~)2=M2s~2(@)~0-' ~0~(0-'i)2F-O--~J ]' "/or [ a2F
= -ff
* Corresponding author. Fax: +49-234-7094 336; e-maih [email protected].
F = -M
(lb)
'
• Bex t +
1 2 2Ks 2 ~ / z o M cos2~9+ ---~-sin O
1 + ~ - K l ( s i n 2 ( 2 0 ) + sin40 s i n 2 ( 2 ~ ) ) .
(2)
Solving Eq. (1) and minimizing the free energy (2) from the three different orientations one can deduce the magnetic parameters from the FMR line positions. As a result of the temperature-dependent measurements, Fig. 1 shows the resonance line position for the configuration with the external magnetic field Bext parallel to [110]. The data are plotted for a rather thick (d = 20 nm) and a rather thin ( d = 2 nm), Fe film, respectively. The high-field lines (squares) correspond to the 'aligned case', i.e. the magnetization precesses around the external
0304-8853/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved
SSDI 0 3 0 4 - 8 8 5 3 ( 9 5 ) 0 0 1 8 1 - 6
82F )
where ~ is the microwave frequency, A oJ the linewidth, 3' the gyromagnetic ratio, M the saturation magnetization and c~ the damping parameter. @ and • are the polar and azimuth angles, respectively, o f the magnetization M. The free energy of the system under investigation consists of the following major contributions given in order of appearance in Eq. (2) below: Zeeman energy, demagnetizing energy, surface anisotropy energy and magnetoeryslalline anisotropy energy (first-order)
2. Results and discussion The uniform mode o f the FMR measures the precession amplitude of the magnetization M in the effective internal magnetic field Beff consisting of the external magnetic field B¢~t and the anisotropy fields. The theoretical model used to analyze the experimental data proceeds from the
1
+ sin=(O
(18)
140
R. Meckenstock et al. /Journal of Magnetisrn and Magnetic Materials 148 (1995) 139-140
magnetic field Bext. This line position is the same for both samples at each temperature. The small differences arise f r o m a misalignment o f the samples o f approximately 0.5 ° when being fixed in the cavity. The 'aligned c a s e ' , resonance line is essentially effected by K 1 and M , but not b y the surface anisotropy K s (no thickness dependence!). The low-field lines corresponds to a ' n o n - a l i g n e d case', i.e. the magnetization precesses around the internal magnetic field Beff not being aligned with Bext. F o r thin Fe films with thicknesses d < 4 nm this line position is influenced not only b y K 1 and M but also b y K s, thus resulting ix different line positions for the 2 and 20 nm thick films. A s for the 2 nm film the second line vanishes at 220 K in the in-plane hard direction, the in-plane easy direction [100] is needed for the evaluation o f the temperature-dependent magnetic parameters (rhombi in Fig. 1). Because o f the thickness-dependent influence o f the surface anisotropy K s additional out-of-plane temperature-dependent measurements (Bextl[001]) were carried out on the thin samples. In Fig. 2 the values o f the crystalline anisotropy constant K 1 (circles) and o f the magnetization M (rhombi) deduced from the line positions o f the two films are plotted versus the temperature. For both Fe films the crystalline anisotropy as well as the magnetization are in very good agreement with the literature values for bulk Fe [4]. The slightly higher values o f K 1 for the thin F e film at low temperatures (T < 70 K) are most probably due to additional anisotropy terms such as stress which are not taken into account in the calculation. The reason for the small deviation from literature values o f K t around room temperature for thick samples cannot be explained but coincides vAth the results o f angle-dependent measurements at anabient temperature [2]. 150,
120
I~]B go •d == 2~ n m e~ ~
aligned case
"~
\
60 / n II [ 1 1 o ] / " 30 ~ zwt, allgnededme 0~
,0.-. . . . . . . . ,
i 100
,
~ O o o :e-****
0%
i 200
,
B I l [100]
i 300
temperature
(O01)-Fe-film
/ d = 20 nnl Oooo00 ,
i 400
%0 ,
t 500
,1.8
1!:
1.7 ~ 1..6 1.5
~o
1.4 ~ 4
' anisoIz'opY c°nlstant; K 1 1.3
o
10o
z~0 temperature
3~o
4~o
~
s ~ '2
(K)
Fig. 2. Temperature dependence of the crystalline anisotropy constant K t ( 0 , O ) and the magnetization M (4% ~ ) for two Fe films with d = 2 nm (filled symbols) and d = 20 nm (open symbols), respectively. For comparison, the literature values for bulk Fe [4] are also given (full line). In general, the error bars are smaller than the size of the symbols; the error bars for the d = 20 nm film are due to uncertainty of the resonance line position for Bextll[ll0] and M not aligned with Boxr This line vanishes in the remanence of the electromagnet for T ----450 K.
The surface anisotropy K s has to be taken into account in thin samples ( d --- 4.0, 2.0, 1.0 nm). The resulting values o f K s for one surface (Ks.top + gs.bonom = 2 K s ) are constant within the limits o f uncertainty: K s --- (0.55 ___0.10) m J / m 3. However, there is a tendency for a small increase with decreasing temperature. The F M R resonance line widths A B ( T ) are found to decrease markedly with increasing temperature, roughly following an inverse power law in the range 150 K < T < 550 K for the thicker samples. Although a 1 / T behaviour w o u l d support a dynamical mechanism, the magnitude o f the observed effects seems too large for it to be attributed to a temperature dependence o f the d a m p i n g parameter only. Therefore, w e assume that inhomogenieous strain broadening and its relaxation with increasing temperature yield an important contribution to A B ( T ) . Acknowledgements: The authors w o u l d like to thank M. Seh~ifer, R. Schreiber and P. Griinberg (IFF4, K F A Jiilich) for preparing the samples. This work was supported b y the Deutsche Forsehungsgemeinschaft, S F B 166. References
,
600
T OK)
Fig. 1. Temperature dependence of the resonance line positions for a d = 2 nm ( 0 , B, 4,) and a d = 2 0 nm ( O , 1:3) (001) Fe film. The squares represent the 'aligned ease' (Bextl[[ll0] in the film plane, .N aligned with Best), the circles represent the 'nonaligned case' (Bestll[ll0], M not aligned with B). The rhombi give the line positions for the thin ( d = 2 nm) film with Bestll[100].
[i] J.A. Wolf, PhD Thesis, Universitiit Ktiln (1993), published as "Bericht des Forsehungszentmms Jiilieh" Jiil-2743. [2] E.C. da Silva et al., J. Magn. Magn. Mater. 121 (1993) 528; R. Meckenstoek et aL, J. Appl. Phys. (June 1995). [3] H. Suhl, Phys. Rev. 97 (1955) 555. [4] Landolt-B6rnstein, Numerical Data and Functional Relationships in Science and Technology, New Series, Vol. llI19a, Magnetle Properties of Metals (Springer Berlin, 1986).
Journal of magnetism and magnetic materials
ELSEVIER
Temperature-dependent FMR investigations on epitaxial Fe (001) films with different thicknesses R. Meckenstock *, K. Harms, O. yon Geisau, J. Pelzl Institut fiir Experimentalphysil¢, AG Festki~rperspektroskopie, Ruhr-Universitiit, D-44780 Bochum, Germany
Abstract The temperature dependence of ferromagnetic resonance (FMR) spectra o f single epitaxial (001) Fe films of different thicknesses ( d = 1.0, 2.0, 4.0, 20.0 nm) were examined in the range from 4 to 570 K. Two resonance lines were observed. The change in line position is essentially governed by the strong temperature dependence of the crystalline 8nisotropy constant K 1 which was found to be close to the value o f bulk Fe. The linewidth of the observed resonances decreases roughly with the inverse power of temperature. The narrowing is attributed to the decrease of the crystalline anisotropy and of the magnetostriction.
1. Experiment The experiments were carried out on samples with the following principal structure: (001) (~aAs substrate, 1 nm ((301) Fe seed layer, 150 nm Ag layer, principal Fe film, 2 nm Ag and 50 nm ZnS [1]. Conventional ferromagnetic resonance (FMR) investigations at 9.2 GHz were performed with a commercial EPR spectrometer covering a temperature range from 4 to 570 K. At room temperature, the angular dependence of the FMR spectra was recorded as a function of the orientation of the external magnetic field Bext for three configurations: (a) Bex t in the fihn plane and (b), (c) Bext out-of-plane starting in-plane in the [100] and [110] crystallographic orientations, respectively. From these measurements the magnetization M, the crystalline anisotropy constants K 1 and K 2, the surface anisotropy K s and an additional uniaxial anisotropy K u were deduced self-consistently [2]. These angular dependent measurements were used to determine the exact orientations of the samples for the temperature-dependent measurements treated in this paper.
FMR dispersion relation expressed in terms of the partial derivatives of the free energy density F [3]:
1 [02F 02F ~2t (-~)2=M2s~2(@)~0-' ~0~(0-'i)2F-O--~J ]' "/or [ a2F
= -ff
* Corresponding author. Fax: +49-234-7094 336; e-maih [email protected].
F = -M
(lb)
'
• Bex t +
1 2 2Ks 2 ~ / z o M cos2~9+ ---~-sin O
1 + ~ - K l ( s i n 2 ( 2 0 ) + sin40 s i n 2 ( 2 ~ ) ) .
(2)
Solving Eq. (1) and minimizing the free energy (2) from the three different orientations one can deduce the magnetic parameters from the FMR line positions. As a result of the temperature-dependent measurements, Fig. 1 shows the resonance line position for the configuration with the external magnetic field Bext parallel to [110]. The data are plotted for a rather thick (d = 20 nm) and a rather thin ( d = 2 nm), Fe film, respectively. The high-field lines (squares) correspond to the 'aligned case', i.e. the magnetization precesses around the external
0304-8853/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved
SSDI 0 3 0 4 - 8 8 5 3 ( 9 5 ) 0 0 1 8 1 - 6
82F )
where ~ is the microwave frequency, A oJ the linewidth, 3' the gyromagnetic ratio, M the saturation magnetization and c~ the damping parameter. @ and • are the polar and azimuth angles, respectively, o f the magnetization M. The free energy of the system under investigation consists of the following major contributions given in order of appearance in Eq. (2) below: Zeeman energy, demagnetizing energy, surface anisotropy energy and magnetoeryslalline anisotropy energy (first-order)
2. Results and discussion The uniform mode o f the FMR measures the precession amplitude of the magnetization M in the effective internal magnetic field Beff consisting of the external magnetic field B¢~t and the anisotropy fields. The theoretical model used to analyze the experimental data proceeds from the
1
+ sin=(O
(18)
140
R. Meckenstock et al. /Journal of Magnetisrn and Magnetic Materials 148 (1995) 139-140
magnetic field Bext. This line position is the same for both samples at each temperature. The small differences arise f r o m a misalignment o f the samples o f approximately 0.5 ° when being fixed in the cavity. The 'aligned c a s e ' , resonance line is essentially effected by K 1 and M , but not b y the surface anisotropy K s (no thickness dependence!). The low-field lines corresponds to a ' n o n - a l i g n e d case', i.e. the magnetization precesses around the internal magnetic field Beff not being aligned with Bext. F o r thin Fe films with thicknesses d < 4 nm this line position is influenced not only b y K 1 and M but also b y K s, thus resulting ix different line positions for the 2 and 20 nm thick films. A s for the 2 nm film the second line vanishes at 220 K in the in-plane hard direction, the in-plane easy direction [100] is needed for the evaluation o f the temperature-dependent magnetic parameters (rhombi in Fig. 1). Because o f the thickness-dependent influence o f the surface anisotropy K s additional out-of-plane temperature-dependent measurements (Bextl[001]) were carried out on the thin samples. In Fig. 2 the values o f the crystalline anisotropy constant K 1 (circles) and o f the magnetization M (rhombi) deduced from the line positions o f the two films are plotted versus the temperature. For both Fe films the crystalline anisotropy as well as the magnetization are in very good agreement with the literature values for bulk Fe [4]. The slightly higher values o f K 1 for the thin F e film at low temperatures (T < 70 K) are most probably due to additional anisotropy terms such as stress which are not taken into account in the calculation. The reason for the small deviation from literature values o f K t around room temperature for thick samples cannot be explained but coincides vAth the results o f angle-dependent measurements at anabient temperature [2]. 150,
120
I~]B go •d == 2~ n m e~ ~
aligned case
"~
\
60 / n II [ 1 1 o ] / " 30 ~ zwt, allgnededme 0~
,0.-. . . . . . . . ,
i 100
,
~ O o o :e-****
0%
i 200
,
B I l [100]
i 300
temperature
(O01)-Fe-film
/ d = 20 nnl Oooo00 ,
i 400
%0 ,
t 500
,1.8
1!:
1.7 ~ 1..6 1.5
~o
1.4 ~ 4
' anisoIz'opY c°nlstant; K 1 1.3
o
10o
z~0 temperature
3~o
4~o
~
s ~ '2
(K)
Fig. 2. Temperature dependence of the crystalline anisotropy constant K t ( 0 , O ) and the magnetization M (4% ~ ) for two Fe films with d = 2 nm (filled symbols) and d = 20 nm (open symbols), respectively. For comparison, the literature values for bulk Fe [4] are also given (full line). In general, the error bars are smaller than the size of the symbols; the error bars for the d = 20 nm film are due to uncertainty of the resonance line position for Bextll[ll0] and M not aligned with Boxr This line vanishes in the remanence of the electromagnet for T ----450 K.
The surface anisotropy K s has to be taken into account in thin samples ( d --- 4.0, 2.0, 1.0 nm). The resulting values o f K s for one surface (Ks.top + gs.bonom = 2 K s ) are constant within the limits o f uncertainty: K s --- (0.55 ___0.10) m J / m 3. However, there is a tendency for a small increase with decreasing temperature. The F M R resonance line widths A B ( T ) are found to decrease markedly with increasing temperature, roughly following an inverse power law in the range 150 K < T < 550 K for the thicker samples. Although a 1 / T behaviour w o u l d support a dynamical mechanism, the magnitude o f the observed effects seems too large for it to be attributed to a temperature dependence o f the d a m p i n g parameter only. Therefore, w e assume that inhomogenieous strain broadening and its relaxation with increasing temperature yield an important contribution to A B ( T ) . Acknowledgements: The authors w o u l d like to thank M. Seh~ifer, R. Schreiber and P. Griinberg (IFF4, K F A Jiilich) for preparing the samples. This work was supported b y the Deutsche Forsehungsgemeinschaft, S F B 166. References
,
600
T OK)
Fig. 1. Temperature dependence of the resonance line positions for a d = 2 nm ( 0 , B, 4,) and a d = 2 0 nm ( O , 1:3) (001) Fe film. The squares represent the 'aligned ease' (Bextl[[ll0] in the film plane, .N aligned with Best), the circles represent the 'nonaligned case' (Bestll[ll0], M not aligned with B). The rhombi give the line positions for the thin ( d = 2 nm) film with Bestll[100].
[i] J.A. Wolf, PhD Thesis, Universitiit Ktiln (1993), published as "Bericht des Forsehungszentmms Jiilieh" Jiil-2743. [2] E.C. da Silva et al., J. Magn. Magn. Mater. 121 (1993) 528; R. Meckenstoek et aL, J. Appl. Phys. (June 1995). [3] H. Suhl, Phys. Rev. 97 (1955) 555. [4] Landolt-B6rnstein, Numerical Data and Functional Relationships in Science and Technology, New Series, Vol. llI19a, Magnetle Properties of Metals (Springer Berlin, 1986).