- Email: [email protected]
FeCo
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 286 (2005) 262–266 www.elsevier.com/locate/jmmm
Ferromagnetic resonance in soft Cu/FeCo James O. Rantschlera,b,, Chester Alexander Jra, Hong-Sik Junga a Center for Materials in Information Technology, University of Alabama, Tuscaloosa, AL 34587-0209, USA Magnetic Materials Group, MSEL, National Institute of Standards and Technology, 100 Bureau Rd., Mail Stop 8552, Gaithersburg, MD 20899-0003, USA
b
Abstract We present the results of ferromagnetic resonance (FMR) measurements of soft Fe65Co35 thin films grown on a seed layer of Cu. FMR is investigated at different magnetic field orientations and over a broad range of frequencies from 3 to 94 GHz. The observation of spin wave resonances in the perpendicular orientation allows us to estimate the exchange stiffness. r 2004 Elsevier B.V. All rights reserved. PACS: 75.50.Bb; 76.50.+g Keywords: Dissipation; FeCo; Spin-wave resonance; Ferromagnetic resonance; Landau–Lifshitz–Gilbert equation
1. Introduction The need for increased data transfer rates in future storage devices drives concern over the high-frequency performance of hard drive components [1]. Some systems of FeCo thin films grown on metallic seed layers are suitable candidates for the write heads of hard drives, having shown good soft properties—the coercivity is on the order of 10 Oe and the anisotropy field is about 30 Oe—and Corresponding author. Magnetic Materials Group, MSEL, National Institute of Standards and Technology, 100 Bureau Rd., Mail Stop 8552, Gaithersburg, MD 20899-0003, USA. Tel.: +1 301 975 8876; fax: +1 301 975 4553. E-mail address: [email protected] (J.O. Rantschler).
a high saturation magnetization of approximately 23 kG [2–5]. In this paper, we give an overview of the high-frequency properties of 50 nm Fe65Co35 grown on a 1 nm copper seed layer [4,5]. The switching speed of a ferromagnetic device is related to the phenomenological parameter found in the governing equations for the magnetization dynamics such as the Bloch–Bloembergen (BB) or Landau–Lifshitz–Gilbert (LLG) damping formulations. This is true for coherent [6] as well as heatassisted switching [7]. An experimentally mature method for exploring the dynamics of the magnetization is ferromagnetic resonance (FMR), which can determine the damping parameter from linewidth data. FMR data in this study is taken over a wider range of frequencies (3–93.9 GHz) and
0304-8853/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2004.09.076
ARTICLE IN PRESS J.O. Rantschler et al. / Journal of Magnetism and Magnetic Materials 286 (2005) 262–266
applied fields (200–60,000 G) than usual, and we use this breadth to extract information about the dissipation that would be impossible with a very small range of frequencies. We also use FMR to supplement and check data about the magnetization and anisotropy found by magnetometry. In the course of the investigation, we determine the exchange stiffness A of FeCo from spin wave resonances.
demagnetization field induced in the film and any planar or uniaxial contribution with a rotation axis along the film normal such as surface or crystal anisotropy. If a film has an in-plane, uniaxial anisotropy, as the Cu/FeCo system does, then the free energy density used for the sample is f ¼ 2pM 2s cos2 y K 1 cos2 y K U sin2 y sin2 f HM s cosðy bÞcosðf aÞ;
2. Experimental details Thin polycrystalline Fe65Co35 films were deposited on glass by DC magnetron sputtering at a target–substrate distance of 6.2 cm with a vacuum of better than 5 107 Torr. A magnetic field of about 300 Oe was applied in the film plane to obtain uniaixial anisotropy. FeCo samples were deposited in an Ar atmosphere of 3 mTorr and timecalibrated to produce a layer 50 nm thick atop a 1 nm copper seed layer to induce soft properties. A 5 nm layer of Ta was then deposited to protect the film from oxidization. These properties were found to come about from the reduction of the mean grain diameter D to 9 nm from the observed 50 nm for films sputtered directly onto glass [5]. FMR was taken using several spectrometers. Measurements from 3.5 to 18.5 GHz were taken with stripline FMR systems in a 2 T iron core magnet. Cavity spectrometers were used to supplement the data from 9 to 94 GHz. Measurements at X-, K-, and Ka-Band (9.38, 25.6, and 34.5 GHz, respectively) were taken using home-built spectrometers within an iron core magnet, and a Ka-Band probe were constructed to take perpendicular data in a 9 T superconducting magnet. Both arrangements used klystrons as frequency sources and resonant cavities for detection. A commercial, cavity-type spectrometer in a 6 T superconducting magnet was used for obtaining W-Band (93.9 GHz) data.
3. Discussion FMR is sensitive to the total perpendicular anisotropy of a sample H?, which combines the
263
ð1Þ
where K1 is the out-of-plane uniaxial anisotropy energy, KU is the in-plane uniaxial anisotropy energy, H is the applied field, and f and a are the azimuthal and y and b are the colatitudinal angles for the magnetization and applied field, respectively. The FMR frequency or is found by solving the Smit–Beljers relation, coming from the torque equation near equilibrium [8] 2 or 1 ¼ 2 2 ð f yy f ff f 2yf Þ (2) g M s sin y in conjunction with the stability relation found from the first derivatives of the free energy, putting the internal torque to zero f y ¼ 0;
(3)
f f ¼ 0;
(4)
where subscripts refer to partial derivatives in the magnetization angle. The constant g is the gyromagnetic ratio and Hk ¼ 2KU/Ms is the anisotropy field. Two rotations are particularly useful. The first is an in-plane rotation, which can determine Hk to high precision and the second is an out-of-plane rotation, which can determine H?. Because of the high saturation moment of FeCo, however, only the W-band instrument in a superconducting magnet could be used for a full 901 rotation. We use the resonance fields to confirm our results from static magnetometry. In-plane rotations were performed at X-, K-, and Ka-band and fit with Eqs. (2) and (4). The resultant estimates for Hk lie between 31 and 33 Oe, agreeing closely with the 29 Oe obtained from magnetometer and torque measurements [5]. Fig. 1 shows resonance fields for
ARTICLE IN PRESS J.O. Rantschler et al. / Journal of Magnetism and Magnetic Materials 286 (2005) 262–266
264
series of rotations from the in-plane easy axis of the FeCo to the film normal for Ka- and W-band measurements. The fits are to Eqs. (2) and (3) and data at both frequencies show a perpendicular anisotropy of 23.4 kG and a gyromagnetic ratio of 2.91 MHz/Oe (which conforms to a Lande´ g-factor of 2.08). Since measurements taken with a vibrating sample magnetometer allowed for an estimate of 23.1 kG for 4pMs, we conclude that K1 is negligible [5]. From time to time, a ferromagnetic metal sharing an interface with another material will display several odd harmonic spin wave resonance lines. Spins are pinned at the interface and produce oscillations through the depth of the film. In the case of the Cu/FeCo system, the agent inducing the soft magnetic properties also produces these modes. These lines all have resonance fields lower than the uniform FMR mode by a factor DHn that is related to the film thickness d, the magnetization Ms, the exchange stiffness A, and the mode number n [9] DH n ¼
2p2 n2 A Msd2
(5a)
The linewidth data is found by the same method after including a LLG-type damping term [10] DoLLG a 1 ¼ f f þ ; (5b) M s yy sin2 y ff g which uses a dimensionless constant a (called the Gilbert parameter) to characterize the dissipation, or the BB transverse relaxation rate T2 for the small oscillations DoBB ¼
1 : T2
(6)
The consideration of more damping formulations is beyond the scope of this paper. For sufficiently small linewidths, this can be rewritten as the halfpower linewidth DH 1=2 of the absorption curve using dH DH 1=2 ¼ (7) Do1=2 do and in order to compare this directly to derivative data, an additional conversion of pffiffiffi (8) DH pp ¼ DH 1=2 = 3
and when the two such modes that are visible in the perpendicular W-Band spectrum are fitted with the uniform FMR mode to Eq. (5a) in Fig. 2, we estimate the exchange stiffness of the system to be A ¼ 1:75 106 erg=cm; which is comparable Permalloy and FeN-based soft, high-moment films.
for a Lorentzian line must be used to find the peak-to-peak linewidth DH pp [11]. The differences between these two formulations are best seen by comparing the way the FMR linewidth behaves when the bias field is applied along the in-plane easy axis or along the film normal. For LLG, both orientations show a linear dependence on frequency with the same Gilbert
Fig. 1. The resonance field as a function of angle found at both 34.5 (diamonds) and 93.9 GHz (circles). The lines are fit to the torque equation.
Fig. 2. Spin wave resonances in the perpendicular orientation at 93.9 GHz. The points are the relative positions of the spin wave resonance lines and the line is the fit used to estimate the exchange stiffness.
ARTICLE IN PRESS J.O. Rantschler et al. / Journal of Magnetism and Magnetic Materials 286 (2005) 262–266
Fig. 3. The linewidth as a function of frequency in two orientations. The circles represent in-plane measurements, the diamonds indicate out-of-plane measurements, the solid symbols are from cavity spectrometers, and the open symbols are from the stripline spectrometer. The lines are fits to the LLG equation.
parameter. For BB, the perpendicular orientation has a constant linewidth of 2/gT2, but the in-plane linewidth varies as DH 1=2 ¼
2o 1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ; g2 T 2 2 H ? þ 4 o=g
(9)
where the total perpendicular anisotropy field H? is 4pM s 2K 1 =M s : It is usual to add a positive constant to account for inhomogeneous broadening [12]. Fig. 3 shows the linewidth as a function of frequency. Both the in-plane and out-of-plane changes are linear, meaning that BB is not acceptable as a phenomenological formulation for the Cu/FeCo system. When we fit the LLG, however, we obtain different damping estimates. For the lower curve we find a Gilbert parameter of 0.004(5), and for the upper curve, we find a Gilbert parameter of 0.006. In accordance with Eq. (8), there is 21 Oe worth of broadening in the absorption spectrum. This is in line with the previous results and is probably due to the small grain size [13]. We turn to rotation data to help us interpret the difference in the Gilbert parameter in the two orientations. The linewidth has a minimum out-ofplane for both curves, and we will therefore use
265
Fig. 4. Linewidth as a function of field angle for 34.5 (diamonds) and 93.9 GHz (circles) rotation measurements. The lines are fits to the LLG equation.
this as the baseline for our fits in Fig. 4, which shows linewidth data at both Ka- and W-band. The fits are based upon Eqs. (2,5b) and (7). It is seen from the W-band data that the fit follows the measured linewidth when the applied field is near the film normal, and mirrors it when nearly inplane with a shift occurring very near the point where the magnetization angle is 451. This shift is consistent with a 2-magnon contribution to a causing the difference of slopes in Fig. 3 [14]. To review, although we have seen that the general behavior of the FMR linewidth of the Cu/ FeCo system is incompatible with BB damping and conforms qualitatively to a LL or LLG dissipation formulation, we see that the use of a single damping parameter for the system is impossible. We have also seen that the total perpendicular anisotropy is within 1.2% of that found by magnetometry data, indicating that there is no significant perpendicular anisotropy contribution in the estimate of the magnetization. Finally, we have been able to measure the exchange stiffness of soft FeCo and found it to be 1.75 106 erg/cm.
Acknowledgments This study was funded by Seagate Research, NSIC-NSF 542417-55139 and by the University of Alabama; shared equipment was funded from
ARTICLE IN PRESS 266
J.O. Rantschler et al. / Journal of Magnetism and Magnetic Materials 286 (2005) 262–266
NSF-DMR 0213985 and NSF award #0079498 for the W-band Spectrometer. The authors would like to thank Bob McMichael for helpful discussions. References [1] K.B. Klassen, R.G. Hirko, J.T. Contreras, IEEE Trans. Magn. 34 (1998) 1822. [2] T. Thomson, P.C. Tiedi, C.L. Platt, A.E. Berkowitz, IEEE Trans. Magn. 34 (1998) 1045. [3] N.X. Sun, S.X. Wang, J. Appl. Phys. 92 (2002) 1477. [4] H.S. Jung, W.D. Doyle, J.E. Wittig, J.F. Al-Sharab, J. Bentley, Appl. Phys. Lett. 81 (2002) 2415. [5] H.S. Jung, W.D. Doyle, S. Matsunuma, J. Appl. Phys. 93 (2003) 6462.
[6] [7] [8] [9] [10]
[11] [12] [13] [14]
R. Kikuchi, J. Appl. Phys. 27 (1956) 1352. H.N. Bertram, Appl. Phys. Lett. 79 (2001) 4402. H. Suhl, Phys. Rev. 94 (1955) 555. D.D. Stancil, Theory of Magnetostatic Waves, Springer, New York, 1993. G.V. Skrotskii, L.V. Kurbatov, in: S.V. Vonsovskii (Ed.), Ferromagnetic Resonance, Israel Program for Scientific Translations, Jerusalem, 1964, pp. 9–59. C.P. Poole Jr., Electron Spin Resonance, Wiley, New York, 1983. B. Heinrich, F. Cochran, R. Hasegawa, J. Appl. Phys. 57 (1985) 3690. J.O. Rantschler, C. Alexander Jr., J. Appl. Phys. 93 (2003) 6665. R.D. McMichael, Krivosik, IEEE Trans. Magn. 40 (2004) 2.
Journal of Magnetism and Magnetic Materials 286 (2005) 262–266 www.elsevier.com/locate/jmmm
Ferromagnetic resonance in soft Cu/FeCo James O. Rantschlera,b,, Chester Alexander Jra, Hong-Sik Junga a Center for Materials in Information Technology, University of Alabama, Tuscaloosa, AL 34587-0209, USA Magnetic Materials Group, MSEL, National Institute of Standards and Technology, 100 Bureau Rd., Mail Stop 8552, Gaithersburg, MD 20899-0003, USA
b
Abstract We present the results of ferromagnetic resonance (FMR) measurements of soft Fe65Co35 thin films grown on a seed layer of Cu. FMR is investigated at different magnetic field orientations and over a broad range of frequencies from 3 to 94 GHz. The observation of spin wave resonances in the perpendicular orientation allows us to estimate the exchange stiffness. r 2004 Elsevier B.V. All rights reserved. PACS: 75.50.Bb; 76.50.+g Keywords: Dissipation; FeCo; Spin-wave resonance; Ferromagnetic resonance; Landau–Lifshitz–Gilbert equation
1. Introduction The need for increased data transfer rates in future storage devices drives concern over the high-frequency performance of hard drive components [1]. Some systems of FeCo thin films grown on metallic seed layers are suitable candidates for the write heads of hard drives, having shown good soft properties—the coercivity is on the order of 10 Oe and the anisotropy field is about 30 Oe—and Corresponding author. Magnetic Materials Group, MSEL, National Institute of Standards and Technology, 100 Bureau Rd., Mail Stop 8552, Gaithersburg, MD 20899-0003, USA. Tel.: +1 301 975 8876; fax: +1 301 975 4553. E-mail address: [email protected] (J.O. Rantschler).
a high saturation magnetization of approximately 23 kG [2–5]. In this paper, we give an overview of the high-frequency properties of 50 nm Fe65Co35 grown on a 1 nm copper seed layer [4,5]. The switching speed of a ferromagnetic device is related to the phenomenological parameter found in the governing equations for the magnetization dynamics such as the Bloch–Bloembergen (BB) or Landau–Lifshitz–Gilbert (LLG) damping formulations. This is true for coherent [6] as well as heatassisted switching [7]. An experimentally mature method for exploring the dynamics of the magnetization is ferromagnetic resonance (FMR), which can determine the damping parameter from linewidth data. FMR data in this study is taken over a wider range of frequencies (3–93.9 GHz) and
0304-8853/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2004.09.076
ARTICLE IN PRESS J.O. Rantschler et al. / Journal of Magnetism and Magnetic Materials 286 (2005) 262–266
applied fields (200–60,000 G) than usual, and we use this breadth to extract information about the dissipation that would be impossible with a very small range of frequencies. We also use FMR to supplement and check data about the magnetization and anisotropy found by magnetometry. In the course of the investigation, we determine the exchange stiffness A of FeCo from spin wave resonances.
demagnetization field induced in the film and any planar or uniaxial contribution with a rotation axis along the film normal such as surface or crystal anisotropy. If a film has an in-plane, uniaxial anisotropy, as the Cu/FeCo system does, then the free energy density used for the sample is f ¼ 2pM 2s cos2 y K 1 cos2 y K U sin2 y sin2 f HM s cosðy bÞcosðf aÞ;
2. Experimental details Thin polycrystalline Fe65Co35 films were deposited on glass by DC magnetron sputtering at a target–substrate distance of 6.2 cm with a vacuum of better than 5 107 Torr. A magnetic field of about 300 Oe was applied in the film plane to obtain uniaixial anisotropy. FeCo samples were deposited in an Ar atmosphere of 3 mTorr and timecalibrated to produce a layer 50 nm thick atop a 1 nm copper seed layer to induce soft properties. A 5 nm layer of Ta was then deposited to protect the film from oxidization. These properties were found to come about from the reduction of the mean grain diameter D to 9 nm from the observed 50 nm for films sputtered directly onto glass [5]. FMR was taken using several spectrometers. Measurements from 3.5 to 18.5 GHz were taken with stripline FMR systems in a 2 T iron core magnet. Cavity spectrometers were used to supplement the data from 9 to 94 GHz. Measurements at X-, K-, and Ka-Band (9.38, 25.6, and 34.5 GHz, respectively) were taken using home-built spectrometers within an iron core magnet, and a Ka-Band probe were constructed to take perpendicular data in a 9 T superconducting magnet. Both arrangements used klystrons as frequency sources and resonant cavities for detection. A commercial, cavity-type spectrometer in a 6 T superconducting magnet was used for obtaining W-Band (93.9 GHz) data.
3. Discussion FMR is sensitive to the total perpendicular anisotropy of a sample H?, which combines the
263
ð1Þ
where K1 is the out-of-plane uniaxial anisotropy energy, KU is the in-plane uniaxial anisotropy energy, H is the applied field, and f and a are the azimuthal and y and b are the colatitudinal angles for the magnetization and applied field, respectively. The FMR frequency or is found by solving the Smit–Beljers relation, coming from the torque equation near equilibrium [8] 2 or 1 ¼ 2 2 ð f yy f ff f 2yf Þ (2) g M s sin y in conjunction with the stability relation found from the first derivatives of the free energy, putting the internal torque to zero f y ¼ 0;
(3)
f f ¼ 0;
(4)
where subscripts refer to partial derivatives in the magnetization angle. The constant g is the gyromagnetic ratio and Hk ¼ 2KU/Ms is the anisotropy field. Two rotations are particularly useful. The first is an in-plane rotation, which can determine Hk to high precision and the second is an out-of-plane rotation, which can determine H?. Because of the high saturation moment of FeCo, however, only the W-band instrument in a superconducting magnet could be used for a full 901 rotation. We use the resonance fields to confirm our results from static magnetometry. In-plane rotations were performed at X-, K-, and Ka-band and fit with Eqs. (2) and (4). The resultant estimates for Hk lie between 31 and 33 Oe, agreeing closely with the 29 Oe obtained from magnetometer and torque measurements [5]. Fig. 1 shows resonance fields for
ARTICLE IN PRESS J.O. Rantschler et al. / Journal of Magnetism and Magnetic Materials 286 (2005) 262–266
264
series of rotations from the in-plane easy axis of the FeCo to the film normal for Ka- and W-band measurements. The fits are to Eqs. (2) and (3) and data at both frequencies show a perpendicular anisotropy of 23.4 kG and a gyromagnetic ratio of 2.91 MHz/Oe (which conforms to a Lande´ g-factor of 2.08). Since measurements taken with a vibrating sample magnetometer allowed for an estimate of 23.1 kG for 4pMs, we conclude that K1 is negligible [5]. From time to time, a ferromagnetic metal sharing an interface with another material will display several odd harmonic spin wave resonance lines. Spins are pinned at the interface and produce oscillations through the depth of the film. In the case of the Cu/FeCo system, the agent inducing the soft magnetic properties also produces these modes. These lines all have resonance fields lower than the uniform FMR mode by a factor DHn that is related to the film thickness d, the magnetization Ms, the exchange stiffness A, and the mode number n [9] DH n ¼
2p2 n2 A Msd2
(5a)
The linewidth data is found by the same method after including a LLG-type damping term [10] DoLLG a 1 ¼ f f þ ; (5b) M s yy sin2 y ff g which uses a dimensionless constant a (called the Gilbert parameter) to characterize the dissipation, or the BB transverse relaxation rate T2 for the small oscillations DoBB ¼
1 : T2
(6)
The consideration of more damping formulations is beyond the scope of this paper. For sufficiently small linewidths, this can be rewritten as the halfpower linewidth DH 1=2 of the absorption curve using dH DH 1=2 ¼ (7) Do1=2 do and in order to compare this directly to derivative data, an additional conversion of pffiffiffi (8) DH pp ¼ DH 1=2 = 3
and when the two such modes that are visible in the perpendicular W-Band spectrum are fitted with the uniform FMR mode to Eq. (5a) in Fig. 2, we estimate the exchange stiffness of the system to be A ¼ 1:75 106 erg=cm; which is comparable Permalloy and FeN-based soft, high-moment films.
for a Lorentzian line must be used to find the peak-to-peak linewidth DH pp [11]. The differences between these two formulations are best seen by comparing the way the FMR linewidth behaves when the bias field is applied along the in-plane easy axis or along the film normal. For LLG, both orientations show a linear dependence on frequency with the same Gilbert
Fig. 1. The resonance field as a function of angle found at both 34.5 (diamonds) and 93.9 GHz (circles). The lines are fit to the torque equation.
Fig. 2. Spin wave resonances in the perpendicular orientation at 93.9 GHz. The points are the relative positions of the spin wave resonance lines and the line is the fit used to estimate the exchange stiffness.
ARTICLE IN PRESS J.O. Rantschler et al. / Journal of Magnetism and Magnetic Materials 286 (2005) 262–266
Fig. 3. The linewidth as a function of frequency in two orientations. The circles represent in-plane measurements, the diamonds indicate out-of-plane measurements, the solid symbols are from cavity spectrometers, and the open symbols are from the stripline spectrometer. The lines are fits to the LLG equation.
parameter. For BB, the perpendicular orientation has a constant linewidth of 2/gT2, but the in-plane linewidth varies as DH 1=2 ¼
2o 1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ; g2 T 2 2 H ? þ 4 o=g
(9)
where the total perpendicular anisotropy field H? is 4pM s 2K 1 =M s : It is usual to add a positive constant to account for inhomogeneous broadening [12]. Fig. 3 shows the linewidth as a function of frequency. Both the in-plane and out-of-plane changes are linear, meaning that BB is not acceptable as a phenomenological formulation for the Cu/FeCo system. When we fit the LLG, however, we obtain different damping estimates. For the lower curve we find a Gilbert parameter of 0.004(5), and for the upper curve, we find a Gilbert parameter of 0.006. In accordance with Eq. (8), there is 21 Oe worth of broadening in the absorption spectrum. This is in line with the previous results and is probably due to the small grain size [13]. We turn to rotation data to help us interpret the difference in the Gilbert parameter in the two orientations. The linewidth has a minimum out-ofplane for both curves, and we will therefore use
265
Fig. 4. Linewidth as a function of field angle for 34.5 (diamonds) and 93.9 GHz (circles) rotation measurements. The lines are fits to the LLG equation.
this as the baseline for our fits in Fig. 4, which shows linewidth data at both Ka- and W-band. The fits are based upon Eqs. (2,5b) and (7). It is seen from the W-band data that the fit follows the measured linewidth when the applied field is near the film normal, and mirrors it when nearly inplane with a shift occurring very near the point where the magnetization angle is 451. This shift is consistent with a 2-magnon contribution to a causing the difference of slopes in Fig. 3 [14]. To review, although we have seen that the general behavior of the FMR linewidth of the Cu/ FeCo system is incompatible with BB damping and conforms qualitatively to a LL or LLG dissipation formulation, we see that the use of a single damping parameter for the system is impossible. We have also seen that the total perpendicular anisotropy is within 1.2% of that found by magnetometry data, indicating that there is no significant perpendicular anisotropy contribution in the estimate of the magnetization. Finally, we have been able to measure the exchange stiffness of soft FeCo and found it to be 1.75 106 erg/cm.
Acknowledgments This study was funded by Seagate Research, NSIC-NSF 542417-55139 and by the University of Alabama; shared equipment was funded from
ARTICLE IN PRESS 266
J.O. Rantschler et al. / Journal of Magnetism and Magnetic Materials 286 (2005) 262–266
NSF-DMR 0213985 and NSF award #0079498 for the W-band Spectrometer. The authors would like to thank Bob McMichael for helpful discussions. References [1] K.B. Klassen, R.G. Hirko, J.T. Contreras, IEEE Trans. Magn. 34 (1998) 1822. [2] T. Thomson, P.C. Tiedi, C.L. Platt, A.E. Berkowitz, IEEE Trans. Magn. 34 (1998) 1045. [3] N.X. Sun, S.X. Wang, J. Appl. Phys. 92 (2002) 1477. [4] H.S. Jung, W.D. Doyle, J.E. Wittig, J.F. Al-Sharab, J. Bentley, Appl. Phys. Lett. 81 (2002) 2415. [5] H.S. Jung, W.D. Doyle, S. Matsunuma, J. Appl. Phys. 93 (2003) 6462.
[6] [7] [8] [9] [10]
[11] [12] [13] [14]
R. Kikuchi, J. Appl. Phys. 27 (1956) 1352. H.N. Bertram, Appl. Phys. Lett. 79 (2001) 4402. H. Suhl, Phys. Rev. 94 (1955) 555. D.D. Stancil, Theory of Magnetostatic Waves, Springer, New York, 1993. G.V. Skrotskii, L.V. Kurbatov, in: S.V. Vonsovskii (Ed.), Ferromagnetic Resonance, Israel Program for Scientific Translations, Jerusalem, 1964, pp. 9–59. C.P. Poole Jr., Electron Spin Resonance, Wiley, New York, 1983. B. Heinrich, F. Cochran, R. Hasegawa, J. Appl. Phys. 57 (1985) 3690. J.O. Rantschler, C. Alexander Jr., J. Appl. Phys. 93 (2003) 6665. R.D. McMichael, Krivosik, IEEE Trans. Magn. 40 (2004) 2.