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Anisotropic Gilbert damping in epitaxial Fe films on InAs(0 0 1)
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 272–276 (2004) 1203–1204
Anisotropic Gilbert damping in epitaxial Fe films on InAs(0 0 1) R. Meckenstocka, D. Spoddiga,*, Z. Fraitb, V. Kamberskyb, J. Pelzla a
Institut fur . Experimentalphysik III AG, Ruhr-Universitaet-Bochum, Universitaetsstr. 150, D-44780 Bochum, Germany b Institute of Physics, Academy of science, Na Slovance 2, CZ-182 21 Praha 8, Czech Republic
Abstract In this paper, we present frequency dependent ferromagnetic resonance (FMR) measurements on Fe films grown on InAs(0 0 1). The Gilbert damping parameter a was determined from the observed linear dependence of the FMR line width on the microwave frequency. a is reduced by 35% along the intermediate magnetic axis as compared to the hard and easy axes. This effect is attributed to the structural growth of Fe on InAs. r 2003 Elsevier B.V. All rights reserved. PACS: 75.70.Cn; 76.50.+g Keywords: Ferromagnetic resonance; Gilbert damping
In 3d-metal semiconductor heterostructures the interaction of the magnetic film with the semiconductor substrate governs not only the static magnetic properties of the film but also the dynamics of the magnetic moments which are important for the spin injection into the semiconductor. In this context the structural and electronic mismatch of film and substrate play a very important part in the damping of the magnetic moment [1]. The investigation of the angle and frequency dependent ferromagnetic resonance (FMR) line width allows the separation of the intrinsic Gilbert damping and the inhomogeneous line broadening which are due to the degree of structural disorder in the magnetic film. The samples investigated were epitaxial Fe-films grown on InAs(0 0 1) characterized by in situ scanning tunnelling microscopy (STM) and low energy electron diffraction (LEED) [2]. The iron starts to grow island like aligning in small ellipsoids along the 4 2-reconstruction lines [1 1 0] of the InAs substrate. The ellipsoids have there long axis perpendicular to these reconstruction lines.
*Corresponding author. Tel.: +49-234-32-23590; fax: +49234-32-14336. E-mail address: [email protected] (D. Spoddig).
FMR experiments were carried out with six different conventional FMR spectrometers in a frequency range from 9 to 69 GHz. Extensive angle dependent FMR measurements were performed at 9 GHz in a cavity setup. Shortened waveguide setups were used for measurements at higher frequencies in the 8 different in plane orientations described below. Angle dependent FMR measurements were described by free energy density (F ) formalism taking into account the partial derivatives with respect to the crystalline axes [3]. For a thin film F consists of the following major contributions: Zeeman energy, demagnetizing energy, surface anisotropy energy, in plane magnetocrystalline anisotropy energy and uniaxial in plane anisotropy energy. The intrinsic FMR line width is then derived from F by the relation ga q2 F 1 q2 F qB Do ¼ Do; ð1Þ ; DB ¼ þ M qY2 sin2 ðYÞ qF2 qo where Do is the intrinsic frequency line width, g is the gyromagnetic ratio, a is the damping factor, M is the saturation magnetization and DB the intrinsic magnetic field line width. Y and F are the polar and azimuthal angles. In the lowest approximation the intrinsic line width increases linearly with the microwave frequency proportional to the damping factor a [4]. Taking into
0304-8853/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.12.047
ARTICLE IN PRESS 1204
R. Meckenstock et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) 1203–1204
account extrinsic influences like roughness or local inhomogeneities of the different contributions to the free energy a frequency independent contribution DB0 has to be added yielding the relation for the total line width: DB ¼ DB0 þ 2ao=g: The in situ STM and LEED investigations reveal an epitaxial growth of iron on InAs(0 0 1) [2]. Due to the large lattice mismatch of 5.5% one gets laterally strained thin Fe films and relaxed bulk like thick Fe films below and above a critical Fe film thickness of 2.3 nm, proven by angle dependent FMR measurements [5]. The easy axis of the uniaxial anisotropy of the magnetization lies along the [1–1 0], which is also the long axis of the small ellipsoids growing on the InAs and is one of the hard axis of the crystalline anisotropy. Thus, the hard direction of the magnetization in the film plane is [1 1 0]. The frequency dependence of the FMR lines was investigated in the eight distinct in plane configurations representing the hard, intermediate and easy axes of the Fe film. In Fig. 1 DB is plotted versus the frequency for the in plane hard [1 1 0], intermediate [11 0] and easy [1 0 0] axes of the magnetization showing the expected linear behaviour [3]. The inhomogeneous part DB0 exhibits extremely low values (o0.1 mT) for the thin films (here, for example, 1.14 nm) in all orientations except the [1 1 0] orientation (2 mT) (see Fig. 1a). This behaviour is due to the forming of ellipsoid columns along the InAs reconstruction lines [2,5]. For the thick films (see Fig. 1b) increasing misalignments of the crystallites lead to a larger inhomogeneous contribution of DB0 reaching values of 1 and 3 mT for the easy and the intermediate axes, respectively. The most intriguing result, however, is the observed anisotropy of the Gilbert damping parameter a: It is reduced by about 35% for the external field along the same easy axis for both thin and thick films. This behaviour can be explained due to the fact that electrons with their k-vector along the dislocation planes or ellipsoids formed during the Fe growth are less scattered than those with k-vector perpendicular. Generally the thin films show a higher a than the thick ones due to the fact that damping is higher in strained films as in relaxed films. The value of a is 4.1 103 (cgs: G ¼ 1:2 108 s1) for the thin and 2.8 103 (cgs: G ¼ 8:3 107 s1) for the thick films and thus well within the smallest values found in literature for Fe on semiconducting substrates [6,7]. In conclusion, the anisotropy of the Gilbert damping factor of epitaxial Fe layers on the (0 0 1) InAs surface is a consequence of the well-oriented dislocation planes as a result of an elongated island like growth of iron on the 4 2 reconstructed InAs surface. The magnitude of the
Fig. 1. Peak-to-peak line width versus frequency of hard (K), intermediate (’) and easy (J) axis: (a) for the 1.14 nm film and (b) for the 2.3 nm film.
observed effects can only be explained if the scattering of the electrons by the dislocation planes is taken into consideration.
References [1] B. Heinrich, Spin Relaxation in Magnetic Metallic Layers and Multilayers, Ultrathin Magnetic Structures, Vol. III, Springer, Berlin, 2003. [2] M. Kneppe, et al., Appl. Phys. A, doi:10.1007/S00339-0032096-6. [3] S.V. Vonsovskii, Ferromagnetic Resonance, Pergamon Press, Oxford, 1960. [4] B. Heinrich, et al., Adv. Phys. 42 (1993) 523. [5] J. Pelzl, et al., J. Phys.: Condens. Matter 15 (2003) S451. [6] R. Urban, et al., Phys. Rev. B 65 (2001) 020402(R). [7] B. Heinrich, et al., J. Magn. Magn. Mater. 258 (2003) 376.
Journal of Magnetism and Magnetic Materials 272–276 (2004) 1203–1204
Anisotropic Gilbert damping in epitaxial Fe films on InAs(0 0 1) R. Meckenstocka, D. Spoddiga,*, Z. Fraitb, V. Kamberskyb, J. Pelzla a
Institut fur . Experimentalphysik III AG, Ruhr-Universitaet-Bochum, Universitaetsstr. 150, D-44780 Bochum, Germany b Institute of Physics, Academy of science, Na Slovance 2, CZ-182 21 Praha 8, Czech Republic
Abstract In this paper, we present frequency dependent ferromagnetic resonance (FMR) measurements on Fe films grown on InAs(0 0 1). The Gilbert damping parameter a was determined from the observed linear dependence of the FMR line width on the microwave frequency. a is reduced by 35% along the intermediate magnetic axis as compared to the hard and easy axes. This effect is attributed to the structural growth of Fe on InAs. r 2003 Elsevier B.V. All rights reserved. PACS: 75.70.Cn; 76.50.+g Keywords: Ferromagnetic resonance; Gilbert damping
In 3d-metal semiconductor heterostructures the interaction of the magnetic film with the semiconductor substrate governs not only the static magnetic properties of the film but also the dynamics of the magnetic moments which are important for the spin injection into the semiconductor. In this context the structural and electronic mismatch of film and substrate play a very important part in the damping of the magnetic moment [1]. The investigation of the angle and frequency dependent ferromagnetic resonance (FMR) line width allows the separation of the intrinsic Gilbert damping and the inhomogeneous line broadening which are due to the degree of structural disorder in the magnetic film. The samples investigated were epitaxial Fe-films grown on InAs(0 0 1) characterized by in situ scanning tunnelling microscopy (STM) and low energy electron diffraction (LEED) [2]. The iron starts to grow island like aligning in small ellipsoids along the 4 2-reconstruction lines [1 1 0] of the InAs substrate. The ellipsoids have there long axis perpendicular to these reconstruction lines.
*Corresponding author. Tel.: +49-234-32-23590; fax: +49234-32-14336. E-mail address: [email protected] (D. Spoddig).
FMR experiments were carried out with six different conventional FMR spectrometers in a frequency range from 9 to 69 GHz. Extensive angle dependent FMR measurements were performed at 9 GHz in a cavity setup. Shortened waveguide setups were used for measurements at higher frequencies in the 8 different in plane orientations described below. Angle dependent FMR measurements were described by free energy density (F ) formalism taking into account the partial derivatives with respect to the crystalline axes [3]. For a thin film F consists of the following major contributions: Zeeman energy, demagnetizing energy, surface anisotropy energy, in plane magnetocrystalline anisotropy energy and uniaxial in plane anisotropy energy. The intrinsic FMR line width is then derived from F by the relation ga q2 F 1 q2 F qB Do ¼ Do; ð1Þ ; DB ¼ þ M qY2 sin2 ðYÞ qF2 qo where Do is the intrinsic frequency line width, g is the gyromagnetic ratio, a is the damping factor, M is the saturation magnetization and DB the intrinsic magnetic field line width. Y and F are the polar and azimuthal angles. In the lowest approximation the intrinsic line width increases linearly with the microwave frequency proportional to the damping factor a [4]. Taking into
0304-8853/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.12.047
ARTICLE IN PRESS 1204
R. Meckenstock et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) 1203–1204
account extrinsic influences like roughness or local inhomogeneities of the different contributions to the free energy a frequency independent contribution DB0 has to be added yielding the relation for the total line width: DB ¼ DB0 þ 2ao=g: The in situ STM and LEED investigations reveal an epitaxial growth of iron on InAs(0 0 1) [2]. Due to the large lattice mismatch of 5.5% one gets laterally strained thin Fe films and relaxed bulk like thick Fe films below and above a critical Fe film thickness of 2.3 nm, proven by angle dependent FMR measurements [5]. The easy axis of the uniaxial anisotropy of the magnetization lies along the [1–1 0], which is also the long axis of the small ellipsoids growing on the InAs and is one of the hard axis of the crystalline anisotropy. Thus, the hard direction of the magnetization in the film plane is [1 1 0]. The frequency dependence of the FMR lines was investigated in the eight distinct in plane configurations representing the hard, intermediate and easy axes of the Fe film. In Fig. 1 DB is plotted versus the frequency for the in plane hard [1 1 0], intermediate [11 0] and easy [1 0 0] axes of the magnetization showing the expected linear behaviour [3]. The inhomogeneous part DB0 exhibits extremely low values (o0.1 mT) for the thin films (here, for example, 1.14 nm) in all orientations except the [1 1 0] orientation (2 mT) (see Fig. 1a). This behaviour is due to the forming of ellipsoid columns along the InAs reconstruction lines [2,5]. For the thick films (see Fig. 1b) increasing misalignments of the crystallites lead to a larger inhomogeneous contribution of DB0 reaching values of 1 and 3 mT for the easy and the intermediate axes, respectively. The most intriguing result, however, is the observed anisotropy of the Gilbert damping parameter a: It is reduced by about 35% for the external field along the same easy axis for both thin and thick films. This behaviour can be explained due to the fact that electrons with their k-vector along the dislocation planes or ellipsoids formed during the Fe growth are less scattered than those with k-vector perpendicular. Generally the thin films show a higher a than the thick ones due to the fact that damping is higher in strained films as in relaxed films. The value of a is 4.1 103 (cgs: G ¼ 1:2 108 s1) for the thin and 2.8 103 (cgs: G ¼ 8:3 107 s1) for the thick films and thus well within the smallest values found in literature for Fe on semiconducting substrates [6,7]. In conclusion, the anisotropy of the Gilbert damping factor of epitaxial Fe layers on the (0 0 1) InAs surface is a consequence of the well-oriented dislocation planes as a result of an elongated island like growth of iron on the 4 2 reconstructed InAs surface. The magnitude of the
Fig. 1. Peak-to-peak line width versus frequency of hard (K), intermediate (’) and easy (J) axis: (a) for the 1.14 nm film and (b) for the 2.3 nm film.
observed effects can only be explained if the scattering of the electrons by the dislocation planes is taken into consideration.
References [1] B. Heinrich, Spin Relaxation in Magnetic Metallic Layers and Multilayers, Ultrathin Magnetic Structures, Vol. III, Springer, Berlin, 2003. [2] M. Kneppe, et al., Appl. Phys. A, doi:10.1007/S00339-0032096-6. [3] S.V. Vonsovskii, Ferromagnetic Resonance, Pergamon Press, Oxford, 1960. [4] B. Heinrich, et al., Adv. Phys. 42 (1993) 523. [5] J. Pelzl, et al., J. Phys.: Condens. Matter 15 (2003) S451. [6] R. Urban, et al., Phys. Rev. B 65 (2001) 020402(R). [7] B. Heinrich, et al., J. Magn. Magn. Mater. 258 (2003) 376.