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GaAs heterostructure
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Magnetization dynamics and Gilbert damping in a hybrid Fe/GaAs heterostructure Haixiao Gao, Jun Lu, Jianhua Zhao, Xinhui Zhang n State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, P.O. Box 912, Beijing 100083, PR China
art ic l e i nf o
a b s t r a c t
Article history: Received 19 March 2014 Received in revised form 15 April 2014 Accepted 5 May 2014 by M. Grynberg
In this paper, we studied the ultrafast magnetization dynamics and damping process in a hybrid epitaxial Fe/GaAs structure by using time-resolved magneto-optical measurements over various temperatures. The phenomenological Gilbert damping constant depended strongly on both the direction and strength of the applied magnetic field. The damping process was revealed to be dominated by incoherent spinflip scattering, with involvement of the Fe/GaAs interfacial defects mediated two-magnon scattering. The intrinsic damping parameter was extracted at sufficiently high magnetic fields (or magnetization precession frequencies). Our results allow for better understanding of magnetization relaxation of Fe/GaAs heterostructure for its potential application in novel spintronic devices. & 2014 Published by Elsevier Ltd.
Keywords: A. Fe/GaAs B. MBE D. Gilbert damping E. TR-MOKE
1. Introduction The rapid development of spintronics demands new insights into magnetization relaxation on the sub-nanosecond time scale. In recent years, many researchers have theoretically studied the origin of the Gilbert damping in ferromagnetic films. Local and non-local Gilbert damping have been found to be related to the differences in the location of energy dissipation [1]. In local damping the spin energy is transferred to the lattice via spin– orbit coupling (SOC) and magnon scattering within the ferromagnetic layer [2]. In contrast, in non-local damping the spin energy dissipates through the interface into the normal metal via spin current or spin waves at the interface between the ferromagnetic layer and non-magnetic layer [3]. The magnetization precession can be triggered by a magnetic field pulse, femtosecond laser pulse, or spin-polarized currents [4–7]. The real-space trajectory of the magnetization precession can be well described by the Landau–Lifshitz–Gilbert equation, which contains a Gilbert damping term that describes the dissipation of magnetic energy [8]. The Gilbert damping parameter is one key factor in spin-transfertorque systems [9]. Studies have shown that damping can also originate from electronic transitions induced by spin–orbit interaction, similar to Elliot–Yafet spin relaxation in metals and semiconductors [4], and can be described simply by α p ξ2D(εF),
n
Corresponding author. Tel.: þ 86 10 82304486. E-mail addresses: [email protected] (H. Gao), [email protected] (J. Lu), [email protected] (J. Zhao), [email protected] (X. Zhang).
where ξ is the spin–orbit interaction energy and D(εr) is the density of states at the Fermi surface [10]. Hybrid structures of semiconductor and ferromagnetic films are important for next-generation spintronic devices. Epitaxial Fe/GaAs (001), a widely adopted spin injection and tunneling magnetoresistive-junction heterostructure, has received great attention in the past decade [11–14] for its promise in spintronic devices. However, little is known about the magnetization dynamics and related damping in this heterojunction, especially at low temperatures. Understanding these properties is important for improving the spin injection efficiency and magnetoresistivity ratio. In this paper, we studied the magnetization dynamics in a Fe/GaAs heterojunction by using the time-resolved magneto-optic Kerr effect (TR-MOKE). We found that the phenomenological Gilbert damping constant depended strongly on the direction and strength of the applied magnetic field, suggesting the involvement of extrinsic magnetic damping mechanisms in addition to Gilbert-type damping. We found that the magnetizationrelaxation time-independent Gilbert damping constant is isotropic. And the intrinsic damping parameter was extracted at high magnetic fields
2. Experimental An epitaxial Fe film was prepared on a GaAs (001) wafer using ultrahigh vacuum molecular beam epitaxy (UHV-MBE). First, a 100 nm n -doped GaAs layer with a free carrier density of 6 1017 cm 3 was grown on a GaAs buffer layer. Then, a 15 nm
http://dx.doi.org/10.1016/j.ssc.2014.05.003 0038-1098/& 2014 Published by Elsevier Ltd.
Please cite this article as: H. Gao, et al., Solid State Commun (2014), http://dx.doi.org/10.1016/j.ssc.2014.05.003i
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high-density n þ -GaAs layer with a free carrier density of 7 1018 cm 3 was grown on the n -GaAs layer to form a Schottky junction. Finally, a 10 nm Fe film was grown on the n þ -GaAs layer. Growth was performed at room temperature in UHV. The doping level of GaAs was determined by the Hall measurement for a few pieces of GaAs test samples before the final sample was prepared under the identical growth condition. This Fe/GaAs interface forms a Schottky contact with a narrow depletion width of o20 nm. To stimulate magnetization precession of the thin Fe film in our TRMOKE experiment, we used a Ti:sapphire laser pulse with a pulse duration of 150 fs and repetition rate of 80 MHz. The pump beam was focused onto the sample at nearly normal incidence, with a focus diameter of 100 μm and a power density of I 2 mJ/cm2. A much weaker probe beam was incident on the sample at 241, and the reflected probe beam was detected by a balanced photodetector after passing the beam through a Wollaston prism. As previously reported [15], the magnetization precession response gets a lot smaller when tuning the excitation wavelength of laser above the GaAs band gap, therefore the excitation wavelength of both the linearly polarized pump and probe beams was centered at 800 nm to ensure the maximum magnetization precession response.
3. Results and discussions Fig. 1 shows the typical ultrafast magnetization evolution of the Fe film under optical excitation with external magnetic fields of 10–1000 Oe, applied along [100] and [110] crystallographic directions. Note that the optical pumping power density, as low as 2 mJ/cm2 in this work, adequately stimulated magnetization precession. This power density is much lower than that required for optically excited demagnetization and magnetization precession in normal ferromagnetic thin films, which often require power densities of 1–10 mJ/cm2 [2,3,16–18]. Previous reports have suggested that magnetization precession triggered by ultra-low power densities can be caused by an effective planar magnetic field induced by the transient photo-induced current through the Schottky heterojunction upon ultrafast laser excitation [15,19]. The
resulting magnetic field H induced by the pumped electron–hole pairs at the ferromagnetic film/semiconductor interface generates ! ! a torque with a magnitude of jM H j on the magnetization M, producing nonlocal magnetization precession at the interface. The damped oscillation response observed in our TR-MOKE data fit very well to the following equation:
θk ¼ a þ b expð t=t 0 Þ þ A expð t=τÞ sin ðωt þ φÞ
ð1Þ
where A, τ, ω, and φ are the amplitude of the oscillation, the magnetization relaxation time, the oscillation frequency, and the phase of the magnetization precession, respectively. a, b, and t0 are related to the background signal in the slow-recovery process. This slow-recovery process was suggested to result from the thermal relaxation of lattice (phonon contribution) upon laser heating [20]. The oscillating signal of the TR-MOKE response corresponds to the uniform magnetization precession, with an oscillating period (or magnetization precession frequency) dependent on both the strength and direction of the external field. When the external magnetic field was applied along the [110] crystallographic direction, the period of the oscillations increased from 113 to 126 ps at smaller external magnetic fields and then decreased from 126 to 75 ps at larger external magnetic fields. In contrast, when the magnetic field was applied along the [100] direction, both the period and amplitude of the magnetization precession changed monotonically with the external magnetic field. Fig. 2(a) and (b) shows the extracted magnetization precession frequency and relaxation time, respectively, obtained by fitting the TR-MOKE data measured with the in-plane field applied along [100], [110], and [11̄0] directions. Previous studies on 10-nm-thick Fe epitaxially grown on GaAs have shown the presence of two intermediate magnetic (hard-axis) anisotropy directions, along the [110] and [11̄0] [14,21,22]. Fig. 2(a) demonstrates those same magnetic anisotropic properties, in which the field-dependent precession frequency fits well to the Kittel equation for the uniform spin-precession mode [23], with the minimum precession frequency appearing in our Fe films at a static anisotropy field of 400 to 450 Oe [15]. The field-dependent magnetization-relaxation time in Fig. 2(b) clearly shows that it is anisotropic along different crystallographic directions, again with the minimum
Fig. 1. (Color online) Typical time-resolved Kerr response of the Fe/GaAs hybrid structure, with the external magnetic field applied along the [100] and [110] crystallographic directions.
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Fig. 2. (Color online) (a) Extracted magnetization-precession frequency and (b) extracted magnetization-relaxation time of the Fe/GaAs hybrid structure as functions of the external magnetic field, with the field applied along the [100] (black points), [110] (red points), and [11̄0] (blue points) crystallographic directions.
Fig. 3. (Color online) (a,b) TR-MOKE response (points) of the Fe/GaAs hybrid structure, measured with an applied external magnetic field of 400 Oe along the [100] and [110] crystallographic directions, respectively; the lines are fits to Eq. (1). (c,d) Dependence of the extracted phenomenological Gilbert damping parameter on the external magnetic field and magnetization-relaxation time, for fields applied along the [100] (black points) and [110] (red points) crystallographic directions.
relaxation time appearing near the static anisotropy field. The strong dependence of the relaxation time on both the strength and direction of the applied field was likely caused by the inhomogeneous excitation nature of the magnetization created by the transient photocurrent along the Schottky diode [15,19,24]. To explore the energy dissipation, and thus how fast the magnetization will align itself with the equilibrium orientation through both intrinsic and extrinsic damping processes, we
extracted the apparent magnetic damping parameter α from the fitting parameters of TR-MOKE results by using the relation τ ¼1/ωα, where τ is the characteristic exponential decay time (the magnetization relaxation time) and ω is the magnetic-precession frequency [25]. Fig. 3(a) and (b) show the raw TR-MOKE data, with the external magnetic field of 400 Oe applied along the [100] and [110] crystallographic directions, respectively. The red lines show the best fits to Eq. (1). Fig. 3(c) shows the external-field-dependent
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magnetic damping factors along the [1 0 0] and [1 1 0] directions. The damping factor was not constant and exhibited strong anisotropy with field direction at relatively small fields. For both directions, as the magnetic field increased, the Gilbert damping factor gradually became a constant value of 0.03. However, when we normalized the damping factor to the magnetization relaxation time, this anisotropic dependence on field direction disappeared, as shown in Fig. 3(d). This behavior implies that the apparent anisotropy of the damping factor in the present system can be ascribed to the field-dependent magnetization relaxation time. We found that the magnetization-relaxation-time–independent Gilbert damping constant α is isotropic with respect to the field direction and could be accurately determined from the TRMOKE data at a magnetization relaxation time τ near 250 ps. To further investigate the different damping mechanisms in our Fe/GaAs heterostructure, we studied the temperature dependent damping process; a summary of these results is shown in Fig. 4(a). As the temperature increased from 10 to 80 K, the apparent Gilbert damping constant increased from 0.07 to 0.12, with the external field applied along the [11̄0] direction at an excitation power density of 2 mJ/cm2. The apparent Gilbert damping constant of 0.12 at 80 K was almost equal to that measured at room temperature under the same experimental conditions (with an excitation wavelength of 800 nm and a pumping power density of 2 mJ/cm2). Bhagat et al. [26] reported that the ferromagnetic relaxation parameter λ of pure Fe remained constant over 4 K oT o300 K. In our hybrid Fe/GaAs junction, the nonlocal magnetization precession triggered by the transient photocurrent demonstrates a different low-temperature magnetic damping behavior from that reported by Bhagat et al. For pure Fe over 300 K, reports have shown a slow and monotonic increase of magnetic damping with temperature [27], which agrees with the model by Heinrich et al. that the damping is caused by incoherent spin-flip scattering of electron–hole pair excitation by phonons and magnons [28]. In this model, the intrinsic damping is dominated by the spin-flip exchange interaction between the itinerant s electrons and the localized d orbital moments, and it is expected that the magnetic damping will increase with temperature (known as resistivity-like
behavior), transferring the spin angular momentum to the lattice via spin–orbit coupling in ferromagnetic metals [29,30]. However, the magnetic damping caused by interactions that conserve electron spin, as described by the breathing Fermi surface model [31–33], is consistent with the increased damping in Ni at lower temperatures, known as conductivity-like magnetic damping [34]. The torque-correlation model developed by Kamberský [35] qualitatively explained the unified non-monotonic temperature dependence of the magnetic-damping behavior. This theory has been developed further by Gilmore [36] and Liu [37], who used first-principle calculations to give more quantitative descriptions of the damping mechanisms. Reports have shown that the resistivity of Fe/GaAs heterostructures increase with temperature and with applied magnetic field at room temperature [38–40]. The general increase of the apparent damping parameter with temperature in our Fe/GaAs heterostructure implies that the magnetic damping process is dominated by incoherent spin-flip scattering (resistivity-like behavior) and that the role of the conductivity-like mechanism is negligible [36,37]. To further clarify this resistivitylike behavior, we examined the photo-excited thermal electron relaxation time by measuring the time-resolved reflectivity measurement simultaneously with TR-MOKE measurements, with a beamsplitter placed before the photodetector. The electron relaxation time was extracted by fitting the time-resolved reflectivity data with an exponential decay function. And the extracted electron relaxation times were displayed by the blue circles in Fig. 4(a). When the temperature increased from 10 to 50 K, the relaxation time of the hot electrons rapidly decreased from 130 to 25 ps, and then became almost constant above 50 K. In contrast, up to 50 K the apparent damping parameter only moderately increased, and then rapidly increased above 50 K. Though these results roughly show that the magnetic damping was inversely proportional to the electronic relaxation time, as predicted by incoherent spin-flip scattering, the different temperature dependence of the damping and electron relaxation time at low temperatures implies that other damping mechanisms are involved along with spin-flip scattering, either at the Fe/GaAs interface or in the GaAs barrier resulting from diffusion of Fe into
Fig. 4. (Color online) (a) Effective damping factors and electron-relaxation times as functions of temperature; (b) Effective damping factors as a function of the magnetization-precession frequency for fields applied along the [100] (black points) and the [110] (red points) crystallographic directions.
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the barrier. The Fe/GaAs interface defects mediated two-magnon scattering has been suggested to contribute to the damping behavior at low magnetic field regime observed in the present work [24,41]. As shown in Fig. 4(b), the apparent damping parameter depended strongly on the precession frequency, independently of the direction of the applied field. The drastic increase in damping parameter at smaller precession frequencies further implies the importance of two-magnon scattering, which becomes more dominant at small magnetic fields, where most spin wave modes are degenerate [24]. When the external field is increased to sufficiently increase the precession frequency, the magnon degeneracy is removed and fewer degenerate magnons will be excited [24], leading to much weaker two-magnon scattering and decrease of the apparent damping parameter, which remained almost constant above a precession frequency of 14 GHz. 4. Conclusions We studied the ultrafast magnetization dynamics and damping in a hybrid epitaxial Fe/GaAs structure by using time-resolved magneto-optical measurements at various temperatures. The phenomenological Gilbert damping constant depended strongly on both the direction and strength of the applied magnetic field, but the magnetization-relaxation time-independent Gilbert damping constant was isotropic. The damping process was dominated by incoherent spin-flip scattering, with the contribution from Fe/ GaAs interface defects mediated two-magnon scattering involved. The intrinsic damping parameter was extracted at sufficiently high magnetic fields (or magnetization precession frequencies). Our results are important for better understanding the magnetization relaxation in ferromagnetic heterostructures. We hope this work will stimulate more experimental and theoretical studies on temperature-dependent magnetization damping to realize novel spintronic devices based on ferromagnetic films. Acknowledgment This work was supported by the National Basic Research Program of China (Nos. 2011CB922200 and 2013CB922303). References [1] M.D. Kaufmann, Magnetization Dynamics in All-optical Pump–Probe Experiments: Spin–Wave modes and Spin–Current Damping (Ph.D. thesis), Georg August Universität Gö ttingen, 2006. [2] J. Walowski, M.D. Kaufmann, B. Lenk, C. Hamann, J. McCord, M. Münzenberg, J. Phys. D 41 (2008) 164016.
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Contents lists available at ScienceDirect
Solid State Communications journal homepage: www.elsevier.com/locate/ssc
Magnetization dynamics and Gilbert damping in a hybrid Fe/GaAs heterostructure Haixiao Gao, Jun Lu, Jianhua Zhao, Xinhui Zhang n State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, P.O. Box 912, Beijing 100083, PR China
art ic l e i nf o
a b s t r a c t
Article history: Received 19 March 2014 Received in revised form 15 April 2014 Accepted 5 May 2014 by M. Grynberg
In this paper, we studied the ultrafast magnetization dynamics and damping process in a hybrid epitaxial Fe/GaAs structure by using time-resolved magneto-optical measurements over various temperatures. The phenomenological Gilbert damping constant depended strongly on both the direction and strength of the applied magnetic field. The damping process was revealed to be dominated by incoherent spinflip scattering, with involvement of the Fe/GaAs interfacial defects mediated two-magnon scattering. The intrinsic damping parameter was extracted at sufficiently high magnetic fields (or magnetization precession frequencies). Our results allow for better understanding of magnetization relaxation of Fe/GaAs heterostructure for its potential application in novel spintronic devices. & 2014 Published by Elsevier Ltd.
Keywords: A. Fe/GaAs B. MBE D. Gilbert damping E. TR-MOKE
1. Introduction The rapid development of spintronics demands new insights into magnetization relaxation on the sub-nanosecond time scale. In recent years, many researchers have theoretically studied the origin of the Gilbert damping in ferromagnetic films. Local and non-local Gilbert damping have been found to be related to the differences in the location of energy dissipation [1]. In local damping the spin energy is transferred to the lattice via spin– orbit coupling (SOC) and magnon scattering within the ferromagnetic layer [2]. In contrast, in non-local damping the spin energy dissipates through the interface into the normal metal via spin current or spin waves at the interface between the ferromagnetic layer and non-magnetic layer [3]. The magnetization precession can be triggered by a magnetic field pulse, femtosecond laser pulse, or spin-polarized currents [4–7]. The real-space trajectory of the magnetization precession can be well described by the Landau–Lifshitz–Gilbert equation, which contains a Gilbert damping term that describes the dissipation of magnetic energy [8]. The Gilbert damping parameter is one key factor in spin-transfertorque systems [9]. Studies have shown that damping can also originate from electronic transitions induced by spin–orbit interaction, similar to Elliot–Yafet spin relaxation in metals and semiconductors [4], and can be described simply by α p ξ2D(εF),
n
Corresponding author. Tel.: þ 86 10 82304486. E-mail addresses: [email protected] (H. Gao), [email protected] (J. Lu), [email protected] (J. Zhao), [email protected] (X. Zhang).
where ξ is the spin–orbit interaction energy and D(εr) is the density of states at the Fermi surface [10]. Hybrid structures of semiconductor and ferromagnetic films are important for next-generation spintronic devices. Epitaxial Fe/GaAs (001), a widely adopted spin injection and tunneling magnetoresistive-junction heterostructure, has received great attention in the past decade [11–14] for its promise in spintronic devices. However, little is known about the magnetization dynamics and related damping in this heterojunction, especially at low temperatures. Understanding these properties is important for improving the spin injection efficiency and magnetoresistivity ratio. In this paper, we studied the magnetization dynamics in a Fe/GaAs heterojunction by using the time-resolved magneto-optic Kerr effect (TR-MOKE). We found that the phenomenological Gilbert damping constant depended strongly on the direction and strength of the applied magnetic field, suggesting the involvement of extrinsic magnetic damping mechanisms in addition to Gilbert-type damping. We found that the magnetizationrelaxation time-independent Gilbert damping constant is isotropic. And the intrinsic damping parameter was extracted at high magnetic fields
2. Experimental An epitaxial Fe film was prepared on a GaAs (001) wafer using ultrahigh vacuum molecular beam epitaxy (UHV-MBE). First, a 100 nm n -doped GaAs layer with a free carrier density of 6 1017 cm 3 was grown on a GaAs buffer layer. Then, a 15 nm
http://dx.doi.org/10.1016/j.ssc.2014.05.003 0038-1098/& 2014 Published by Elsevier Ltd.
Please cite this article as: H. Gao, et al., Solid State Commun (2014), http://dx.doi.org/10.1016/j.ssc.2014.05.003i
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high-density n þ -GaAs layer with a free carrier density of 7 1018 cm 3 was grown on the n -GaAs layer to form a Schottky junction. Finally, a 10 nm Fe film was grown on the n þ -GaAs layer. Growth was performed at room temperature in UHV. The doping level of GaAs was determined by the Hall measurement for a few pieces of GaAs test samples before the final sample was prepared under the identical growth condition. This Fe/GaAs interface forms a Schottky contact with a narrow depletion width of o20 nm. To stimulate magnetization precession of the thin Fe film in our TRMOKE experiment, we used a Ti:sapphire laser pulse with a pulse duration of 150 fs and repetition rate of 80 MHz. The pump beam was focused onto the sample at nearly normal incidence, with a focus diameter of 100 μm and a power density of I 2 mJ/cm2. A much weaker probe beam was incident on the sample at 241, and the reflected probe beam was detected by a balanced photodetector after passing the beam through a Wollaston prism. As previously reported [15], the magnetization precession response gets a lot smaller when tuning the excitation wavelength of laser above the GaAs band gap, therefore the excitation wavelength of both the linearly polarized pump and probe beams was centered at 800 nm to ensure the maximum magnetization precession response.
3. Results and discussions Fig. 1 shows the typical ultrafast magnetization evolution of the Fe film under optical excitation with external magnetic fields of 10–1000 Oe, applied along [100] and [110] crystallographic directions. Note that the optical pumping power density, as low as 2 mJ/cm2 in this work, adequately stimulated magnetization precession. This power density is much lower than that required for optically excited demagnetization and magnetization precession in normal ferromagnetic thin films, which often require power densities of 1–10 mJ/cm2 [2,3,16–18]. Previous reports have suggested that magnetization precession triggered by ultra-low power densities can be caused by an effective planar magnetic field induced by the transient photo-induced current through the Schottky heterojunction upon ultrafast laser excitation [15,19]. The
resulting magnetic field H induced by the pumped electron–hole pairs at the ferromagnetic film/semiconductor interface generates ! ! a torque with a magnitude of jM H j on the magnetization M, producing nonlocal magnetization precession at the interface. The damped oscillation response observed in our TR-MOKE data fit very well to the following equation:
θk ¼ a þ b expð t=t 0 Þ þ A expð t=τÞ sin ðωt þ φÞ
ð1Þ
where A, τ, ω, and φ are the amplitude of the oscillation, the magnetization relaxation time, the oscillation frequency, and the phase of the magnetization precession, respectively. a, b, and t0 are related to the background signal in the slow-recovery process. This slow-recovery process was suggested to result from the thermal relaxation of lattice (phonon contribution) upon laser heating [20]. The oscillating signal of the TR-MOKE response corresponds to the uniform magnetization precession, with an oscillating period (or magnetization precession frequency) dependent on both the strength and direction of the external field. When the external magnetic field was applied along the [110] crystallographic direction, the period of the oscillations increased from 113 to 126 ps at smaller external magnetic fields and then decreased from 126 to 75 ps at larger external magnetic fields. In contrast, when the magnetic field was applied along the [100] direction, both the period and amplitude of the magnetization precession changed monotonically with the external magnetic field. Fig. 2(a) and (b) shows the extracted magnetization precession frequency and relaxation time, respectively, obtained by fitting the TR-MOKE data measured with the in-plane field applied along [100], [110], and [11̄0] directions. Previous studies on 10-nm-thick Fe epitaxially grown on GaAs have shown the presence of two intermediate magnetic (hard-axis) anisotropy directions, along the [110] and [11̄0] [14,21,22]. Fig. 2(a) demonstrates those same magnetic anisotropic properties, in which the field-dependent precession frequency fits well to the Kittel equation for the uniform spin-precession mode [23], with the minimum precession frequency appearing in our Fe films at a static anisotropy field of 400 to 450 Oe [15]. The field-dependent magnetization-relaxation time in Fig. 2(b) clearly shows that it is anisotropic along different crystallographic directions, again with the minimum
Fig. 1. (Color online) Typical time-resolved Kerr response of the Fe/GaAs hybrid structure, with the external magnetic field applied along the [100] and [110] crystallographic directions.
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Fig. 2. (Color online) (a) Extracted magnetization-precession frequency and (b) extracted magnetization-relaxation time of the Fe/GaAs hybrid structure as functions of the external magnetic field, with the field applied along the [100] (black points), [110] (red points), and [11̄0] (blue points) crystallographic directions.
Fig. 3. (Color online) (a,b) TR-MOKE response (points) of the Fe/GaAs hybrid structure, measured with an applied external magnetic field of 400 Oe along the [100] and [110] crystallographic directions, respectively; the lines are fits to Eq. (1). (c,d) Dependence of the extracted phenomenological Gilbert damping parameter on the external magnetic field and magnetization-relaxation time, for fields applied along the [100] (black points) and [110] (red points) crystallographic directions.
relaxation time appearing near the static anisotropy field. The strong dependence of the relaxation time on both the strength and direction of the applied field was likely caused by the inhomogeneous excitation nature of the magnetization created by the transient photocurrent along the Schottky diode [15,19,24]. To explore the energy dissipation, and thus how fast the magnetization will align itself with the equilibrium orientation through both intrinsic and extrinsic damping processes, we
extracted the apparent magnetic damping parameter α from the fitting parameters of TR-MOKE results by using the relation τ ¼1/ωα, where τ is the characteristic exponential decay time (the magnetization relaxation time) and ω is the magnetic-precession frequency [25]. Fig. 3(a) and (b) show the raw TR-MOKE data, with the external magnetic field of 400 Oe applied along the [100] and [110] crystallographic directions, respectively. The red lines show the best fits to Eq. (1). Fig. 3(c) shows the external-field-dependent
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magnetic damping factors along the [1 0 0] and [1 1 0] directions. The damping factor was not constant and exhibited strong anisotropy with field direction at relatively small fields. For both directions, as the magnetic field increased, the Gilbert damping factor gradually became a constant value of 0.03. However, when we normalized the damping factor to the magnetization relaxation time, this anisotropic dependence on field direction disappeared, as shown in Fig. 3(d). This behavior implies that the apparent anisotropy of the damping factor in the present system can be ascribed to the field-dependent magnetization relaxation time. We found that the magnetization-relaxation-time–independent Gilbert damping constant α is isotropic with respect to the field direction and could be accurately determined from the TRMOKE data at a magnetization relaxation time τ near 250 ps. To further investigate the different damping mechanisms in our Fe/GaAs heterostructure, we studied the temperature dependent damping process; a summary of these results is shown in Fig. 4(a). As the temperature increased from 10 to 80 K, the apparent Gilbert damping constant increased from 0.07 to 0.12, with the external field applied along the [11̄0] direction at an excitation power density of 2 mJ/cm2. The apparent Gilbert damping constant of 0.12 at 80 K was almost equal to that measured at room temperature under the same experimental conditions (with an excitation wavelength of 800 nm and a pumping power density of 2 mJ/cm2). Bhagat et al. [26] reported that the ferromagnetic relaxation parameter λ of pure Fe remained constant over 4 K oT o300 K. In our hybrid Fe/GaAs junction, the nonlocal magnetization precession triggered by the transient photocurrent demonstrates a different low-temperature magnetic damping behavior from that reported by Bhagat et al. For pure Fe over 300 K, reports have shown a slow and monotonic increase of magnetic damping with temperature [27], which agrees with the model by Heinrich et al. that the damping is caused by incoherent spin-flip scattering of electron–hole pair excitation by phonons and magnons [28]. In this model, the intrinsic damping is dominated by the spin-flip exchange interaction between the itinerant s electrons and the localized d orbital moments, and it is expected that the magnetic damping will increase with temperature (known as resistivity-like
behavior), transferring the spin angular momentum to the lattice via spin–orbit coupling in ferromagnetic metals [29,30]. However, the magnetic damping caused by interactions that conserve electron spin, as described by the breathing Fermi surface model [31–33], is consistent with the increased damping in Ni at lower temperatures, known as conductivity-like magnetic damping [34]. The torque-correlation model developed by Kamberský [35] qualitatively explained the unified non-monotonic temperature dependence of the magnetic-damping behavior. This theory has been developed further by Gilmore [36] and Liu [37], who used first-principle calculations to give more quantitative descriptions of the damping mechanisms. Reports have shown that the resistivity of Fe/GaAs heterostructures increase with temperature and with applied magnetic field at room temperature [38–40]. The general increase of the apparent damping parameter with temperature in our Fe/GaAs heterostructure implies that the magnetic damping process is dominated by incoherent spin-flip scattering (resistivity-like behavior) and that the role of the conductivity-like mechanism is negligible [36,37]. To further clarify this resistivitylike behavior, we examined the photo-excited thermal electron relaxation time by measuring the time-resolved reflectivity measurement simultaneously with TR-MOKE measurements, with a beamsplitter placed before the photodetector. The electron relaxation time was extracted by fitting the time-resolved reflectivity data with an exponential decay function. And the extracted electron relaxation times were displayed by the blue circles in Fig. 4(a). When the temperature increased from 10 to 50 K, the relaxation time of the hot electrons rapidly decreased from 130 to 25 ps, and then became almost constant above 50 K. In contrast, up to 50 K the apparent damping parameter only moderately increased, and then rapidly increased above 50 K. Though these results roughly show that the magnetic damping was inversely proportional to the electronic relaxation time, as predicted by incoherent spin-flip scattering, the different temperature dependence of the damping and electron relaxation time at low temperatures implies that other damping mechanisms are involved along with spin-flip scattering, either at the Fe/GaAs interface or in the GaAs barrier resulting from diffusion of Fe into
Fig. 4. (Color online) (a) Effective damping factors and electron-relaxation times as functions of temperature; (b) Effective damping factors as a function of the magnetization-precession frequency for fields applied along the [100] (black points) and the [110] (red points) crystallographic directions.
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the barrier. The Fe/GaAs interface defects mediated two-magnon scattering has been suggested to contribute to the damping behavior at low magnetic field regime observed in the present work [24,41]. As shown in Fig. 4(b), the apparent damping parameter depended strongly on the precession frequency, independently of the direction of the applied field. The drastic increase in damping parameter at smaller precession frequencies further implies the importance of two-magnon scattering, which becomes more dominant at small magnetic fields, where most spin wave modes are degenerate [24]. When the external field is increased to sufficiently increase the precession frequency, the magnon degeneracy is removed and fewer degenerate magnons will be excited [24], leading to much weaker two-magnon scattering and decrease of the apparent damping parameter, which remained almost constant above a precession frequency of 14 GHz. 4. Conclusions We studied the ultrafast magnetization dynamics and damping in a hybrid epitaxial Fe/GaAs structure by using time-resolved magneto-optical measurements at various temperatures. The phenomenological Gilbert damping constant depended strongly on both the direction and strength of the applied magnetic field, but the magnetization-relaxation time-independent Gilbert damping constant was isotropic. The damping process was dominated by incoherent spin-flip scattering, with the contribution from Fe/ GaAs interface defects mediated two-magnon scattering involved. The intrinsic damping parameter was extracted at sufficiently high magnetic fields (or magnetization precession frequencies). Our results are important for better understanding the magnetization relaxation in ferromagnetic heterostructures. We hope this work will stimulate more experimental and theoretical studies on temperature-dependent magnetization damping to realize novel spintronic devices based on ferromagnetic films. Acknowledgment This work was supported by the National Basic Research Program of China (Nos. 2011CB922200 and 2013CB922303). References [1] M.D. Kaufmann, Magnetization Dynamics in All-optical Pump–Probe Experiments: Spin–Wave modes and Spin–Current Damping (Ph.D. thesis), Georg August Universität Gö ttingen, 2006. [2] J. Walowski, M.D. Kaufmann, B. Lenk, C. Hamann, J. McCord, M. Münzenberg, J. Phys. D 41 (2008) 164016.
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