Frequency dependence of spin pumping in Pt/Y3Fe 5O12 film

Kazuya Harii; Toshu An; Yosuke Kajiwara; Kazuya Ando; Hiroyasu Nakayama; Tatsuro Yoshino; Eiji Saitoh

doi:10.1063/1.3594661

Frequency dependence of spin pumping in Pt/Y₃Fe ₅O₁₂ film

Kazuya Harii, Toshu An, Yosuke Kajiwara, Kazuya Ando, Hiroyasu Nakayama, Tatsuro Yoshino, Eiji Saitoh

Advanced Institute for Materials Research (AIMR)

Research output: Contribution to journal › Article › peer-review

36 Citations (Scopus)

Abstract

The frequency dependence of magnetization precession in spin pumping has been investigated using the inverse spin-Hall effect in a Pt/ Y 3 Fe 5 O 12 bilayer film. We found that the magnitude of a spin current generated by the spin pumping depends weakly on the applied microwave frequency. This weak dependence, which is attributed to the compensation between the frequency change in the spin-pumping cycle and the dynamic magnetic susceptibility, is favorable for making a spin-current-driven microwave demodulator. This behavior is consistent with a model calculation based on the Landau-Lifshitz-Gilbert equation combined with the spin mixing.

Original language	English
Article number	116105
Journal	Journal of Applied Physics
Volume	109
Issue number	11
DOIs	https://doi.org/10.1063/1.3594661
Publication status	Published - 2011 Jun 1

ASJC Scopus subject areas

Physics and Astronomy(all)

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@article{3a5ef88cdba040669686706ddf8382bc,

title = "Frequency dependence of spin pumping in Pt/Y3Fe 5O12 film",

abstract = "The frequency dependence of magnetization precession in spin pumping has been investigated using the inverse spin-Hall effect in a Pt/ Y 3 Fe 5 O 12 bilayer film. We found that the magnitude of a spin current generated by the spin pumping depends weakly on the applied microwave frequency. This weak dependence, which is attributed to the compensation between the frequency change in the spin-pumping cycle and the dynamic magnetic susceptibility, is favorable for making a spin-current-driven microwave demodulator. This behavior is consistent with a model calculation based on the Landau-Lifshitz-Gilbert equation combined with the spin mixing.",

author = "Kazuya Harii and Toshu An and Yosuke Kajiwara and Kazuya Ando and Hiroyasu Nakayama and Tatsuro Yoshino and Eiji Saitoh",

note = "Funding Information: 3 Fe 5 O 12 film Harii Kazuya 1,2,3 a) An Toshu 2,3 Kajiwara Yosuke 2 Ando Kazuya 2,3 Nakayama Hiroyasu 2,3 Yoshino Tatsuro 2 Saitoh Eiji 2,3,4,5 1 Department of Applied Physics and Physico-Informatics, Keio University , Yokohama 223-8522, Japan 2 Institute for Materials Research, Tohoku University , Sendai 980-8577, Japan 3 CREST, Japan Science and Technology Agency , Sanbancho, Tokyo 102-0075, Japan 4 The Advanced Science Research Center, Japan Atomic Energy Agency , Tokai, Ibaraki 319-1195, Japan 5 PRESTO, Japan Science and Technology Agency , Sanbancho, Tokyo 102-0075, Japan a) Author to whom correspondence should be addressed. Electronic mail: kharii@imr.tohoku.ac.jp . 01 06 2011 109 11 116105 02 10 2010 11 04 2011 15 06 2011 2011-06-15T09:12:15 2011 American Institute of Physics 0021-8979/2011/109(11)/116105/3/ $30.00 The frequency dependence of magnetization precession in spin pumping has been investigated using the inverse spin-Hall effect in a Pt/ Y 3 Fe 5 O 12 bilayer film. We found that the magnitude of a spin current generated by the spin pumping depends weakly on the applied microwave frequency. This weak dependence, which is attributed to the compensation between the frequency change in the spin-pumping cycle and the dynamic magnetic susceptibility, is favorable for making a spin-current-driven microwave demodulator. This behavior is consistent with a model calculation based on the Landau-Lifshitz-Gilbert equation combined with the spin mixing. Spin pumping, the generation of spin currents from a magnetization precession excited by a microwave, has attracted much attention recently. 1–15 In a ferromagnetic/paramagnetic film, the spin pumping driven by a magnetization precession injects a spin current into the paramagnetic layer. This injected spin current is converted into a dc electric voltage using the inverse spin-Hall effect (ISHE) in the paramagnetic layer. This effect can be used as amplitude demodulation in an amplitude-modulation signal transmission using microwave demodulation, because the spin pumping generates a rectified electric voltage that is proportional to the microwave amplitude, 5 only when a microwave frequency fulfills the ferromagnetic resonance condition. Here, in this amplitude demodulation method, the frequency tuning is achieved by controlling the strength of an external magnetic field. The spin pumping originates from dynamical coupling between magnetization and conduction-electron spins, and thus higher-frequency operation is basically favorable. Because a spin current is emitted to an attached paramagnetic metal in each cycle of the magnetization precession, the spin current generated by the spin pumping is expected to be proportional to the precession frequency f FMR : j s ∝ f FMR . 1 Here we show that, in an operation of the spin pumping in a magnetic film, the generated spin current varies rather moderately with f FMR . Figures 1(a) and 1(b) show a schematic illustration of the sample used in this study. The sample is a paramagnetic Pt/ferrimagnetic insulator Y 3 Fe 5 O 12 (111) (YIG) bilayer film comprising a 10-nm-thick Pt layer and a 2.4- μ m -thick single-crystal YIG layer. The surface of the YIG layer is of a 1.3 mm × 3.5 mm rectangular shape. The YIG film was grown on a Gd 3 Ga 5 O 12 (111) single-crystal substrate via liquid phase epitaxy. The Pt layer was fabricated on the YIG layer via ion-beam sputtering. Two electrodes are attached to the ends of the Pt layer. The sample system is placed on a microstrip-microwave guide. During the measurement, a 20-mW-excitation microwave with a frequency f generated by a vector-network analyzer was introduced to the microstrip waveguide, and an external magnetic field H along the film plane was applied perpendicular to the direction across the electrodes (see Fig. 1(b) ). The magnetization precession excited by the applied microwave injects a dc pure spin current with a spin polarization σ parallel to the magnetization-precession axis into the paramagnetic layer under the spin-wave resonance condition. 15 This injected spin current can be detected electrically by means of the strong ISHE in the Pt layer. 4,9,15 Because YIG is an insulator, this ISHE measurement is not interfered with by effects in the ferromagnetic layer, e.g., the anomalous-Hall effect. Here, the relation between the electric field E ISHE induced by the ISHE, the spatial direction of the spin current j s , and σ is given by 16,17 E ISHE ∝ σ × j s . (1) The spin-wave resonance signal of the Pt/YIG film can be detected by measuring the S 11 parameter using the vector-network analyzer. We measured the spin-wave resonance signal and the electric voltage between the electrodes attached to the Pt layer. All of the measurements were performed at room temperature. Figure 1(c) shows the spin-wave resonance spectrum, or S 11 (dB), for the Pt/YIG film as a function of the microwave frequency f . In this spectrum, multiple resonance signals appear. These multiple signals are attributed to the spin-wave mode in the YIG layer. Here, we define the ferromagnetic resonance (FMR) frequency for the most prominent peak (FMR mode) as f FMR . The peaks for f > f FMR are magnetostatic surface modes (MSSW), and the peaks for f < f FMR are magnetostatic backward volume modes (MSBVW). 18 Figure 1(d) shows the dc electric voltage signals for the Pt/YIG film when the external magnetic field is applied perpendicular ( θ = 0 ) and parallel ( θ = 90 ∘ ) to the direction across the electrodes. At θ = 0 , voltage signals appear at the spin-wave resonance and FMR fields, indicating that the electromotive force is induced by the ISHE in the Pt layer affected by the spin-wave resonance in the YIG layer. 15 We confirmed that the electromotive force disappears at θ = 90 ∘ , a situation consistent with Eq. (1) . The spectral shape of the electromotive force is well reproduced by using a sum of Lorentz functions as shown in Fig. 1(d) (solid line), consistent with the prediction of the spin pumping. 6,15 Figures 2(a) and 2(b) show the f dependence of the spin-wave resonance spectra and the electric voltage signals. In the frequency range under 3 GHz, the FMR peak in the S 11 spectrum is strongly suppressed by the Suhl instability. 18,19 Here, by changing H , f FMR is varied systematically, consistent with Kittel{\textquoteright}s formula: 20 f FMR = ( μ 0 γ eff / 2 π ) H FMR ( H FMR + M s ) , as shown in Fig. 2(c) , where γ eff = 1.78 × 10 11 ( T · s ) - 1 is the effective gyromagnetic ratio and μ 0 M s = 0.172 T is the saturation magnetization for the YIG film estimated from the resonance frequency f FMR . 21 The microwave-absorption power P ab at f FMR is proportional to the incident microwave power P in , as shown in Fig. 2(d) , indicating that P ab for P in ≤ 20 mW is lower than the saturation of the FMR absorption when f FMR = 3.51 GHz. Here, P ab is estimated as the S 11 spectrum for the resonance in the YIG layer from which the spectrum without resonance ( H is changed) is subtracted. In Fig. 3 , the ω{\~ } ≡ 2 π f FMR / ( γ eff μ 0 M s ) dependence of V ISHE / h 2 is shown (solid circles). V ISHE is the voltage at f FMR . h is the rf-field amplitude at f FMR estimated by the relation h 2 = P ab / ( ν π f FMR μ 0 χ FMR ″ ) . Here, ν is a volume in which the irradiated microwave is absorbed. Because ν cannot be estimated accurately, we assume that ν is the whole volume of the YIG layer, ν YIG . χ FMR ″ is the imaginary part of the complex magnetic susceptibility under FMR conditions: χ FMR ″ = 1 + 4 ω{\~ } 2 + 1 2 α ω{\~ } 1 + 4 ω{\~ } 2 , (2) where α is the Gilbert damping coefficient for the YIG/Pt film. In the frequency range without the Suhl instability, V ISHE / h 2 was found to decrease slightly with increasing ω{\~ } , as shown in Fig. 3 . Given that V ISHE is proportional to j s ≡ | j s | as shown in Eq. (1) , this result indicates that the spin current induced by the spin pumping decreases with increasing f FMR , rather than the intuitively expected state of j s ∝ f FMR . This behavior is explained by the compensation between the magnetization-precession frequency and the spin current generated by a cycle of the precession j s 1 (Ref. 1 ); they both depend on the frequency, but in different manners: j s = f FMR · j s 1 , where j s 1 ≡ ℏ 2 g r ↑ ↓ 1 M s 2 ∫ 0 1 / f FMR 1 2 π 〈 M ( t ) × d M ( t ) d t 〉 z d t . (3) Here, g r ↑ ↓ is the real part of the mixing conductance and 〈 M ( t ) × d M ( t ) / d t 〉 z is the z component of M ( t ) × d M ( t ) / d t . The z axis is directed along the magnetization-precession axis. Using Eq. (3) and the Landau-Lifshitz-Gilbert equation, we find j s / h 2 to be j s / h 2 = ℏ g r ↑ ↓ μ 0 γ eff 4 π α 2 M s 1 + 4 ω{\~ } 2 + 1 2 ( 1 + 4 ω{\~ } 2 ) . (4) The decrease in V ISHE / h 2 is reproduced by Eq. (4) as shown in Fig. 3 (solid line). Here, θ SHE is the spin-Hall angle in Pt, or the efficiency of the conversion of the spin current to an electric current. 22 We use α = 4.34 × 10 - 4 , estimated by the S 11 spectrum, and g r ↑ ↓ θ SHE ≈ 1.73 × 10 16 m - 2 , which is larger than in our previous study. 15 A possible reason for this difference is that the approximation of ν = ν YIG is over-estimated. In this analysis, we assumed that g r ↑ ↓ θ SHE is constant for the whole frequency range. The slight decrease in V ISHE / h 2 is explained by a decrease in j s 1 . Because j s 1 is proportional to the area of the magnetization-precession trajectory 7 S , S decreases with increasing f FMR due to the decrease in the magnetization-precession angle with the increase in the external magnetic field H FMR that is necessary for achieving ferromagnetic resonance. In summary, we measured the frequency dependence of magnetization-precession in spin pumping in a Pt/ Y 3 Fe 5 O 12 film using the inverse spin-Hall effect. We found that in this film, the spin-current density decreases slightly with increasing precession frequency, which is well reproduced by a model calculation based on the Landau-Lifshitz-Gilbert equation combined with a standard model of spin pumping. This result is favorable for making a microwave demodulator detection device based on spin pumping and the inverse spin-Hall effect. The authors thank S. Takahashi, Y. Fujikawa, and H. Kurebayashi for valuable discussions. This work was supported by a Grant-in-Aid for Scientific Research in Priority Area “Creation and control of spin current” (19048028) from MEXT, Japan, a Grant-in-Aid for Scientific Research (A 21244058) from MEXT, Japan, Global COE for the Materials Integration International Center of Education and Research from MEXT, Japan, a Grant for Industrial Technology Research from NEDO, Japan, and Fundamental Research Grants from CREST-JST, PRESTO-JST, and TRF, Japan. FIG. 1. (Color online) (a) A schematic illustration of the spin pumping and inverse spin-Hall effect in the Pt/ Y 3 Fe 5 O 12 film. M ( t ) is the magnetization in the Y 3 Fe 5 O 12 layer. j s denotes the spatial direction of the generated spin current. σ denotes the spin polarization carried by the spin current. (b) A schematic illustration of the Pt/ Y 3 Fe 5 O 12 film used in the present study. H is an external magnetic field. h is a rf-magnetic field. (c) The microwave frequency ( f ) dependence of S 11 for the Pt/ Y 3 Fe 5 O 12 film. The peak labeled “FMR” is a uniform mode (ferromagnetic resonance mode), the peaks in the area labeled “MSBVW” are magnetostatic backward volume modes, and the peaks in the area labeled “MSSW” are magnetostatic surface modes. (d) Microwave frequency ( f ) dependence of the electromotive force for the Pt/ Y 3 Fe 5 O 12 film. The solid circles and the open circles represent the experimental data when the external magnetic field is applied perpendicular (solid circles) and parallel (open circles) to the direction across the electrodes. The solid curve shows a fitting result using a sum of five Lorentz functions for the solid circles. FIG. 2. (Color online) (a) Microwave frequency ( f ) dependence of the spin-wave resonance spectra for the Pt/ Y 3 Fe 5 O 12 film. The transition of the line colors corresponds to an increase of the external magnetic field. (b) Microwave frequency ( f ) dependence of the electric voltage signals for the Pt/ Y 3 Fe 5 O 12 film. (c) Field ( H ) dependence of the FMR frequency ( f FMR ) for the Pt/ Y 3 Fe 5 O 12 film. The solid circles represent the experimental data. The solid line shows a fitting result using Kittel{\textquoteright}s formula with the effective gyromagnetic ratio for the Y 3 Fe 5 O 12 layer. (d) The microwave-absorption power ( P ab ) due to FMR plotted against the power of incident microwave ( P in ) for the Pt/ Y 3 Fe 5 O 12 film. The solid circles represent the experimental data, and the solid line shows a linear fitting result. FIG. 3. (Color online) ω{\~ } ≡ 2 π f FMR / ( γ eff μ 0 M s ) dependence of V ISHE / h 2 for the Pt/ Y 3 Fe 5 O 12 film, where V ISHE and h 2 are the electric voltage due to the ISHE and the square of the rf-field strength at FMR frequency, respectively. The solid circles represent the experimental data with a changing external magnetic field. The solid line shows the fitting result using Eq. (4) . The inset shows the ω{\~ } dependence of the rf-field amplitude at FMR frequency. ",

year = "2011",

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language = "English",

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journal = "Journal of Applied Physics",

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TY - JOUR

T1 - Frequency dependence of spin pumping in Pt/Y3Fe 5O12 film

AU - Harii, Kazuya

AU - An, Toshu

AU - Kajiwara, Yosuke

AU - Ando, Kazuya

AU - Nakayama, Hiroyasu

AU - Yoshino, Tatsuro

AU - Saitoh, Eiji

N1 - Funding Information: 3 Fe 5 O 12 film Harii Kazuya 1,2,3 a) An Toshu 2,3 Kajiwara Yosuke 2 Ando Kazuya 2,3 Nakayama Hiroyasu 2,3 Yoshino Tatsuro 2 Saitoh Eiji 2,3,4,5 1 Department of Applied Physics and Physico-Informatics, Keio University , Yokohama 223-8522, Japan 2 Institute for Materials Research, Tohoku University , Sendai 980-8577, Japan 3 CREST, Japan Science and Technology Agency , Sanbancho, Tokyo 102-0075, Japan 4 The Advanced Science Research Center, Japan Atomic Energy Agency , Tokai, Ibaraki 319-1195, Japan 5 PRESTO, Japan Science and Technology Agency , Sanbancho, Tokyo 102-0075, Japan a) Author to whom correspondence should be addressed. Electronic mail: kharii@imr.tohoku.ac.jp . 01 06 2011 109 11 116105 02 10 2010 11 04 2011 15 06 2011 2011-06-15T09:12:15 2011 American Institute of Physics 0021-8979/2011/109(11)/116105/3/ $30.00 The frequency dependence of magnetization precession in spin pumping has been investigated using the inverse spin-Hall effect in a Pt/ Y 3 Fe 5 O 12 bilayer film. We found that the magnitude of a spin current generated by the spin pumping depends weakly on the applied microwave frequency. This weak dependence, which is attributed to the compensation between the frequency change in the spin-pumping cycle and the dynamic magnetic susceptibility, is favorable for making a spin-current-driven microwave demodulator. This behavior is consistent with a model calculation based on the Landau-Lifshitz-Gilbert equation combined with the spin mixing. Spin pumping, the generation of spin currents from a magnetization precession excited by a microwave, has attracted much attention recently. 1–15 In a ferromagnetic/paramagnetic film, the spin pumping driven by a magnetization precession injects a spin current into the paramagnetic layer. This injected spin current is converted into a dc electric voltage using the inverse spin-Hall effect (ISHE) in the paramagnetic layer. This effect can be used as amplitude demodulation in an amplitude-modulation signal transmission using microwave demodulation, because the spin pumping generates a rectified electric voltage that is proportional to the microwave amplitude, 5 only when a microwave frequency fulfills the ferromagnetic resonance condition. Here, in this amplitude demodulation method, the frequency tuning is achieved by controlling the strength of an external magnetic field. The spin pumping originates from dynamical coupling between magnetization and conduction-electron spins, and thus higher-frequency operation is basically favorable. Because a spin current is emitted to an attached paramagnetic metal in each cycle of the magnetization precession, the spin current generated by the spin pumping is expected to be proportional to the precession frequency f FMR : j s ∝ f FMR . 1 Here we show that, in an operation of the spin pumping in a magnetic film, the generated spin current varies rather moderately with f FMR . Figures 1(a) and 1(b) show a schematic illustration of the sample used in this study. The sample is a paramagnetic Pt/ferrimagnetic insulator Y 3 Fe 5 O 12 (111) (YIG) bilayer film comprising a 10-nm-thick Pt layer and a 2.4- μ m -thick single-crystal YIG layer. The surface of the YIG layer is of a 1.3 mm × 3.5 mm rectangular shape. The YIG film was grown on a Gd 3 Ga 5 O 12 (111) single-crystal substrate via liquid phase epitaxy. The Pt layer was fabricated on the YIG layer via ion-beam sputtering. Two electrodes are attached to the ends of the Pt layer. The sample system is placed on a microstrip-microwave guide. During the measurement, a 20-mW-excitation microwave with a frequency f generated by a vector-network analyzer was introduced to the microstrip waveguide, and an external magnetic field H along the film plane was applied perpendicular to the direction across the electrodes (see Fig. 1(b) ). The magnetization precession excited by the applied microwave injects a dc pure spin current with a spin polarization σ parallel to the magnetization-precession axis into the paramagnetic layer under the spin-wave resonance condition. 15 This injected spin current can be detected electrically by means of the strong ISHE in the Pt layer. 4,9,15 Because YIG is an insulator, this ISHE measurement is not interfered with by effects in the ferromagnetic layer, e.g., the anomalous-Hall effect. Here, the relation between the electric field E ISHE induced by the ISHE, the spatial direction of the spin current j s , and σ is given by 16,17 E ISHE ∝ σ × j s . (1) The spin-wave resonance signal of the Pt/YIG film can be detected by measuring the S 11 parameter using the vector-network analyzer. We measured the spin-wave resonance signal and the electric voltage between the electrodes attached to the Pt layer. All of the measurements were performed at room temperature. Figure 1(c) shows the spin-wave resonance spectrum, or S 11 (dB), for the Pt/YIG film as a function of the microwave frequency f . In this spectrum, multiple resonance signals appear. These multiple signals are attributed to the spin-wave mode in the YIG layer. Here, we define the ferromagnetic resonance (FMR) frequency for the most prominent peak (FMR mode) as f FMR . The peaks for f > f FMR are magnetostatic surface modes (MSSW), and the peaks for f < f FMR are magnetostatic backward volume modes (MSBVW). 18 Figure 1(d) shows the dc electric voltage signals for the Pt/YIG film when the external magnetic field is applied perpendicular ( θ = 0 ) and parallel ( θ = 90 ∘ ) to the direction across the electrodes. At θ = 0 , voltage signals appear at the spin-wave resonance and FMR fields, indicating that the electromotive force is induced by the ISHE in the Pt layer affected by the spin-wave resonance in the YIG layer. 15 We confirmed that the electromotive force disappears at θ = 90 ∘ , a situation consistent with Eq. (1) . The spectral shape of the electromotive force is well reproduced by using a sum of Lorentz functions as shown in Fig. 1(d) (solid line), consistent with the prediction of the spin pumping. 6,15 Figures 2(a) and 2(b) show the f dependence of the spin-wave resonance spectra and the electric voltage signals. In the frequency range under 3 GHz, the FMR peak in the S 11 spectrum is strongly suppressed by the Suhl instability. 18,19 Here, by changing H , f FMR is varied systematically, consistent with Kittel’s formula: 20 f FMR = ( μ 0 γ eff / 2 π ) H FMR ( H FMR + M s ) , as shown in Fig. 2(c) , where γ eff = 1.78 × 10 11 ( T · s ) - 1 is the effective gyromagnetic ratio and μ 0 M s = 0.172 T is the saturation magnetization for the YIG film estimated from the resonance frequency f FMR . 21 The microwave-absorption power P ab at f FMR is proportional to the incident microwave power P in , as shown in Fig. 2(d) , indicating that P ab for P in ≤ 20 mW is lower than the saturation of the FMR absorption when f FMR = 3.51 GHz. Here, P ab is estimated as the S 11 spectrum for the resonance in the YIG layer from which the spectrum without resonance ( H is changed) is subtracted. In Fig. 3 , the ω ̃ ≡ 2 π f FMR / ( γ eff μ 0 M s ) dependence of V ISHE / h 2 is shown (solid circles). V ISHE is the voltage at f FMR . h is the rf-field amplitude at f FMR estimated by the relation h 2 = P ab / ( ν π f FMR μ 0 χ FMR ″ ) . Here, ν is a volume in which the irradiated microwave is absorbed. Because ν cannot be estimated accurately, we assume that ν is the whole volume of the YIG layer, ν YIG . χ FMR ″ is the imaginary part of the complex magnetic susceptibility under FMR conditions: χ FMR ″ = 1 + 4 ω ̃ 2 + 1 2 α ω ̃ 1 + 4 ω ̃ 2 , (2) where α is the Gilbert damping coefficient for the YIG/Pt film. In the frequency range without the Suhl instability, V ISHE / h 2 was found to decrease slightly with increasing ω ̃ , as shown in Fig. 3 . Given that V ISHE is proportional to j s ≡ | j s | as shown in Eq. (1) , this result indicates that the spin current induced by the spin pumping decreases with increasing f FMR , rather than the intuitively expected state of j s ∝ f FMR . This behavior is explained by the compensation between the magnetization-precession frequency and the spin current generated by a cycle of the precession j s 1 (Ref. 1 ); they both depend on the frequency, but in different manners: j s = f FMR · j s 1 , where j s 1 ≡ ℏ 2 g r ↑ ↓ 1 M s 2 ∫ 0 1 / f FMR 1 2 π 〈 M ( t ) × d M ( t ) d t 〉 z d t . (3) Here, g r ↑ ↓ is the real part of the mixing conductance and 〈 M ( t ) × d M ( t ) / d t 〉 z is the z component of M ( t ) × d M ( t ) / d t . The z axis is directed along the magnetization-precession axis. Using Eq. (3) and the Landau-Lifshitz-Gilbert equation, we find j s / h 2 to be j s / h 2 = ℏ g r ↑ ↓ μ 0 γ eff 4 π α 2 M s 1 + 4 ω ̃ 2 + 1 2 ( 1 + 4 ω ̃ 2 ) . (4) The decrease in V ISHE / h 2 is reproduced by Eq. (4) as shown in Fig. 3 (solid line). Here, θ SHE is the spin-Hall angle in Pt, or the efficiency of the conversion of the spin current to an electric current. 22 We use α = 4.34 × 10 - 4 , estimated by the S 11 spectrum, and g r ↑ ↓ θ SHE ≈ 1.73 × 10 16 m - 2 , which is larger than in our previous study. 15 A possible reason for this difference is that the approximation of ν = ν YIG is over-estimated. In this analysis, we assumed that g r ↑ ↓ θ SHE is constant for the whole frequency range. The slight decrease in V ISHE / h 2 is explained by a decrease in j s 1 . Because j s 1 is proportional to the area of the magnetization-precession trajectory 7 S , S decreases with increasing f FMR due to the decrease in the magnetization-precession angle with the increase in the external magnetic field H FMR that is necessary for achieving ferromagnetic resonance. In summary, we measured the frequency dependence of magnetization-precession in spin pumping in a Pt/ Y 3 Fe 5 O 12 film using the inverse spin-Hall effect. We found that in this film, the spin-current density decreases slightly with increasing precession frequency, which is well reproduced by a model calculation based on the Landau-Lifshitz-Gilbert equation combined with a standard model of spin pumping. This result is favorable for making a microwave demodulator detection device based on spin pumping and the inverse spin-Hall effect. The authors thank S. Takahashi, Y. Fujikawa, and H. Kurebayashi for valuable discussions. This work was supported by a Grant-in-Aid for Scientific Research in Priority Area “Creation and control of spin current” (19048028) from MEXT, Japan, a Grant-in-Aid for Scientific Research (A 21244058) from MEXT, Japan, Global COE for the Materials Integration International Center of Education and Research from MEXT, Japan, a Grant for Industrial Technology Research from NEDO, Japan, and Fundamental Research Grants from CREST-JST, PRESTO-JST, and TRF, Japan. FIG. 1. (Color online) (a) A schematic illustration of the spin pumping and inverse spin-Hall effect in the Pt/ Y 3 Fe 5 O 12 film. M ( t ) is the magnetization in the Y 3 Fe 5 O 12 layer. j s denotes the spatial direction of the generated spin current. σ denotes the spin polarization carried by the spin current. (b) A schematic illustration of the Pt/ Y 3 Fe 5 O 12 film used in the present study. H is an external magnetic field. h is a rf-magnetic field. (c) The microwave frequency ( f ) dependence of S 11 for the Pt/ Y 3 Fe 5 O 12 film. The peak labeled “FMR” is a uniform mode (ferromagnetic resonance mode), the peaks in the area labeled “MSBVW” are magnetostatic backward volume modes, and the peaks in the area labeled “MSSW” are magnetostatic surface modes. (d) Microwave frequency ( f ) dependence of the electromotive force for the Pt/ Y 3 Fe 5 O 12 film. The solid circles and the open circles represent the experimental data when the external magnetic field is applied perpendicular (solid circles) and parallel (open circles) to the direction across the electrodes. The solid curve shows a fitting result using a sum of five Lorentz functions for the solid circles. FIG. 2. (Color online) (a) Microwave frequency ( f ) dependence of the spin-wave resonance spectra for the Pt/ Y 3 Fe 5 O 12 film. The transition of the line colors corresponds to an increase of the external magnetic field. (b) Microwave frequency ( f ) dependence of the electric voltage signals for the Pt/ Y 3 Fe 5 O 12 film. (c) Field ( H ) dependence of the FMR frequency ( f FMR ) for the Pt/ Y 3 Fe 5 O 12 film. The solid circles represent the experimental data. The solid line shows a fitting result using Kittel’s formula with the effective gyromagnetic ratio for the Y 3 Fe 5 O 12 layer. (d) The microwave-absorption power ( P ab ) due to FMR plotted against the power of incident microwave ( P in ) for the Pt/ Y 3 Fe 5 O 12 film. The solid circles represent the experimental data, and the solid line shows a linear fitting result. FIG. 3. (Color online) ω ̃ ≡ 2 π f FMR / ( γ eff μ 0 M s ) dependence of V ISHE / h 2 for the Pt/ Y 3 Fe 5 O 12 film, where V ISHE and h 2 are the electric voltage due to the ISHE and the square of the rf-field strength at FMR frequency, respectively. The solid circles represent the experimental data with a changing external magnetic field. The solid line shows the fitting result using Eq. (4) . The inset shows the ω ̃ dependence of the rf-field amplitude at FMR frequency.

PY - 2011/6/1

Y1 - 2011/6/1

N2 - The frequency dependence of magnetization precession in spin pumping has been investigated using the inverse spin-Hall effect in a Pt/ Y 3 Fe 5 O 12 bilayer film. We found that the magnitude of a spin current generated by the spin pumping depends weakly on the applied microwave frequency. This weak dependence, which is attributed to the compensation between the frequency change in the spin-pumping cycle and the dynamic magnetic susceptibility, is favorable for making a spin-current-driven microwave demodulator. This behavior is consistent with a model calculation based on the Landau-Lifshitz-Gilbert equation combined with the spin mixing.

AB - The frequency dependence of magnetization precession in spin pumping has been investigated using the inverse spin-Hall effect in a Pt/ Y 3 Fe 5 O 12 bilayer film. We found that the magnitude of a spin current generated by the spin pumping depends weakly on the applied microwave frequency. This weak dependence, which is attributed to the compensation between the frequency change in the spin-pumping cycle and the dynamic magnetic susceptibility, is favorable for making a spin-current-driven microwave demodulator. This behavior is consistent with a model calculation based on the Landau-Lifshitz-Gilbert equation combined with the spin mixing.

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