Abstract
Coupling between conduction electrons and localized magnetization is responsible for a variety of phenomena in spintronic devices. This coupling enables to generate spin currents from dynamical magnetization. Due to the nonlinearity of magnetization dynamics, the spincurrent emission through the dynamical spinexchange coupling offers a route for nonlinear generation of spin currents. Here, we demonstrate spincurrent emission governed by nonlinear magnetization dynamics in a metal/magnetic insulator bilayer. The spincurrent emission from the magnetic insulator is probed by the inverse spin Hall effect, which demonstrates nontrivial temperature and excitation power dependences of the voltage generation. The experimental results reveal that nonlinear magnetization dynamics and enhanced spincurrent emission due to magnon scatterings are triggered by decreasing temperature. This result illustrates the crucial role of the nonlinear magnon interactions in the spincurrent emission driven by dynamical magnetization, or nonequilibrium magnons, from magnetic insulators.
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Introduction
Dynamical magnetization in a ferromagnet emits a spin current^{1,2}, enabling to explore the physics of spin transport in metals and semiconductors^{3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22}. The dynamical spincurrent emission has been achieved utilizing ferromagnetic metals, semiconductors and insulators^{23,24,25,26}. In particular, the discovery of the spincurrent emission from a magnetic insulator yttrium iron garnet, Y_{3}Fe_{5}O_{12}, has drawn intense experimental and theoretical interests, opening new possibilities to spintronics based on metal/insulator hybrids, where angular momentum can be carried by both electrons and magnons.
A ferrimagnetic insulator yttrium iron garnet, Y_{3}Fe_{5}O_{12}, is characterized by the exceptionally small magnetic damping, making it a key material for the development of the physics of nonlinear magnetization dynamics^{27,28,29}. The nonlinear magnetization dynamics in Y_{3}Fe_{5}O_{12} has been extensively studied both experimentally and theoretically in the past half a century, benefited by the exceptional purity, high Curie temperature and simplicity of the lowenergy magnon spectrum^{28,29,30,31}. Recently, the nonlinear magnetization dynamics has been found to affect the spincurrent emission from the magnetic insulator; the spincurrent emission is enhanced by magnon scattering processes [see Fig. 1(a)], triggered by changing the excitation frequency or power of the magnetization dynamics^{14,15,32}. These findings shed new light on the longstanding research on nonlinear magnetization dynamics, promising further development of spintronics and magnetics based on the magnetic insulator.
In this work, we demonstrate that the spincurrent emission from Y_{3}Fe_{5}O_{12} is strongly affected by nonlinear magnetization dynamics at low temperatures. The spincurrent emission is probed by the inverse spin Hall effect (ISHE) in a Pt film attached to the Y_{3}Fe_{5}O_{12} film^{11,33,34}, which enables to measure temperature dependence of the spincurrent emission from the magnetic insulator under various conditions. In spite of the simple structure of the metal/insulator bilayer, we found nontrivial variation of the spincurrent emission; the temperature dependence of the spincurrent emission strongly depends on the microwave frequency and excitation power. This result reveals that nonlinear spincurrent emission due to three and four magnon scatterings emerges by decreasing temperature, even at constant magnon excitation frequency and power. This finding provides a crucial piece of information for understanding the spincurrent emission from ferromagnetic materials and investigating the magnon interactions in the metal/insulator hybrid.
Results
Temperature evolution of spincurrent emission
A singlecrystal Y_{3}Fe_{5}O_{12} (111) film (3 × 5 mm^{2}) with a thickness of 5 μm was grown on a Gd_{3}Ga_{5}O_{12} (111) substrate by liquid phase epitaxy (purchased from Innovent e.V., Jena). After the substrates were cleaned by sonication in deionized water, acetone and isopropanol, a piranha etching process, a mixture of H_{2}SO_{4} and H_{2}O_{2} (with the ratio of 7:3), was applied, then to be able to remove any residuals an oxygen plasma cleaning was performed outside a sputtering chamber. On the top of the film, a 10nmthick Pt layer was sputtered in an Ar atmosphere. Prior to sputtering 10nmthick Pt layer, an argon plasma cleaning was also performed insitu. The Pt/Y_{3}Fe_{5}O_{12} bilayer film was placed on a coplanar waveguide, where a microwave was applied to the input of the signal line as show in Fig. 1(b). Two electrodes were attached to the edges of the Pt layer. The signal line is 500 μm wide and the gaps between the signal line and the ground lines are designed to match to the characteristic impedance of 50 Ω. An inplane external magnetic field H was applied parallel to the signal line, or perpendicular to the direction across the electrodes^{11}. Figure 1(c) shows the inplane magnetic field H dependence of the microwave absorption P measured by applying a 10 mW microwave with the frequency of f_{0} = 7.6 GHz at T = 300 K. Under the ferromagnetic resonance condition H = H_{R}, dynamical magnetization in the Y_{3}Fe_{5}O_{12} layer emit a spin current j_{s} into the Pt layer, resulting in the voltage generation through the ISHE as shown in Fig. 1(d)^{1,2}. The sign of the voltage is changed by reversing H, consistent with the prediction of the spincurrent emission from the magnetic insulator^{35}. Here, the absorption spectrum comprises multiple resonance signals due to spinwave modes, including magnetostatic surface waves and backwardvolume magnetostatic waves in addition to the ferromagnetic resonance. To extract the damping constant for the Pt/Y_{3}Fe_{5}O_{12} film, we have plotted dV/dH in Fig. 1(e), which allows rough estimation of the damping constant, .
Figure 2(a) shows temperature dependence of V_{ISHE}/P_{abs}, where V_{ISHE} and P_{abs} are the magnitude of the microwave absorption and electric voltage, respectively; V_{ISHE}/P_{abs} characterizes the angularmomentum conversion efficiency from the microwaves into spin currents. Notably, V_{ISHE}/P_{abs} increases drastically below T = 150 K by decreasing T at f_{0} = 4.0 GHz. This drastic change is irrelevant to the temperature dependence of the spin pumping and spincharge conversion efficiency in the Pt/Y_{3}Fe_{5}O_{12} bilayer, such as the spin Hall angle θ_{SHE}, the spin pumping conductance g_{eff}, the spin diffusion length λ and the electrical conductivity σ. Figure 2(b) shows the temperature dependence of the electrical conductivity σ and the spin Hall conductivity σ_{s}. The spin Hall conductivity was obtained from the temperature dependence of V_{ISHE}/P_{abs} at 10 mW for f_{0} = 7.6 GHz shown in Fig. 2(a); the value of V_{ISHE}/P_{abs} is insensitive to the excitation power from 5 to 15 mW, indicating that the spincurrent emission is reproduced with a liner spinpumping model^{36}:
where ω_{F} = 3.0 mm and v_{F} = 7.5 × 10^{−11} m^{3} are the width and volume of the Y_{3}Fe_{5}O_{12} film. d = 10 nm is the thickness of the Pt layer. μ_{0}ΔH is the halfmaximum fullwidth of the ferromagnetic resonance linewidth. For the calculation of σ_{s}, we used the measured parameters of the electrical conductivity σ and saturation magnetization M_{s}. The spindiffusion length^{37} λ = 7.7 nm and spin pumping conductance^{38} g_{eff} = 4.0 × 10^{18} m^{−2} were assumed to be independent of temperature, as demonstrated previously^{39}. The spin Hall conductivity of the Pt layer shown in Fig. 2(b) increases with decreasing temperature above 100 K. Below 100 K, the spin Hall conductivity decreases with decreasing temperature. This feature is qualitatively consistent with the previous report^{39}. Although the spin Hall conductivity varies with temperature, the variation of the spin Hall conductivity alone is not sufficient to explain the drastic increase of V_{ISHE}/P_{abs} for f_{0} = 4 GHz shown in Fig. 2(a). Thus, the drastic change in V_{ISHE}/P_{abs} across 150 K at f_{0} = 4.0 GHz can be attributed to the change in the magnetization dynamics in the Y_{3}Fe_{5}O_{12} layer. In fact, by decreasing T, the microwave absorption intensity P_{abs} decreased clearly across T = 150 K as shown in Fig. 2(c), suggesting the change of the magnetization dynamics in the Y_{3}Fe_{5}O_{12} layer across T = 150 K.
Discussion
The origin of the temperatureinduced drastic change of the spinconversion efficiency V_{ISHE}/P_{abs} shown in Fig. 2(a) is enhanced spincurrent emission triggered by the three magnon splitting. The threemagnon splitting creates a pair of magnons with the opposite wavevectors and the frequency f_{0}/2 from the uniform magnon with f_{0} [see also Fig. 1(a)]. The splitting process redistributes the magnons and changes the relaxation rate of the spin system, increasing the steadystate angular momentum stored in the spin system, or resulting in the stabilized enhancement of the spincurrent emission^{14,32}. The splitting is allowed only when f_{0}/2 > f_{min}, where f_{min} is the minimum frequency of the magnon dispersion, because of the energy and momentum conservation laws. This condition can readily be found by finding f_{min} for the thin Y_{3}Fe_{5}O_{12} film from the lowest branch of the dipoleexchange magnon dispersion for the unpinned surface spin condition^{40}:
where Ω = ω_{H} + ω_{M}(D/μ_{0}M_{s})k^{2}, ω_{H} = γμ_{0}H, ω_{M} = γμ_{0}M_{s} and Q = 1 − [1 − exp(−kL)]/(kL). D = 5.2 × 10^{−13} Tcm^{2} is the exchange interaction constant, L = 5 μm is the thickness of the Y_{3}Fe_{5}O_{12} layer and k is the wavenumber of the magnons (see also the Supplementary Information). γ = 1.84 × 10^{11} Ts^{−1} is the gyromagnetic ratio. In Fig. 3(a,b), we show the lowest branch of the magnon dispersion at different temperatures for the Pt/Y_{3}Fe_{5}O_{12} film, calculated using Eq. (2). For the calculation, we used the saturation magnetization M_{s} at each temperature [see Fig. 3(c)], estimated from the ferromagnetic resonance field H_{R} data with Kittel’s formula:, where the resonance condition is independent of the value of D. We assumed that D is independent of temperature, as demonstrated in literature^{32,41,42}; although D varies with temperature, the variation is less than 4% in Y_{3}Fe_{5}O_{12} for T < 350 K and the shape of the magnon dispersion is not sensitive to the small variation of D^{41,42,43}. Figure 3(a,b) demonstrate that the minimum frequency f_{min} decreases with decreasing temperature and the splitting condition f_{0}/2 > f_{min} is satisfied below T = 150 K; the magnon redistribution is responsible for the enhancement of V_{ISHE}/P_{abs}. Thus, this result demonstrates that the enhanced spincurrent emission can be induced not only by changing the excitation frequency or power of the magnetization dynamics, but also by changing temperature.
Figure 4(a,b) show temperature dependence of the spinconversion efficiency V_{ISHE}/P_{abs} at different microwave excitation powers P_{in} for f_{0} = 7.6 and 4.0 GHz, respectively. At f_{0} = 4.0 GHz, the enhancement of V_{ISHE}/P_{abs} due to the threemagnon splitting below 150 K is observed for all the excitation powers as shown in Fig. 4(b). The drop in V_{ISHE}/P_{abs} at T = 50 K for f_{0} = 4.0 GHz is induced by the decrease of the spin Hall conductivity shown in Fig. 2(b); below 100 K, the spin Hall conductivity, or the spin Hall angle, decreases with decreasing temperature, whereas the spincurrent enhancement through the magnon splitting increases by decreasing temperature. The competition gives rise to the peak structure in V_{ISHE}/P_{abs} around 70 K for 4.0 GHz. This result also shows that the enhancement factor is almost independent of the excitation power. In contrast, notably, the variation of V_{ISHE}/P_{abs} depends on the excitation power, especially below 150 K, at f_{0} = 7.6 GHz as shown in Fig. 4(a). These features for f_{0} = 7.6 and 4.0 GHz were confirmed in V_{ISHE}/P_{abs} measured with the reversed external magnetic field [see the experimental data for −H in Fig. 4(a,b)], indicating that the change of the spincurrent emission from the magnetic insulator is responsible for the nontrivial behavior of V_{ISHE}/P_{abs} at low temperatures.
To understand the temperature and power dependences of V_{ISHE}/P_{abs} at f_{0} = 7.6 GHz in details, we plot [V_{ISHE}/P_{abs}]_{100 mW}/[V_{ISHE}/P_{abs}]_{5 mW} in Fig. 4(c). For the spincurrent emission in the linear magnetization dynamics regime, V_{ISHE}/P_{abs} is constant with P_{in}, or [V_{ISHE}/P_{abs}]_{100 mW}/[V_{ISHE}/P_{abs}]_{5 mW} = 1 because the emitted spin current is proportional to P_{in}^{35}. Since the threemagnon splitting is prohibited at f_{0} = 7.6 GHz, [V_{ISHE}/P_{abs}]_{100 mW}/[V_{ISHE}/P_{abs}]_{5 mW} ≈ 1.2, at T = 300 K, demonstrates enhanced spincurrent emission without the splitting of a pumped magnon.
The observed enhancement of the spincurrent emission at T = 300 K is induced by the four magnon scattering, where two magnons are created with the annihilation of two other magnons [see also Fig. 1(a)]^{44,45}. The fourmagnon scattering emerges at high microwave excitation powers P_{in} > P_{th}, known as the second order Suhl instability^{46}, where P_{th} is the threshold power of the scattering. Although this process conserves the number of magnons, the magnon redistribution can decrease the relaxation rate of the spin system through the annihilation of the uniform magnons with large damping η_{0} and creation of dipoleexchange magnons with small damping η_{q}. This results in the steadystate enhancement of the angular momentum stored in the spin system, or the enhanced spincurrent emission^{32}. In the Pt/Y_{3}Fe_{5}O_{12} film, the damping η_{0} of the uniform magnon at low excitation powers is mainly dominated by the twomagnon scattering; the temperature dependence of the ferromagnetic resonance linewidth is almost independent of temperature as shown in the inset to Fig. 5, indicating that the damping η_{0} is not dominated by the temperature peak processes or the KasuyaLeCraw mechanism^{47}. In contrast, the damping η_{q} of the secondary magnons created by the fourmagnon scattering is dominated by the KasuyaLeCraw mechanism, since the twomagnon scattering events are suppressed due to the small group velocity; the group velocity of the secondary dipoleexchange magnons created at the same frequency as the uniform magnon can be close to zero because of the exchangedominated standing spinwave branches [see Fig. 1(a)]^{44,48,49,50}. The exchangedominated branches, i.e. the thickness modes, show the energy minimum not only at the bottom of the dispersion but also at the excitation frequency. Therefore, in the present system, the damping η_{0} of the uniform magnon is dominated by the temperatureindependent twomagnon scattering, whereas the damping η_{q} of the secondary magnon is dominated by temperaturedependent threeparticle confluences, such as the KasuyaLeCraw process^{47}. In the presence of the four magnon scattering, the total number of the nonequilibrium magnons N_{t} is expressed as^{32}
where η_{q} is defined as the average decay rate to the thermodynamic equilibrium of the degenerate secondary magnons for simplicity. The imaginary part of the susceptibility is expressed as
where
Here, η_{sp} is the decay constant of the uniform precession to degenerate magnons at f_{0} due to scattering on sample inhomogeneities. Under the assumption that the spinpumping efficiency is insensitive to the wavenumber k of the nonequilibrium magnons, that is V_{ISHE} ∝ j_{s} ∝ N_{t}, Eq. (3) is directly related to the spinconversion efficiency: V_{ISHE}/P_{abs} ∝ N_{t}/P_{abs}.
The above model reveals that the spincurrent enhancement due to the fourmagnon scattering is responsible for the nontrivial behavior of the voltage generation shown in Fig. 4(a). As shown in Fig. 4(c), the nonlinearity of the spincurrent emission is enhanced by decreasing temperature, from [V_{ISHE}/P_{abs}]_{100 mW}/[V_{ISHE}/P_{abs}]_{5 mW} ≈ 1.2 at T = 300 K to [V_{ISHE}/P_{abs}]_{100 mW}/[V_{ISHE}/P_{abs}]_{5 mW} ≈ 2.4 at 50 K. Figure 5 shows microwave excitation power P_{in} dependence of V_{ISHE}/P_{abs} for f_{0} = 7.6 GHz at different temperatures. This result clearly shows that the threshold power P_{th} of the spincurrent enhancement decreases with decreasing temperature, which is the origin of the nontrivial behavior of the temperature dependence of V_{ISHE}/P_{abs} shown in Fig. 4(a,c). The threshold power of the spincurrent enhancement through the fourmagnon process is very low at low temperatures, making it difficult to observe the threshold behavior. In fact, V_{ISHE}/P_{abs} deviates from the prediction of the linear model even at the lowest microwave excitation power that is necessary to detect the ISHE voltage in the Pt/Y_{3}Fe_{5}O_{12} film at T = 75 K [see the orange circles in Fig. 6]. At T = 300 K, a clear threshold is observed around P_{in} = 40 mW. The threshold power of the fourmagnon scattering is given by^{47} , where h_{th} is the threshold microwave field and σ_{q} is the coupling strength between the uniform and secondary magnons. For simplicity, we neglect the surface dipolar interactions, or L → ∞. Under this approximation, the ferromagnetic resonance condition is given by f_{0} = γμ_{0}H and the coupling strength can be approximated as σ_{q} = γμ_{0}M_{s}. Thus, the threshold power for the fourmagnon scattering is proportional to
Equation (6) predicts that the threshold power of the spincurrent enhancement decreases with decreasing temperature, since M_{s} increases by decreasing temperature as shown in Fig. 3(c). Although the damping η_{0} of the uniform magnon is almost independent of temperature as shown in the inset to Fig. 5, the damping η_{q} of the dipoleexchange magnon tends to decrease the threshold power, since η_{q}, dominated by the KasuyaLeCraw process is approximately proportional to temperature^{47}. At high power excitations, the competition between the increase of the spincurrent enhancement due to the fourmagnon scattering and the decrease of the spin Hall effect by decreasing temperature gives rise to the peak structure in V_{ISHE}/P_{abs} around 100 K for f_{0} = 7.6 GHz [see Fig. 4(a)].
In summary, we have demonstrated that the spincurrent emission from a Y_{3}Fe_{5}O_{12} film is strongly affected by nonlinear magnetization dynamics at low temperatures. The spincurrent emission has been demonstrated to be enhanced even in the absence of the threemagnon splitting^{15}. The experimental results presented in this paper are consistent with this result and further extend the physics of the nonlinear spincurrent emission from the magnetic insulator. Our study reveals that the spincurrent enhancement arises from both the three and four magnon scatterings depending on the excitation frequency and temperature. We show that the enhanced spincurrent emission can be triggered by decreasing temperature, which is evidenced by our systematic measurements for the Pt/Y_{3}Fe_{5}O_{12} film; the spincurrent emission can be enhanced not only by changing the magnon excitation frequency or power, but also by changing temperature. This result demonstrates the generality of the crucial role of magnon interactions in the spincurrent emission, combining the longstanding research on nonlinear spin physics with spintronics.
Additional Information
How to cite this article: Tashiro, T. et al. Spincurrent emission governed by nonlinear spin dynamics. Sci. Rep. 5, 15158; doi: 10.1038/srep15158 (2015).
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Acknowledgements
This work was supported by JSPS KAKENHI Grant Numbers 26220604, 26103004, 26600078, PRESTOJST “Innovative nanoelectronics through interdisciplinary collaboration among material, device and system layers,” the Mitsubishi Foundation, the Asahi Glass Foundation, the Noguchi Institute, the Casio Science Promotion Foundation and the Murata Science Foundation.
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T.T., A.N. and S.M. collected and analyzed the data. S.W., K.K. and H.S. fabricated the device. K.A. developed the explanation and wrote the manuscript. All authors discussed results and reviewed the manuscript.
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Tashiro, T., Matsuura, S., Nomura, A. et al. Spincurrent emission governed by nonlinear spin dynamics. Sci Rep 5, 15158 (2015). https://doi.org/10.1038/srep15158
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DOI: https://doi.org/10.1038/srep15158
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