We report on the efficiency of spin pumping from parametrically excited propagating high-*k* spinwaves in a YIG(25 nm)/Pt(5 nm) bilayer. We observe clear signals, detected using the inverse spin Hall effect. The measured spin pumping efficiency and microwave thresholds needed for parametric excitation indicate that spin pumping is insensitive to the spinwave wavevector magnitude and propagation direction in the range $0\u2264k\u227220\u2009\mu m\u22121$. This finding is consistent with the fact that for thin films, the variation of spin wave amplitude across the film thickness is only weakly dependent on the wavevector. Our results are promising for the development of spin-based devices operated by spinwaves.

Spin pumping from spinwaves allows for angular momentum transfer from high frequency finite wavelength magnetic excitations of a ferromagnet into an adjacent normal metal layer. Most previous spin pumping experiments address the uniform (i.e., *k* = 0) mode of ferromagnetic resonance (FMR).^{1,2} However, angular momentum transfer from excitations with much higher wavevectors *k* is potentially attractive for applications, allowing for further miniaturization and an associated increase of operational frequencies for spintronic devices. An important material for these applications is yttrium iron garnet (YIG), a ferrimagnetic insulator with low magnetic losses, which makes YIG an ideal spinwave conductor.^{3} Spin pumping from spinwaves has been studied previously in thick^{4–10} and thin film YIG.^{11,12} However, the highest wavevector range covered in experiments with thin films^{11} has yet to exceed $k\u22734\u2009\mu m\u22121$ and has only been reported for standing wave modes. This is smaller than spinwave wavevectors used in many spin transfer torque experiments.^{13} Also, the extraordinarily strong spin pumping signals detected in our thin YIG films^{2,14} make it a very promising candidate for spintronics applications, especially in light of the recent demonstration of electrical control of spinwave damping in YIG.^{15,16}

In this letter, we report a systematic study of the wavevector dependence of spin pumping from low and high-k spinwaves in a thin YIG film, *d* = 25 nm. We have developed and implemented parallel and perpendicular parametric pumping schemes able to excite spinwaves with well defined propagation directions and wavevector magnitudes. At fixed microwave frequency, the spinwave spectrum can be tuned with external magnetic field, and hence, we are able to generate a broad range of spinwave wavevectors $0\u2264k\u227220\u2009\mu m\u22121$. A primary result of our study is the demonstration that spin pumping is insensitive to the magnitude and propagation direction of the spinwave wavevector.

The YIG used in this experiment is a (111)-oriented thin film epitaxially grown on a (111) gadolinium gallium garnet substrate.^{14} The spin sensing layer is a 5 nm thick sputtered Pt film with resistance 660 Ohm. Indium contacts are attached to the Pt layer near the edges of the sample, and the center of the sample is covered with a 200 nm thick SiO_{2} layer. The magnetic properties of our YIG/Pt sample were measured to be saturation magnetization $4\pi Ms=1650$ G, saturation field $Hsat=25$ Oe, and uniform mode linewidth $\Delta H=23$ Oe @ 9.65 GHz. The typical linewidth of our YIG films in the absence of Pt^{18} is ∼10 Oe @ 9.65 GHz. The experimental setup is schematically shown in Fig. 1(a). The microwave field **h** is generated by a shorted coaxial resonator.^{19} The loaded quality factors $QL$ and coupling coefficients *β* are measured for all resonator modes used in the experiment. The threshold microwave field $hthm$ above which parametric excitation can occur is given by^{20} $hthm=QL\pi fp\beta 1+\beta Pth$, where $Pth$ is the threshold microwave power. The orientation of the resonator short defines the orientation of microwave field and hence the microwave pumping condition. Pure perpendicular pumping $(H\u22a5h)$ is achieved when the resonator short is collinear with the **z** axis. Quasi-parallel pumping $(H\u2225h)$ is realized when the coaxial short is parallel to the **y** axis, as shown in Fig. 1(a). Note that for this pumping geometry, there is a small perpendicular component of field **h** that is maximum at the edges of the coaxial short. The pumping geometry is selected by rotation of the coaxial resonator short with respect to the film normal. The oscillations of magnetization **M** excited in YIG generate a spin current in the Pt layer that is converted into a charge current via the inverse spin Hall effect (ISHE) and measured as a voltage $VISHE$, shown in Fig. 1(a).

The family of dispersion curves for different spinwave propagation directions defined by the angle *θ _{k}* is presented in Fig. 1(b). In parametric excitation, the microwave photon of frequency $fp$ transfers its energy to two counter propagating spinwaves at $fp/2$, such that energy and momentum are conserved. This is indicated by arrows in Fig. 1(b). Depending on the parametric excitation geometry, the photon excites spinwaves with different propagation angle

*θ*. For quasi-parallel pumping

_{k}^{21–24}geometry, the propagation angle $\theta k\u224890\xb0$, and for perpendicular pumping,

^{22,25}$\theta k\u224845\xb0$. At a fixed frequency $fp$, the magnitude of the spinwave wavevector can be selected by shifting the spinwave dispersion curves along with the frequency of the uniform FMR mode $f0=\gamma H(H+4\pi Ms)$ by adjusting the external field

*H*, such that the excited wavevector

*k*is defined by the intersection of the spinwave dispersion curve with $fp/2$ (see Fig. 1(b)). The maximum excited wavevector

*k*corresponds to the lowest applied field $H=Hsat$. As the magnetic field increases, the excited spinwave wavevector decreases, reaching $k\u22480$ at the resonant field

*H*

_{0}of the quasi-uniform FMR mode at $fp/2$. Further increase of the field leads to the excitation of different spinwaves with a broad distribution

^{23,25}of

*k*and

*θ*.

_{k}The field dependence of $VISHE$ is shown in Figs. 1(c) and 1(d), for parallel and perpendicular microwave pumping geometries, respectively. Below the threshold power, the spin pumping signal arises only from the uniform FMR mode driven at $fp$ ($k\u22480$). At high power levels, above the parametric excitation threshold, lower field features arise in the ISHE voltage, revealing spin pumping from parametrically excited spinwaves at $fp/2$ ($k\u22600$). The observed change in the sign of the voltage with field reversal (panels (c) and (d)) confirms that this is an ISHE signal due to spin pumping.

Figure 2 shows good correlation between the spin pumping signal $VISHE$ and absorbed microwave power $Pabs$ at different levels of the input power $Pin$. The magnitude of $VISHE$ attributed to the parametrically excited spinwaves is as high as 80 *μ*V ($H=160$ Oe), which corresponds to a charge current density $J\u22481.7$ A/cm^{2}. These spin pumping signals strongly surpass those reported in experiments with *μ*m-thick YIG films.^{7,10}

The measured absorbed power allows us to determine the spin pumping efficiency $VISHE$/$Pabs$ which is shown in Fig. 3. This measurement demonstrates that the spin pumping efficiency is insensitive to wavevector *k*. Moreover, the spin pumping efficiency for parametrically excited spinwaves in the range $0\u2272k\u22728\u2009\mu m\u22121$ is nearly the same as it is for the uniform FMR mode ($k\u22480$) driven at $fp$. This is in clear contrast to the results from micrometer-thick YIG films^{4,5,7} where the precession amplitude exhibits a wavevector-dependent suppression with distance from the interface. Because SP is an interfacial effect, this decrease will alter the spin pumping efficiency relative to the film thickness; in contrast, the precession amplitude is constant across the thickness of our thin films.^{17,26} Also, the wavevector independent spin pumping efficiency indirectly shows that the energy loss (transfer) due to spin pumping dominates over multi-magnon processes, for which amplitudes (probabilities) should increase^{22} with *k*. Both of these factors make thin YIG films attractive for spintronic applications where uniformity of the spinwave coupling to the electrical circuit is a requirement.

Also, Fig. 3 shows a decrease of the spin pumping efficiency with increasing microwave power. We identify this as due to a small amount of microwave heating not related to FMR that is indirectly measured^{27} to be $\Delta T<$ 2 K for the maximum applied power $Pin$ = 207 mW.

To extend the measurement of spin pumping efficiency to higher wavevectors, we measured threshold power to determine wavevector dependence of the damping which enabled us to determine that spin pumping is nearly insensitive to spinwave wavevector magnitude in a broad range of wavevectors $0\u2264k\u227220\u2009\mu m\u22121$. Achieving higher wavevector magnitudes requires larger microwave frequency $fp$ at the given fields where, due to diminished signal-noise, it is more reliable to determine spin pumping efficiency from measurements of the threshold power $Pth$. By operating at the onset of parametric excitation, the signal arises from a well-defined wavevector thus avoiding the excitation of a broad range wavevectors and propagation directions that can occur^{24} when using microwave powers exceeding the threshold $Pth$. The inset in Fig. 2 shows a clear power threshold in ISHE signal from the parametrically excited spinwaves at $fp/2$ ($H=$ 160 Oe) in comparison to the almost linear response from the uniform FMR at $fp$ (*H* = 610 Oe). We note that threshold power is that at which the spinwave losses are just balanced by the drive provided by the microwave field. This can be formulated^{28,29} as $Pth\u223chth$ $\u223c\Delta H(k)/Ck$, where $\Delta H(k)$ is for spinwave damping and *C _{k}* defines the coupling efficiency of a given spinwave mode

**k**to microwave field

**h**. Therefore, threshold power $Pth$ is a direct measure of the spinwave damping $\Delta H(k)$ when

*C*is known.

_{k}^{25,30–32}In turn, the damping is dominated by spin pumping for very thin films.

^{14,26}If there is a wavevector-dependence of the spin pumping, it should be accordingly reflected in the measured microwave thresholds $hthm$.

The field dependencies of the measured microwave thresholds for parallel $(H\u2225hRF)$ and perpendicular $(H\u22a5hRF)$ pumping are shown in Fig. 4. In the case of parallel pumping, the thresholds exhibit a slow decrease with increasing magnetic field until $H=H0$. Above the uniform resonance field *H*_{0}, which is indicated by arrows in Fig. 4, the thresholds $hthm$ start to increase rapidly. This behavior is in a good agreement with theory.^{21,33} Following Refs. 21 and 33 and *under the assumption of wavevector independent damping*, i.e., $\Delta H(k)=\Delta H(0)=23$ Oe @ 9.4 GHz, we calculated^{34} threshold fields $hthc$ for our YIG film. It is clear that calculations demonstrate good agreement with experiment in Fig. 4(a) for $H\u227360$ Oe. Note, we use a single fit parameter to scale all the curves to fit calculated thresholds to experimental data.

The experimental threshold power for perpendicular pumping $(H\u22a5hRF)$ is compared in Fig. 4(b) with the expected damping from thin film theory,^{33} calculated^{34} under the assumption of wavevector-independent damping. The relatively good agreement between experiment and theory at low fields supports the validity of wavevector-independent damping for these high wavevectors. For perpendicular pumping, the minimum in the measured threshold, and hence spinwave damping, occurs at fields slightly lower than the predicted minimum at *H*_{0}. The discrepancy between theory and experiment might indicate a wavevector-dependent spinwave damping within this small field range. While this could be an indication of wavevector-dependent spin pumping, this is unlikely to be a factor at these low wavevectors^{26} (i.e., wavevectors $k<5\u2009\mu m\u22121$). Rather, it suggests the existence of enhanced spinwave scattering near the uniform mode, such as coupling to standing spinwave modes.^{25}

Table I summarizes the ranges of field and wavevector presented in Figure 4 throughout which spin pumping is wavevector independent. In particular, we find spin pumping to be independent of wavevector magnitude and propagation direction for *k* ≤ 20 μm^{−1}. This agrees well with the measured spin pumping efficiency shown in Fig. 3. This arises from the uniform distribution of the spinwave amplitude across film thickness for thin YIG films.

Frequency $fp$ (GHz) . | 3.4 . | 4.1 . | 5.2 . | |||
---|---|---|---|---|---|---|

H (Oe) | k (μm^{−1}) | H (Oe) | k (μm^{−1}) | H (Oe) | k (μm^{−1}) | |

$H\u2225hRF,\u2009\theta k=90\xb0$ | $25\u2266H\u2272202$ | $9\u2267k\u22730$ | $60\u2266H\u2272282$ | $12\u2267k\u22730$ | $60\u2266H\u2272416$ | $18\u2267k\u22730$ |

$H\u22a5hRF,\u2009\theta k=45\xb0$ | $25\u2266H\u2266170$ | $14\u2267k\u22674$ | $35\u2266H\u2266237$ | $15\u2267k\u22675$ | … | … |

Frequency $fp$ (GHz) . | 3.4 . | 4.1 . | 5.2 . | |||
---|---|---|---|---|---|---|

H (Oe) | k (μm^{−1}) | H (Oe) | k (μm^{−1}) | H (Oe) | k (μm^{−1}) | |

$H\u2225hRF,\u2009\theta k=90\xb0$ | $25\u2266H\u2272202$ | $9\u2267k\u22730$ | $60\u2266H\u2272282$ | $12\u2267k\u22730$ | $60\u2266H\u2272416$ | $18\u2267k\u22730$ |

$H\u22a5hRF,\u2009\theta k=45\xb0$ | $25\u2266H\u2266170$ | $14\u2267k\u22674$ | $35\u2266H\u2266237$ | $15\u2267k\u22675$ | … | … |

In conclusion, we report the demonstration of large spin pumping signals from propagating high-*k* spinwaves in thin film YIG. The spin pumping efficiency is found to be insensitive to the spinwave wavevector magnitude *k* for different spinwave propagation directions *θ _{k}*. Our findings emphasize the promise of thin YIG films for spinwave-based spintronics by allowing for predictable down-scaling of the devices dimensions and enabling a broad range of operational frequencies.

This research was primarily supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under Award No. DE-FG02-03ER46054 (experimental conception, experimental design, and microwave ISHE measurements). This work was also supported by DOE Award No. DE-SC0001304 (sample growth), Army Research Office Grant No. W911NF-12-1-0587 (technical assistance and data analysis), and by the Center for Emergent Materials, an NSF-funded MRSEC under Award No. DMR-1420451 (sample characterization).

## References

The coaxial resonator consists of a coaxial cable of length 30 cm that is capacitively coupled to the RF generator at one end and terminated with a short at the other end (see, for example, Ref. 20). The unloaded quality factor is Q0 = 260 at f = 3.4 GHz.

The temperature change $\Delta T$ was determined from the change in measured Pt resistance as a function of power.

The threshold field $hthc$ was determined at fixed external field by varying both k and θk in the ranges $0\u2264k\u226430\mu m\u22121$ and $0\u2264\theta k\u226490\xb0$. The propagation angles corresponding to the minimum for $H\u2264H0$ were $\theta k\u223c90$ and $\theta k\u223c45$ for parallel and perpendicular pumping, respectively.