Spin transport parameters of NbN thin films characterized by spin pumping experiments

We present measurements of ferromagnetic resonance driven spin pumping and inverse spin Hall effect in $\mathrm{NbN}/{\mathrm{Y}}_3\mathrm{F}{\mathrm{e}}_5{\mathrm{O}}_{12}$ (YIG) bilayers. A clear enhancement of the (effective) Gilbert damping constant of the thin-film YIG was observed due to the presence of the NbN spin sink. By varying the NbN thickness and employing spin-diffusion theory, we have estimated the room-temperature values of the spin-diffusion length and the spin Hall angle in NbN to be 14 nm and $-1.1\times {10}^{-2}$, respectively. Furthermore, we have determined the spin mixing conductance of the NbN/YIG interface to be $10\mathrm{n}{\mathrm{m}}^{-2}$. The experimental quantification of these spin transport parameters is an important step towards the development of superconducting spintronic devices involving NbN thin films.

Figure 1

Structural and magnetic properties of a bare (111)-oriented YIG film (nominally 60 nm thick) used in this paper and deposited onto GGG. (a) 10 × $10\mu \text{m}$ AFM topography scan showing a root-mean-square roughness of less than 0.16 nm. (b) Magnetization hysteresis loops characterized by a superconducting quantum interference device magnetometer showing a saturation volume magnetization of $140\pm 3\mathrm{emu}\mathrm{c}{\mathrm{m}}^{-3}$. (c) High angle x-ray-diffraction data demonstrating (111) orientation with visible Laue fringes on the (444) and (888) diffraction peaks characteristic of layer-by-layer growth. (d) Low angle x-ray reflectometry data (black) with a best-fit (red) curve from which we estimate a nominal thickness of $60\pm 2\mathrm{nm}$.

Figure 2

(a) A schematic of the spin pumping setup. The lateral area of all samples is $5\times 5\mathrm{m}{\mathrm{m}}^2$. MW magnetic fields $\left(h_{\mathrm{rf}}\right)$ were generated by the transmission line to generate magnetic dynamics in the YIG film. Spin currents $\left(j_s\right)$ were emitted at the YIG/NbN interface, which can induce ISHE voltages detected through the two electrodes attached to the edges of the sample. We simultaneously measured the FMR absorption signal as a voltage in a microwave power meter $\left(V_{\mathrm{P}}\right)$ connected to the microwave line and the ISHE signal $\left(V_{\mathrm{ISHE}}\right)$. (b) FMR absorption measurements for different MW frequencies. (b) FMR absorption measurements for different MW frequencies. Voltages in our MW power detector were measured while magnetic fields were swept. Dots in red, green, blue, cyan, pink, yellow, and black represent measurement results for 3, 4, 5, 6, 8, 10, and 12 GHz, respectively. (c) A plot of frequency vs FMR field $\left(H_{\mathrm{res}}\right)$ for samples with different NbN thicknesses. Dots represent experimental results and curves are produced by fitting using the Kittel formula.

Figure 3

(a) Frequency dependence of FMR linewidth of YIG/NbN samples with different NbN thicknesses. Experimental data (filled points) is fitted by a linear line $\mathrm{\Delta }H=\mathrm{\Delta }{H}_0+\left(4\pi \alpha /\gamma \right)f$, where $\mathrm{\Delta }{H}_0$ and $\gamma$ describe the inhomogeneous broadening and the gyromagnetic ratio respectively, from which the Gilbert damping coefficient α is extracted. (b) Plots of α for different YIG/NbN samples. Equation (1) was used to fit to the thickness dependence with the spin-diffusion length and the real part of mixing conductance as fitting parameters. The inset depicts the resistivity as a function of NbN thickness.

Figure 4

ISHE measurements. Simultaneous measurements of FMR absorption and ISHE voltages for positive (a) and negative (b) magnetic field values for a $t_{\mathrm{NBN}}=20\mathrm{nm}$ sample. Corresponding data for $t_{\mathrm{NBN}}=5\mathrm{nm}$ are depicted in (c) and (d), respectively. Both $V_{\mathrm{P}}$ and $V_{\mathrm{ISHE}}$ peaks appear at the same magnetic field, confirming that the voltages were generated when YIG magnetic moments were precessing. The sign change in voltage peaks observed between the positive and negative magnetic field regions is consistent with the spin pumping/ISHE picture.

Figure 5

Microwave power dependent measurements. (a) ISHE voltage measurements with different insertion powers $\left(P_{\mathrm{MW}}\right)$. (b) A plot of ISHE voltage peak to peak amplitude $\left(V_{\mathrm{ISHE}}^{*}\right)$ as a function of $P_{\mathrm{MW}}$. $V_{\mathrm{ISHE}}$ scales with $P_{\mathrm{MW}}$ as expected from the spin pumping theory in the linear regime.

Figure 6

In-plane (a) and out-of-plane (b) angular dependences of $V_{\mathrm{ISHE}}$ signal peak to peak amplitude $\left(V_{\mathrm{ISHE}}^{*}\right)$. Fit curves in both angular dependences are discussed in the main text. We show fit curves with four different spin-relaxation times $\left({\tau }_s\right)$ in (b) to illustrate how the model curve changes with ${\tau }_s$. The best-fit curve was produced with ${\tau }_s=11\pm 2\mathrm{ps}$. We define three angles $(\varphi ,{\varphi }_M,\theta )$ as depicted in the insets.

Figure 7

$V_{\mathrm{ISHE}}{t}_{\mathrm{NbN}}/{\rho }_{\mathrm{NbN}}$ as a function of NbN thickness. We plot $V_{\mathrm{ISHE}}{t}_{\mathrm{NbN}}/{\rho }_{\mathrm{NbN}}$ to normalize $V_{\mathrm{ISHE}}$ with NbN thickness and resistivity. By using Eq. (3) in the main text, we extract the spin Hall angle $\left({\theta }_{\mathrm{SH}}\right)$ and spin-diffusion length $\left(l_{\mathrm{SD}}\right)$ of NbN to be $1.1\times {10}^{-2}$ and 14 nm. The best-fit curve is shown along with the experimental data.

Figure 8

Comparison of (a) ac and (b) dc $V_{\mathrm{P}}$ measurements. The extracted parameters using equations in Appendix pp1 for each measurement method are depicted in the legends of the figures. We can confirm that the extracted values are almost the same for both measurements.

Figure 9

Eddy current damping contribution. (a) A schematic of our model for the eddy current damping. A chain of magnetic moments (red arrow) lines up along the $y$ direction and we consider the magnetic field at point P $(x$, 0). (b) A plot of calculated eddy current damping as a function of the NbN thickness. The unit of the eddy current damping is arbitrary in order to discuss it qualitatively. The thickness dependence is clearly different from our experimental results in Fig. 3, suggesting that this damping mechanism is not significant in our experiments.

Figure 10

FMR absorption spectra and ISHE voltages as a function of temperature for the $t_{\mathrm{NbN}}=10\mathrm{nm}$ sample. (a) FMR absorption spectra measured at 3 GHz, with temperature ranging from 260 to 3 K. (b) Linewidth evolution with temperature for the 3-GHz measurements. Black data correspond to a YIG/NbN sample and red data correspond to a bare YIG sample. (c) ISHE voltages measured at 3 GHz for the temperature region of 50–300 K. We confirm that the peak height is below the signal-to-noise ratio around 50 K. (d) The normalized ISHE voltage amplitude as a function of temperature. The inset represents our four point probe measurements of NbN resistivity (for $t_{\mathrm{NbN}}=10\mathrm{nm})$.