Propagating spin-wave spectroscopy in nanometer-thick YIG films at millikelvin temperatures

TL;DR

This work demonstrates propagating spin-wave spectroscopy (PSWS) in a 100 nm-thick YIG film at millikelvin temperatures using stripline nanoantennas to excite and detect magnetostatic surface spin waves (Damon–Eshbach mode) across a 10 μm separation. The measurements reveal a fixed ferromagnetic resonance around $f_{\mathrm{FMR}}=3.36$ GHz at low fields, with Gilbert damping increasing from $\alpha_s\approx 6\times10^{-4}$ at room temperature to $\alpha_s\approx 3\times10^{-3}$ at $45$ mK, and a ~50% rise in group velocity due to increased $M_s$ ($142\ \mathrm{kA/m}$ RT vs $189\ \mathrm{kA/m}$ cryogenic). Propagation amplitudes decrease at low temperatures due to stronger damping, and the GGG substrate becomes magnetically active above about $75$ mT, with $M_{GGG}$ reaching up to ~47 kA/m at 45 mK, distorting spin-wave signals. These findings confirm PSWS can operate in nanoscale YIG at millikelvin temperatures and highlight substrate effects that motivate future suspended or nanostructured YIG designs for robust, high-field quantum magnonic circuits.

Abstract

Performing propagating spin-wave spectroscopy of thin films at millikelvin temperatures is the next step towards the realisation of large-scale integrated magnonic circuits for quantum applications. Here we demonstrate spin-wave propagation in a $100\,\mathrm{nm}$-thick yttrium-iron-garnet film at the temperatures down to $45 \,\mathrm{mK}$, using stripline nanoantennas deposited on YIG surface for the electrical excitation and detection. The clear transmission characteristics over the distance of $10\,μ\mathrm{m}$ are measured and the subtracted spin-wave group velocity and the YIG saturation magnetisation agree well with the theoretical values. We show that the gadolinium-gallium-garnet substrate influences the spin-wave propagation characteristics only for the applied magnetic fields beyond $75\,\mathrm{mT}$, originating from a GGG magnetisation up to $47 \,\mathrm{kA/m}$ at $45 \,\mathrm{mK}$. Our results show that the developed fabrication and measurement methodologies enable the realisation of integrated magnonic quantum nanotechnologies at millikelvin temperatures.

Figures (5)

• Figure 1: Overview of the electron-beam lithographed stripline nanoantennas on the yttrium-iron-garnet film. (a) Sketch of the sample used in these measurements. Stripline nanoantennas coupled to coplanar waveguide (CPW) and the reference CPW are fabricated atop a $100\,\mathrm{nm}$-thick yttrium-iron-garnet film on a $500\,\mathrm{\mu m}$-thick gadolinium-gallium-garnet substrate. (b) The coplanar-waveguide coupled nanoantennas are fabricated with electron-beam lithography. These nanoantennas are made of Ti($5\,\mathrm{nm}$)/Au($55\,\mathrm{nm}$) (more details in main text). (c) Optical and secondary-electron images of the CWP nanoantennas used in the manuscript. These nanoantennas are $10\,\mathrm{\mu m}$ spaced apart and have a width of $330\,\mathrm{nm}$ and length of $120\,\mathrm{\mu m}$. The propagating spin waves (PSW) are excited and detected by the stripline nanoantennas 1 and 2 respectively. The transmission is measured through the S-parameters, acquired by a vector network analyser.
• Figure 2: Linear magnitude, real and imaginary part of the $\mathrm{S'_{21}}$ parameters for propagating spin waves (PSW) in the Damon-Eshbach mode, using $\mathbf{50\,\mathrm{\textbf{mT}}}$ of external magnetic field and different temperatures. The applied microwave power was set to $-28\,\mathrm{dBm}$ (at the sample) with an average sampling of 50 for $45\,\mathrm{mK}$-$1\,\mathrm{K}$ and 100 for $1.5\,\mathrm{K}$-$2.5\,\mathrm{K}$. The FMR point ($k=0$) is constant at $3.36\,\mathrm{GHz}$ ($189\,\mathrm{kA/m}$) for all measured PSW.
• Figure 3: Imaginary part of the $\mathrm{S'_{21}}$ parameter, calculated dispersion relation, antenna excitation efficiency and group velocity for PSW (Damon-Eshbach mode), using $\mathbf{50\,\mathrm{\textbf{mT}}}$ external field at different temperatures. The theoretical group velocity is calculated as the derivation of the dispersion relation and measured as $v_g={\delta}f \cdot D$, with the periodicity of the transmission in the Im($\mathrm{S'_{21}}$) parameters ${\delta}f$ and the gap between the nanoantennas $D$ (see Ref. Vlaminck2010). The parameters measured and used for the calculation are the following: (a) $297\,\mathrm{K}$, $M_s=142\,\mathrm{kA/m}$, (b) $500\,\mathrm{mK}$, $M_s=189\,\mathrm{kA/m}$, (c) $45\,\mathrm{mK}$, $M_s=189\,\mathrm{kA/m}$. The effective saturation magnetisation increases and thus group velocity increases by about $50\,\%$ at millikelvin temperatures.
• Figure 4: Linear magnitude, real and imaginary part of the $\mathrm{S'_{21}}$ parameters for PSWS in the Damon-Eshbach mode at different external fields. The applied microwave power was set to $\mathbf{-28\,\mathrm{\textbf{dBm}}}$ (at the sample) with an averaging of 10 (for $\mathbf{297K}$) and 25 (for $\mathbf{0.045K}$). (a) Room temperature ($297\,\mathrm{K}$): The spin-wave propagation can be measured over a wide magnetic field range. (b) Base temperature ($45\,\mathrm{mK}$): The spin-wave propagation for magnetic fields in the range from about $25\,\mathrm{mT}$ to $75\,\mathrm{mT}$ is trackable, while above $75\,\mathrm{mT}$ the magnitude and its propagation characteristics start to be distorted. This effect is a result of the increased magnetisation of the GGG substrate (see Fig. \ref{['fig:Fig6']}).
• Figure 5: Magnetisation of the GGG substrate versus the applied magnetic field. A GGG-only sample is measured using a vibrating sample magnetometer (VSM) at $2\,\mathrm{K}$ (dark-blue dots), leading for example to an effective magnetisation of $28.5 \,\mathrm{kA/m}$. From the data the magnetisation values for $45\,\mathrm{mK}$ are extrapolated (blue dashed line). At $75\,\mathrm{mT}$ the magnetisation increases to about $47 \,\mathrm{kA/m}$.