Controlling Spin-Waves by Inhomogeneous Spin-Transfer Torques

Abstract

We investigate the interplay between spin currents and spin waves in nanofabricated Permalloy waveguides with geometrical constrictions. Using propagating spin-wave spectroscopy, micromagnetic simulations, and analytical modeling, we provide experimental evidence that spin-wave phase can be modulated by inhomogeneous spin-transfer torques generated by current-density gradients shaped by the constriction geometry. Narrower constrictions enhance these gradients and modify the internal field for Damon-Eshbach spin waves, resulting in pronounced changes in spin-wave group velocity and phase. To our knowledge, this constitutes the first demonstration of deterministic phase modulation via engineered nonuniform spin-transfer torques. Beyond enabling a scalable route to magnonic interferometry - a building block for spin-wave-based computing - our findings establish a platform to control spin-wave dynamics in spatially varying current landscapes, relevant for analogue-gravity experiments in condensed matter systems.

Figures (3)

• Figure 1: (a) Optical microscope image of the PSWS device, showing the orientations of the applied DC current ($I_{\mathrm{DC}}$) and the external magnetic field ($H$). (b) Scanning electron microscope image of the antenna region and ferromagnetic strip, featuring a constriction with width $w_{\mathrm{c}} = 1140~\mathrm{nm}$, constriction total tapered length $l = 4.5~\mu\mathrm{m}$ and antenna distance center to center D=6.1 $\mu$m . (c) Example mutual inductance spectra for a device with $w_{\mathrm{c}} = 571~\mathrm{nm}$, showing the real, imaginary, and magnitude components of the signal, as well as the corresponding phase (right axis), measured at $\mu_0 H = +100~\mathrm{mT}$.
• Figure 2: Transmitted spin-wave spectra (mutual inductance amplitude) for (a) a uniform waveguide ($w_{\mathrm{c}} = 2000$ nm) and (b) a constricted waveguide ($w_{\mathrm{c}} = 571$ nm). The dots in (a) represent the extracted group velocity, plotted using the right-hand axis shown in panel (b) for clarity. (c) Minimum applied magnetic field required for detectable spin-wave transmission, plotted as a function of constriction width.
• Figure 3: (a) Real, imaginary, and phase components of the mutual inductance for the sample with $w_{\mathrm{c}} = 286$ nm at $I \approx 0.6$ mA (the noisiest dataset). (b) Absolute change in group velocity, $\Delta v_{\mathrm{g}} = v_{\mathrm{g}}(I) - v_{\mathrm{g}}(0)$, as a function of effective current for various constriction widths. Arrows indicate the relative directions of electron flow ($e^-$) and spin-wave propagation ($k$). (c) Antisymmetric component of the relative group velocity change, with linear fits shown as dashed lines. (d) Slopes of the experimental data fits in (c), from simulations and coefficient of Eq. \ref{['eq:relativevg']} with $M_s=750 \mathrm{~kA}$, $P=0.55$, $g=2.19$, $l=4.5~\mathrm{\mu m}$, $D=6.1~\mathrm{\mu m}$ and $w_0=2000~$nm highlighting the dominant current-induced contribution to $\Delta v_{\mathrm{g}}$ for narrower constrictions (see Supplementary Material for details on simulated slopes and $P$ value extraction).