Predicting tunable nonreciprocal spin wave generation mediated by interfacial Dzyaloshinskii-Moriya interaction in magnonic heterostructures

TL;DR

This work tackles the challenge of achieving and controlling nonreciprocal spin waves in thin films where damping limits propagation. It develops a simple analytic approach based on the spin-wave dispersion and an overlap function to predict maximum nonreciprocity, validated by 1D micromagnetic simulations of a driven region with interfacial DMI. To overcome short propagation lengths, it proposes a magnonic heterostructure that confines iDMI to the driving region while using low-damping material elsewhere, enabling spin waves to travel over several microns. The framework provides a practical design tool for tunable, long-range nonreciprocal magnonic devices and points to future work on anisotropy and interface effects to further optimize performance.

Abstract

Thin, metallic magnetic films can support nonreciprocal spin waves due to the interfacial Dzyaloshinskii-Moriya interaction (iDMI). However, these films typically have high damping, making spin wave propagation distances short (less than one micrometer). In this work, we theoretically study a thin ferromagnetic strip with iDMI and excite spin waves by driving a central segment of the strip. Spin waves propagate with different amplitudes to the left versus to the right from the driving region (i.e. nonreciprocity occurs) due to the iDMI. Our calculation based on spin-wave-dispersion plus our micromagnetic simulations both show that changing the driving segment width, driving frequency and static applied field strength tunes the nonreciprocity. Our calculation based on spin-wave-dispersion, using a so-called "overlap function" will allow researchers to predict conditions of maximum nonreciprocity, without the need for computational solvers. Moreover, to circumvent the issue of short propagation distances, we propose a geometry where iDMI is only present in the driving region and low-damping materials comprise the remainder of the strip. Our calculations show significant spin wave amplitudes over several microns from the excitation region.

Figures (6)

• Figure 1: (a) Schematic diagram of the thin film strip (modeled as a quasi-one-dimensional spin chain) with bias magnetic field applied along $z$ and the oscillatory driving field $\mathbf{h}$ along $x$. (b) Dispersion relation for the system in the presence of DMI (solid line) and when no DMI is present (dashed line). (c) Snapshot of the magnetization ($m^x$) along the $x$ axis after 8 ns of driving for $D_z=$0.8 mJm$^{-2}$ and damping $\alpha=0.01$ across the full chain. The center of the spin-chain is driven ($d=$ 180 nm, shaded region) at a driving frequency $f_d=$11.4 GHz and driving amplitude $h=$ 0.03 mT. The wave vector for left- and right-bound propagating spin waves at $f_d$ are indicated in (b) as $k_L$ and $k_R$, respectively.
• Figure 2: (a) Resonant spin wave frequencies as a function of wavelength for left (dashed) and right (solid line) bound propagation, obtained from the dispersion relation in Fig. \ref{['fig:Dispersion']}(b). The horizontal line shows the case of $f_d=11.4$ GHz that is used throughout this work, with wavelengths corresponding to $k_L$ and $k_R$ labeled. (b) Equivalent overlap function $\vartheta$ as function of driving frequency for a driven region of width $d =$ 180 nm, plotted on a log scale.
• Figure 3: (a) Schematic diagram of the thin film strip (modeled as a quasi-one-dimensional spin chain) with bias magnetic field applied along $z$ and a drive region of width $d$, which is the only region with DMI. We assume that within the driving region, $D_z=$ 0.8 mJm$^{-2}$ and $\alpha=0.01$. Elsewhere, $\alpha=$ 10$^{-4}$. In the gray shaded regions at the ends, $\alpha$ linearly increases from 10$^{-4}$ to 0.2 at the very edges. (b) Snapshot of magnetization motion along the $x$ axis for $f_d=$ 11.4 GHz after driving for 8 ns (91 cycles). (c) Spatial FFT of the data in Fig. \ref{['fig:theta']}(b), termed $\tilde{m}^x(k)$. The dark blue line is obtained by taking the data to the right of the driving region ($+k$), while the cyan line is obtained by taking the data to the left of the drive ($-k$). (d) The maximum FFT value of $\tilde{m}^x(k)$, termed $\mathcal{R}(\pm k)$, for generated spin waves (somewhat equivalent to the overlap function). The dark, blue circles are for right- $(x>0)$ and the cyan squares are for left-propagation $(x<0)$. For clarity, the amplitudes are given on a log scale.
• Figure 4: Nonreciprocity efficiency constant $\eta$ as a function of driving field frequency $f_d$. We compare the micromagnetic solutions $\eta_{\textrm{num}}$ (symbols) with the prediction based on spin wave dispersion $\eta_{\textrm{simple}}$ (solid lines). These are given for three different driving region widths (a) $d=$ 180 nm, (b) $d=$ 90 nm, and (c) $d=$ 360 nm.
• Figure 5: (a) Dispersion relation for two applied fields of $B_0=$ 50 mT (dashed line) and $B_0=$ 150 mT (solid line). Both cases are for a thin strip, considering the presence of iDMI interaction. The nonreciprocity dimensionless parameter $\eta$ for both the numerical simulations ($\eta_{\textrm{num}}$) and predictions based on the dispersion relation ($\eta_{\textrm{simple}}$) are given for (b) $d=$ 180 nm, (c) $d=$ 90 nm and (d) $d=$ 360 nm, all as function of applied field $B_0$. Through (b) to (d) the driving frequency is kept constant, $f_d=$ 11.4 GHz, and other parameters are the same as used in Fig. \ref{['fig:theta']}.