Nonreciprocal Spin-Wave Dynamics in Crescent-Shaped Ferromagnetic Nanowires

TL;DR

This work investigates nonreciprocal spin-wave propagation in infinitely long nanowires with crescent-shaped cross-sections under a perpendicular bias field. Using micromagnetic simulations (TetraX) complemented by analytical modeling, it shows that SW dispersion and nonreciprocity are highly sensitive to mode character and CS geometry, with distinct LF, HA, and HF behaviors including field- and wavenumber-dependent sign changes. A phenomenological ellipticity-based model links nonreciprocity to modal ellipticity, while multimode hybridization explains the HA sign reversal, underscoring complex but tunable nonreciprocity in curved 3D nanostructures. These findings point to the potential of CS nanowires as building blocks for reconfigurable magnonic devices and nonreciprocal signal processing in nanoscale circuits.

Abstract

Recent progress in the study of spin-wave propagation in ferromagnetic waveguides has highlighted the role of nonreciprocity arising from both the interfacial Dzyaloshinskii-Moriya interaction and the chiral nature of dipolar interactions. In this paper, we examine how a nanowire with a crescent-shaped cross-section affects spin-wave propagation along its long axis when a bias magnetic field is applied perpendicular to the axis. Employing micromagnetic simulations supported by analytical modeling, we systematically analyze the effects of geometry and external magnetic field strength on the magnetization dynamics and spin-wave amplitude distribution. The results demonstrate that these factors modify the dispersion relation of spin waves and influence its nonreciprocity, which can vary depending on the mode type. This work advances the fundamental understanding of spin-wave dynamics in curved geometries and offers new perspectives for designing magnonic waveguides with tailored properties.

Figures (13)

• Figure 1: (a) Infinitely long CS nanowire with an external magnetic field $B_{\text{ext}}=0.5$ T applied along the $z$-axis. Arrows indicate the steady-state magnetization distribution. (b) Geometrical construction of the CS cross-section, defined as the set difference of two ellipses: $E_1$ with semi-axes $a_1=125$ nm and $b_1=200$ nm, $E_2$ with semi-axes $a_2=139$ nm and $b_2=135$ nm.
• Figure 2: Hysteresis loops of the CS nanowire illustrating the normalized, cross-sectionally averaged magnetization components, $m_z$ (red line) and $m_x$ (blue line), as a function of the external magnetic field $B_\mathrm{ext}$ applied along the $z$-axis. Arrows indicate the loop orientation for increasing and decreasing field. Insets display the static magnetization configurations at $B_\mathrm{ext} = 0.5$ and 1 T, with the colormap representing magnetization orientation as defined in the diagram in the lower-left corner.
• Figure 3: (a) FMR spectra of the CS nanowire as a function of the external magnetic field $B_{\mathrm{ext}}$ applied along the $z$-axis. Color represents the normalized absorption intensity (scale bar), and the red lines mark the field values taken into closer analysis in (b)-(d). (b)--(d) Spectra at selected field values: $B_{\mathrm{ext}}=$ 0.5 T, 1 T and 2 T, respectively. Insets LF, HA, and HF show the corresponding mode profiles: hue encodes the local precession phase (color wheel), while opacity encodes the normalized precession magnetization amplitude $|m| = \left(|m_x|^2 + |m_y|^2\right)^{1/2}$ (transparent at 0, opaque at 1).
• Figure 4: Dispersion relations of the first, counting from the lowest frequency, 16 SW modes propagating along the CS nanowire at three different values of the external magnetic field applied perpendicular to the nanowire axis. The LF, HA, and HF modes identified in Fig. \ref{['Fig:FMR']} are highlighted with blue, orange, and green dots, respectively.
• Figure 5: Nonreciprocity $\delta f(|k_x|) = f(-|k_x|) - f(|k_x|)$, i.e., the frequency difference between opposite wave vectors as functions of wavenumber $|k_x|$, for the three selected in Fig. \ref{['Fig:FMR']} SW modes: LF (a), HA (b), and HF (c). Results are shown for three values of the bias magnetic field applied perpendicular to the nanowire axis with magnitude $B_{\mathrm{ext}}=$ 0.5, 1.0 and 2.0 T, at which dispersion relations are shown in Fig. \ref{['Fig:dispersions']}.