Unveiling Micrometer-Range Spin-Wave Transport in Artificial Spin Ice

TL;DR

The paper tackles the challenge of achieving long-range spin-wave transport in artificial spin ice (ASI), where purely dipolar coupling limits energy transfer. It introduces a hybrid ASI-PMA architecture that embeds in-plane magnetized ASI nanoelements in a perpendicularly magnetized multilayer to enable exchange-mediated coupling and evanescent spin-wave tunneling across the PMA. Micromagnetic simulations with realistic parameters show edge and bulk spin-wave modes propagating over about one micrometer, with group velocities reaching several hundred meters per second, significantly exceeding ordinary s-ASI. The work demonstrates tunability via vertex gap and external bias, reconfigurability through ASI microstate control, and compatibility with standard nanofabrication, pointing to reconfigurable on-chip magnonic circuits and studies of monopole dynamics.

Abstract

Artificial spin ice (ASI) systems exhibit fascinating phenomena, such as frustration and the formation of magnetic monopole states, and Dirac strings. However, exploring the wave phenomena in these systems is elusive due to the weak dipolar coupling that governs their interactions. In this study, we demonstrate coherent spin-wave propagation in an hybrid ASI system, which is based on a multilayered ferromagnetic thin film with perpendicular magnetic anisotropy and in-plane magnetized nanoelements embedded within it. We show that this system enables spin-wave transmission over a one-micrometer distance via exchange-mediated coupling between subsystems and evanescent spin-wave tunneling through the out-of-plane magnetized parts. This system overcomes the limitations of purely dipolar interactions in standard ASIs while preserving their fundamental properties. Thus, it provides a platform for studying spin-wave phenomena in frustrated ASI systems and paves the way for exploiting them in analog signal processing with spin waves.

Figures (4)

• Figure 1: ASI-PMA structure and resonant modes. (a) Schematic of a 1D chain of square ASI-PMA lattice (nanoelements: 200 × 75 nm²) embedded in Co/Pd multilayer. Yellow regions indicate microwave antennas. (b) Four vertex types (Type 1–4) classified by spin configuration and net charge $Q$. (c) Relaxed magnetization in ASI-PMA ($-2.5$ to $2.5$ µm).The hue represents the in-plane orientation of the magnetization, while the brightness indicates the out-of-plane value (black: $-z$ and white: $+z$). (d) Out-of-plane magnetization ($m_z$) static magnetization cross-sections across the nanoelement core (P1) and edge (P2) positions. The orange vertical stripes mark the antenna used for the SW excitation. (e,f) Mode profiles (dynamic $m_z$ component) of the edge mode (EM, 3.9 GHz) and the bulk mode (BM, 5.3 GHz) spanning distance from $-0.42$ to 0.42 µm around the antenna.
• Figure 2: Spin-wave transmission in s-ASI and ASI-PMA systems. 2D spatial intensity maps (sum of the squared amplitude of $m_x$, $m_y$ and $m_z$ magnetization components) for (a) s-ASI and (b) ASI-PMA systems. Right: Normalized transmission spectra ($S_{21}$) measured at 0.3 µm from the antenna center. (c) and (d) Spatial decay of the intensity of the propagating SW modes along $\pm x$-directions on log scale, showing EM and BM for ASI-PMA (d), and analogous modes for s-ASI (c). Dotted lines: the exponential fits $\propto \exp(-2x/\xi)$. In s-ASI, no bias field, in ASI-PMA $B_{\text{ext},z} = 50$ mT, in both cases the identical excitation was used.
• Figure 3: Tunability and characteristics of propagating spin-waves in ASI-PMA. (a,b) Dependence of SW propagation length on bias field $B_{\text{ext},z}$ and vertex gap $g$, showing monotonic decay for EM and maximum for BM. (c) Spatial distribution of the BM intensity, $A(x,f)$, through a single vertex gap (PMA matrix) and neighboring nanoelements for representative values of $g$.
• Figure 4: Dispersion characteristics of propagating spin waves in ASI-PMA. (a) Dispersion relations of SWs in ASI-PMA system at three selected values of $g$. Vertical dashed black lines mark the Brillouin-zone boundaries. (b) Maximum group velocity $v_\text{g}^{\max}$ derived from despersion relations for the EM and BM bands. All simulations made at 50 mT bias magnetic field.