Magnonic Radar: Spin-Wave Based Detection

• Magnonic radar is a technique that uses spin-wave packets to non-invasively detect and quantify the translational and angular dynamics of domain walls in magnetic systems.
• It operates by launching coherent spin-wave excitations and analyzing dual Doppler frequency shifts—one from translation and one from rotation—to extract key motion parameters.
• The approach enables high temporal and spatial resolution measurements and supports scalable, programmable on-chip implementations for advanced magnonic and memory devices.

Magnonic radar is a paradigm in which spin-wave packets fulfill the role of electromagnetic (photon-based) or acoustic pulses, enabling non-contact, high-bandwidth, and vector-resolved interrogation of dynamic magnetic textures. Conceptually analogous to conventional radar, magnonic radar launches coherent spin-wave excitations toward a dynamic entity—typically a domain wall in a synthetic antiferromagnet—detects the scattered (reflected and transmitted) waves, and analyzes their frequency shifts arising from both translational and internal precessional motion of the domain wall. The extracted information provides direct, time-resolved access to the wall’s position, velocity, and angular dynamics, and is extensible to scalable on-chip implementations leveraging programmable magnonic circuits (Lan et al., 2 Sep 2025, Florio et al., 30 Apr 2026).

1. Fundamental Principles and Physical Platform

Magnonic radar operationalizes the analogy between spin waves and electromagnetic/phononic probes. In magnetic systems, a spin wave is defined as a small-amplitude, propagating oscillation of the magnetization vector $\mathbf{m}(x,t)$, characterized by wavevector $k$ and circular polarization index $\sigma=\pm1$. The target is typically a domain wall—a topological magnetization texture—in a synthetic antiferromagnet (SAF). In SAFs, the domain wall exhibits both translational ($V=dX/dt$) and angular ($\Omega=d\Phi/dt$) degrees of freedom, governed under small damping ($\alpha$) by coupled Thiele equations: $$V = \frac{J\,W\,\varphi_0}{1+\alpha^2}\,e^{-t/\tau},\qquad \Omega = -\frac{J\,\chi_0}{(1+\alpha^2)\,W}\,e^{-t/\tau}$$ with $J$ (interlayer coupling), $W$ (wall width), $\tau\approx (1+\alpha^2)/(\alpha J)$, $k$0, $k$1 (initial tilt and offset).

The spin wave’s interaction with the moving/precessing wall is described by a covariant time derivative in the quantum-like equation of motion: $k$2 Transforming to the moving/rotating wall frame leads to a Doppler-shifted frequency: $k$3 delineating two orthogonal contributions: a translational shift $k$4 and an angular (rotational) shift $k$5.

2. Dual Doppler Effect and Information Extraction

The crux of magnonic radar is the simultaneous extraction of both translational and angular velocities via distinct Doppler-shifted channels:

• Reflected spin waves encode the pure translational Doppler effect, yielding a shift $k$6.
• Transmitted, polarization-resolved spin waves encode the sum of translation and angular effects, $k$7 (leading term for $k$8).

In general, the observable frequency shift is

$k$9

with $\sigma=\pm1$0 for right/left circular polarization. Measuring both reflection and polarization-resolved transmission frequencies enables algebraic solution for $\sigma=\pm1$1 and $\sigma=\pm1$2. The scheme is robust to various internal wall dynamics, including inertial and micro-Doppler (e.g., breathing, twisting mode) features.

3. Experimental Realization and Simulation Methodology

Spin-wave packets are generated using local antenna fields of the form: $\sigma=\pm1$3 where $\sigma=\pm1$4 (central frequency), $\sigma=\pm1$5 (packet width), and field amplitude $\sigma=\pm1$6 set temporal and spectral parameters (e.g., $\sigma=\pm1$7 GHz, $\sigma=\pm1$8 ns). Linear or circular polarization is achieved by phase control of orthogonal antenna components. The SAF nanowire is initialized with a domain wall at $\sigma=\pm1$9, with small perturbations in the Walker-profile initiating finite $V=dX/dt$0 or $V=dX/dt$1.

Detection employs spatially separated monitors for reflected and transmitted packets. Magnetization components (e.g., $V=dX/dt$2, $V=dX/dt$3) are time-resolved and Fourier-transformed (FFT) to yield the power spectrum $V=dX/dt$4. Fitting the spectral peak with a Gaussian allows the extraction of the shifted frequency $V=dX/dt$5 for each channel.

• Non-invasive regime: low $V=dX/dt$6 ensures minimal back-action on wall dynamics, ideal for repeated measurements with constant Doppler shifts.
• Invasive regime: higher $V=dX/dt$7 enables mapping of wall acceleration/deceleration due to magnon momentum transfer, revealing time-dependent $V=dX/dt$8 and $V=dX/dt$9.

4. Frequency-Domain Signal Processing and Quantitative Analysis

The quantitative workflow is:

• Time-to-frequency conversion: signal windowing and FFT per scattered packet.
• Gaussian peak fitting: isolation of $\Omega=d\Phi/dt$0 for reflected and transmitted, polarization-selective channels.
• Velocity extraction:
  • Reflected: $\Omega=d\Phi/dt$1
  • Transmitted ($\Omega=d\Phi/dt$2): $\Omega=d\Phi/dt$3
  • Simultaneous solution yields both $\Omega=d\Phi/dt$4 and $\Omega=d\Phi/dt$5.

Temporal resolution in tracing $\Omega=d\Phi/dt$6, $\Omega=d\Phi/dt$7 is determined by packet repetition interval (few ns), while frequency resolution (controlled by $\Omega=d\Phi/dt$8) typically provides GHz–MHz accuracy. Sensitivity is governed by noise and acquisition window; MHz-scale frequency shifts, corresponding to velocities $\Omega=d\Phi/dt$9 m/s or $\alpha$0 MHz, are measurable. Spatial resolution derives from group-velocity contrast, allowing unambiguous assignment of reflected and transmitted channels over distances of several microns.

5. Programmable Magnonic Meshes for On-Chip Radar Architectures

Programmable integrated magnonic meshes provide a scalable front-end compatible with magnonic radar protocols. Yttrium iron garnet (YIG) circuits synthesized via direct laser writing support:

• Spin-wave propagation: phase-coherent transport over $\alpha$1 wavelengths; bandwidth up to $\alpha$2 GHz.
• Directional couplers: energy transfer between waveguides on length scales $\alpha$3m; loss per coupler $\alpha$4 dB.
• Phase shifters: tunable via applied field $\alpha$5, allowing $\alpha$6 phase control over $\alpha$7m.
• Routers and mesh networks: cascaded stages realizing $\alpha$8 reconfigurable interferometric meshes, with beamforming, splitting, and demultiplexing functionalities.

A canonical magnonic radar front-end is built as follows (Florio et al., 30 Apr 2026):

• Transmit path: single input is split and phase-shifted across $\alpha$9 branches, each feeding a spin-wave antenna. The phase ramp $$V = \frac{J\,W\,\varphi_0}{1+\alpha^2}\,e^{-t/\tau},\qquad \Omega = -\frac{J\,\chi_0}{(1+\alpha^2)\,W}\,e^{-t/\tau}$$0 steers the emitted beam.
• Receive path: scattered spin-wave echoes are re-combined with phase-conjugate settings for SNR maximization in the desired direction, or demultiplexed to parallel detectors for multibeam operation.
• Reconfigurability: switching times $$V = \frac{J\,W\,\varphi_0}{1+\alpha^2}\,e^{-t/\tau},\qquad \Omega = -\frac{J\,\chi_0}{(1+\alpha^2)\,W}\,e^{-t/\tau}$$1s, dynamic reprogramming of phase and amplitude, bandwidth up to 10 GHz.

6. Performance, Resolution, and Applications

Magnonic radar delivers:

• Temporal resolution: $$V = \frac{J\,W\,\varphi_0}{1+\alpha^2}\,e^{-t/\tau},\qquad \Omega = -\frac{J\,\chi_0}{(1+\alpha^2)\,W}\,e^{-t/\tau}$$2 ns; sub-ns possible in low-damping media.
• Frequency shift sensitivity: $$V = \frac{J\,W\,\varphi_0}{1+\alpha^2}\,e^{-t/\tau},\qquad \Omega = -\frac{J\,\chi_0}{(1+\alpha^2)\,W}\,e^{-t/\tau}$$3 of order 10 MHz.
• Spatial discrimination: $$V = \frac{J\,W\,\varphi_0}{1+\alpha^2}\,e^{-t/\tau},\qquad \Omega = -\frac{J\,\chi_0}{(1+\alpha^2)\,W}\,e^{-t/\tau}$$4m-scale channel separation from group-velocity differences.
• Scalability: mesh-based arrays up to $$V = \frac{J\,W\,\varphi_0}{1+\alpha^2}\,e^{-t/\tau},\qquad \Omega = -\frac{J\,\chi_0}{(1+\alpha^2)\,W}\,e^{-t/\tau}$$5 demonstrated without intermediate amplification.

Principal applications:

• Real-time, all-magnonic tracking of domain wall velocities $$V = \frac{J\,W\,\varphi_0}{1+\alpha^2}\,e^{-t/\tau},\qquad \Omega = -\frac{J\,\chi_0}{(1+\alpha^2)\,W}\,e^{-t/\tau}$$6 and precessional rates $$V = \frac{J\,W\,\varphi_0}{1+\alpha^2}\,e^{-t/\tau},\qquad \Omega = -\frac{J\,\chi_0}{(1+\alpha^2)\,W}\,e^{-t/\tau}$$7 for magnetic memory (e.g., racetrack memories).
• In situ calibration and characterization of dynamic magnonic devices, including logic gates and time-varying metamaterials.
• Spectroscopic access to fundamental spin texture dynamics, including inertial response, Walker breakdown, and complex micro-Doppler sidebands.

A plausible implication is that the integration of programmable magnonic meshes with Doppler-based interrogation opens a pathway to entirely on-chip, contactless, and high-throughput domain wall detection systems, compatible with both classical and quantum signal processing modalities.

7. Context, Limitations, and Prospects

The magnonic radar concept fundamentally extends previous electrical and magneto-optical methods by providing a vector-resolved, frequency-domain, and non-invasive probe of domain wall dynamics. Relative to prior work, unique features include dual Doppler sensitivity (translation and angular), high spatial-temporal resolution, and extension to fully integrated chip-scale architectures with programmable routing and beamforming. Realistic limits on velocity and rotation rate resolution are imposed by material damping, antenna bandwidth, and SNR; advances in materials (e.g., low-$$V = \frac{J\,W\,\varphi_0}{1+\alpha^2}\,e^{-t/\tau},\qquad \Omega = -\frac{J\,\chi_0}{(1+\alpha^2)\,W}\,e^{-t/\tau}$$8 YIG) and device engineering continue to enhance attainable precision.

This framework supports exploration of nonequilibrium magnetic phenomena and supports device concepts for magnonic information technologies, where dynamic control and rapid readout of domain wall motion are critical. The documented mesh primitives and radar protocol specify a complete route from physical principle to CMOS-compatible, scalable implementation (Lan et al., 2 Sep 2025, Florio et al., 30 Apr 2026).