Scattering theory of spin waves by lattice dislocation defects

TL;DR

The paper develops a continuum magnetoelastic framework to study spin-wave propagation in magnetic insulators containing lattice dislocations. Dislocation strain fields generate localized magnetic textures that act as effective scattering potentials, producing asymmetric and interference-like transport phenomena across 1D and 2D geometries, and altering domain-wall dynamics. By combining 1D reductions, full 3D simulations, and First Born–type scattering theory, the authors map how dislocation type and magnetoelastic coupling control reflection, transmission, and angular scattering patterns, including the disruption of intrinsic domain-wall reflectionless behavior. The results highlight lattice dislocations as tunable centers for defect engineering in magnonic devices and suggest avenues for defect-assisted control of spin-wave transport in functional spintronic systems.

Abstract

We investigate spin-wave propagation in magnetic insulators in the presence of lattice dislocations. Within a continuum magnetoelastic framework, we show that the strain fields generated by dislocations induce equilibrium magnetic textures. The morphology of these textures depends sensitively on the dislocation type and acts as a localized scattering potential for spin-wave excitations. As a result, the scattering response exhibits pronounced asymmetries and interference effects governed by the magnetoelastic coupling and the dislocation type. By combining numerical simulations with analytical scattering theory, we compute differential cross sections and frequency-dependent transmission coefficients. Furthermore, analysis of the effective potential landscape reveals that the defect forms a barrier that modulates spin-wave transport and, crucially, breaks the intrinsic reflectionless nature of magnetic domain walls. Our findings identify lattice dislocations as tunable scattering centers, opening new avenues for defect engineering in magnonic devices.

Figures (14)

• Figure 1: Schematic of SW scattering by an effective potential, $V_{\text{eff}}$, produced by a dislocation line. The vectors $\bm{k}_{\text{inc}}$ and $\bm{k}_{\text{out}}$ denote the incident and scattered SW vectors, respectively. Similarly, $\theta_{\text{inc}}$ and $\theta_{\text{sc}}$ represent the incident and deflection angles within the $xz$-plane, while $\alpha$ defines the azimuthal angle of incidence within the $xy$-plane.
• Figure 2: Relaxed magnetization profiles for the one-dimensional model in the weak regime. Panels (a)-(c) show the relaxed profiles for the homogeneous boundary conditions, and panels (d)-(f) show the relaxed profiles for the domain wall conditions. Columns correspond to mixed, edge, and screw dislocation types, respectively. Additionally, panel (f) shows the defect-free Bloch wall profile (dashed lines) schryer.
• Figure 3: Magnetic ground states in the presence of different dislocation types. The configurations were obtained from an initial ferromagnetic state along the $y$-axis for a (a) mixed and (b) screw dislocation. For comparison, panels (c) and (d) show the strong coupling regime for a mixed and screw dislocation, respectively. Arrows represent the in-plane magnetization components $(m_x, m_z)$, while the color scale encodes the out-of-plane component $m_y$.
• Figure 4: (a) One-dimensional effective potential profiles for different dislocation types in the quasi-homogeneous case. The inset provides a magnified view of the weak coupling regime (solid lines) near the origin. Dashed lines represent the strong coupling regime, and the horizontal pink line indicates the 5 GHz excitation level. (b) Reflection (left) and transmission (right) coefficients for SW scattering as a function of frequency $\omega$ and incident angle $\alpha$.
• Figure 5: (a) One-dimensional effective potential for the $b_{1,2} = 8\times10^4$ J/m$^3$ limit. Profiles for mixed (black), edge (blue), and screw (red) dislocations are compared to the analytical Pöschl-Teller potential (dashed black line). The horizontal pink line indicates the 0.7 GHz excitation level. (b) Reflection (left) and transmission (right) coefficients for SW scattering as a function of frequency $\omega$ and incident angle $\alpha$.