Establishing the Magnetoelastic Origin of Spin-Wave Routing through Focused Ion Beam Patterning

TL;DR

This work addresses how Ga$^{+}$ FIB patterning steers spin waves in YIG by engineering local dispersion through irradiation-induced lattice dislocations. It combines trMOKE-determined dispersion with magnetoelastic modeling, AFM-measured thickness changes, and SRIM-based damage profiling to extract a magnetoelastic field $H_{mel}$ that evolves through three deformation regimes (elastic, plastic, partial amorphization). Micromagnetic simulations using the derived strain tensors reproduce the observed non-monotonic wavelength shifts, establishing a quantitative magnetoelastic basis for FIB-engineered GRIN spin-wave landscapes. The results enable magnetoelastically programmable magnonic devices and highlight the potential for reversible control by operating within the elastic regime, while also outlining the limitations of the current SRIM-based and tensor-simplified approaches.

Abstract

Spin waves are promising information carriers for analog and wave-based computing, requiring compact and precisely engineered scattering landscapes. Focused ion beam (FIB) irradiation enables such control by locally modifying the spin-wave dispersion in yttrium iron garnet (YIG), yet the underlying crystallographic mechanisms remain unclear. Here, we present an experimentally validated framework that attributes FIB-induced spin-wave steering to magnetoelastic effects arising from irradiation-induced lattice dislocations. Following FIB irradiation and wet-chemical etching, local height profiles were obtained by atomic force microscopy (AFM) and used as fixed geometric constraints in fits of spin-wave dispersion relations measured by time-resolved magneto-optical Kerr effect (trMOKE) microscopy. The dispersion relation was extended by an explicit magnetoelastic field term, treated as a fit parameter. Its evolution reveals three successive deformation regimes, elastic, plastic, and partial amorphization, explaining the observed non-monotonic dependence of the spin-wave wavelength on ion dose. A three-phase deformation scenario based on SRIM simulations reproduces the extracted magnetoelastic field trends, validating the fitting approach. Micromagnetic simulations incorporating strain tensors derived from the experimental magnetoelastic field reproduce the characteristic non-monotonic wavelength behavior. These results establish a physical basis for FIB-engineered graded-index (GRIN) spin-wave landscapes and magnetoelastically programmable magnonic devices.

Figures (11)

• Figure 1: Schematic overview of a $100~nm$ YIG thin film deposited by RF-Sputtering on a $500~µm$ GGG substrate. Spin wave excitation is provided by a $2~µm$ wide, $110~nm$ thick Ti($10~nm$)/Au($100~nm$) MSL. Adjacent to the antenna, squares of $50\times50~µm\squared$ (red), were irradiated with $\mathrm{Ga}^{+}$ ion doses ranging from $2$ to $60\times10^{12}~ions\per cm\squared$ in steps of $2\times10^{12}~ions\per cm\squared$. In the FVSW configuration, spin waves are excited at a $k_0$ wave vector directly beneath the antenna. Upon entering the irradiated regions, the wave vector changes to $k_{\mathrm{FIB}}$, and returns to $k_0$ after leaving the region.
• Figure 2: trMOKE measurement of a $t = 100~nm$ wet-chemically etched YIG film at $2.305~GHz$ and $8~\mathrm{dBm}$ input power with $\mu_{0}H_{\mathrm{ext,OOP}} = 250~mT$. (a) trMOKE image of coherently excited spin waves across $30$ distinct $\mathrm{Ga}^{+}$-implanted regions (irradiated at $30~keV$) over a propagation distance of $45~µm$. (b) Line-wise Fourier transformations of the spin-wave profiles in (a) reveal wavelength shifts as a function of ion dose. Three prominent wavelength regims are observed: I between the unimplanted reference ($0 \times 10^{12}~ions\per cm\squared$) and the first turning point at $12 \times 10^{12}~ions\per cm\squared$; II between $12 \times 10^{12}~ions\per cm\squared$ and $34 \times 10^{12}~ions\per cm\squared$; and III extending from $34 \times 10^{12}~ions\per cm\squared$ to a saturation regime near $60 \times 10^{12}~ions\per cm\squared$.
• Figure 3: Schematic stress–strain curve of a crystal under continuous irradiation, illustrating elastic and plastic deformation up to the breakdown of the crystalline structure.
• Figure 4: Illustration of the dislocation formation. (a) An incident ion beam initiates collision cascades that displace atoms from their lattice sites, creating a vacancy-rich core surrounded by interstitial atoms that aggregate into a defect cluster. (b) With increasing defect concentration, the cluster collapses into an energetically favored edge dislocation ($\perp$) loop. (c) A vacancy-type dislocation loop corresponds to a missing atomic plane, causing the surrounding lattice to bend inward toward the vacant lattice sites. (d) An interstitial-type dislocation loop corresponds to an additional atomic plane, pushing the lattice outward from the additional plane.
• Figure 5: Conceptual illustration of strain potential wells that translate dislocation dynamics into a three-phase scenario of irradiation-induced deformations. Phase I: Dislocations ($\perp$) nucleate and accumulate within the strain well at the ion-damage source, progressively filling it in a process known as source hardening. Phase II: As the local strain exceeds the potential threshold, dislocations overcome the barrier and migrate into neighboring wells, initiating plastic deformation. Phase III: Migrated dislocations pile up against obstacles such as surfaces, defects, or grain boundaries, producing friction hardening and ultimately leading to partial amorphization (//).