Tuning Microwave Resonance in FeCoBSi Stripe‑Patterned Films: Thickness‑Dependent Magnetic Characterization

Background

Electromagnetic interference (EMI) poses a growing challenge to high‑frequency communication systems. To counteract this, broadband, tunable resonances in magnetic films are essential for effective EMI shielding. A high damping factor at the target frequency further enhances absorption performance.

In-plane uniaxial anisotropy, often induced during deposition or by post‑annealing, yields soft magnetic behavior at gigahertz frequencies. However, achieving controllable broadband response requires additional design strategies. Patterned magnetic films, engineered with shape anisotropy through lithography, offer a robust, scalable route to tailor resonance characteristics.

Our prior work on double‑stripe FeCo films demonstrated a dual‑peak resonance, confirming that independent magnetic stripes can superimpose to broaden the response. Building on this insight, the present study introduces a five‑stripe design, each stripe differing in width, to further extend the resonance band. We analyze the resulting microwave behavior using the Landau–Lifshitz–Gilbert (LLG) framework, accounting for demagnetization effects, and confirm that the broadened band is mathematically predictable and experimentally realizable.

Experiment

Fe₆₆Co₁₇B₁₆Si₁ films were deposited by DC magnetron sputtering onto Si(111) substrates at room temperature. A 500 Oe field aligned along the substrate’s short axis induced in‑plane uniaxial anisotropy (Fig. 1a). UV lithography followed by lift‑off defined the combined stripe pattern, comprising stripes of 5, 10, 15, 20, and 25 µm widths, separated by 5 µm gaps. Film thicknesses ranged from 45 to 135 nm.

The deposition scheme (a) and resulting stripe pattern (b). Widths: 5, 10, 15, 20, 25 µm; gap: 5 µm.

Thickness was verified by cross‑sectional SEM. Static magnetic properties were measured with a vibrating sample magnetometer (VSM). Microwave permeability was obtained using a shorted micro‑strip line perturbation method coupled to a vector network analyzer, covering 0.5–6 GHz.

Results and discussion

The deposition geometry (Fig. 1a) ensured a 500 Oe field during growth, imparting a clear in‑plane easy axis. Post‑deposition lift‑off produced the intended stripe pattern (Fig. 1b). XRD revealed no crystalline peaks aside from Si(111), confirming the amorphous or nanocrystalline nature of the films.

Hysteresis loops (Fig. 2) illustrate pronounced uniaxial anisotropy: coercivity along the hard axis (H_ch) drops from 32 Oe at 45 nm to 13 Oe at 135 nm, consistent with the random‑anisotropy model of Herzer. The low H_ce values (< 13 Oe) confirm the soft‑magnetic quality of the films.

Hysteresis loops for 45–135 nm films, showing easy and hard axes. Thickness increases from (a) to (d).

Permeability spectra (Fig. 3) reveal split resonance peaks for the 45 nm film: μ′ ≈ 170 at f_low ≈ 3.2 GHz and f_high ≈ 5 GHz. As thickness grows, f_low shifts upward; for 135 nm, f_low reaches 4.2 GHz while f_high likely lies beyond 6 GHz. The FWHM expands to over 4 GHz at 45 nm, surpassing the 2 GHz width observed in double‑stripe films. This enhancement stems from distinct shape‑anisotropy fields in the five stripe widths, each acting independently due to the 5 µm separation.

To model the dynamics, we employed the LLG equation incorporating demagnetization factors (N_x, N_y, N_z) for each stripe:

Using N_x and N_y expressions (Eqs. 3–5), the resonance frequency for each stripe width was calculated (Fig. 4). With α = 0.03, M_s = 1345 emu cm⁻³, and H_e = 40 Oe, the model predicts resonance frequencies that shift upward with thickness, broadening the overall band. When the film exceeds 110 nm, the 5 µm stripe’s resonance surpasses the 6 GHz measurement limit, reducing the FWHM relative to the 45 nm sample.

Calculated resonance frequencies for stripes of 5–25 µm across thicknesses. The blue band marks the 6 GHz measurement window.

Figure 5 compares the measured imaginary permeability of the combined‑stripe film (red band) with the calculated single‑stripe response. The excellent overlap confirms that the broadened band arises from the superposition of independent stripe resonances.

Measured and calculated imaginary permeability for 45 nm film; red area indicates the combined‑stripe FWHM. Calculated single‑stripe curves demonstrate the origin of the broad band.

Conclusions

By engineering a five‑stripe FeCoBSi pattern and controlling film thickness, we achieved a 4 GHz wide resonance band—an improvement over previous double‑stripe designs. The tunability afforded by stripe width and thickness makes this approach highly suitable for next‑generation EMI shielding and microwave devices.

Abbreviations

EMI:

Electromagnetic interference

FWHM:

Full width at half maximum

LLG:

Landau–Lifshitz–Gilbert