Frequency-thickness normalized electromagnetic parameter design for broadband electromagnetic wave absorption in FeCoCu alloy foams

Electromagnetic wave absorbing materials (EWAMs) are critical for mitigating electromagnetic (EM) pollution, yet achieving broadband absorption with thin coatings remains challenging because clear criteria for EM parameters optimization are still lacking. Herein, a frequency-thickness normalized EM parameters construction strategy is proposed based on transmission line theory. By quantitatively correlating complex permittivity, frequency, and coating thickness with reflection-loss minimization, the optimal complex permittivity for thin broadband absorption is constructed as $$ \varepsilon_{\mathrm{r}}^{\prime}=\left(\frac{76}{f d}\right)^{2} \\ $$, and $$ \varepsilon_{\mathrm{r}}^{\prime \prime}=\frac{95}{f d} \\ $$ (f in GHz and d in mm), thereby identifying the target complex permittivity distribution. The results show that pure conduction loss inherently deviates from the required parameter evolution and limits effective absorption bandwidths (EABs), whereas polarization and magnetic losses provide additional tunable degrees of freedom to approach optimal absorption conditions. To validate this theory-guided design principle, FeCoCu alloy foams with tunable Cu contents were synthesized. Cu incorporation regulates conduction loss and induces body-centered cubic (BCC)/face-centered cubic (FCC) dual phases, generating abundant heterogeneous interfaces for interfacial polarization, while the FeCo matrix preserves desirable magnetic loss. An equivalent circuit model further elucidates the dielectric loss mechanism, revealing that Cu mainly enhances interfacial polarization intensity rather than changing relaxation dynamics. Benefiting from the optimized coupling of conduction loss, polarization loss, magnetic loss, impedance matching, and quarter-wavelength cancellation, the Fe₆₅Co₃₀Cu₅ foam achieves an effective absorption bandwidth of 7.36 GHz with a coating thickness of 1.74 mm. This work provides a theory-guided framework for constructing optimal EM parameters and understanding dielectric loss mechanisms toward thin, efficient, and broadband EWAMs.