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Hao et al. Soft Sci. 2025, 5, 39 https://dx.doi.org/10.20517/ss.2025.48 Page 7 of 25

[72]
which a spinel phase is dispersed within a rock salt matrix . By leveraging the significant polarization loss
inherent to high-entropy oxides and the spatial distribution of functional units, the resulting composite
[72]
demonstrates outstanding electromagnetic wave absorption performance .

Microwave absorption mechanisms of mesoscopic metacomposites
Dielectric materials primarily exhibit the polarization response and conduction response when subjected to
electromagnetic fields. The permittivity (ε = ε ’ - jε ’’) characterizes the response behavior of dielectric
r
r
r
materials in electromagnetic fields. The real part of the permittivity indicates the ability to store
electromagnetic energy, while the imaginary part reflects the capacity to dissipate electromagnetic energy .
[73]
According to the metal back-panel theory, reflection loss (RL) represents microwave absorption
performance, which was simulated using measured electromagnetic parameters through

where Z and Z = 377 Ω denote the material impedance and vacuum impedance; d, c, and f represent the
in
0
absorber thickness, velocity of light, and measured frequency, respectively . μ is the permeability, with a
[74]
r
value of 1 in dielectric materials. When the RL is below -10 dB, 90% microwave attenuation was expected.
Here, the frequency range with RL below -10 dB was considered as the effective absorbing bandwidth
(EAB). The characterization of electromagnetic parameters can be performed through two primary
methodologies: rectangular waveguide techniques and coaxial transmission-reflection measurements. The
coaxial approach demonstrates distinct advantages in the 2-18 GHz frequency range, offering both
measurement efficiency and standardization benefits. This method accommodates test specimens with
uniform dimensions (ϕ = 7 mm, ϕ = 3.04 mm, thickness d = 2 mm), significantly simplifying sample
in
out
preparation procedures. Conversely, waveguide characterization presents inherent technical constraints.
The method’s effectiveness is limited by three key factors: (1) cutoff frequency requirements; (2) mode
matching complexities; and (3) resonant oscillation interference. These limitations necessitate the use of
frequency-specific sample geometries (X-band: 22.8 × 10.16 mm; Ku-band: 15.90 × 8.03 mm) to ensure
accurate absorption property evaluation across different operational bands.

As given in the Debye equation ε ’’ = ε ’’ + ε ’’ = (ε - ε )ωτ/(1 + ω²τ(T)²) + σ(T)/(ε ω), here, ε , ε , ε , ω, τ, σ
r
s
p
c
0
s
0
∞
∞
represent the permittivity of free space, the static permittivity, the relative permittivity at the high-frequency
[75]
limit, the relaxation time, the angular frequency, and the conductivity, respectively . ε ’’ indicates
c
conductivity loss, which is closely associated with the conductivity of the material. Qin et al. divided
conductive losses into two models . The first type is the electron transfer model. Free charges can rapidly
[76]
migrate within the material under the influence of an external electric field. The latter is the electronic
hopping model. The presence of various interfaces and defects in dielectric materials makes it difficult for
free charges to migrate quickly. Nonetheless, the establishment of macroscopic conductive networks
reduces the energy barrier for electron hopping, enhancing charge transfer in microwave-absorbing
materials . With the rise of temperature, the intensification of electron thermal motion promotes the
[77]
increase of conductivity. However, excessively high conductivity undoubtedly leads to impedance
mismatches.
Conductive loss serves a pivotal role in MSMCs, particularly for units incorporating conductive
components such as carbon-based materials and conductive polymers. Under the action of the
electromagnetic wave electric field, charge carriers (electrons or holes) inside the functional unit undergo
directed migration, forming a conductive current. In the process of migration, the carriers collide with the
lattice and impurities, converting electromagnetic energy into thermal energy to achieve efficient microwave