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Sun et al. Soft Sci. 2025, 5, 35 https://dx.doi.org/10.20517/ss.2025.21 Page 9 of 16

Figure 4. (A) Real permittivity (ε'), (B) imaginary permittivity (ε''), (C) tanδ , (D) real permeability (μ'), (E) imaginary permeability (μ''),
ε
(F) tanδ and (G) average complex permittivity of FCNZ-500, FCNZ-600 and FCNZ-700 composites; Cole-Cole curves of composites
μ
of (H) FCNZ-500, (I) FCNZ-600 and (J) FCNZ-700.
The dielectric loss includes the conduction loss and the polarization loss, the relationship between ε' and ε''
can be expressed as [52,53] :

One semicircle in the Cole-Cole plot of ε' - ε'' stands for a Debye relaxation process . In Figure 4H-J,
[54]
FCNZ-500, FCNZ-600, and FCNZ-700 show multiple Cole-Cole semicircles. Meanwhile, interfacial and
[55]
dipole polarization may exist due to the different electronegativity between atoms . Furthermore, the Cole-
Cole curve intuitively reflects that FCNZ-600 has multiple active and distinguishable relaxation processes in
wider frequency band.

Based on the complex permeability results, FCNZ-500, FCNZ-600, and FCNZ-700 present good magnetic
loss capability. Generally, the magnetic loss is mainly composed of natural, exchange resonance and eddy
current loss. By investigating C -f - the relationship between the eddy current constant and the frequency -
0
which is further analyzed, the eddy current loss can be evaluated using :
[54]