## 3.1 XRD patterns

The crystalline structures of the powders are identified by XRD. The XRD patterns of Ni0.5Zn0.5Fe2O4, CI and CB powders are shown in Fig. 2. For the Ni0.5Zn0.5Fe2O4 pattern, nine diffraction peaks are noticed, which conform to (hkl) planes of (111), (220), (311), (222), (400), (422), (511), (440) and (533), respectively. The ideal spinel structure is noticed by the peaks of NiZn ferrite [12]. All the observed peaks of Ni0.5Zn0.5Fe2O4 are matched with the standard XRD pattern (JCPDS, PDF no. 08–0234). On the other hand, for the carbonyl iron pattern, three characteristic peaks are noticed, which conform to (hkl) planes of (100), (200), and (211), respectively. The XRD pattern of carbonyl iron resembles crystallites in which the sample mainly contains α-Fe phase [13]. All the observed peaks of CI are matched with the standard XRD pattern (JCPDS, PDF no. 06-0696). Finally, for the CB pattern, two characteristic peaks are noticed, which conform to (hkl) planes of (002) and (100), respectively [14].

## 3.2 FTIR spectra

The FTIR spectra of the Ni0.5Zn0.5Fe2O4, CI and CB powders is shown in Fig. 3. For the Ni0.5Zn0.5Fe2O4 nanoparticles, two peaks at 565.4 cm− 1 and 432.3 cm− 1 are referring to the stretching vibration of (Fe-O), which emphasizes the formation of the metal-oxygen in ferrite-based [15]. On the other hand, the peak at 1630.4 cm− 1 in Ni0.5Zn0.5Fe2O4, CI, and CB is referring to C = O stretching vibration, and the peaks at 2348 cm− 1 and 3452 cm− 1 are referring to O-H stretching vibration [16, 17].

## 3.4 EMI shielding and MA properties

There are two general methods that cope with the interference of incident electromagnetic waves: the first one is electromagnetic interference (EMI) shielding and the second one is microwave absorption (MA). For the EMI shielding method (Fig. 5a), the significant point is to attenuate the transmitted power of the EM waves (\({p}_{T}\)). On the other hand, for the microwave absorption method (Fig. 5b), though, a metal plate is put to reflect the transmitted power of the EM waves. As a consequence, the transmitted power of the EM waves is negligible in microwave absorption. EMI shielding and MA properties of the prepared samples are estimated with the free-space technique as shown in Fig. 6. EM waves are generated by a microwave generator in the frequency band of 8.8–12 GHz (with wavelengths λ = 2.5–3.4 cm), where a microwave generator is connected by a WR90 waveguide instrument (IEC Standard R100, X Band). The incident EM waves (\({p}_{in}\)) are measured by the horn antenna connected to an oscilloscope (Fig. 6), then the prepared sample perpendicularly is placed between a microwave generator and the horn antenna to measure the transmitted power of the EM waves (\({p}_{T}\)) by an oscilloscope. As a result, SE can be calculated for the EMI shielding by applying the Eq. (1) [18]:

$$SE \left(dB\right)={SE}_{R }+{SE}_{A}+{SE}_{M}=10 log\frac{{p}_{in}}{{p}_{T}}$$

1

It is significant to note that the multiple reflection loss (\({SE}_{M}\)) can be ignored if the absorption shielding (\({SE}_{A}\)) of EMI shielding material is higher than 10 dB and Eq. (1) then can be rewritten as [18]:

$$SE \left(dB\right)={SE}_{R }+{SE}_{A}=10 log\frac{{p}_{in}}{{p}_{T}}$$

2

In addition to that, the reflected power of the EM waves (\({p}_{ref}\)) is measured when the EM waves are incident on the sample surface at an angle of 45° by an oscilloscope. As a result, the shielding by reflection (\({SE}_{R }\)) can be calculated for the EMI shielding by applying the Eq. (3).

$${SE}_{R }\left(dB\right)=-10\text{log}\left(1-R\right)=-10\text{log}\left(1-\frac{{p}_{ref}}{{p}_{in}}\right) \left(3\right)$$

Finally, the shielding by absorption (\({SE}_{A}\)) is calculated by Eq. (4) [19, 20]:

$${SE}_{A} \left(dB\right)=-10\text{log}\left(\frac{T}{1-R}\right)= -10\text{log}\left(\frac{{p}_{T}}{{p}_{in}-{p}_{ref}}\right) \left(4\right)$$

Figure 7 represents the shielding efficiency (SE) of F/CI/CB composites in the frequency band of 8.8–12 GHz with various thicknesses (2–4–6 mm). The results illustrate that the maximum shielding efficiency is 21.7 dB at the frequency of 11.0 GHz for the thickness of 4 mm of the F/CI/CB-111 composite sample. Figure 8 shows the SER and SEA of F/CI/CB composites with various thicknesses (2–4–6 mm) at the frequency of 11.5 GHz.

For the microwave absorption method, the prepared sample is placed on the metal plate at an angle of 45° to measure the reflected power of the EM waves (\({p}_{ref}\)) by an oscilloscope. As a result, RL can be calculated by applying the Eq. (5) [19, 20]:

$$Rl \left(dB\right)=10log\frac{{p}_{in}}{{p}_{ref}} \left(5\right)$$

Figure 9 illustrates the RL of F/CI/CB composites with various thicknesses (2–4–6 mm) at the weight percentage of the absorber within a paraffin matrix (40% w/w). Figure 9 illustrates that the RL attenuation peaks of samples moved to lower frequencies with increasing sample thickness. This phenomenon may be defined by the quarter-wavelength (λ/4) cancellation model, as shown in Eq. (6) [21–23]:

$${t}_{m}=\frac{c}{4{f}_{m}\sqrt{\left|{\mu }_{r}\right|\left|{\epsilon }_{r}\right|}}$$

6

Where |εr| and |µr| are the modulus of the measured complex relative permittivity (\({\epsilon }_{r })\) and permeability (\({\mu }_{r })\) at matching frequency (fm), respectively. c is the velocity of light.

Table 2 shows the reasonable surface density (SD) of all the prepared absorbers. As a result, one can notice the impact of incorporating Ni0.5Zn0.5Fe2O4 and CI (magnetic loss materials) and CB (dielectric loss material) on the EMI and MA properties of the prepared absorber. This incorporation drives an effective and low thickness absorber with a wide BW− 10dB [24].

Table 2

MA behavior of Ni0.5Zn0.5Fe2O4/CI/CB composites at various thicknesses (2–4–6 mm).

Composite samples | t (mm) | RLmin (dB) | fm (GHz) | BW− 10 dB (GHz) | SD (kg/m2) | BW− 10 dB /SD (GHz.m2/kg) |

F/CI/CB-111 | 2 | -18.3 | 11.5 | 3.2 | 3.86 | 0.83 |

4 | -18.5 | 10.3 | 3.2 | 3.87 | 0.83 |

6 | -19.4 | 9.9 | 3.2 | 3.89 | 0.82 |

F/CI/CB-112 | 2 | -17.3 | 11.3 | 3.2 | 3.62 | 0.88 |

4 | -16.3 | 10.4 | 2.9 | 3.64 | 0.80 |

6 | -15.5 | 9.8 | 2.8 | 3.65 | 0.77 |

F/CI/CB-211 | 2 | -18.4 | 11.7 | 3.2 | 4.01 | 0.80 |

4 | -17.3 | 10.9 | 3.2 | 4.02 | 0.80 |

6 | -15.8 | 10.0 | 3.2 | 4.04 | 0.79 |