Crystal structure engineering of GdFeO3/Mxene composites with excellent electromagnetic wave absorption: role of phase transition and high polarizability

The development of new materials that can absorb electromagnetic waves (EMW) is needed to address the problem of signal interference and crosstalk. In this study, a new composite material consisting of MXene and GdFeO 3 nanoparticles has been synthesized using crystal structure engineering to improve EMW attenuation performance between 2 and 18 GHz. The GFO nanoparticles, with a size of 30–40 nm, are evenly distributed on the surface of the MXene layers. The XRD and Raman spectra of the composite material show different phases of GdFeO 3 , which have different crystal symmetries and coordination states. The XPS and EPR measurements indicate the coexistence of various valence states of Fe, which leads to oxygen vacancies in the lattice. The addition of MXene greatly increased the speci�c surface area and dielectric properties of the composite material. Due to the improved polarization and phase transition behavior, the P-E loop, DM constant, and attenuation constant were signi�cantly enhanced. The combination of good ferroelectric GdFeO 3 and disordered crystal phase into the multilayered MXene matrix resulted in an enhancement of conductive and magnetic losses. Experimental results demonstrated that the Pbnm GdFeO 3 /MXene composites exhibited excellent EMW absorption performance. At a thickness of 4 mm, the minimum re�ection loss was − 61.5 dB, and a maximum effective absorption bandwidth of 8.62 GHz was achieved at 10.8 GHz due to the good dielectric, magnetic, and multiple re�ections contributing to superior EMW absorption performance with a broad band.


Introduction
Electromagnetic wave absorption (EWA) materials have garnered signi cant attention due to their potential applications in various elds such as radar stealth technology, communication, and electronic warfare [1]. However, current EMA materials often suffer from limitations such as narrow bandwidth, low absorption capacity, and poor thermal stability [2]. The mechanism of EM absorption is based mainly on the electromagnetic wave-matter interaction which consists dielectric loss and magnetic loss [3,4]. When the EMA passes through a material, the electric eld of the wave causes the electrons in the material to oscillate, resulting in energy dissipation (dielectric loss), while the magnetic eld of the wave causes the magnetic domains in the material to rotate, resulting in energy dissipation, particularly in the lower frequency ranges where magnetic elds play a more dominant role. (magnetic loss) [5][6][7][8][9][10][11][12]. Therefore, the dielectric constant and magnetic property are crucial for EMA.
To overcome these limitations, nano-composites are appealing to realize the broadband absorption, particularly through combining dielectric loss-type nanomaterials, such as MXene [13][14][15][16] with magnetic loss-type nanomaterials such as Fe 3 O 4 [17]. Much promising impedance match and broadband absorbing capacity have been achieved due to the enhanced interfacial polarization loss capability and the synergistic effects coupling dielectric and magnetic losses [18][19][20].
MXene is a two-dimensional transition metal carbide or nitride with promising electrical conductivity, high speci c surface area, and tunable surface chemistry. The layer structure and the combination of different elements in MXene enables the formation of a conductive network, leading to improved conductivity and electromagnetic wave absorption performance [14]. The high surface area is one of the most attractive properties of MXene which provides a large contact area between the material and EM waves, resulting in e cient absorption [20][21][22][23]. MXene has a high conductivity and low dielectric constant, which means it can absorb a wide range of EM waves, from radio waves to microwave and even terahertz waves.
These composites exhibited a decreased minimum re ection loss (RL) of -49.38 dB at 14.2 GHz [23], -38.9 dB at 4.82 GHz [24], -47 dB at 12.8 GHz [25] with an increased EMA performance, respectively. The results indicated that the incorporation of magnetic component with MXene is an e cient method to obtaining good EMA property.
Despite the promising results achieved in previous studies, there are still some limitations that need to be addressed. For example, the high electrical conductivity of MXene induces the impedance mismatch between composites and air, yielding much re ection and transmission, and reducing the absorption of electromagnetic wave. [26]. The magnetic susceptibility loss, the conductivity and the stability of the composites also need to be optimized to achieve e cient EW absorption.
To address these issues, GdFeO 3 (GFO) was proposed to composites with MXene for the EMA application in this study. By virtue of the co-existence of multi-valences and multi-coordination, transition metal GdFeO 3 is a complex magnetic oxide material that exhibits various types of magnetic ordering and different crystal phases at different temperatures [27]. Firstly, GdFeO 3 has good magnetic properties, such as high magnetic permeability, this makes GFO a promising material for EMA. The strong magnetic properties of GdFeO 3 are attributed to the presence of Gd and Fe ions, which have unpaired electrons that produce magnetic moments. The magnetism of GdFeO 3 can be further enhanced by the Gd →Fe magnetic moments exchange interaction [28][29][30].
Secondly, GdFeO 3 commonly undergoes a structural phase transition from an orthorhombic phase (Pbnm space group) to a rhombohedral phase (R3c space group) upon increasing temperature or pressure [31]. The orthorhombic phase is characterized by a reduction in the symmetry of the crystal structure compared to the rhombohedral phase. The transition is driven by the competition between the exchange interaction and the crystal eld interaction in GdFeO 3 , which is sensitive to the crystal symmetry [27]. In GFO, the A-site polyhedron GdO 12 expands more rapidly versus temperature than the B-site and FeO 6 sites [32], thus stabilizing the R3c phase at higher temperature. The distortion of crystal structure and the tilting of the FeO 6 octahedra break the cubic symmetry and increase the polarizability of structure.
Importantly, the phase transition in GdFeO 3 is always associated with a change in the electric, polarizability and magnetic ordering [28,29]. For example, the P-E curves of GdFeO 3 exhibit signi cant changes across the structural phase transition [30]. In the rhombohedral phase, the P-E curve is linear and exhibits weak ferroelectric behavior. However, in the orthorhombic phase, the P-E curve shows a more pronounced hysteresis loop with a higher polarization value, indicating stronger ferroelectric behavior.
These studies demonstrate the potential of the phase transition in GdFeO 3 to enhance its EMA properties, highlighting the importance of understanding the underlying physics and chemistry of this material for potential applications in electromagnetic absorption and related technologies. However, the phase transition mechanism is not fully understood, especially related to the EMA property of GFO-composites.
In this study, for the rst time a new MXene/GFO composites was synthesized, the EMA performance were investigated in terms of the phase transition, polarizability and magnetic ordering of the composites. GdFeO 3 nanoparticles are synthesized via a sol-gel method. 15mmol gadolinium nitrate hexahydrate, 15mmol iron (III) nitrate nonahydrate, dissolved in equimolar acetic acid and ethylene glycol (40 mL) and magnetically stirred for 90 minutes at 40°C. The mixture is stirred at 80°C for 4 hrs until a homogeneous gel was formed, then the gel was dried at 120°C for 8 hrs. Then heated the resultant product at 600°C and 900°C (with 6 hours' subsequent ball-milling) for 4 hrs to form the GdFeO 3 nanoparticles in different crystal phases. The corresponding samples are labeled as GFO6 and GFO9, respectively.

Synthesis of GFO/MXene composites
The MXene was synthesized using a two-step etching process. 10 g Ti 3 AlC 2 powder was rst immersed in a mixture of hydro uoric acid and hydrochloric acid (200 mL, 39%) at 40°C through magnetic stirring for up to 36 hrs to remove the aluminum layers, followed by a washing step with deionized water. The resulting Ti 3 C 2 T x was then immersed in an ammonium uoride solution to remove the surface terminations and obtain Ti 3 C 2 .
GFO/MXene composites was synthesized through mixing the GFO nanoparticles and Ti 3 C 2 (GFO: Ti 3 C 2 = 1:1 mol:mol)in acetic acid and ethylene glycol in a ratio of 1:1 (0.01M) and stirring/sonicated for 10 min at room temperature. The prepared solution was stirred and sonicated for 2 hrs at 80°C. Then rinsed the nal product for several times with deionized water and was put in a drying oven at 60°C for 3 hrs. Figure 1 shows the synthesis scheme of GFO/MXene composites.

Characterization
X-ray diffractometer (XRD, Bruker D8) was used to con rm the crystal structure and phase purities of samples with a Cu Kα radiation source and angle range10-70°C. Using XRD data, Rietveld re nements were conducted to calculate the lattice parameters. Raman spectra was recorded to analyze the vibrational modes of samples using 633 nm laser. Surface and morphology of composites were investigated using Transmittance electron microscopy (TEM, FEI, Tecnai G20) with Energy Dispersive X-Ray Analysis (EDX) for compositional analysis. The Binding energies of elements in the composites were checked using X-ray photoelectron spectroscopy (XPS, AXIS Supra). The dielectric parameters were measured using HITESTERLCR meter. The polarization versus electric eld hysteresis loop was traced.
The microwave absorption was test through mixing samples with para n wax (Sample: Para n = 7:3) in a coaxial ring (inner/outer diameter of 3/7 mm). The electromagnetic parameters of the material were measured by a vector network analyzer (VAN; Agilent, N5234A) with working frequency of 2 ~ 18 GHz (E5071C, Agilent). EMW absorption capability was evaluated with re ection loss (RL), which was calculated based on the transmission-line theory and metal back-panel model [33].  [32]. The distinct diffraction pattern indicates the good crystallinity which is also in good agreement with the standard JCPDS 78-0451, and other previously published literatures [34][35][36][37]. No other satellite peaks were found, suggesting the purity of GFO.

Phase transition of GFO in composites
The GFO9 treated at 900°C with ball-milling for 4 hours shows a different pattern in Fig. 2a . On the other hand, the pattern is rather broader than GFO6 due to the relative smaller particle size. Based on the Debye-Scherrer formula, the size of GFO6 and GFO8 were estimated to be 26 and 22 nm, respectively. Figure 2b shows the XRD patterns of GFO/MXene composites along with that of T 3 AlC 2 and etched Mxene. Ti 3 AlC 2 shows the strongest characteristic diffraction peak at 2θ = 9.7, 19.1, 39 ° which was indexed to the (002), (004) and (008) crystal plane according to JCPDS 52-0875 [37]. After the etching process, 3 main peaks at 2θ = 8.65, 18.2 and 61.4 ° were observed corresponding to the (002), (004) and (100) planes of MXene, respectively. The (008) plane of T 3 AlC 2 disappeared while the peak at 2θ = 9.7 °o f (002) plane signi cantly shifted to 8.65 °. This peak shift toward a lower angle shows an increase in the interplanar distance, con rming the broken of Ti-Al metal bond, and the removing of the Al atom can increase the plane spacing [39]. At the same time, the great decreases in the peak intensity of MXene indicates the loss of crystalline nature of the MAX powder after aluminum etching [34]. Both the XRD patterns of GFO6/MXene and GFO9/MXene in Fig. 1b exhibit the mix of R3c /Pnma phases of GFO with the MXene. In order to verify the crystal phase of GFO in the composites, Rietveld re nement of XRD patterns of GFO9/MXene and GFO6/MXene are shown in Fig. 1c and 1d, respectively, the lattice parameters obtained are listed in Table 1. From Fig. 1c and 1d, the calculation curves matched well with the experimental data with very small differences.
From Table 1, the GFO in GFO6/MXene composite was ascertained to be orthorhombic perovskite with Pbnm space group, the lattice parameters are: a = 5.349 Å, b = 5.611 Å, c = 7.669 Å, and α = β = γ = 90 °w hich are in good agreement with reported data [40]. The Rietveld re nement of XRD of two composites revealed that Fe 3+ was coordinated with 6 O 2− in octahedral unit. However, the Fe-O angle is larger while Fe-O length of GFO9 is smaller than that of GFO6, ensuring a big distortion in octahedral FeO 6 of Pbnm structure along the C axis. The Gd-O length is larger than that of Fe-O due to relative larger ionic radius of Gd, while both of them decreased for GFO9, indicating that the phase transition and tilting of FeO6 squeezed the Gd-O distance. The re nement results in Table 1 also indicate that the synthesis process of composites well remained the original crystal structure of GFO due to the relative lower temperature (80°C).   [33]. The bonds between the layers are weaker than the bonds within the layers, resulting in the layers being able to slide past one another.
This sliding motion makes the Pbnm phase more exible and less prone to cracking than the R3c phase. As comparison, the R3c GFO has a rhombohedral unit cell which is organized in a three-dimensional lattice, with the Gd and Fe ions and oxygen atoms situated at the lattice points [32]. The oxygen atoms in octahedral FeO 6 form chains along the z directions and occupy tetrahedral voids in the lattice. They are slightly tilted along the z directions, forming a network of corner-sharing octahedral around the Gd and Fe cations. Fe and Gd ions occupy octahedral sites and are arranged in a distorted perovskite structure.
The Raman spectra are shown in Fig. 4a to evaluate the molecular vibrations in the composites and the phase transition of GFO. From Fig. 4a, the Raman spectra of composites are divided into peaks due to GFO (yellow dashed lines) and Mxene (blue dashed lines) vibrations. The GFO generally exhibits 24 Raman-active vibrational modes (7A g , 7B 1g , 5B 2g and 5B 3g ) [41]. In this study, GFO6 (Pbnm) shows four cm − 1 and above 500 cm − 1 , respectively. From the comparison of GFO6 and GFO9, the GFO6 shows much higher intensity in the range of 200 to 500 cm − 1 , indicating a much stronger tilting and bending vibration of FeO 6 units. This is accordance with literatures [41]. On the contrary, the peak at 507 cm − 1 due to A g (3) vibration disappeared in R3c crystal. And R3c phase shows relative weaker FeO 6 rotation and bending modes. It is known that the Raman modes especially the A g (3) and A g (5) are sensitive to the changes of A site of perovskite [13]. Based on the Landau theory, signi cant wavenumber shifts stand for the large contribution from phase transition and highly asymmetry. And such shift is linearly proportional to the tilting/distortion degree of FeO 6 . From Fig. 1a, the A g (5) of R3c crystal phase was merged with B 2g (5) while A g (3) disappeared. Therefore, these changes of Raman spectrum attest that octahedron tilting and structural distortion which agree with the XRD analysis. Such differences can be observed in the Raman spectra of GFO6/MXene and GFO9/MXene composites. The vibrational characters of Pbnm and R3c of GFO are well remained after being composited with Mxene.
The spectrum of MXene is shown in Fig. 1a. TEM images in Fig. 5a2 shows that layer feature with the characteristic spacing between the lattice fringes of d = 0.956 nm in the corresponding the (002) plane of MXene [39]. Similarly, the surface topography in Fig. 5b2 shows that a large number of GFO is loaded on MXene layer, where the measured spacing between lattice fringes of 0.345 nm which is indexed to the (111) crystal plane of GFO (Pbnm) [43]. The distribution of GFO (Pbnm) is plotted in the inset of Fig. 5b1. From the plot, the average size of GFO (Pbnm) is 30 nm which is slightly smaller than that of GFO (R3c) (38 nm) in the inset of Fig. 5c1. The lattice fringes in Fig. 5c2 is 0.297 nm which is corresponding to the (110) plane of GFO (R3c), con rming the rhombohedral crystal structure of GFO [34].    and 4f valence electrons in this composite [45].
The XPS spectrum of Fe2p in Fig. 7e displays two peaks centered at 712.1 and 724.9 eV for Fe 2p 3/2 and Fe 2p 1/2 , respectively with a spin orbit energy separation of 12.8 eV. In general, the Fe 3+ shows a typical characteristic of Fe2p 3/2 -Fe2p 1/2 separation energy of 12.9 eV [32]. Therefore, the value of 12.8 eV suggests there is probably other valence of Fe (i.e. Fe 2+ ). Another possible reason is the existence of spin-orbit coupling between the 2p core hole and the unpaired 3d electrons of the Fe. From Fig. 7e It is known that surface oxygen vacancies play. The presence of Fe 2+ -induced charge imbalance would result in surface oxygen vacancies which play signi cant role in the EMA process. The oxygen vacancies can be detected from the core level energy of O1s (Fig. 7f). From Fig. 7f, the O1s spectrum of GFO6/MXene shows two peaks at 533.1 and 531.2 eV. The deconvolution of this spectrum exhibits 4 sub-peaks. The sub-peaks at highest bonding energy 534 eV is due to the loosely bonded oxygen on the surface which corresponds to the dangling bond i.e. oxygen vacancy [34]. This is because all lanthanide oxide materials present hygroscopicity nature including the GFO. Such it is easy to absorb oxygen on its surface such as H The oxygen vacancies were con rmed by the EPR analysis in Fig. 8. One sign cant strong asymmetric single EPR feature was detected at 160 mT for all samples with gyromagnetic (g) factor g = 4.3. This is the characteristic signal of Fe 3+ ions, indicating that the + 3 valence state is the dominant charge of Fe in samples. The signal at g = 4.3 shows the highest intensity for GFO9/MXene composites, also the intensity of GFO6/MXene at this value is much higher than that pristine GFO. This discover implies that the combination with MXene enhanced the spin-orbit coupling of Fe ions, which is very plausible for subsequent EMA performance. The EPR spectra in Fig. 8 also present another relative strong asymmetric signal at g = 2 with a similar tendency of intensity to that g = 4.3. The signal at g = 2 is corresponding to oxygen vacancies defect in the structure of composite [41] which was not detected in the pristine GFO. This result suggests that the defects were associated with the MXene, agreeing well with the XPS analysis. From the spectra, this signal becomes broader and more asymmetric at 360 mT which con rms the existence of oxygen vacancies on the surface of Ti 3+ layers [46]. Another wide and less intense signal around 500 mT (g = 1.613) is associated with Fe 2+ ions due to the reduction of MXene which is absent for pristine GFO. The intensity of this signal agrees with the Fe2p core level energy result. From Fig. 8, EPR intensity of this signal was very close to each other for Pbnm and R3c GFO phases. In general, the change in EPR intensity depends on the various factors, such as defect valence state, low to high spin con guration, and spin-lattice distortion [33]. In case of this study, the relative higher intensities of EPR signal of Pbnm GFO at g = 4.3 and g = 2 is due to the oxygen vacancies (V o ) and spin-lattice defect formation through the charge compensation process. The slight deviation of the g-factor (with respect to that standard g values of unpaired electrons of Fe) veri ed the spin-orbit coupling. In addition, the broader line-width feature of Pbnm GFO/MXene indicates stronger magnetic dipolar-dipolar interaction within the sample.
The asymmetric parameter magneto-crystalline anisotropy (P) can be calculated from the EPR spectra through P = h U /h L , referring to ratio of the maximum height of upper/lower peak above/below the baseline [47]. After calculation, the value of Pbnm of GFO (2.26) at g = 4.3 is higher than other two (1.24 for R3c GFO and 1.73 for GFO9/MXene), indicating a stronger magnetic interaction. This is mainly because the Fe 3+ has signi cant higher magneto-crystalline anisotropy (1.4cm − 1 /ion) than that of Gd 3+ , while the bond length of Fe-O is smaller than that of Gd-O (Table 1), particularly in R3c GFO. Therefore, the short length and high magneto-crystalline anisotropy resulted in strong magnetization which is good to EMA applications.

Dielectric, magnetic and polarization study
The materials interact with the electromagnetic wave mainly through polarization (dielectric constant ε′) and magnetization (magnetic permeability µ′) responses in materials [1]. The ε′ represents the polarization intensity under the action of EMW and shows the ability to consume the EM energy in the form of electrical energy. Therefore, the ε′ and dielectric loss are important factors for EMA samples. Figure 9a shows the ε′ and dielectric loss (inset) of GFO/MXene composites. It is known that the pure phase MXene (Ti 3 C 2 ) shows dielectric constant within 14.06 ~ 24.21 [3]. This is because MXene do not possess intrinsic polarization due to their metal-like nature, which makes them unable to support a signi cant internal electric eld. Therefore, the ε′ is comparatively low. However, ferroelectric GFO has asymmetrical arrangement of ions within the crystal lattice, and GFO possesses a spontaneous polarization which aligns in a particular direction under external electromagnetic eld, leading to an increase in dipole moment and hence the dielectric constant. From Fig. 9a, the ε′ of GFO6 (1000) and GFO9 (400) are much higher than that of MXene and the values are close to that in literatures (300-1200) [23]. In addition, we notice that the ε′ of Pbnm GFO (GFO6) is higher than that of R3c (GFO9) due to the lower crystal symmetry of the Pbnm phase. The lower symmetry allows for more complex polar structures that can store more electrical charge, leading to a higher dielectric constant. On the contrary, R3c phase has fewer complex polar structures due to its relative higher symmetry, resulting in a lower dielectric constant. On the other hand, the orthorhombic structure of GFO has a larger unit cell, which allows for more atomic dipoles to align with the electric eld, leading to a higher dielectric constant compared to the rhombohedral structures [33].
From Fig. 9a, the ε′ of all samples decreases rapidly from lower to higher frequency region due to the rapid polarization occurring in samples. However, a clear high frequency-independent behavior of ε′ was observed for all samples. This is because the electric dipoles do not comply with the eld at high frequency, and then lag behind the eld [6]. Similar to the ε′, dielectric losses in Fig. 9b show dispersion behavior of GFO6 and GFO9. This is because the space charge of GFO cannot sustain at higher frequency and the values of dielectric loss gets diminished with external eld. On the other hand, at higher frequency, domain wall rotation of GFO predominate their motion, resulting in low dielectric losses [11]. However, the GFO based composites show much stronger dielectric loss, particularly at higher frequency range due to the contribution of MXene. Firstly, MXene akes have a large surface area and highly conductive nature, which leads to high interfacial polarization and electrical conductivity losses in the composite material. Secondly, the dielectric properties of GFO/MXene are highly sensitive to their surface termination, with commonly used terminations such as -O, -OH, and -F exhibiting relatively high losses at higher frequencies. Thirdly, the presence of residual water molecules or other polar impurities can also contribute to high dielectric loss at higher frequencies in MXene-based composites [34]. Finally, the morphology and alignment of MXene akes in the composite structure can also affect the dielectric loss. For example, the GFO6/MXene with less ordered structures shows higher losses at higher frequencies than GFO9/MXene. The much higher dielectric loss indicates the complementary advantages of GFO and MXene which is very welcome for EMA application.
When a material is exposed to an electromagnetic wave, it will experience an oscillating electric eld that can cause polarization within the material, and such polarization process consumed and absorbed the energy of EM wave. In general, the polarization behavior is dependent on the crystal structure and associated symmetry degree, different crystal phases possess different crystal symmetries, leading to variations in their polarization-electric eld response. Figure 9c shows the polarization versus electric eld performance. From Fig. 9c, both GFO6 (Pbnm) and GFO6/MXene have a steep slope in the P-E curve at low electric eld strengths. This means that even small electric elds can induce signi cant polarization, allowing for greater absorption of the electromagnetic waves. Additionally, a high maximum polarization at high electric eld strengths was observed which is bene cial for absorbing strong electromagnetic waves. In this study, the Pbnm and R3c crystal structures of GFO have different symmetry properties, which gave rise to different polarization-electric eld (P-E) behaviors. From Fig. 9c, the R3c (GFO9) and R3c based composites show relative lower polarization than that of Pbnm GFO due to the lower crystal symmetry of Pbnm structure. This result agrees well with literatures in which the orthorhombic phase of GdFeO 3 also exhibited stronger polarization-electric properties than rhombohedral and cubic phases [45].
The much lower symmetry of orthorhombic Pbnm results in a larger number of active modes for ferroelectricity and a greater degree of distortion in the crystal lattice, allowing for a stronger P-E coupling under an applied electric eld. On the contrary, R3c crystal structure has a more symmetric lattice and fewer active modes for ferroelectricity. As a result, under an applied electric eld, the distortion in the R3c structure is lower, leading to a weaker P-E coupling. In addition, the active modes in Pbnm phase has a preferred to growth orientation while that of R3c tends to be more random in orientation. Thus the Pbnm phase presents a highly polarizable feature. That is why both Pbnm GFO and Pbnm GFO based composite show much stronger P-E performances in Fig. 9c.
The EMA performance of sample is also greatly affected by the magnetic permeability (µ′ or magneticdielectric MD) constant which describes the ability to store magnetic energy inside materials. Figure 9e-9h shows the MD constant of GFO and GFO based composites. Materials with a high µ′ can effectively attenuate the amplitude of electromagnetic waves as they pass through the materials. The µ′ is the ratio of the magnetic dipole moment to the magnetic eld that causes it. When a magnetic eld is applied to a material, the magnetic dipole moment of its atoms or molecules will align with the eld. However, the degree of alignment and the resulting MD constant depend on the frequency. As can be seen from Fig. 9e-9h, at low frequencies, the magnetic moments of the atoms or molecules of all samples align with the magnetic eld as ferromagnetic resonance, therefore, the MD constant is relatively high at this resonance frequency due to the strong alignment of the magnetic moments. However, at higher frequencies, the magnetic moments of the atoms or molecules no longer keep pace with the changing magnetic eld and their alignment (ferromagnetic resonance) was disrupted, resulting in a signi cant decrease in the MD constant. At very high frequencies, the magnetic moments no longer follow the magnetic eld at all and become completely randomized. At this point, the MD constant approaches zero [22]. From Fig. 9e-9h, the MD constant of Pbnm GFO is slightly higher than that of R3c, but the compositing with MXene greatly enhanced the MD constant of samples. This is because GFO Pbnm has a high net magnetic moment orientation, causing more energy to be dissipated within GFO Pbnm during electromagnetic wave propagation, thereby contributing to an increase in attenuation constant in Fig. 9d

Re ection loss and EMA property
The EMA capability of material is closely associated with the minimum re ection loss (RL min ), thickness of material, and the effective bandwidth [48]. The re ection loss can be obtained using Eqs. (2) and (3): Where, the f, d, c Z 0 and Z in refer to the frequency, thickness, light speed, free-space impedance, and the input impedance, respectively. Figure 10 shows the simulated re ection loss and 3D re ection loss plane and contour maps samples. The RL min , thickness, frequency, and effective bandwidth lists are compared, and presented in Table 1. The sharp peak observed in the re ection loss curve is known as a resonance peak or absorption peak, and it occurs at the frequency where the material strongly absorbs the incident electromagnetic wave. The location, shape and intensity of peak are dependent on dielectric constant, magnetic permeability, thickness, and structure. It can be seen from Fig. 10 that the maximum EMA of GFO6 and GFO9 appears at 7.2 and 9.5 GHz, with RL min of -24.9 and − 32.8 dB at thickness of 3, and 2.5 mm, respectively. The effective bandwidth (EWB) is 3.36 GHz at 2.5 mm and 3.11 GHz at 3 mm thickness. From Fig. 10a, the re ection peaks of GFO9 are broad while that of GFO6 are sharp and stronger. The effective bandwidth of EMA of GFO9 is also smaller than that of GFO6. From precious studies, Pbnm GFO possess larger ', polarization and µ'. In general, a higher ' induces RL min appear at lower frequencies due to the strong ability to store energy in an electric eld. While a higher µ' causes the resonance peak to occur at higher frequencies [23]. The rhombohedral phase GFO in Fig. 10a  magneto-electric resonance frequency around 9 GHz. The broad absorption peak occurs due to the random orientation of dipoles within the material, which leads to ine cient energy absorption at speci c frequencies. On the contrary, the orthorhombic phase of GFO in Fig. 10b exhibits a sharp re ection loss peak at around 11 GHz due to the alignment of its electric and magnetic dipole moments along a particular axis. This alignment leads to the formation of an electric and magnetic polariton, which results in a strong and narrow resonance peak. From 3D re ection loss maps in Fig. 10a1 and Fig. 10b1, the GFO6 clearly exhibits a broader EMA bandwidth than GFO9, indicating strong absorption over a wide range of frequencies.
From Fig. 10c and 10d, after incorporation GFO with MXene, the composites show much enhanced EMA performance with RL min of -51.6 and − 61.5 dB for GFO9/MXene and GFO6/MXene at 15.2 GHz (3 mm) and 10.08 GHz (4 mm), respectively. The EWB is 6.44 GHz at 3 mm and 8.62 GHz at 4 mm thickness. The greatly improvement on EMA property mainly due to the large surface area and highly conductivity of MXene. Based on the Debye theory [43], dielectric loss mainly originates the conduction loss and polarization loss [44]. The highly conductive MXene has layered structure which provides a conduction pathway for carrying and attenuating the EMW, at the same time, the electron polarization, dipole polarization, ion polarization on MXene surface contributed the high EMA of GFO6/MXene composite as well. From the maps in Fig. 10d1, the resonance peaks appear at both low and high frequencies due to the both higher ' and µ' values of GFO6, resulting in a signi cant broadening of effective bandwidth of EMA.
The impedance matching contour plots are shown in Fig. 11. As addressed, the impedance matching between samples and air is critical for EMA performance. In the contour maps in Fig. 11, the colors represent different levels of impedance. The blue, red, and yellow colors in the plot typically represent regions of poor, fair, and good impedance matching, respectively. Thus, for a good impedance match, we would expect to see more yellow color in the plot. Besides the color, the shape of the impedance matching contour plot provide impedance matching characters. For example, a steeply sloping curve may indicate that the impedance matching is particularly sensitive to changes in frequency (not steady and constant matching), while a broad, shallow curve may suggest a constant and broad matching of impedance.
From Fig. 11a, the pristine GFO (R3c) shows a stripe from top to bottom with more red color, indicating that the impedance matching is not constant across the frequency range of interest. In addition, the narrow stripe reveals that the EMA bandwidth is narrow. However, the impedance matching of GFO6 in Fig. 11b is broader contour shape which exhibits more yellow area, however, the line still is steep which decreases sharply from top to bottom across the whole frequency, suggesting that the impedance matching is not stable and constant. This issue was signi cantly optimized in Fig. 11d and particularly in Fig. 11c, not only the line become atter and broader, but also more and more yellow color present in the contour plot. From the indicator bar, the yellow color stands for the best impedance matching value of 1. Therefore, this result implies that the composites, particularly the GFO6/MXene reach the best impedance matching with air. The synergistic effect between Mxene and GFO improved the impedance matching of the composite and make EMW easier to enter the material. In addition, the at/shallow and broad curve also indicate a steady and broader-band impedance matching capabilities for EMA [48].  Table 2 lists the EMA values of work of this study and from literatures. From the comparison in Table 2, the values obtained in this study are superior. The mechanism of enhanced EMA property of GFO6/MXene composite is illustrated in Fig. 12. As addressed previously, GFO shows promising EMA properties due to its strong coupling between electric and magnetic degrees of freedom. The Pbnm and R3c phases of GFO exhibited different EMA properties due to differences in their dielectric constant, dipole polarization, magnetic loss, and crystal defects such as low symmetry lattice and highly distortion of FeO6 units. These factors provided more active sites and much stronger dipolar polarization, resulting in the higher EMA for Pbnm GFO. In addition, the combination of MXene with Pbnm GFO take advantages of the high surface area, layered structure and broad-band absorption of MXene, giving rise to greatly enhanced EMA behavior. Figure 12 shows various contributions to the EMA of Pbnm GFO/MXene composites.
From Fig. 12, the excellent EMA property has various contributions and 5 main sources are displayed.
The rst contribution is the strong Gd 3+ → Fe 3+ and Fe 3+ → Fe 3+ dipole coupling between electric and magnetic degrees of freedom [46-52]. From Fig. 9e-9h, the GFO6/MXene owns high magnetic permeability constant µ' and exhibits stronger ferromagnetic ordering than the R3c phase. In addition, the lower crystal symmetry in the Pbnm phase allows for greater magnetic anisotropy, which enhances the alignment of the magnetic moments along a preferred direction. The vibration of the dipoles within GFO/MXene under an applied electric eld, leading to energy dissipation in the form of heat. All of these factors contributed to the much high attenuation loss of EMA in GFO6/MXene (Fig. 9d).
The second main contribution to EMA of GFO6/MXene is the high ' and dielectric loss as shown in Fig. 9a and 9b. When EMW passes through the sample, the movement, collision and oscillation of electrons inside sample exhausted a large number of EM energy in electric form. is owe to the large dielectric constant which yield high dielectric loss which transferred much EM energy. The third source is the interfacial polarization loss or oxygen defects. From previous FT-IR, XPS, EPR analysis, the existence of functional groups, oxygen vacancies, dislocations, grain boundaries and lattice defects on the surface of MXene can form interfacial polarization and enhance the polarization loss. These defects can act as scattering centers for electromagnetic waves, leading to a consumption of EM energy. The formation of hetero-structured interfaces between GFO and MXene layer is conducive to improving the interface polarization, thus increasing the polarization loss; On the other hand, when the EMW touch the interface, electrons on the surface was polarized near the surface and such polarization process consumed a lot of EM energy as well. This can be con rmed from the high P-E loop in Fig. 9c. Other sources such as the Eddy current loss, multi-re ection loss, thermal loss and good impedance matching all contributed to the high EMA performance of GFO6/MXene composite.

Conclusion
In this study, two different crystal phases of GdFeO 3 were composited with MXene to obtain novel composites with high EMA property and broad bandwidth. The synergic effect of multilayered interfaces with both dielectric and magnetic elements enhanced the wave absorption effect. The Pbnm GFO/Mxene composite obtained at 600°C showed highly asymmetry and strong polarization, exhibiting more active sites for electron and magnetic dipolar coupling which jointly improved the impedance matching and MD constant. The minimum RL reached − 61.5 dB (with a frequency of 10.08 GHz, and 4 mm thickness), and maximum EAB of 8.62 GHz. The R3c GFO/MXene obtained at 800°C also exhibited excellent EMA performance with RLmin -− 51.6 dB (with a frequency of 15.2 GHz, and 3 mm thickness), and maximum EAB of 6.44 GHz. In addition, the composites of GFO/MXene is a novel composites and for the rst time for EMA application to provide excellent EMA property and broad bandwidth which is promising for EMA applications such as the defense, environments, medical and energy elds.

Declarations
Funding: None 49. Xu H, Yin X, Li X, Thermal stability and dielectric properties of 2D  Figure 1