3.1 Crystal structure and high-entropy phases
The XRD patterns and Rietveld refinements in Fig. 2 offer insights into the crystallization and crystal phases of CsMBr3 (M = Pb, Fe, Co, Ni, Mn) with varying Cs: M2+ ratios. In Fig. 2a, CPB1 demonstrates distinct crystallographic peaks at 2θ = 15.6°, 21.06˚, 30.83˚, 37.86˚, and 44.22˚, corresponding to the (100), (110), (200), (211), and (220) planes of cubic CsPbBr3, as per JCPDS No.29–073 [17]. Upon reaching a Cs: M2+ ratio of 1:2, CPB2's XRD pattern diverges from CPB1. Noticeable are intensified peaks at 2θ = 15.6°, 21.66˚, 30.83˚, 37.86˚, and 44.22˚. However, the peaks at 15.6°, 30.83˚, and 37.86˚ display splitting into two sub-peaks, signifying significant characteristics of orthorhombic CsPbBr3, per JCPDS 97–851 [18]. Additionally, in CPB3's XRD pattern, beyond the crystal peaks of orthorhombic CsPbBr3, three extra peaks appear at 2θ = 12°, 23.8°, and 48.2°, corresponding to planes of a new phase known as tetrahedral CsPb2Br5 (JCPDS: 25–0211) [19] due to the high M2+ content.
The phase evolution in Fig. 2a, based on the M2+ content, is most likely a result of the mismatch in ionic radii, lattice energy, and ionic bonding between Fe2+, Co2+, Ni2+, Mn2+ ions, and the original Pb2+ ions. The introduction of these significantly smaller ions into the crystal lattice creates an inherent size discrepancy, causing compression of the surrounding lattice and distorting the ideal geometry of the octahedral MBr6 unit. This distortion leads to the emergence of new phases with distinct symmetries.
Conversely, the sizes of ions involved also impact the bonding within the crystal lattice. The presence of multiple ionic sizes induces variations in the strength of ionic bonds, resulting in a reduction of Gibbs free energy. These alterations influence the arrangement of atoms and disrupt the delicate equilibrium that upholds the stability of the crystal structure, thereby initiating phase transitions from cubic to orthorhombic and tetrahedral.
The investigation into crystallization and phase transition was extended using Rietveld refinement, as demonstrated in Fig. 2b and 2c, revealing a remarkable alignment between the simulated and actual data, with minimal disparity between the two datasets. The corresponding lattice parameters can be accessed in Table 1.
Analysis of Table 1 unveils that CPB1 exhibits lattice parameters of approximately a = b = 8.171 Å, c = 11.833 Å, and α = β = γ = 90°, confirming its cubic geometric configuration as CsPbBr3. In contrast, CPB2's diffraction peaks indicate lattice parameters of a = 7.973 Å, b = 8.062 Å, c = 11.611 Å, and α = β = γ = 90°, pointing to its orthorhombic phase. The parameters for CPB3 divulge a coexistent scenario: the presence of orthorhombic CsPbBr3 and tetragonal CsPb2Br5 (a = b = 8.4822 Å, c = 15.25 Å, α = β = γ = 90°), harmonizing effectively with the XRD pattern depicted in Fig. 2a.
The variation in M2+ content within the structure of CsPbBr3 yields interesting lattice behavior. Initially, with an increase in M2+ content, the lattice constants a, b, c, and volume experience a reduction, followed by a slight increment. This pattern suggests the integration of doped Fe, Co, Ni, and Mn ions into the CsPbBr3 structure, effectively replacing Pb ions at the B-site.
This substitution introduces smaller dopant ions compared to the larger Pb2+ ions, resulting in a lattice contraction. The greater electronegativity of the larger Pb2+ ions contributes to this contraction. The cubic phase's high symmetry gives way to increased distortion in the crystal structure during the orthorhombic phase. Consequently, the Pb-Br bond length increases due to the tilting and rotating of the PbBr6 octahedral, causing atoms to rearrange and elongate the Pb-Br bond lengths. Meanwhile, the Cs⁺ ions adopt an 8-coordinate geometry, bonded to eight Br⁻ atoms. As the orthorhombic distortion takes effect, the arrangement of surrounding Br⁻ ions shifts, leading to a reduction in the Cs-Br bond length. These structural modifications elucidate the XRD pattern splitting observed in the CPB2 and CPB3 samples (Fig. 2a). Notably, the values of χ2 (2.76 and 1.39) underscore the absence of significant impurities in the present samples.
When the Cs/M2+ ratio reached 1:3, the lattice parameters and volume increased slightly due to the formation of a tetragonal crystal structure. In a tetragonal crystal structure, the lattice can be elongated in one direction compared to the other two perpendicular directions. This elongation can lead to larger lattice parameters and volume along the elongated direction, making it occupy more space.
Table 1
Refined structural parameters of samples
Parameters | CPB1 | CPB2 | CPB3 |
Crystal type | cubic | orthorhombic | Orth./tetra |
Space group | Pm3m | Pbnm | Pbnm/P-42m |
a(Å) ± 0.001 | 8.171 | 7.973 | 8.1814 |
b(Å) ± 0.001 | 8.171 | 8.062 | 8.1814 |
c(Å) ± 0.001 | 11.833 | 11.611 | 13.125 |
Angle | α = β = γ = 90° | α = β = γ = 90° | α = β = 90° |
V(Å) | 800.86 | 769.16 | 824.04 |
Pb-Br (Å) | 3.02 | 3.05 | 3.06 |
Cs-Br (Å) | 3.72 | 2.61 | 3.62 |
Rp(%) | 11.3 | 12.62 | 12.47 |
Rexp | 3.88 | 10.22 | 11.2 |
χ2 | 2.82 | 2.03 | 1.19 |
Figure 3 shows the atomic models of various phases of CsPbBr3 computed using Vesta software. The crystal structure of cubic CsPbBr3 (Pm3m) is characterized by corner-sharing MBr6 octahedra, with each M²⁺ ion bonded to six Br⁻ atoms, forming a three-dimensional network [20]. The M-Br bond lengths and angles within each PbBr6 octahedron exhibit high symmetry. Cs ions occupy interstitial sites in this network, resulting in a highly symmetrical cubic lattice. Cs cations are at the cube's corners, M cations are at the center, and Br anions occupy face-centered positions. This arrangement ensures overall charge neutrality.
Contrasting the cubic phase, the orthorhombic phase (space group Pnma) possesses a rectangular unit cell with varying dimensions along each axis. Each M ion is surrounded by six Br ions, forming a distorted octahedral coordination geometry with varying edge lengths and angles between faces. Cs⁺ ions adopt an 8-coordinate geometry with eight Br⁻ atoms. While Cs remains centered, the arrangement of M and Br ions changes, causing MBr6 octahedral to tilt and rotate at angles of 19–27° [21]. Consequently, the crystal structure becomes more distorted. Pb–Br bond lengths increased, and Cs–Br bond lengths decreased on the contrary.
As the M2+ concentration reaches 3, the crystal lattice loses its charge balance due to insufficient Br⁻ ions to coordinate with extra M2+ ions. To adapt, the crystal structure undergoes a phase transition. The crystal system reorganizes, forming new coordination environments for M2+ ions and Br⁻ anions, resulting in a tetrahedral CsM2Br5 structure (P-42m) [32, 33]. In the tetragonal CsM2Br5 structure, each M2+ ion isn't directly bonded to Cs but forms separate MBr6 octahedral units. Cesium atoms are arranged in tetrahedral coordination with Br⁻ anions. The structure consists of layers, with one layer of Cs⁺ ions between two Pb2Br5 − layers. These M2Br5 − layers involve Pb2+ Fe2+, Co2+, Ni2+, Mn2+ atoms coordinated with eight Br⁻ ions, resulting in an elongated polyhedral shape (staggered arrangement). As a result, both Pb-Br and Cs-Br bond lengths, as well as the volume, increase.
GIWAXS patterns and curves are shown in Fig. 4 to further analyze the high structural order within the crystal structure. In the GIWAXS pattern of CPB1 in Fig. 4a, the circular scattering patterns depicted in a light blue color symbolize different diffraction peaks. These regular circular patterns represent the ordered arrangement of atoms within the cubic crystal structure. The high symmetry of the cubic phase results in symmetrical and well-defined circular scattering patterns, with the different color points corresponding to various diffraction angles.
In Fig. 4b, the GIWAXS pattern of CPB2 reveals more intricate circular scattering patterns, highlighted with yellow and red color points to signify unique diffraction peaks. The orthorhombic crystal structure's varying dimensions along different axes result in slightly elongated and subtly distorted circular patterns. These color-coded points within the patterns correspond to specific diffraction angles, and their alignment with the findings in Fig. 2a confirms their accuracy.
In Fig. 4c, the GIWAXS pattern of CPB3 presents a complex and distinct scattering pattern, characterized by numerous circular features. Different color points within this pattern represent characteristic diffraction peaks. This intricate pattern emerges due to the layered arrangement of tetrahedral CsPb2Br5 and its mixture with the orthorhombic phase [22]. The scattering pattern blends well-defined circular motifs with broader arcs, all distinguished by distinct color points corresponding to specific diffraction angles. Notably, the prevalence of red color within the circles signifies the merging of the two phases, where strong diffraction peaks are observed, highlighting the coexistence of these phases.
Through the analysis of Fig. 4a–c, it becomes evident that the diffraction peaks experience subtle shifts in positions with varying Pb/Fe/Co/Ni/Mn content. Notably, Fig. 4c demonstrates pronounced alterations in diffraction positions when the Pb/Fe/Co/Ni/Mn content is raised to 3. This substantial shift indicates a noteworthy transformation in the crystal structure of CsPbBr3 due to the high-entropy alloying [23]. Additionally, the in-plane line cuts in Fig. 4d illustrate distinct and observable changes in the characteristic diffraction peaks across all three samples, agreeing well with Fig. 2a.
Figure 4e offers an enlarged view of the (110) plane peaks extracted from the GIWAXS patterns, revealing a discernible trend. As additional secondary elements are introduced, the diffraction peak becomes progressively more asymmetric and multicomponent. For our analysis, we employed multicomponent Gaussian fitting for each pattern based on the number of secondary elements present in the system. Notably, a distinct emergence of five sets of diffractive components within the (110) plane is observed across the three samples. These components correspond to the Pb, Fe, Co, Ni, and Mn constituents.
The arrangement of the five sub-peaks in Fig. 4e corresponds to an increasing order of atomic numbers: Pb (82), Ni (28), Co (27), Fe (26), and Mn (25). This relationship between atomic number (Z) and scattering angle (qz value) is significant as it reflects the unique atomic scattering factors possessed by different elements, influencing their X-ray scattering capabilities. It's important to emphasize that each element has distinct atomic scattering factors that determine its efficiency in scattering X-rays. Furthermore, various elements may exhibit preferences for specific crystallographic sites within the lattice, contributing to the observed variations in peak intensities, even when molar compositions are equivalent. These scattering factors lead to the observed intensity differences in Fig. 4e.
The findings depicted in Fig. 4e unveil a crucial aspect of the nature of high-entropy CsMBr3 perovskites - they are multiphase systems compared to the pure CPB (CsPbBr3) in the bottom of Fig. 4e. This multiphase nature arises due to two contrasting effects. On one hand, the smaller Fe, Co, Ni, and Mn ions can occupy interstitial spaces within the lattice, resulting in the expansion of the crystal structure. Conversely, the substitution of smaller ions into sites originally occupied by larger Pb2+ ions leads to lattice contraction. Consequently, a delicate balance is achieved between lattice expansion and contraction, ultimately stabilizing the crystal structure. This balance is pivotal for maintaining the integrity and stability of the high-entropy CsMBr3 perovskites.
3.2 Morphology, composition and chemical valence analysis
The morphology, particle distribution, and selected area electron diffraction (SAED) patterns of the samples are presented in Fig. 5 to further investigate the impact of high entropy alloying on the size and phases of CsPbBr3. As illustrated in Figs. 5a-5c, the CsPbBr3 nanocrystals within all samples exhibit a uniform square shape and even distribution, displaying no noticeable agglomerations. By combining the TEM images with corresponding histograms (insets), it is evident that the average size of CsPbBr3 is 65 nm in CPB1, which reduces to 58 nm for CPB2 and 60 nm for CPB3. This reduction in size implies that the increase in high entropy M2+ content, characterized by smaller ionic radii, aligns with the decrease in Gibbs free energy in accordance with the Gibbs Free Energy Minimization Principle [24]. A decrease in Gibbs free energy signifies enhanced stability of the CsPbBr3 nanocrystals. On the other hand, the smaller size of the Fe, Co, Ni, and Mn ions will not fill the same space as the larger Pb ions, leaving gaps in the crystal lattice that can reduce the overall size of the particles. Similar outcomes were also documented in previous studies involving Co-doped CsPbBr3 perovskite materials [25].
Figures 5a’ to 5c’ present the SAED patterns for CPB1, CPB2, and CPB3, respectively. Notably, CPB1 displays an inter-planar spacing of 3.22 Å, which corresponds to the (200) plane of cubic CsPbBr3 with a spacing of 3.21 Å [26]. On the other hand, CPB2 exhibits a slightly smaller d-space of 3.16 Å, aligning well with the (200) plane of orthorhombic CsPbBr3 at 3.14 Å [27]. The introduction of excessive B-site metal cations in CPB3 results in the observation of irregularly shaped layered nanocrystals alongside mostly square ones. Upon thorough SAED pattern analysis, the lattice spacing of 3.27 Å and 3.16 Å are attributed to the (211) plane of tetrahedral CsPb2Br5 and the (200) plane of orthorhombic CsPbBr3, respectively [27]. These findings confirm the coexistence of different phases and the occurring phase transition, in line with the XRD results depicted in Fig. 2 and Table 1.
The N2 adsorption–desorption isotherms and pore size distribution for CPB1, CPB2, and CPB3 are illustrated in Figs. 5d, 5e, and 5f, respectively. According to the IUPAC classification, all four samples exhibit type IV physio-adsorption isotherms, indicative of their mesoporous nature (with pore sizes ranging from 2–50 nm). In terms of surface properties, CPB1, CPB2, and CPB3 possess surface areas of 45.52 m2/g, 48.33 m2/g, and 51.78 m2/g, respectively. Furthermore, with the increase in M content, there is a corresponding slight reduction in the average pore size. These changes in surface characteristics, specifically the increase in surface area and reduction in pore size, are favorable for enhancing electromagnetic wave absorption. This is attributed to the heightened surface polarization effects, which will be elaborated upon in the subsequent section.
Figure 6 displays the EDX compositional analysis of two distinct nanocrystal positions within CPB3 (as shown in the inset of Fig. 6a) to further confirm the presence of a high-entropy alloyed multicomponent. The analysis reveals the presence of all elements (Cs, Br, Pb, Fe, Co, Ni, and Mn) in the samples, indicating the successful alloying of Fe, Co, Ni, and Mn into the crystal lattice. Notably, there is a discrepancy in the intensity of M elements (Pb, Fe, Co, Ni, Mn) between the two points, suggesting two different compositions and phases. Subsequent calculations based on the atomic percentage of all elements from the histogram (inset of Fig. 6a) reveal that the stoichiometric formula for point 1 is CsPbBr3, while that for point 2 is CsPb2Br5. This discovery aligns well with the XRD and GIWAXS results.
Figure 6b presents the element distribution within the CPB3 sample, illustrating that Cs, Pb, Br, Fe, Co, Ni, and Mn are uniformly distributed without any noticeable segregation. This homogeneity of each element within the crystal structure plays a crucial role in ensuring the stable performance of the material.
The multivalence states of transition metal ions are well-known to manifest during the synthesis process. In the context of CsPbBr3, the valence states of Fe, Co, Ni, and Mn play a critical role in determining crystal stability and properties. In Fig. 7a, we observe the overall XPS core energy levels of CsPbBr3, including Cs3d, Br3d, Pb4d, Pb4f, Fe2p, Co2p, Ni2p, and Mn2p, which originate from the reagents used in the synthesis. Additionally, the presence of O1s is notable, and likely introduced during the synthesis process. A minimal amount of C1s may be attributed to incomplete decomposition of organic components.
In Fig. 7b, the binding energies of Pb4f are observed at 143.7 eV for Pb4f 5/2 and 138.9 eV for Pb4f 7/2, indicating a + 2 valence state for Pb atoms [16]. However, upon deconvolution fitting, both Pb4f5/2 and Pb4f 7/2 peaks are resolved into two sub-peaks. This suggests the existence of different chemical environments or coordination states of Pb atoms. Referencing our XRD and TEM analyses, we can attribute these two sub-peaks of Pb4f 5/2 and Pb4f 7/2 to PbBr6 in the orthorhombic CsPbBr3 and PbBr8 in the tetrahedral CsPb2Br5. The varying bonding interactions of Pb atoms in PbBr6 and PbBr8 units give rise to the appearance of secondary sub-peaks.
In Fig. 7c, the XPS spectra for Br3d reveal a broad peak centered at 70 eV. This broad peak was deconvoluted into six sub-peaks, each corresponding to distinct chemical environments based on electronegativity and position within the crystal lattice. These sub-peaks were identified as Br-Cs at 71.5 eV, Br-Pb at 70.6 eV, Br-Mn at 69.7 eV, Br-Fe at 69.1 eV, Br-Co at 68.5 eV, and Br-Ni at 67.6 eV. This observation provides further confirmation of the successful alloying of Fe, Co, Ni, and Mn into the CsPbBr3 structure.
Moving to Fig. 7d, we examine the core energy level of Cs3d spectra, which displays two distinctive peaks at 739.5 and 726.2 eV, corresponding to the Cs3d3/2 and Cs 3d5/2 of Cs+ in CPB3, respectively [28].
In Fig. 7e to Fig. 7h, we explore the XPS spectra of the alloyed components Fe2p, Co2p, Ni2p, and Mn2p, respectively. Notably, these spectra reveal a prominent feature – the presence of a + 3 valence state for these elements. In Fig. 4b, the Fe 2p XPS spectrum reveals two spin-orbit peaks, Fe 2p1/2 (726.05 eV) and Fe 2p1/2 (712.2 eV), along with their corresponding satellite peaks at 733 and 718.5 eV. These observations suggest the presence of Fe2+ and Fe3+ oxidation states [2, 15].
Turning to Fig. 7f, the Co2p XPS spectrum can be divided into two spin-orbit peaks, Co 2p3/2 and Co 2p1/2, accompanied by corresponding satellite peaks (785 eV and 802.6 eV, respectively). The peaks of Co 2p3/2 and Co 2p1/2 consist of two valence states, Co3+ (777.1 and 793.5 eV) and Co2+ (778.3 eV and 795 eV) [25]. Figure 7g displays the Ni2p XPS spectrum, where the peaks of Ni 2p3/2 and Ni 2p1/2 are situated at approximately 858 and 873.2 eV, with two satellite peaks centered at 864 and 880 eV. Four fitted peaks for Ni 2p3/2 and Ni 2p1/2 are deconvoluted into Ni2+ (858 eV, 874 eV) and Ni3+ (861.6 eV, 876 eV), respectively [20]. Moving to Fig. 7h, the Mn 2p spectrum illustrates two main peaks at 653 and 642.3 eV, corresponding to Mn2p1/2 and Mn2p3/2, respectively. Similarly, these two peaks were deconvoluted into four sub-peaks at 654 and 643.3 eV for Mn3+ and 652.5 and 641.5 eV for Mn2+ [16].
The presence of both + 3 and + 2 valence states in Fe, Co, Ni, and Mn can primarily be attributed to oxidation during the ball-milling process, consistent with the observed minimal oxygen content in Fig. 6a and the O1s signal in Fig. 7a. However, when evaluating the integrated areas of these two valence states, it becomes apparent that the + 2 valence state predominates and is significantly more prominent than the + 3 state. This prevalence of + 2 valence states plays a pivotal role in maintaining the stability of the crystal structure in CsPbBr3. Nevertheless, the emergence of the + 3 valence state has the potential to disrupt the charge balance within CsPbBr3, potentially resulting in an excess positive charge and introducing defects into the crystal structure. These alterations could have notable implications for charge carrier dynamics, non-radiative recombination processes, and overall electronic properties. Consequently, further studies are essential to gain a comprehensive understanding of these effects.
3.3 Magnetic properties of CsM(Pb, Fe, Co, Ni, Mn)Br3
The magnetic hysteresis (M-H) loop behavior in Fig. 8a illustrates the characteristics of the present sample. In our previous study, non-magnetic CsPbBr3 exhibited weak diamagnetic behavior. However, the introduction of potent magnetic elements, specifically Fe, Co, Ni, and Mn, into the crystal lattice led to the development of robust ferromagnetic properties in various CsM(Pb, Fe, Co, Ni, Mn)Br3 compounds with different Cs/M ratios. Notably, the saturation magnetization (Ms) steadily increased from 12 Am2/Kg (CPB1) to 50 Am2/Kg (CPB2) and 75.5 Am2/Kg (CPB3) as the M content in these compounds rose, primarily due to the heightened concentration of Fe, Co, Ni, and Mn ions. In the original CsPbBr3, neither Cs nor Pb ions displayed evident magnetic behavior. However, when replaced by the strong magnetic Fe, Co, Ni, and Mn ions, the magnetic properties experienced significant enhancement. In ferromagnetic CsM(Pb, Fe, Co, Ni, Mn)Br3 samples, ferromagnetism originates from the exchange interaction between neighboring electron spins, resulting in the alignment of magnetic moments.
In this study, Fe, Co, Ni, and Mn atoms possess partially filled d-orbitals in their electron configurations. According to the Pauli Exclusion Principle, no two electrons within an atom can have the same set of quantum numbers (n, l, ml, ms). Consequently, electrons from adjacent atoms engage in exchange interactions, specifically exchange coupling between neighboring magnetic ion electrons, leading to the observed enhancement of ferromagnetization shown in Fig. 8a.
From Fig. 8a, it can be observed that the coercivity of the sample also increases with the M content. The magnetic coercivity is primarily influenced by the crystal structure and anisotropy, which can give rise to preferred magnetization directions, making it challenging to alter the magnetic alignment in specific orientations. Conversely, crystal defects and grain boundaries act as pinning sites, rendering it more difficult for magnetic domains to reorient and, consequently, increasing coercivity.
In the context of this study, the introduction of multiple components into the Pb sites within the lattice of CsPbBr3 unquestionably enhances the disorder and anisotropy of the crystal structure [29]. This is substantiated by the formation of highly distorted orthorhombic and tetrahedral phases. Such disorder and the imbalance of charge valence within the lattice induce a greater number of defects. These instances of anisotropy and defects culminate in an elevation of coercivity in the samples.
Among these four elements, Fe and Co exhibit robust magnetic moments. Conversely, the + 3 valence state of Fe, Co, and Ni yields higher magnetic moments compared to the + 2 valence state. For instance, the magnetic moments of Fe3+, Co3+, and Ni3+ are 5.92 µB, 3.8 µB, and 4.9 µB, respectively, while those of Fe2+, Co2+, and Ni2+ are 4.89 µB, 3.88 µB, and 2.83 µB. Therefore, the introduction of the + 3 valence states not only introduces defects into the lattice, potentially increasing the effective magnetic anisotropy (EMA), but also yields stronger magnetic moments in the samples, which is crucial for EMA enhancement.
The X-band EPR spectra (9.5 GHz) of the samples are depicted in Fig. 8b, enabling a deeper exploration of the spin states of Fe, Co, Ni, and Mn ions and their contribution to magnetization. In Fig. 8b, all samples exhibit two asymmetric EPR resonance signals within the ranges of 135–250 mT and 330–370 mT.
The EPR peak at approximately 135 mT, characterized by a g-value of 5.11, is attributed to octahedral Co2+ ions in a high spin state. High-spin (HS) Co2+ ions within octahedral coordination environments typically manifest EPR peaks with g-values ranging from 4.7 to 6.1, depending on the specific coordination geometry and surrounding conditions [30]. High-spin Co2+ ions possess three unpaired electrons (d7 electron configuration), and their EPR spectrum reflects the interactions of these unpaired electrons with an external magnetic field.
The most prominent peak in Fig. 8b, occurring at 150 mT with a g-value of 4.5, arises from a combination of the EPR signal of high-spin octahedral Fe2+ ions at g = 4.7 and transitions involving high-spin Fe3+ ions in octahedral coordination at g = 4.3. As previously addressed, Fe ions possess the largest magnetic moment; therefore, at the same molar ratio, the intensity of the Fe EPR signal is the most pronounced. High-spin Fe2+ ions have two unpaired electrons in their 3d orbitals. Under the influence of an external magnetic field, the energy levels of these electrons split due to the Zeeman effect, giving rise to the observed EPR signals. The EPR signals of Ni2+ ions appear at 160 mT, while the peak of Mn2+ is observed at 215 mT, indicating their octahedral coordination as well. Due to the contribution of these high-spin octahedral M2+ ions in the B sites of CsPbBr3, the magnetization in Fig. 8a was notably enhanced.
In addition to the EPR signals of M2+ ions, M3+ ions also exhibit EPR signals within a lower g-value range of around 330 mT. In high-spin states, multiple unpaired electrons with parallel spins align their magnetic moments with the applied field, resulting in a stronger interaction between electrons and the magnetic field, thus yielding a higher g-value. Figure 8b shows that the EPR peak of M3+ is broader than that of individual M2+ ions. This broadening occurs because the EPR signals of Fe3+, Co3+, Ni3+, and Mn3+ ions are all situated within the same range with g-values of 2-2.2, causing the broader peak due to the overlap of all M3+ ions. Additionally, the presence of multiple lines in the EPR spectrum indicates that M ions in the CsMBr3 structure confirm the anisotropic octahedral coordination geometry [31].
Notably, in Fig. 8b, there is also a peak at 350 mT with a g-value of 1.946, which can be attributed to lattice defects present in all samples. Similar to the other EPR peaks in Fig. 8b, the intensity of this peak increases with the M content. These progressively increasing defects are induced by crystal structure deformations and charge imbalances resulting from the presence of M3+ ions. These defects can be advantageous for enhancing the absorption of electromagnetic waves.
The XANES L2,3-edge absorption spectra of Fe, Co, Ni, and Mn within CsMBr3 crystals are presented in Fig. 9, shedding light on the magnetic spin states and electron transitions of these metal ions within the CsPbBr3 matrix. In Fig. 9, the metal ions (Fe, Co, Ni, and Mn) within the octahedral MBr6 coordination environment exhibit distinct features in their XANES spectra. Specifically, they display a pre-edge peak resulting from dipole-allowed electron transitions 1s → 3d, an L3 peak originating from electron transitions between the 2p → 3d orbitals (2p1/2), and an L2 peak arising from electron transitions involving the 1s → 3d (4s) orbitals (2p3/2). Notably, the L3 edge exhibits a sharp and intense peak, whereas the L2 peak appears broader and weaker [32].
The broadening of the L2-edge XANES spectrum can be attributed to the involvement of multiple electron transitions, including the excitation of the 1s core electron to both 3d and 4s states. The intricate interactions between these electronic states result in the observed spectral broadening. Furthermore, the higher energy levels of the 4s states contribute to their overlap with the 3d states, further contributing to the broadening effect. This broadening is also indicative of the mixing of different valence states in the system.
Examining Fig. 9a, it becomes evident that the pre-edge and L3 peaks increase notably with the M content, and the intensity of the Fe2+ peak surpasses that of Fe3+. This observation suggests that Fe2+ predominantly exists within CsMBr3, which plays a pivotal role in maintaining structural stability. Importantly, the coordination number of M (Fe, Co, Ni, Mn) was distinguished to be octahedral MBr6 based on the analysis of Fig. 9. This determination was made evident by the notable pre-edge peak and intense L3 peak observed in the XANES spectrum. Octahedral M2+ ions commonly exhibit a prominent pre-edge peak followed by a sharp L3 peak in the XANES spectrum. Additionally, the prevalence of the high spin (HS, shoulder) state of Fe2+ over the low spin (LS) state contributes significantly to the enhanced magnetic properties observed in Fig. 8a.
The XANES spectra of Co, Ni, and Mn exhibit similar characteristics to those of Fe. From Figs. 9a to 9d, the sharp and intense L3 peaks in these elements' spectra indicate highly active electron transitions between the 2p → 3d orbitals. These active super-exchange interactions between electrons at the 2p and 3d orbitals contribute to the ferromagnetic properties observed in the samples, providing an explanation for the significant enhancements in magnetization (Ms) and coercively.
3.4 Dielectric constant, P-E curve and MCD spectra
The electromagnetic properties of CsM(Pb, Fe, Co, Ni, Mn)Br3 at various Cs/M ratios are presented in Fig. 10. These materials primarily absorb electromagnetic waves through two mechanisms: polarization, characterized by real and imaginary permittivity (ε' and ε''), and magnetization, represented by magnetic permeability (µ'), as depicted in Fig. 10a, 10b, and 10c, respectively. In Figs. 10a and 10b, it's observed that the real and imaginary components of the dielectric constant for all samples decrease as the EMW frequency increases. This phenomenon occurs because dielectric polarization struggles to keep pace with the rapid changes in the alternating electric field at higher frequencies. However, as the content of high-entropy element M increases within CsM(Pb, Fe, Co, Ni, Mn)Br3, both the ε' and ε'' values show significant augmentation. This increase in ε'' has an interesting consequence on the resistivity (ρ) of CsM(Pb, Fe, Co, Ni, Mn)Br3, as explained by the free electron theory ε'' ≈ 1/πε0ρf, where ε0 represents the free space impedance and f denotes the frequency [33]. Consequently, the rise in ε'' indicates a decrease in resistivity, signifying improved conductivity loss during the process of EMW absorption as a result of the higher entropy alloying.
This phenomenon can be understood from a different perspective. In CPB1, which has a lower M content and a cubic CsMBr3 structure, the crystal exhibits cubic symmetry with minimal distortions and lacks intrinsic polarization. This characteristic of CPB1 limits the support for a significant internal electric field, resulting in relatively low values for both ε' and ε'' (real and imaginary dielectric constants).
Conversely, CPB2, with a higher M content, features an asymmetrical orthorhombic ion arrangement within the crystal lattice. This arrangement leads to spontaneous polarization aligning in a specific direction when subjected to an external electromagnetic field. This alignment results in an increased dipole moment and, consequently, a higher dielectric constant. Similarly, in CPB3, the crystal structure exhibits even stronger asymmetry and disorder, combining orthorhombic and tetrahedral configurations. The lower crystal symmetry of CPB3 allows for the formation of more complex polar structures capable of storing a greater amount of electrical charge. This complexity leads to a higher dielectric constant [33].
The magnetic permeability (µ') as depicted in Fig. 10c exhibits a notable increase with the introduction of a high-entropy component in CsMBr3. Specifically, in CPB1, µ' is approximately 1.2 H/m, but this value increases to 1.3 H/m for CPB2 and further to 1.55 H/m for CPB3. This observed trend aligns with the relationship between µ' and magnetic susceptibility (χ), which is obtained from VSM data as shown in Fig. 8a. According to the relationship µ' = 1 + χ, the elevation of µ' is primarily attributed to the rise in χ, indicating a heightened capacity for dissipating the electric energy carried by incident electromagnetic waves (EMW). Remarkably, the µ'' values of all the current samples also demonstrate a substantial increase with increasing M content, owing to the heightened magnetization, as illustrated in Fig. 8a. Materials with high µ′ can effectively diminish the amplitude of electromagnetic waves as they pass through them. Consequently, the dissipation of magnetic energy is elevated, which is advantageous for the electromagnetic absorption (EMA) property of these materials.
The intrinsic impedance ratio, denoted as Z, plays a crucial role in determining the ease with which electromagnetic waves (EMW) penetrate a material. A higher intrinsic impedance ratio, typically exceeding 0.3, indicates favorable conditions for the ingress of EMW into the material's interior [34]. This intrinsic impedance ratio, a transmission property, characterizes how electromagnetic waves propagate through a given medium and can be computed using Eq. (6).
$$Z=\sqrt{\raisebox{1ex}{${\mu }^{{\prime }}$}\!\left/ \!\raisebox{-1ex}{${\epsilon }^{{\prime }}$}\right.}$$
6
When the intrinsic impedance of a material closely approximates that of free space, it results in reduced reflection of electromagnetic waves at the material's interface. This diminished reflection translates into lower signal loss and more efficient energy transfer, which are pivotal for effective Electromagnetic Absorbers. A rule of thumb is that when Z exceeds 0.3, electromagnetic waves can smoothly and abundantly infiltrate the absorbing material [35]. A higher intrinsic impedance ratio ensures a greater quantity of EMW propagates into the absorber.
Figure 10d provides insights into these principles. CPB1 exhibits a value below 0.3, indicating less favorable conditions for EMW penetration. Conversely, CPB2 and CPB3 boast much higher intrinsic impedance ratios, well surpassing 0.3, across the 2–18 GHz frequency range. This suggests that CPB2 and CPB3 exhibit excellent transmittance for high-frequency EMW and can effectively attenuate incoming electromagnetic waves.
When samples are subjected to the electromagnetic wave, they experience an oscillating electric field, resulting in polarization and the absorption of electromagnetic energy. This polarization response is intricately linked to the crystal structure and its corresponding level of symmetry, with different crystal phases displaying diverse reactions to applied electric fields. Figure 10e reveals intriguing trends in the polarization-electric field (P-E) curves of our samples, where polarization consistently rises with increasing M (Fe, Co, Ni, and Mn) content. Notably, CPB3 exhibits a steeper slope on its P-E curve compared to CPB1 and CPB2, despite the application of relatively low electric fields. This observation underscores the material's remarkable response to even modest electric fields. The heightened polarization in CPB3 can be attributed to multiple factors, with crystal structure playing a pivotal role. Our previous X-ray diffraction (XRD) analysis unveiled key insights: CPB2 adopts an orthorhombic structure, whereas CPB3 consists of a mixture of orthorhombic and tetrahedral phases, both featuring highly asymmetric structures. The lower symmetry in the CPB3 structure makes it more susceptible to polarization under an applied electric field. This increased susceptibility arises from a greater degree of lattice distortion, which provides a wealth of active modes for ferroelectricity, resulting in a more pronounced coupling between polarization and the electric field.
In addition to structural considerations, the introduction of M elements (Fe, Co, Ni, and Mn) has a notable impact on charge distribution within the crystal lattice, particularly involving elements with varying + 2 and + 3 valences. The process of charge transfer between these elements induces changes in the electronic structure, thereby fostering higher polarization. Importantly, the distinct charge-donation and -acceptance behaviors of these elements contribute to alterations in the distribution of charge carriers within the crystal, further enhancing the overall polarization response. Therefore, the improved polarization can be attributed to high-entropy induced- structural (crystal symmetry and lattice distortion) and electronic factors (charge distribution and transfer) which collectively yield the observed increase in polarization, even under relatively mild electric field conditions.
The attenuation constant (α) holds significant importance in electromagnetic wave (EMW) absorption performance. In Fig. 10f, it is evident that the capacity to attenuate incident EMW gradually improves with the increase in M content and EMA frequency. Importantly, all three samples exhibit attenuation constants exceeding 100 across the entire frequency spectrum, indicating their effective ability to absorb incident EMW [1]. The substantial increase in attenuation loss can be primarily attributed to two main factors. Firstly, the heightened presence of M elements (Fe, Co, Ni, and Mn) introduces additional electron energy levels within the bandgap of CsPbBr3, leading to heightened absorption and the potential for increased attenuation loss. Secondly, the coexistence of different phases with grain boundaries amplifies the scattering of electromagnetic waves, consequently elevating attenuation loss. Additionally, defects and distortions within the crystal structure consume electromagnetic energy, further contributing to the overall rise in attenuation loss.
3.5 Reflection loss and EMA property
The Effective Electromagnetic Absorption (EMA) parameters, namely Minimum Reflection Loss (RLmin), material thickness, and Effective Absorption Bandwidth (EAB), play a crucial role in characterizing electromagnetic wave absorption. In Table 2, we summarize RLmin, thickness, frequency, and EAB.
In Fig. 11, we provide a visual representation of the simulated reflection loss (RL) through 3D reflection loss plane maps, contour maps, and the Zin/Z0 ratio for various samples. As depicted in Fig. 11, all samples exhibit distinctive peaks in RL, indicating their strong absorption of incident electromagnetic waves at specific frequencies, resulting in high reflection losses. Specifically, for CPB3, the maximum EMA occurs at 10.2 GHz, achieving an RLmin of 75 dB with a thickness of 2.5 mm. Notably, CPB3 outperforms CPB2, which achieves an RLmin of 58.5 dB at 12.4 GHz with a thickness of 1.5 mm, and CPB1, which achieves a modest RLmin of 23.8 dB at 9.2 GHz with a thickness of 3.5 mm.
Furthermore, when comparing Fig. 11a, 11b, and 11c, it becomes evident that CPB3 exhibits a significantly broader bandwidth. For example, the resonance peaks in Fig. 11a appear at both low and high frequencies due to CPB3's higher dielectric constant (ɛ') and magnetic permeability (µ'), resulting in a significant broadening of the Effective Absorption Bandwidth (EAB 8.8 GHz). This suggests that CPB3 is capable of absorbing electromagnetic waves across a wider frequency range compared to CPB2 (5.6 GHz) and CPB1(4.4 GHz). This superiority can be attributed to the mixture of orthorhombic and tetrahedral phases in CPB3, which possess notably higher ɛ', polarization, µ', intrinsic impedance, and attenuation loss due to the large content of high-entropy alloying.
On the flip side, a larger specific surface area also plays a role in enhancing RLmin. As depicted in Fig. 5, CPB3 boasts a higher specific surface area (51.78 m2/g), offering more surface sites or interfaces. This augmentation facilitates surface polarization effects, ultimately leading to improved electromagnetic radiation absorption and enhanced EMA performance, as observed in Figs. 11a and 11a1.
In this study, the introduction of high-entropy elements such as Fe, Co, Ni, and Mn, which are highly conductive, creates a pathway for the conduction and attenuation of electromagnetic waves. Simultaneously, the electron polarization, dipole polarization, and ion polarization on the enhanced surface area contribute to CPB3's superior EMA characteristics.
Furthermore, the normalized Zin/Z0 ratio characteristics of CPB3, CPB2, and CPB1 are illustrated in Figs. 11a2, 11b2, and 11c2, respectively, to assess impedance matching. From Fig. 11, it's evident that at the maximum peak frequency, the input impedance ratio Zin/Z0 of each sample is close to 1.0 (highlighted in yellow), and the absorption strength decreases when the maximum peak frequency corresponds to Zin/Z0 ≠ 1.0. This indicates that these samples exhibit excellent impedance matching with electromagnetic waves, a crucial factor for efficient power transfer, minimal reflection, reduced signal loss, improved signal integrity, and reduced heat generation. This aspect is crucial for optimizing the absorption or transmission of electromagnetic waves in materials.
The contour plots in Fig. 12 illustrate impedance-matching characteristics, with different colors denoting varying impedance levels. Specifically, blue, red, and yellow regions correspond to poor, fair, and excellent impedance matching, respectively. Moreover, the contour shape provides insights into these matching properties. For instance, in Fig. 12c, a steeply sloping curve suggests that CPB1 experiences non-steady impedance matching, with a fluctuating stripe pattern across different frequencies [36]. In contrast, Fig. 12a exhibits a much flatter and broader contour, indicating consistent and superior impedance matching across a wide frequency range. Figure 12b, while broader than CPB1, fails to cover the entire desired frequency range, and CPB2 maintains a steep contour line, signifying sharp variations in impedance matching across all frequencies, indicating instability.
Additionally, examining the colors, CPB1 predominantly displays red in its stripe pattern, whereas CPB2 and CPB3 are dominated by yellow. The color scale on the left side of each figure indicates that yellow corresponds to an optimal impedance matching value of 1. This suggests that CPB3 achieves the best impedance matching with air, facilitating the penetration of electromagnetic waves into CPB3. Consequently, the flat, shallow, and broad curves seen in CPB3 imply steady and broader-band impedance matching capabilities for EMA [37].
In Fig. 12d, a comparison is made among three samples in terms of EMB, thickness, and RLmin. Notably, CPB3 significantly outperforms the other two samples.
The results of the present study were compared with relevant literature, and a summary is provided in Table 2. Specifically, the study evaluated the electromagnetic absorption (EMA) performance.
In Table 2, you can observe a summary of comparisons with other materials and studies. For instance, materials with high-entropy transition metals in MB2 (M = Cr, Zr, Hf, Nb, Ta) exhibited high entropy and good EMA characteristics. Similarly, MAlx (M = Fe, Co, Ni, Mn) alloys with high entropy, particularly the FeCoNiMn combination, demonstrated favorable EMA properties.
It's worth noting that the documented use of CsPbBr3 for EMA applications was limited to CsPbBr3/carbon nanotube composites. Another relevant study involved MAPbI3/graphene composites for EMA. Upon comparing these findings in Table 2, it becomes evident that the CPB3 material examined in this study holds great promise and potential for EMA applications.
Table 2
Comparison of EMA parameters between present samples and relevant literature materials.
EMA materials | RLmin (dB) | Bandwidth(GHz) | References |
TMB2(Cr, Zr, Hf, Nb, Ta) | -59.6 (8.48GHz, 2.68mm) | 7.6 | [] |
FeCoNiMn0.5Alx | -42.851(4.4GHz, 3mm) | / | [a] |
CsPbBr3/CNT | -51.74(7.8GHz, 3.23mm) | 5.56 | [6] |
MAPbI3/graphene | -10.78(13.2GHz, 1.82mm) | 6.04 | [23] |
Cs (Pb, Fe, Co, Ni, Mn)Br3 | -23.8(9.2GHz,3.5mm) | 4.2 | This study |
-58.5(12.4GHz,1.5mm) | 5.6 | This study |
-75(10.2GHz,2.5mm) | 8.8 | This study |
The mechanism underlying the enhanced Electromagnetic Absorption (EMA) properties of the current samples is elucidated in Fig. 13, considering high-entropy and phase regulation engineering. As depicted in Fig. 8, the initial step of high-entropy alloying, incorporating magnetic elements such as Fe, Co, Ni, and Mn into CsPbBr3, notably elevates magnetic susceptibility and permeability by introducing localized magnetic moments within the crystal. This increase in magnetic permeability influences how electromagnetic waves propagate through the material, potentially enhancing wave-matter interactions and dipolar polarization. Furthermore, Fig. 5 demonstrates that the augmented specific surface area contributes to an increased surface polarization effect. Figure 8 illustrates that the M-H hysteresis loop of the present sample expands with higher high-entropy M content, indicating that magnetic moments within CPB3 reorient themselves in response to an oscillating magnetic field. Additionally, from Fig. 10, the P-E curve reveals a significant enhancement in the polarization of CPB3. These findings collectively lead to energy dissipation in the form of heat within the sample, resulting in high EMA.
The occurrence of resonance loss within the GHz range is primarily attributed to the anisotropic magnetic susceptibility of CPB3. Moreover, the coexistence of stronger Fe3+ and Co3+ ions significantly enhances magnetic couplings between various elemental species and charge carriers. Secondly, as demonstrated in Fig. 10, high entropy alloying induces an increase in dielectric constant and attenuation loss. When electromagnetic waves traverse the material, electrons' movement, collision, and oscillation consume a substantial amount of energy in the form of electricity. A high dielectric constant leads to increased dielectric loss, transferring a significant amount of electromagnetic energy.
Another substantial contributor to high EMA is the phase regulation of the current sample. Analysis through SAED, GIWAXS, and Rietveld refinement of XRD patterns indicates that the elevated high-entropy M content triggers lattice distortion and the coexistence of orthorhombic and tetrahedral phases. This diversity in elemental types, with varying ionic sizes, electronegativity, and arrangements in the crystal structure, results in a disordered microstructure. This diverse microstructure creates multiple interfaces and boundaries within the material, leading to multiple reflection and scattering centers for incident electromagnetic waves, thereby enhancing EMA.
On the other hand, EPR analysis reveals that high entropy alloying and phase transition within the crystal, especially with + 3 valence states, generate oxygen deficiencies and lattice defects, increasing vacancy loss and lattice distortion loss. For example, the lower crystal symmetry and higher distortion of MBr6 units in tetrahedral and orthorhombic phases provide more active sites and stronger dipolar polarization within CPB2 and CPB3, resulting in significantly higher EMA compared to the cubic phase in CPB1, attributable to the dielectric relaxation theory. In highly ordered structures, dipoles or charges have well-defined orientations and can respond more efficiently to the applied field, resulting in lower losses. Conversely, in less ordered structures, dipoles or charges have a more random arrangement, leading to less efficient responses and higher losses.