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Article

The Raman Spectra of Co-, Fe-, and Mn-doped Bi2Se3 Single Crystals

by
Ligang Liu
1,
Min Zhang
1 and
Qiya Liu
2,*
1
School of Physics and Astronomy, China West Normal University, Nanchong 637002, China
2
College of Optoelectronic Technology, Chengdu University of Information Technology, Chengdu 610225, China
*
Author to whom correspondence should be addressed.
Crystals 2023, 13(3), 456; https://doi.org/10.3390/cryst13030456
Submission received: 18 December 2022 / Revised: 6 February 2023 / Accepted: 2 March 2023 / Published: 5 March 2023
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Abstract

:
In this study, single crystals of TrxBi2Se3 (Tr = Co, Fe, and Mn) were produced via a melt-grown reaction. All crystals are c-axis oriented with an excellent single crystalline phase. The smaller ionic radius of the transition metal elements makes the QLs of Bi2Se3 thinner. Their abundant magnetism will provide spin–phonon coupling channels when the phonons are scattering in the system. Both Stokes and anti-Stokes Raman spectroscopy were performed for the three optical phonon modes of the Bi2Se3 crystals. These peaks were centered at 74.5 cm−1, 133.4 cm−1, and 175.2 cm−1 and were attributable to the A1g(1), Eg(2), and A1g(2) modes, respectively. With an increase in the doping concentration, the magnetic and compressive strains induced by impurities dominate the phonon dynamics of materials. The results provide an effective scheme to regulate the thermoelectric properties of a Bi2Se3 system.

1. Introduction

Bismuth selenide (Bi2Se3) is a topological insulator (TI) material, and its thermoelectric properties have been noted by some groups [1,2,3]. It possesses a layered three-dimensional (3D) structure, as shown in Figure 1a. This highly symmetric layered structure consists of Se(1)-Bi- Se(2)-Bi- Se(1) quintuple layers (QLs). The quintuple layered structure is bonded by a van der Walls force [4]. The 3D Bi2Se3 exhibits topological insulating properties due to the presence of surface states and a bandgap of 0.3 eV in the bulk [5,6]. The peculiar electronic structure of the 3D Bi2Se3 is caused by a strong spin–orbit interaction, which is topologically protected against backscattering crystalline defects and distortion of the surface state. Therefore, its application in spintronic devices and fault-tolerant quantum computing has been suggested [7,8,9]. Many TIs are known as excellent thermoelectric (TE) materials. This is because TI and TE compounds usually favor the same material features, such as being heavy elements and possessing a smaller energy gap. Thus, the excellent thermoelectric property of Bi2Se3 means that it can be utilized in a variety of diverse applications [10,11]. In principle, a temperature gradient creates an electric potential in TE materials; thus, these materials could be used as TE converters for the purposes of power generation. A TE converter could be used for the conversion of a part of low-grade waste heat (such as that which is generated by engines, industrial furnaces, gas pipes, etc.) to electricity (such as through thermoelectric conduction devices [10] and infrared THz detectors [11]). The phonon dynamics of Bi2Se3 and their coupling with complex environments are critical for understanding their thermal conductivity and heat-to-electricity conversion [12,13] and hence improving their device performances [14,15].
The measurements of coherent phonons have been conducted for various TE materials, which have thus revealed the dynamics of phonons [11,12,13,14,15]. Phonon–phonon coupling and electron–phonon coupling play an important role in the study of phonon dynamics in Bi2Se3. According to the reports, the phonon dynamics in Bi2Se3 crystals were studied via using femtosecond spectroscopy. In addition, these so-called coherent phonons cause a modulation in the transient reflectivity or transmissivity via a change in the electric susceptibility with those vibrational frequencies [15,16,17]. Bi2Se3 crystals have a rhombohedral crystal structure composed of hexagonal close-packed atomic layers that are stacked along the c axis (shown in Figure 1a). The zone-center phonons consist of 2Eg + 2A1g + 2Eu + 2A2u, where the Eg and A1g modes are Raman active, while the Eu and A2u modes are infrared active [18]. Evidently, these crystals’ phonon properties have been studied extensively using Raman spectroscopy [18,19]. Raman scattering (RS) is a powerful and sensitive technique in the study of phonon dynamics, microscopic structures [20], and the defects [21] of samples for doped solid materials [22]. There are many excellent works that have reported the dynamics of phonons in Bi2Se3 [23,24,25]. Zhang et al. reported their findings regarding the Raman spectroscopy of few-quintuple layer topological insulator Bi2Se3 nanoplates. The results indicated that a significant reduction in the phonon lifetime of the in-plane vibrational modes is most likely due to an enhanced electron–phonon coupling in the few-QL regime [23]. Humlíček et al. observed three narrow Raman bands in the Bi2Se3 films out of the four resulting from crystalline symmetry, thus confirming the excellent quality of the epitaxial films [24]. Using Raman spectroscopy, the Raman spectra of Bi2Se3 nanostructures were analyzed in detail by Yang et al. [25]. Their results show that Raman shifts are correlated directly to the identities (i.e., nature, order, length, and energy) of the representative bond of the specimen. Cheng et al. studied the structure and properties of seven sesqui-chalcogenides (Bi2Te3, Bi2Se3, Bi2S3, Sb2Te3, Sb2Se3, Sb2S3, and β-As2Te3) using the first principles. Their results indicated that unconventional bonding leading to physical properties are distinctively different from those caused by covalent, metallic, or ionic bonding. Furthermore, their experiments revealed that this bonding mechanism prevails in four sesqui-chalcogenides, which were characterized by rather short interlayer distances at the van-der-Waals-like gaps—thereby suggesting a significant interlayer coupling in the materials [26]. Moreover, we have studied the anharmonic effects in Bi2Se3 crystals via using femtosecond (fs) transient optical spectroscopy at 5–280 K, as well as a vibration frequency and dephasing time of a A1g(1) mode decreasing with an increasing temperature and a lattice parameter c [27]. At present, the studies on the phonon dynamics of Bi2Se3 mainly focus on pure Bi2Se3 crystals. As such, the phonon dynamics of doped samples are rarely studied. However, during the synthesis of a Bi2Se3 single crystal, it is easy to form n-type semiconductor materials rather than topological insulator materials, which is due to the Se vacancy [28]. To solve these problems, element-doping schemes have been used by multiple groups in order to modulate the material properties [28,29,30,31,32,33]. In doped samples, the structural and topological phase transitions caused by impurities may lead to changes in the properties (topological properties, thermoelectric properties, mechanical properties, optical properties, electromagnetic properties, etc.), and even induce novel properties (i.e., the anomalous quantum Hall effect (AQHE) and superconductivity) [7,8,9,17,26]. Therefore, it is incredibly valuable to study the phonon properties of doped Bi2Se3 crystals.
The chemical doping method has been widely used to regulate the Fermi level, the lattice, the thermal conductivity, the Dirac point position, and the surface chemical potential [28,29,30,31,32,33]. A series of different element substituting experiments have been performed on Bi2Se3 to study the influence of impurities on the phonon dynamics from a different processing [29,33]. The phonon dynamics of the Cu-intercalated Bi2Se3 have been studied with different temperatures, such as at T = 3 K, and the helical scattering continuum was amplified with weak doping [9]. The Raman scattering spectra of sputtered amorphous Ge25Se75-xBix films demonstrate that the lattice vibration was changed. Furthermore, with the different Bi concentrations, it was observed where the 175 cm−1 line intensity increased and the position of the 200, 265, and 255 cm−1 lines decreased by 10 cm−1 [34]. Among the many doped elements, the transition metals are special because of their strong spin electrons, as well as their doping with a magnetic atom, which can regulate the surface states of TI. This is a source of time-reversal symmetry breaking, which can lead to the realization of the novel magneto-electronic properties of the system [32,35,36,37]. Previously, the electronic properties of Bi2Se3 were doped by 3D transition metals (i.e., Mn, Fe, Co, or Ni), in which the ions were calculated by Ptok et al. [36]. In addition, the density of states and the projected band structure were also investigated; the shift of the Fermi level was observed and the existence of nearly dispersionless bands around the Fermi level associated with substituted atoms was confirmed. Ptok et al. also discussed the modification of the electron localization function, as well as the charge and spin redistribution in the system. Their study shows a strong influence regarding the transition metal-Se bond on the local modifications of the physical properties. The results are also discussed in the context of the interplay between the energy levels of the magnetic impurities and topological surface states. Cermak et al. studied the phonon dynamics of Cr-doped Bi2Se3 crystals and their thermoelectric properties via the use of first principles [37]. The results indicated the changes induced by the Cr doping lead to extraordinary behavior regarding the transport properties of Bi2Se3. The extraordinary behavior of the Seebeck coefficient and carrier mobility lead to an enhanced power factor in the doped crystals. In our previous report, we studied the following: the phase structure; the electrical and magnetic transport properties; as well as the Hall mobility and Hall resistivity for the transition-metal (Co, Fe, and Mn)-doped topological insulators (TI) of CoxBi2-xSe3, FexBi2-xSe3, and MnxBi2-xSe3 [38,39,40]. However, the lattice dynamics of transition-metal-doped Bi2Se3 have not been systematically discussed. In this work, we pay attention to the phonon dynamics of the different vibration modes in transition-metal-doped Bi2Se3 crystals.
As demonstrated in studies of phonons and electron–phonon coupling in graphene in a few-layer regime [41], Bi2Se3 displays a layered structure with five atomic layers in the basic unit cell. The electron–phonon coupling is important because it sets a fundamental limit on the conductivity of electrons in topologically protected surface states [42,43]. The Raman-active modes of Bi2Se3 single crystals with the transition metal doping are shown in Figure 1b. Additionally, the Raman shifts of different modes of symmetry for Bi2Se3 are shown in Table 1. According to the reports, the Raman shifts and intensity of Bi2Se3 can be changed because of its thickness, temperature, doping, pressure, laser wavelength, and QLs [9,12,29,33].
In order to explore the lattice vibration dynamics of the single crystals of CoxBi2-xSe3, FexBi2-xSe3, MnxBi2-xSe3, and the Raman spectra measurements that were performed on the new cleaved pristine surface of the samples, the lattice vibration dynamics of the single crystals of CoxBi2-xSe3, FexBi2-xSe3, and MnxBi2-xSe3 are discussed. Additionally, the crystal structure and morphology of the samples were characterized by X-ray diffraction (XRD) and the field emission scanning electron microscope (FESEM). In addition, we also calculate the phonon spectra of 3D Fe-doped Bi2Se3 structures via using the first principles to further verify our experimental results.

2. Experimental

The single crystals of CoxBi2-xSe3, FexBi2-xSe3, and MnxBi2-xSe3 were prepared by melting a stoichiometric mixture with a high-purity bismuth (99.999%), selenium (99.999%), and Co, Fe, and Mn-balt (99.99%) powder. After being ground and pressed, the pellets were sealed in evacuated quartz glass tubes (<10-5 torr). The tubes were kept in a muffle furnace to induce sintering, and the quartz tubes were heated at 850 ℃ for 8 h. Then, the furnace was slowly cooled to 620 ℃ for 50 h and kept at this temperature for 24 h. Finally, the quenching was carried out in water, whereby high-quality single crystal samples were obtained.
In our work, the crystal structure analysis was performed via using X-ray diffraction (XRD, X’Pert Panalytical). A field emission scanning electron microscope (FESEM, JSM-7001F) was used to detect the morphology of the samples. The Raman scattering measurements were carried out through quasi-backscattering geometry at 295 K. In addition, the excitation lines of λ = 532.1 nm, with a power of less than 2 mW, were used to obtain the incidence of the samples’ surface. Lastly, the single crystal Si-substrate Raman modes were used as the internal frequency reference.
Simultaneously, the density of the phonon states of the Fe-doped Bi2Se3, as well as the Bi2Se3, was calculated via the first principles, which was achieved with the Vienna Ab Initio Simulation Package (VASP), which includes the density functional theory (DFT) and plane wave pseudopotential method. In this paper, the 2 × 2 × 1 supercell contains 36 Se atoms and 24 Bi atoms, which were used to calculate the influence of the Fe atom on Bi2Se3. Density functional theory (DFT) was performed to achieve optimized geometrical and electronic structures with a projector augmented wave (PAW) [44]. Further, the Perdew–Burke–Ernzerhof (PBE) generalized gradient approximation (GGA) exchange-correlation functional method was adopted; the kinetic energy cutoff was 520 eV. A Brillouin zone (BZ) integration was performed on grids Γ-centered 5 × 5 × 1 k-points grids for the structural relaxation and electronic structure calculations. Total energy and the all forces on atoms converged to less than 10−6 eV and 0.01 eV/Å. All calculations were performed using the DFT/GGA method. Moreover, the van der Waals interaction (a DFT-D3 method with Becke–Jonson damping) was incorporated [45,46]. The spin-orbital coupling (SOC) was also considered and the data were processed by Origin 9.0.

3. Results and Discussion

In order to obtain the crystal structure of CoxBi2-xSe3, the detection of XRD was performed, the results of which are shown in Figure 2a. All the peaks with the same orientation were attributable to the (0 0 L) family, thus confirming that the CoxBi2-xSe3 crystals are parallel to the c-axis. Meanwhile, the impurity peaks were not observed in this experiment. This indicates that the Co atoms were incorporated into the tetradymite structure by occupying the Bi lattice sites [47,48]. As the atomic radius of Co (1.25 Å) is smaller than Bi (1.63 Å), the lattice constant c decreases with the increasing Co content, as shown in Figure 2b. The typical FE-SEM images of the CoxBi2-xSe3 crystals with x = 0.00 and 0.06 are shown in Figure 2c,d, respectively. These results display a layered structure with flat, smooth, and crack-free surfaces. Compared to pure Bi2Se3 crystals, the layers of the Co-doped samples become more compact, and the steps are thinned. This implies that the QLs of the CoxBi2-xSe3 crystals are compressed, which is caused by the smaller atomic radius of the Co atomic. In addition, the Co–Se bond is shorter, and more compact layer structures can be found. This result is consistent with the conclusion obtained following the XRD analysis. Simultaneously, similar SEM results were found for the FexBi2-xSe3 and MnxBi2-xSe3 crystals [39,40].
Figure 3a shows the Raman spectra of the CoxBi2-xSe3 crystals with x varying from 0 to 0.12. Three obvious Raman shift peaks of Bi2Se3 were centered at 74.5 cm−1, 133.4 cm−1 and 175.2 cm−1, respectively; the Raman active mode corresponded to A1g(1), Eg(2), and A1g(2) [9,18]. Meanwhile, the Raman shift peaks from the impure phase were not observed, thus rendering them consistent with the XRD results. The phonon vibration frequency of Eg(2) and A1g(2) was blue-shifted with an increasing Co concentration, the results of which are shown in Figure 3b. The phonon frequency of the out-of-plane vibrational A1g(1) moved to the smaller wavelength (red-shift), and the intensity of the Raman peak at 74.5 cm−1 decreased when the Co content increased. According to previous studies on the phonon dynamics of topological insulators, these results may be caused by the magnetic order and lattice distortion that arise from impurities in the system [49,50,51,52,53]. Generally, a blue-shift of the Raman optical phonons was observed with an increasing strain. It has been suggested that the size-induced phonon red-shift (blue-shift) is activated by surface disorder [49], surface stress [51], and phonon quantum confinement [52]. The phonon confinement model suggested that strong phonon damping happens with a decreasing solid size [53]. In this work, when Co is doped into a Bi2Se3 system, the impurity induces a strain enhancement in the material, and the frequencies of the two optical phonons, Eg(2) and A1g(2), are blue-shifted. Compared with the Bi–Se bond, the Co–Se bond is shorter, the QLs become more compact, extra compression strain occurs, and the enhanced van der Waals interaction results in a higher phonon vibration frequency. However, with the increase in doping, the signals of the A1g(1) mode is weakened and the frequency is almost constant. It is reported that the A1g(1) mode is more sensitive to layer structures because it reflects the out-of-plane vibrations, whereby the corresponding vibration frequency is lower [23,26,54]. Therefore, it is necessary to consider spin–phonon coupling to explain the result. Transition metals have strong 3D spin electrons that can interact with different phonons. In addition, spin–phonon coupling may inhibit the A1g(1) phonon scattering. Zhang et al.’s results also show that Co-doped Bi2Se3 topological insulators would introduce additional spin. Further, the Bi2Se3 matrix is diamagnetic, and the doped sample is a superposition of ferromagnetism (FM) and paramagnetism (PM) behavior at low temperature. Two possible explanations have been proposed for the origin of ferromagnetism in Co-doped Bi2Se3. One is the magnetic ordering from the nanoclusters of a Co–Se compound in the crystals. The other is through a Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction between the magnetic impurities [38]. Therefore, it is appropriate to consider the effects of the van der Waals interlayer magnetic coupling, as well as the spin–phonon coupling that is caused by the impurities on the phonon vibration frequency in Co-doped systems. In the process of CoxBi2-xSe3 crystal growth, the lattice constant c decreases as the Co atomic radius becomes smaller (Figure 2b). When the Co–Se(1) spacing becomes smaller, the stack of adjacent atomic layers become compact and the broadening of the in-plane vibrational mode Eg(2) becomes wider, thereby suggesting that the layer-to-layer stacking affects the intralayer bonding [23,26]. The A1g(1) of Co-doped Bi2Se3 single crystals was found to red-shift. The broadening of the Eg(2) mode became wider due to the Co atomic substitute for Bi atomic in Bi2Se3 single crystals.
Figure 4a shows the XRD patterns of FexBi2-xSe3 (x = 0.00, 0.04, 0.06, 0.10, and 0.15). Lv et al. reported the crystal structure, morphology, as well as the electrical and magnetic transport properties of Fe-doped in the Bi2Se3 single crystals [39]. With the increase in Fe doping amounts, the tetradymite structure of Bi2Se3 saw no change due to the fact that all the diffraction peaks corresponded to the (0 0 L) reflections of the rhombohedral Bi2Se3. Furthermore, there was no impure phase, thus indicating that the majority of the Fe impurity was substituted for in the Bi atomic sites. The lattice constant c firstly decreased and then increased gradually with the increasing Fe content, as shown in Figure 4b. This implies that Fe atomic interposed to the Bi2Se3 materials [55], and the change in lattice parameters with the Fe impurity concentration confirms this conclusion. In order to further confirm the lattice distortion of the FexBi2-xSe3 crystals samples, the Raman scattering measurements were carried out at 295 K. (The Raman spectra of the FexBi2-xSe3 e crystals are shown in Figure 4c.) Two remarkable Raman peaks in the FexBi2-xSe3 samples appeared in the Raman shifts = 132.9 cm−1 and 175.4 cm−1. These were similar to the phonon frequency of the Bi2Se3 crystals [9,18]. The Raman-active mode corresponded to Eg(2) and A1g(2), and the Raman peaks of impurity were not detected. The results are consistent with the XRD results, which once again proved that the Fe atoms were incorporated into the tetradymite structure. However, with the increasing Fe doping amount, the phonon vibration frequency of A1g(2) and Eg(2) firstly red-shifted and then blue-shifted, the results of which are shown in Figure 4d. This indicated that two lattice aberrations were formed due to the Fe doping, which also fit with the results of Figure 4b. However, this result was different from that of the Co-doped Bi2Se3. As such, the theory of impurity-induced lattice distortion may not be applicable in terms of explaining the phonon dynamics of this system [51]. Therefore, to analyze the phonon’s vibration frequency of FexBi2-xSe3, we are more concerned with the magnetic order and disorder of the impurities. Due to the complex magnetism of the Fe element [39], the spin electrons of impurity interact with the laser-excited Raman active phonons; further, the phonon scattering may be inhibited [49,50].
Lv et al. reported that the Fe2+ and Fe3+ ions coexist in Fe-doped Bi2Se3 crystals. Additionally, Fe2+ ions mainly form around defect regions due to the existence of Fe–Se compounds, while Fe3+ ions plays an important role in determining carrier concentration as a substitution effect. The substitution defect of Fe3+ ions replacing Bi3+ ions produces no extra electrons; however, more electronegative Fe atoms tend to bond more strongly with Se atoms than they do with Bi atoms. The Fe3+ ion substitution for Bi3+ ions cannot affect the free carrier concentration directly, but the interaction between Fe atoms and native defects does lead to a decrease in Se vacancies [39]. Therefore, three types of nano-scaled Fe-enriched defects may be induce complex spin–phonon interactions. In order to further confirm the above experimental conclusions, the phonon state density of Fe-doped Bi2Se3 and pure Bi2Se3 were calculated using the first principles, the results of which are shown in Figure 5.
In this paper, we used the cold phonon method to calculate the phonon dispersion relationship and the states density of phonons with Fe atoms at the Bi site. Its atomic structure is shown in Figure 5a. For the pure Bi2Se3 and the Fe-doped Bi2Se3 models, all structures were fully optimized until the convergent threshold for energy was at 10−8 eV/atom, as well as when the Hellmann–Feynman force acting on each atom was 10−6 eV/Å. In addition, the force constant was calculated by the PAW method.
From Figure 5b,c, it can be seen that the high frequency vibration (~4.2 THz) of Bi2Se3 was mainly contributed by Se atoms. Meanwhile, the low frequency vibration (~1.8 THz) was mainly contributed by Bi atoms. Further, Fe was mainly combined with the Se atoms to form a Fe–Se bond, which restrains the high frequency vibration. These results are consistent with the report by Lv et al., whereby the crystal defects caused by Fe impurities may lead to external structural strains and spin [39]. The spin–phonon interaction was enhanced, and the phonon scattering may be inhibited, thus resulting in a red-shift of the vibration frequency. The calculated results are in agreement with the experimental results, which shows that our analysis of the experimental results is reliable.
The Mn element can effectively adjust the Dirac point to the energy gap, as well as modulate the surface state of Bi2Se3 [56]. The XRD patterns of Mn-doped Bi2Se3 in Figure 6a and the multiple diffraction peaks of different crystal planes were detected. The lattice parameters along the a-axis and the c-axis were calculated, as shown in Figure 6b. The lattice constant c and a of MnxBi2-xSe3 decreases with the increasing Mn content. This indicates that the Mn atomic substitute for the Bi atomic in the processing of the Bi2Se3 crystal’s growth. Further, the Mn atomic radius was found to be less than the Bi atomic radius, the Mn–Se(1) spacing of MnxBi2-xSe3 became smaller, and the thinner QLs layers were tightly stacked. The Raman spectra of MnxBi2-xSe3 crystals were detected in the same method, as shown in Figure 6c. The frequency of the two Raman active phonons were 133.5 cm−1 and 175.2 cm−1, respectively, which were ascribed to the vibration frequencies of the A1g(2) and Eg(2) modes of Bi2Se3. The dependence of the phonon vibration frequency on the doping concentration is shown in Figure 6d. The vibration frequencies of the A1g(2) mode were also observed, whereby they increased first and then decreased with the increase in the Mn concentration. The results imply that thinner QLs may obtain additional compressive strain, and that the phonon vibration frequency was blue-shifted [51]. In addition, the experimental results of Lv et al. showed that the magnetic order introduced by impurities gradually increases with the increase in Mn content. Furthermore, the magnetization data of the samples suggested the existence of an antiferromagnetic interaction between the Mn ions, and the strength of those couplings increased with the concentration of the Mn ions [40]. Thus, the van der Waals interlayer magnetic coupling and spin–phonon coupling was also considered. The strong spin–phonon coupling may inhibit phonon scattering and reduce phonon vibration frequency [49,50]. With respect to Eg(2), the vibration mode of which differs from A1g(2), the compressive strain of the a-axis and the spin–phonon coupling influenced the phonon scattering in the material, thereby resulting in an almost constant phonon frequency [49,50,51]. It was also noted that the broadening of A1g(2) and Eg(2) became wider, which confirmed that the lattice changed. The results of this are shown in Figure 6d. The reason for these phenomena are explained in detail in the previous description of the CoxBi2-xSe3 single crystals and FexBi2-xSe3 single crystals. The Mn–Se bonds are formed, and the Bi–Se bonds are broken; thus, the overall broadening increases.

4. Conclusions

Transition-metal (Co, Fe, and Mn)-doped Bi2Se3 crystals were prepared. The surface morphology of the samples were detected by FESEM. The results displayed a layered structure with flat, smooth, and crack-free surfaces. Compared to a pure Bi2Se3 crystal, the layers are more compact and the steps more thinned, which were caused by impurities that possessed smaller ionic radii. Raman spectroscopy and XRD were performed to characterize the crystal structure and the lattice vibration mode of the single crystals of CoxBi2-xSe3, FexBi2-xSe3, and MnxBi2-xSe3. The results demonstrated that the samples did not undergo a structural phase transition. However, the lattice constant c of the samples decreases with increasing dope content as the additional compressive strain and magnetic order induced by the impurities influence the phonon vibration frequency of the materials. Magnetism, in particular, likely leads to different phonon frequency dependencies. The results suggest that the different transition metal elements have different ionic radii and magnetic properties, which may lead to a different dependence of optical phonon vibration frequencies on different impurity concentrations in a Bi2Se3 system.

Author Contributions

Conceptualization, L.L.; Q.L. and M.Z.; methodology, Q.L. and M.Z.; software, L.L. and Q.L.; validation, L.L.; Q.L. and M.Z.; formal analysis, L.L.; Q.L. and M.Z.; investigation, L.L. and Q.L.; resources, Q.L. and M.Z.; data curation, Q.L. and M.Z.; writing—review and editing, L.L. and Q.L.; visualization, L.L. and Q.L.; supervision, Q.L. and M.Z.; project administration, Q.L. and M.Z.; funding acquisition, M.Z. All authors have read and agreed to the published version of the manuscript.

Funding

The research was supported by Sichuan Provincial Science and Technology Project (Grant No. 23ZDYF0311), Nanchong Science and Technology Project (Grant No. 21GXJS0014), Enterprise Project (Grant No. 401918), Sichuan Provincial Education Department Project (Grant No. CJF21006).

Data Availability Statement

The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest

The authors declared that they have no conflicts of interest to this work.

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Crystals 13 00456 g001 550
Figure 1. (a) Schematic of the Bi2Se3 crystal structure showing the quintuple layer and the location of the van der Waals gaps. (b) Atomic displacements of the four Raman-active modes.
Figure 1. (a) Schematic of the Bi2Se3 crystal structure showing the quintuple layer and the location of the van der Waals gaps. (b) Atomic displacements of the four Raman-active modes.
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Crystals 13 00456 g002 550
Figure 2. With different Co concentrations: (a) the XRD patterns of CoxBi2-xSe3; (b) the decreasing lattice constant c amount (the stars represent the lattice parameters of c in the (006) direction with the different Co doping concentrations); (c) the typical FESEM images of the CoxBi2-xSe3 crystals with x = 0.00; and (d) x = 0.06.
Figure 2. With different Co concentrations: (a) the XRD patterns of CoxBi2-xSe3; (b) the decreasing lattice constant c amount (the stars represent the lattice parameters of c in the (006) direction with the different Co doping concentrations); (c) the typical FESEM images of the CoxBi2-xSe3 crystals with x = 0.00; and (d) x = 0.06.
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Crystals 13 00456 g003 550
Figure 3. (a) The Raman spectra of CoxBi2-xSe3 single crystals; (b) the position of Raman peaks. (Note: the red points, blue triangers and black squares represent the Raman shift of the Eg(1), A1g(2) and A1g(2) vibration mode of the samples with the different Co doping concentrations.).
Figure 3. (a) The Raman spectra of CoxBi2-xSe3 single crystals; (b) the position of Raman peaks. (Note: the red points, blue triangers and black squares represent the Raman shift of the Eg(1), A1g(2) and A1g(2) vibration mode of the samples with the different Co doping concentrations.).
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Crystals 13 00456 g004 550
Figure 4. With different Fe concentrations: (a) the XRD patterns of FexBi2-xSe3; (b) the lattice constant c decreasing (the red points represent the lattice parameters of c in the (006) direction with the different Fe doping concentrations); (c) the Raman spectra of the FexBi2-xSe3 single crystals; and (d) the position of the Raman peaks.
Figure 4. With different Fe concentrations: (a) the XRD patterns of FexBi2-xSe3; (b) the lattice constant c decreasing (the red points represent the lattice parameters of c in the (006) direction with the different Fe doping concentrations); (c) the Raman spectra of the FexBi2-xSe3 single crystals; and (d) the position of the Raman peaks.
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Figure 5. (a) The 60-atom layered crystal structure of Fe-doped Bi2Se3; (b) the phonon state density of Fe-doped Bi2Se3; and (c) the phonon state density of Bi2Se3. (Note: the black line shows the phonon state density of Se atoms; the red line shows the phonon state density of Bi atoms; the blue line shows the phonon state density of Fe atoms).
Figure 5. (a) The 60-atom layered crystal structure of Fe-doped Bi2Se3; (b) the phonon state density of Fe-doped Bi2Se3; and (c) the phonon state density of Bi2Se3. (Note: the black line shows the phonon state density of Se atoms; the red line shows the phonon state density of Bi atoms; the blue line shows the phonon state density of Fe atoms).
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Crystals 13 00456 g006 550
Figure 6. With different Mn concentrations: (a) the XRD patterns of MnxBi2-xSe3, (“*”, it represents the position of the XRD diffraction peak of Mn); (b) the lattice constant a and c decreases in amount,(the blue squares represent the lattice parameters of c in the (006) direction with the different Mn doping concentrations; and the black circle represent the lattice parameters of a with the different Mn doping concentrations.); (c) the Raman spectra of the MnxBi2-xSe3 single crystals; and (d) the position of the Raman peaks.
Figure 6. With different Mn concentrations: (a) the XRD patterns of MnxBi2-xSe3, (“*”, it represents the position of the XRD diffraction peak of Mn); (b) the lattice constant a and c decreases in amount,(the blue squares represent the lattice parameters of c in the (006) direction with the different Mn doping concentrations; and the black circle represent the lattice parameters of a with the different Mn doping concentrations.); (c) the Raman spectra of the MnxBi2-xSe3 single crystals; and (d) the position of the Raman peaks.
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Table
Table 1. Raman shifts of the different modes of symmetry for Bi2Se3.
Table 1. Raman shifts of the different modes of symmetry for Bi2Se3.
Modes
Symmetry		Frequencies (cm−1)
Reference [18]Reference [9]
Eg(1)41.4938.9
A1g(1)75.4273.3
Eg(2)137.06132.9
A1g(2)171.02175.4
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Liu, L.; Zhang, M.; Liu, Q. The Raman Spectra of Co-, Fe-, and Mn-doped Bi2Se3 Single Crystals. Crystals 2023, 13, 456. https://doi.org/10.3390/cryst13030456

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Liu L, Zhang M, Liu Q. The Raman Spectra of Co-, Fe-, and Mn-doped Bi2Se3 Single Crystals. Crystals. 2023; 13(3):456. https://doi.org/10.3390/cryst13030456

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Liu, Ligang, Min Zhang, and Qiya Liu. 2023. "The Raman Spectra of Co-, Fe-, and Mn-doped Bi2Se3 Single Crystals" Crystals 13, no. 3: 456. https://doi.org/10.3390/cryst13030456

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