Manipulating electronic properties of two-dimensional MXenes Cr₂TiC₂FCl by phonon vibration

Summary

Although the manipulation of physical properties is common in applications of two-dimension (2D) materials, it is rare to tailor electronic properties by phonon vibration. In this article, we tailor the electronic band structure of Cr₂TiC₂FCl monolayer from indirect semiconducting state to metallic state by phonon modes (${\mathrm{A}}_1^2$, ${\mathrm{A}}_1^5$, and ${\mathrm{A}}_1^6$ mode) with the Raman and infrared active. The ${\mathrm{A}}_1^4$ mode makes Cr₂TiC₂FCl monolayer become direct semiconductor with a little gap, which can elevate the optical absorption efficiency of Cr₂TiC₂FCl monolayer, especially in the visible region. Meanwhile, both the conduction band minimum (CBM) and valence band maximum (VBM) are contributed by the spin-down channel; so, the electron hopping between VBM and CBM also does not need the participation of spin flipping and chiral phonon in Cr₂TiC₂FCl monolayer under the ${\mathrm{A}}_1^4$ mode. These results are significant for the application of 2D materials in the semiconductor laser, solar cell, and photodetector.

Graphical abstract

Highlights

• •We modulate the band structure of antiferromagnetic monolayer via phonon vibration
• •The ${\mathrm{A}}_1^4$ mode makes Cr₂TiC₂FCl monolayer become a direct semiconductor
• •The ${\mathrm{A}}_1^4$ mode makes the CBM and VBM of Cr₂TiC₂FCl both from spin down
• •${\mathrm{A}}_1^2$, ${\mathrm{A}}_1^5$, and ${\mathrm{A}}_1^6$ modes make Cr₂TiC₂FCl become metal from indirect semiconductor

Physics; nanoscience; applied sciences

Introduction

Recently, two-dimensional (2D) transition metal carbides and carbonitrides (MXenes) have attracted substantial attentions due to their high melting points, large metallic conductivities, extreme volumetric capacitance, and nanoscale magnetism,^1,2 which reveals that MXenes can be used in flexible electronics,³ ion batteries,⁴ supercapacitors,⁵ and spintronics.⁶ Unlike ferromagnets, antiferromagnetic (AFM) MXenes possess robustness against magnetic-field perturbation and ultrahigh speed of device operation. In 2019, Shenoy et al.⁷ functionalized the MXenes by surface terminations and investigated the magnetism in Janus M₂XO_xF_2-x and predicted their high Néel temperatures. He et al.⁸ also designed AFM Janus Cr₂TiC₂FCl with a Néel temperature of 901 K, much higher than room temperature, and the conduction band minimum (CBM) and valence band maximum (VBM) exhibit opposite spin directions. This surface functionalization can be realized by introducing atom to MXenes in synthesis as chemical dopants.^9,10

In the process of device manufacturing, it is of significance to manipulate the electronic and magnetic properties of MXenes effectively. In past years, numerous strategies have been proposed to tailor the electronic and magnetic properties of 2D materials, such as substitutional doping,^11,12 vacancy defect,¹³ strain,^14,15 adsorption,^16,17 optical driving,^18,19,20 heterostructure,^21,22 and applying external electrical field.^23,24 For instance, Tezze et al.²⁵ manipulated 2D MnPS₃ from pristine AFM state to complex magnetic textures by combing the intercalation and vacancy defect. Henríquez-Guerra et al.²⁶ enhanced the magnetic anisotropy of 2D CrSBr experimentally by compressive biaxial strain. Niu et al.²⁷ found the interlayer magnetic phase transition of a three-layer CrI₃ under external electrical field. It is rare to tailor electronic band structure by phonon vibration. The physical meaning of phonon is a quasi-particle produced by quantizing the collective vibration of a continuous lattice. The phonon can reflect the thermal stability, geometrical structure, bonding, and anharmonicity. Meanwhile, it has been unveiled that there always is indelible spin-phonon coupling in magnetic materials,^28,29 and this spin-phonon coupling often is owed to the electron transfer between ions. Samanta et al.³⁰ discovered the improvement of the magnetic stability of organic-molecule-intercalated 2D Cr₂Ge₂Te₆ by Raman spectroscopy, and attributed this improvement to electron transfer between tetrabutyl ammonium and Cr³⁺ ions. Therefore, the phonon vibration should also have impacts on the electronic properties of magnetic materials, but there are only a few studies discussing it.

In this article, we would explore the effects of phonon vibration on the electronic properties by the first-principles calculations with framework of density functional theory. According computation and analysis, we find that the imposition of phonon vibration can tailor the band structure of Cr₂TiC₂FCl monolayer effectively. For instance, the ${\mathrm{A}}_1^2$, ${\mathrm{A}}_1^5$, and ${\mathrm{A}}_1^6$ optical phonon modes can change the band structure of Cr₂TiC₂FCl monolayer from indirect semiconducting state to metallic state, while ${\mathrm{A}}_1^4$ mode makes Cr₂TiC₂FCl monolayer become a direct semiconductor with a little gap. All of these phonon modes are both Raman and infrared active and can be stimulated by laser with specific wavelength. These results pave a way for manipulating electronic properties of 2D materials by phonon vibration, which may be significant for the application of 2D materials in the optoelectronic devices.

Results and discussion

Structure and dynamical stability of Cr₂TiC₂FCl monolayer

Cr₂TiC₂FCl monolayer is designed by functionalizing MXenes Cr₂TiC₂ asymmetrically, as shown in Figure 1, while Cr₂TiC₂ is obtained by deleting Al in MAX phase Cr₂TiAlC₂. In Figures 1A and 1B the green, red, blue, cyan, and gray balls represent Cl, C, Cr, Ti, and F atoms, respectively. The black solid line highlights the unit cell of Cr₂TiC₂FCl monolayer. The lattice constants are a = b = 3.147 Å for our relaxed Cr₂TiC₂FCl monolayer, which is consistent with the results of He et al.⁸ well. In Cr₂TiC₂FCl monolayer, there are seven sublayers, including one Ti sublayer, two C sublayers, two Cr sublayers, one F sublayer, and one Cl sublayer. Ti atom in the third sublayer bonds with two C atoms forming a hexagonal ring, while Cr atom sublayer inserts the center of C-Ti-C hexagonal ring. Meanwhile, in a unit cell (u.c), two Cr atoms bond with F and Cl, respectively. To determine the magnetic state of Cr₂TiC₂FCl monolayer, we calculated the total energy under four different magnetic configurations, including ferromagnetic (FM), AFM-a, AFM-b, and AFM-c, as shown in Figure S1. The total energy of AFM-c configuration is −109.86 eV, smaller 205.89, 424.25, 494.38 meV/u.c than the FM, AFM-a, and AFM-b, respectively. As a result, the AFM-c configuration is the magnetic ground state of Cr₂TiC₂FCl monolayer. Moreover, this magnetic ground state can be validated by the spin charge density distribution in Figure 2. The magenta and cyan isosurfaces represent the spin up and spin down, respectively, and the isosurfaces were separated by ± 0.05 Bohr/ų. Figure 2 reveals the spin in Cr₂TiC₂FCl mainly arises from the Cr³⁺, and magnetic moments on the two Cr³⁺ ions in the u.c arrange antiparallelly while that on Cr³⁺ ions in the same sublayer ally parallelly. The sampling path for the irreducible Brillouin zone is shown in Figure 1C, which would be used in the calculations of phonon dispersion and band structures.

Figure 1.

Different views of crystal structure and the irreducible Brillouin zone

Top (A) and side (B) views of atomic model of Cr₂TiC₂FCl monolayer and (C) the k-point path in the irreducible Brillouin zone.

Figure 2.

Spin density of Cr₂TiC₂FCl monolayer

(A) Top and (B) side views of spin density with the magenta (spin up) and cyan (spin down) isosurfaces separated by ± 0.05 Bohr/ų.

To identify the stability, the elements in elastic constants matrix were calculated as C₁₁ = C₂₂ = 189.612 N/m, C₁₂ = C₂₁ = 42.543 N/m, C₆₆ = 73.490 N/m. According to the Born-Huang stability criteria,³¹ our relaxed Cr₂TiC₂FCl monolayer is mechanically stable, because $C_{11}{C}_{22}-C_{12}^2>0$ and C₆₆ > 0. The Young’s modulus and Poisson’s ratio of Cr₂TiC₂FCl monolayer are ∼180 N/m and 0.224. Besides, the phonon dispersion and phonon DOS were calculated to identify the dynamic stability, as shown in Figure 3. There is a slightly imaginary frequency about ∼0.012 THz around Γ point, which is common in 2D materials including graphene.^32,33 There are 21 branches, including three acoustic, and 18 optical branches, in the phonon dispersion of Cr₂TiC₂FCl, due to seven atoms in the u.c. It can be discovered from phonon DOS that the high frequency in phonon dispersion can be attributed to the C atom, while low frequency mainly arises from the Cr, Cl, and Ti. At Γ point, due to the frequency degeneration, these 18 optical phonon modes can be deconstructed as:

$${\mathrm{\Gamma }}_{\text{optical}}=6{\mathrm{A}}_1\left(\mathrm{R}\&\text{IR}\right)+6\mathrm{E}\left(\mathrm{R}\&\text{IR}\right)\text{,}$$ (Equation 1)

where R (IR) represents the phonon mode with Raman (infrared) active. Obviously, all of these optical modes are both Raman active and infrared active, which can be stimulated by laser with the corresponding frequency. The intrinsic vibration modes of optical phonons are exhibited in Figure 4 where arrow indicates vibration direction. These vibrations will be imposed to Cr₂TiC₂FCl by moving these seven atoms from their equilibrium positions. The distance away from equilibrium position is determined by the moduli of eigenvector of dynamic matrix.

Figure 3.

Dynamical stability of Cr₂TiC₂FCl monolayer

Phonon dispersion (A) and phonon density of states (DOS) (B) of Cr₂TiC₂FCl monolayer.

Figure 4.

Vibration mode of optical phonons in Cr₂TiC₂FCl monolayer

Band structure and projected DOS of Cr₂TiC₂FCl monolayer

Before studying the effect of phonon vibration on electronic band structure, we calculated the electronic band structure and projected DOS of pristine Cr₂TiC₂FCl monolayer as benchmark, as shown in Figure S2 in SI. The red and blue solid lines represent the spin-up and spin-down channel, respectively. The positive and negative values in projected DOS indicate the spin-up and spin-down states, respectively. Meanwhile, the Fermi energy level has been set as 0 eV. It is obvious that the Cr₂TiC₂FCl monolayer is an indirect semiconductor because the VBM occurs at different high-symmetry point with CBM. VBM can be found at Γ point while CBM appears on the Γ-M path. Furthermore, the obvious spin splitting can be observed from projected DOS and the CBM mainly contain the spin-up state while VBM can be attributed to the spin-down state. Interestingly, He et al.⁸ manipulated the positions of CBM and VBM by applying a gate voltage, due to the opposite spin state of VBM and CBM. Here, we would try to control the CBM and VBM by the phonon vibration.

In the phonon dispersion of Cr₂TiC₂FCl, there are three acoustic phonon branches whose eigenvectors describe the translation of the unit cell along x, y, and z axes, respectively, so they are named as longitudinal acoustic, transverse acoustic, and out-of-plane acoustic phonons, respectively. The electronic band structure under these three acoustic phonon modes also were calculated and presented in Figure S3 in SI. It can be found there is little difference between these three band structures and that of pristine Cr₂TiC₂FCl, including the channels, positions and values of VBM and (CBM). There it can be concluded acoustic phonon has little impact on the electronic band structure of Cr₂TiC₂FCl. The electronic band structure under optical phonon modes were plotted in Figure 5. We can find from Figure 5 that all of the optical phonon mode can shift the Fermi energy level, although the Fermi energy level is set as 0 eV. As a result, metal state appears when some phonon mode is imposed, such as ${\mathrm{A}}_1^2$, ${\mathrm{A}}_1^5$, and ${\mathrm{A}}_1^6$ modes. Among of these, ${\mathrm{A}}_1^2$ mode makes CBM and VBM at the same point (Γ point), and both are contributed by the spin-down channel. For ${\mathrm{A}}_1^5$ mode, both the VBM and CBM go across the Fermi level, resulting in a metal state. Similar to ${\mathrm{A}}_1^5$ mode, ${\mathrm{A}}_1^6$ mode also makes the VBM and CBM cross the Fermi level, and moves the CBM to the M point. Meanwhile, E¹ mode moves the CBM near the M point, while ${\mathrm{A}}_1^1$, E², E³, E⁴, ${\mathrm{A}}_1^3$, E⁵, and E⁶ modes make the CBM moving near the K point. Interestingly, the ${\mathrm{A}}_1^4$ mode also makes CBM and VBM at the same point (Γ point) with a small gap of 0.081 eV, rending the Cr₂TiC₂FCl monolayer a direct semiconductor. Then, the electron transition does not require the participation of phonons in Cr₂TiC₂FCl monolayer under the ${\mathrm{A}}_1^4$ mode. Furthermore, both the CBM and VBM are composed by the spin-down state in Cr₂TiC₂FCl monolayer under the ${\mathrm{A}}_1^4$ mode, and the electron transition between VBM and CBM also does not need the spin flipping and the participation of chiral phonon. Therefore, the imposition of ${\mathrm{A}}_1^4$ mode can elevate the optical absorption efficiency of Cr₂TiC₂FCl monolayer, especially in the visible region, which is desired in designing and fabricating light emitting diode, semiconductor laser, solar cell, photodetector. Besides, the ${\mathrm{A}}_1^4$ mode of 12.65 THz is a single-phonon mode without any phonon DOS degeneration in Figure 4, which is rare in condensed matter. This single-phonon mode is more easily stimulated and generated stable frequency output by laser than other modes, which renders Cr₂TiC₂FCl monolayer a promising candidate for quantum mechanical resonator with high cooling temperature. Meanwhile, it is convenient to change the Cr₂TiC₂FCl monolayer to direct semiconductor by laser excitation.

Figure 5.

Band structures of Cr₂TiC₂FCl monolayer under intrinsic optical phonon vibration modes, obtained by obtained by DS-PAW

It can be concluded that the intrinsic phonon mode has an impressive on the electronic properties and can tailor the band structure effectively. However, why the electronic band structure of Cr₂TiC₂FCl monolayer can be changed by the phonon vibration? To answer this question, we plotted the projected DOS of Cr and Ti ions in Cr₂TiC₂FCl monolayer, when the optical phonon vibrations were imposed. It can be discovered from Figure S2B that the magnetism and spin splitting mainly come from the Cr ion and slightly from the Ti ion, because both of them has underoccupied d orbit and obvious asymmetry of DOS. We can find from Figure 6 that the phonon mode can affect the DOS near the Fermi level significantly by the charge transferring induced by the atomic vibration, making the peak shift of DOS. Although ${\mathrm{A}}_1^2$, ${\mathrm{A}}_1^5$, and ${\mathrm{A}}_1^6$ modes change the Cr₂TiC₂FCl monolayer from indirect semiconducting state to metallic state, there still is a little DOS can be observed near the Fermi level. Because there are few numbers of energy bands going across the Fermi level, so the possibility of electrons occupying these energy bands is low and the DOS is too small to be observed.

Figure 6.

Projected density of states (DOS) for atoms in Cr₂TiC₂FCl monolayer

The projected DOS of Cr (A) and Ti (B) ions in Cr₂TiC₂FCl monolayer under optical phonons, obtained by obtained by DS-PAW.

Conclusions

In this article, we investigated the impacts of phonon vibration mode on the electronic band structure of AFM Cr₂TiC₂FCl monolayer using the first-principles calculations. Firstly, we identified the mechanical and dynamical stability of our relaxed Cr₂TiC₂FCl monolayer, and analyzed the vibration mode of 18 optical phonons at the Γ point in the irreducible Brillouin zone. Then, we imposed these vibration modes to Cr₂TiC₂FCl monolayer and calculated the band structures. According to computations, we find that phonon vibration can shift the Fermi level in the band structure significantly, resulting in the change of electrical conductivity. For instance, the ${\mathrm{A}}_1^2$, ${\mathrm{A}}_1^5$, and ${\mathrm{A}}_1^6$ modes can make the band structure of Cr₂TiC₂FCl monolayer change from the indirect semiconducting state to a metallic state, while Cr₂TiC₂FCl monolayer becomes direct semiconductor with a little gap under the ${\mathrm{A}}_1^4$ mode. There is no requirement for the participation of phonons during electron hopping in this direct semiconductor, and this little gap can be crossed by absorbing photons with frequencies in the visible region. Hence, the applications of Cr₂TiC₂FCl monolayer in semiconductor laser, solar cell, and photodetector can be expanded. Finally, we explained the origin of the change of band structure under phonon vibration by projected DOS. This study paves a way for manipulating electronic properties of 2D materials by phonon vibration, which is of significance for the application of 2D materials in optoelectronics.

Limitations of the study

In this study, we investigated the impacts of phonon vibration on electronic properties by the first-principles calculations implemented on the DS-PAW and VASP software. We find that the imposition of phonon vibration can tailor the band structure of Cr₂TiC₂FCl monolayer effectively. The ${\mathrm{A}}_1^2$, ${\mathrm{A}}_1^5$, and ${\mathrm{A}}_1^6$ modes change the band structure of Cr₂TiC₂FCl monolayer from indirect semiconductor to a metallic state, while the ${\mathrm{A}}_1^4$ mode makes Cr₂TiC₂FCl monolayer become a direct semiconductor. The largest limitation of the study is the 2D AFM Cr₂TiC₂FCl has not been successfully prepared, and it is difficult to verify its physical properties and regulatory functions by experiments, especially the Néel temperature of Cr₂TiC₂FCl monolayer. Based on the latest advances in material preparation technologies, we propose synthesizing 2D Cr₂TiC₂FCl layers via chemical vapor deposition, which presents a pivotal direction for future research endeavors on 2D AFM Cr₂TiC₂FCl.

Resource availability

Lead contact

Further information and requests for resources and reagents should be directed to and will be fulfilled by the lead contact, Zhigang Pan (panzhigang0703@126.com).

Materials availability

This study did not generate new unique materials.

Data and code availability

• •Data reported in this article will be shared by the lead contact upon request.
• •This article does not report original codes.
• •Any additional information required to reanalyze the data reported in this article is available from the lead contact upon request.

Acknowledgments

K.W. acknowledges the support from the National Natural Science Foundation of China (NNSFC) (12204373). K.R. acknowledges the support from the Natural Science Foundation of Jiangsu Province, China (grant no. BK20220407). Y.L. acknowledges the support from the Shaanxi Provincial Department of science and Technology (QINCHUANGYUAN, “scientist + engineer” team construction: 2024QCY-KXJ-188). We gratefully acknowledge HZWTECH for providing computation facilities.

Author contributions

Conceptualization, K.W., K.R., and Z.P.; methodology, K.W. and J.L.; investigation, K.W. and J.L.; software, Z.C. and K.W.; writing – original draft, K.W., K.R., Y.L., and Z.P.; writing – review and editing, K.W. and Z.P.; funding acquisition and project administration, K.W., K.R., and Y.L.

Declaration of interests

The authors declare no competing interests.

STAR★Methods

Key resources table

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Software
Device Studio (DS-PAW) 2022	HONGZHIWEI TECHNOLOGY	https://cloud.hzwtech.com/web/product-service?id=6
VASP5.4.1	VASP team	https://www.vasp.at/
PHONOPY1.11.2	PHONOPY team	https://phonopy.github.io/phonopy/

Experimental model and study participant details

Our study does not use experimental models typical in the life sciences.

Method details

The atomic model of 2D Cr₂TiC₂FCl monolayer was built by open-source VESTA program package. To suppress the coupling between adjacent layers, a 20 Å vacuum space was imposed along the out-of-plane direction. Afterward, the unit cell of 2D Cr₂TiC₂FCl monolayer was relaxed with cutoff of 550 eV until the energy difference and atomic force converge to 10⁻⁸ eV and 0.001 eV/Å, respectively. All calculations of the mechanical constants, electronic band structure, and electronic DOS were implemented by DS-PAW software integrated in Device Studio program.^34,35 DS-PAW is an open-source software, focusing on the balance between accuracy and computational efficiency. For the conventional property calculations, such as the structure relaxation, stability analysis, and basic electronic properties of MXenes, DS-PAW can be used as an “efficient alternative” to VASP. Under the same system, DS-PAW has faster calculation speed and lower memory consumption, which is suitable for scenarios requiring batch calculation or large system relaxation. The Monkhorst-Pack (MP) grid of 7 × 7×1 was used in structural relaxation, while a dense grid (13 × 13×1) was applied to obtain more accurate electronic band structure and DOS. The optimized lattice parameter of Cr₂TiC₂FCl is 3.15 Å, which is well agreed with the geometric structure predicted by He et al.⁸ Due to the d-orbital electron around Cr ion, the Hubbard U of 3 eV was used in all first-principles calculations. In all first-principles calculations, the projector augmented wave (PAW) method was used and the Perdew-Burke-Ernzerhof (PBE) of generalized gradient approximation was chosen as the exchange-correlation functional.^36,37 It is worth noting that the phonon dispersion was calculated by PHONOPY (Version 1.11.2) and VASP (Version 5.4.1) codes, based on the density functional perturbation theory (DFPT).³⁸ Because the optical phonon vibration modes cannot be obtained through DS-PAW, so we employed VASP and PHONOPY to perform the calculations of phonon.

Quantification and statistical analysis

Our study does not include statistical analysis or quantification.

Published: December 18, 2025