First-principles study of magnetism in some novel MXene materials

Magnetic two-dimensional materials have gained considerable attention in recent years due to their special topologies and promising applications in electronic and spintronic devices. As a new family of two-dimensional materials, MXene materials may have unusual magnetic properties. In this work, the structural stabilities and electronic properties of 1H and 1T type pristine M2C (M = Sc, Ti, Fe, Co, Ni, Cu, Zn) MXenes with different magnetic configurations were calculated and compared. The critical temperatures of the magnetic MXenes were evaluated through Monte Carlo simulations using the spin–exchange coupling parameters. The results suggest that the ground-state 1T-Ti2C and 1T-Fe2C, 1H-Co2C MXenes are antiferromagnetic or ferromagnetic materials with high Néel or Curie temperatures. Different from the other pristine M2C MXenes with metallic properties, indirect band gaps were found for the 1T-Ti2C and 1T-Ni2C MXenes, which may be useful for their application in information storage or sensors. The findings are expected to promote the development of novel devices based on MXenes and their magnetic properties.


Introduction
Since the discovery of graphene in 2004, two-dimensional (2D) nanomaterials have been considered as prospective materials in various disciplines including electronics, optoelectronics, energy, and sensing. 1,2 The exploration of new 2D nanomaterials such as h-BN 3 and transition metal dichalcogenides 4 has attracted attention worldwide and is still ongoing. Meanwhile, numerous theoretical and experimental works have produced rapid advances related to magnetism in 2D materials because of their potential applications in electronic and spintronic devices. [5][6][7][8] However, the utilization of most known 2D materials in spintronics is limited by their intrinsically nonmagnetic (NM) properties. Therefore, several approaches such as strain engineering, doping or defect generation, and surface decoration have been adopted to introduce magnetism into 2D materials, [9][10][11][12] and the effects on the magnetic properties have been discussed. 13,14 Simultaneously, new magnetic 2D materials are in demand. MXenes, a unique family of metal carbides and/or nitrides with the chemical formula M n+1 X n , where M is the transition metal that potentially generates the intrinsic magnetic moment, X can be carbon and/or nitrogen, and n varies between 1 and 3, were discovered in 2011 and have attracted extensive research interest in recent years. [15][16][17][18][19] MXenes can be fabricated from conventional MAX phases or other layered compounds such as Zr 3 Al 3 C 5 and Mo 2 Ga 2 C through chemical etching, [20][21][22] forming the functionalized MXenes M n+1 X n T x , 15 where T indicates the surface-terminating groups (-H, -F, -Cl, ]O, or -OH) originating from the etching agent. [23][24][25][26] Chemical vapor deposition (CVD) is another growth method for fabricating high-quality 2D MXene materials. 27 Both methods are currently under development, and many attempts to improve their efficiency and purity of the products are found in the literature.
Theoretical calculations have been widely employed to obtain insight into the relevance of the electronic structures of MXene materials and their properties to better understand and utilize MXene materials. [28][29][30][31] To date, several pristine MXenes such as Ti 4 C 3 , Ti 3 CN, Cr 2 C, Cr 2 N, and Zr 2 C have been predicted to possess magnetic moments; however, synthesizing these materials and retaining the magnetic behaviors when they are exfoliated into monolayers remain challenging. 31,32 He and coworkers 33,34 studied the structure and magnetic properties of some V-, Cr-, and Mn-based MXenes and discussed the substrate effect of MXenes on the SiC(0001) surface. Depending on the functional group, these MXenes can be half-metals, metals, or semiconductors. Zhang et al. found that the Mn 2 C monolayer can transform from the antiferromagnetic (AFM) state to the ferromagnetic (FM) state under hydrogenation or oxygenation. 35 At present, it is recognized that understanding the intrinsic magnetism of MXenes is a key step in promoting their application. This work focuses on the magnetism of pristine MXenes, whose geometric structures are similar to transition metal chalcogenides in two common phases (1H and 1T). 36,37 Theoretical exploration via rst-principles calculations was conducted on the stability, magnetism, and electronic properties of the 1H and 1T M 2 C MXenes with various transition metals (M ¼ Sc, Ti, Fe, Co, Ni, Cu, Zn). The corresponding parameters, including the lattice parameters, total energies, magnetic moments, and spin exchange coupling parameters, were calculated and compared, and the critical temperatures T c for particular magnetic MXenes were evaluated through Monte Carlo (MC) simulations. The ndings provide valuable reference information toward the application of MXene materials in industry based on the magnetic characteristics.

Computational details
First-principles density functional theory (DFT) calculations were carried out based on projector augmented-wave (PAW) potentials 38 in reciprocal space represented by a generalized gradient approximation (GGA). 39 The Perdew-Burke-Emzerhof (PBE) exchange-correlation function was used, and the calculations were implemented in VASP code. 40 Plane waves with energies of up 550 eV were employed to describe the electronic wave functions, and the Brillouin zone was sampled using a set of G-centered 12 Â 12 Â 1 k-points. Specically, the highly accurate non-empirical density functional meta-GGA strongly constrained and appropriately normed (SCAN) + rVV10 was employed. 41,42 In the structural optimization, the maximum force on each atom was 10 À3 eVÅ À1 , and the total energies converged within 10 À7 eV. A lattice parameter of 30Å for the caxis perpendicular to the MXene surface was set to avoid any articial interaction between the layers and their images. The Hubbard "U" correction was also employed within the rotationally invariant DFT + U approach 43 as a comparison. A correction of U eff ¼ U À J ¼ 3 eV was used for Sc, Ti, Fe, Co, and Ni based on relevant previous reports 33,44 on the magnetic conguration and band structure calculations. The PHONOPY soware 45 combined with the VASP code was utilized for phonon dispersion calculations using density functional perturbation theory 46 to conrm the structural stabilities. To predict the electrical conductivity, linearized Boltzmann transport calculations based on the constant relaxation time approximation and rigid-band approximation were performed using the BoltzTraP2 code. 47 For a given T and m, the carrier concentration was obtained from the density of states, and the electrical conductivities were calculated using the transport distribution function. The relaxation time s was variable and could be obtained by tting the experimental data 48 or using s ¼ 10 À14 s as a general approximation to estimate the electrical conductivity. 49

Results and discussion
First, the geometries of the 1H and 1T pristine M 2 C (M ¼ Sc, Ti, Fe, Co, Ni, Cu, Zn) MXenes shown in Fig. 1 were examined. Three possible initial magnetic congurations have been considered for the M 2 C MXene 1 Â 1 unit cell containing two transition-metal atoms: the AFM conguration with the magnetic moments of the two metal atoms in opposite directions; the FM conguration with the magnetic moments of the two atoms in the same direction; and the NM conguration with zero atomic magnetic moment. For the M 2 C MXenes in the FM conguration, the spin-up and spin-down states are not symmetrical. Meanwhile, the M 2 C MXenes in the AFM and NM congurations exhibit zero total magnetic moments; the difference between the AFM and NM congurations is that the atomic magnetic moments for the AFM conguration are nonzero. Based on the above initial magnetic congurations, the optimized lattice constants, total energies, and magnetic properties of the M 2 C MXenes from the self-consistent calculations are listed in Table S1 † with the most stable congurations highlighted in bold. From the table, the 1T M 2 C MXenes calculated in our work exhibit lower total energies than the 1H MXenes except for Co 2 C and Cu 2 C. The 1H M 2 C MXenes usually possess smaller lattice constants than the 1T ones, and the small differences in lattice constants vary by magnetic conguration, suggesting that the magnetic properties may have slight effects on the chemical bonds at equilibrium. From the calculations, the Ni 2 C, Cu 2 C, and Zn 2 C MXenes present zero atomic magnetic moments. This may be attributed to the absence of unpaired d electrons, which are necessary for atomic magnetic moments. Cu and Zn, which have 10 d electrons, cannot have unpaired electrons, and the magnetic moment for Ni is zero due to electron transfer and rearrangement in the electronic conguration. 50 Since phonon dispersion can be used to measure the dynamic stability of a material, the phonon dispersion plots of the lowestenergy congurations of the M 2 C MXenes along the highsymmetry directions in the Brillouin zone are given in Fig. S1. † According to the gure, the Sc 2 C (1T-FM), Ti 2 C (1T-AFM), Fe 2 C (1T-FM), Co 2 C (1H-FM), and Ni 2 C (1T-NM) MXenes are dynamically stable with all their phonon branches non-negative. Thus, these MXenes could possibly be synthesized experimentally. The structures of the Cu 2 C and Zn 2 C MXenes with imaginary phonon modes require further study. The phonon dispersions of some higher-energy congurations are also plotted in Fig. S1 † for comparison. The absence of imaginary phonon modes suggests that the Sc 2 C (1T-AFM and NM), Ti 2 C (1T-FM and NM), Fe 2 C (1H-FM), Co 2 C (1H-AFM and NM), and Ni 2 C (1H-NM) MXenes are all dynamically stable, and the small differences in the phonon branches for the M 2 C MXenes with different magnetic congurations imply that the magnetic states have slight effects on the vibrational modes. This means that MXenes may exhibit different mechanical and thermal properties that do not exist in the ground magnetic states.
Aer investigating the basic structural and stability properties, a 2 Â 1 supercell containing four metal atoms was employed to further study the magnetic properties of the 1T-Sc 2 C, 1T-Ti 2 C, 1T-Fe 2 C, and 1H-Co 2 C MXenes. Four possible magnetic congurations (three AFM and one FM) were considered; the top and side views are shown in Fig. 2(a) and (c), respectively. The spin system was typically identied by a Hamiltonian function in the 2D Ising model with the spin exchange coupling parameters J 0 , J 1 , and J 2 [paths shown in Fig. 2 where J 0 is the intralayer exchange coupling interaction between nearest neighbors, J 1 and J 2 are the interlayer exchange coupling interactions between the nearest and next-nearest neighbors, respectively, and s takes the value of AE1 for spin-up and spindown. Correspondingly, for the 1T type, the total energies E FM , E AFM1 , E AFM2 , and E AFM3 can be expressed as follows: where J 0 , J 1 , and J 2 are then expressed as Similarly, for the 1H type, E FM , E AFM1 , E AFM2 , and E AFM3 can be expressed as follows: with J 0 , J 1 and J 2 expressed as: From the obtained relative energies listed in Table 1, Sc 2 C and Ti 2 C are predicted to possess antiferromagnetism with the magnetic congurations AFM3 and AFM2, as shown in Fig. 2,   1T (a, b) and 1H (c, d) M 2 C MXenes. Black and red represent spin-up and spin-down, respectively. and the spin charge density distributions are plotted in Fig. 3(a) and (b), respectively. Fe 2 C and Co 2 C MXenes are predicted to be ferromagnetic, and the spin charge density distributions are shown in Fig. S2. † The spin exchange coupling parameters J 0 , J 1 , and J 2 were calculated with formulas (3) and (5). We note that the absolute value of parameter J 1 for the Sc 2 C MXene with a small interaction distance is abnormally less than J 2 . This may be due to the fact that every spin-polarized charge center for Sc 2 C is actually located on the top of the Sc atomic layer at the center of the three Sc atoms arranged in an equilateral triangle [ Fig. 2(a)], different from Ti 2 C, Fe 2 C, and Co 2 C, in which the spin charges are around the metal atoms. The spin charge shielding effects of the metal atoms and superexchange interaction may affect the relative magnitude of the interlayer coupling parameters J 1 and J 2 . The spin exchange interactions for 1H type Co 2 C are mainly dominated by the interlayer exchange coupling parameter J 1 . MC simulations were then performed on a NVIDIA Tesla K80 Graphics Processing Unit with the Metropolis algorithm using the coupling parameters to evaluate the critical temperature T c . In the MC simulations, 1024 Â 1024 supercells were adopted. For every spin ip operation, the change in exchange interactions before and aer the trial switch of the selected s i spin DH ¼ H a À H o was calculated, and the acceptance probability was determined as W m ¼ exp(ÀDH/k B T), where k B is the Boltzmann constant, and T is the temperature. A random number R (0 < R < 1) was generated. If R was less than W m , the selected spin was ipped; otherwise, the spin remained unchanged. The average magnetization orientation as a function of temperature is shown in Fig. S3. † The predicted T c values are 110, 875, 965, and 1497 K for 1T-Sc 2 C, 1T-Ti 2 C, 1T-Fe 2 C, and 1H-Co 2 C MXenes, respectively. Consequently, the ground-state Ti 2 C or Fe 2 C, Co 2 C MXenes are AFM or FM materials with Néel or Curie points above room temperature.
To further understand the magnetic and electronic properties of the ground-state Sc 2 C, Ti 2 C, Fe 2 C, Co 2 C, and Ni 2 C MXenes, their band structures were calculated and are plotted in Fig. 4. The Fe 2 C and Co 2 C MXenes show observable spin splitting around the Fermi level with a metallic feature; meanwhile, the spin-up and spin-down bands of the Sc 2 C and Ti 2 C MXenes with AFM congurations are entirely coincident. In addition, the Ti 2 C MXene presents a band gap of 0.17 eV, and the 1T type Ni 2 C MXene also shows an indirect band gap. The band structures with DFT + U correction are provided in Fig. 4(f)-(j) for comparison. The similarities in band structures with the exceptions of shis in some bands indicate the validity Table 1 Calculated magnetic characteristics of the 1T-Sc 2 C, 1T-Ti 2 C, 1T-Fe 2 C, and 1H-Co 2 C MXenes. For relative energy, the ground-state are set as zero and indicated in bold

Relative energy
Exchange interaction of the SCAN meta-GGA calculations. The transport coefficients s xx /s at 300 K versus the chemical potential m for magnetic Ti 2 C, Fe 2 C, and Co 2 C with critical temperature above 300 K and Ni 2 C MXenes were calculated and are plotted in Fig. 5. For the Ti 2 C MXene, the s xx /s at zero chemical potential approaches zero because of the band gap near their Fermi level, and doping with electrons and holes within a certain range can both lead to a signicant increase in the transport coefficient s xx /s. Owning a special ground spin conguration, high Néel temperature, and adjustable transport coefficient, the AFM Ti 2 C MXene is a promising material for 2D spintronics. Moreover, a nearly zero s xx /s value at zero chemical potential and increase in s xx /s with doping content are found for the Ni 2 C MXene. The 1H Co 2 C MXene shows a higher transport coefficient than the MXenes. Due to their diversity, more members of the MXene and 2D material family with magnetism and potential for application in spintronic devices require further study.

Conclusions
In summary, the structures, magnetic and electronic properties, and total energies for 1H and 1T pristine M 2 C (M ¼ Sc, Ti, Fe, Co, Ni, Cu, Zn) MXenes with different magnetic congurations were calculated and compared. Most MXenes studied herein are stable in the 1T type, while Co 2 C is unique in that it possesses a 1H FM ground conguration. The spin exchange coupling parameters were calculated to predict the critical temperature T c . The 1T-Ti 2 C, 1T-Fe 2 C, and 1H-Co 2 C MXenes show relatively high Néel or Curie temperatures of 875, 965, and 1497 K, respectively. Different from the other pristine M 2 C MXenes with metal properties, the 1T AFM ground conguration of the Ti 2 C MXene presents a band gap of 0.17 eV, indicating great potential for high-efficiency spintronic devices. The results provide new insights into the application of magnetic MXene materials in electronic and spintronic devices.

Conflicts of interest
There are no conicts to declare.  Relationship between the chemical potential m and transport coefficient s xx /s at 300 K for 1T-Ti 2 C, 1T-Fe 2 C, 1H-Co 2 C, and 1T-Ni 2 C MXenes.