High Curie temperature and carrier mobility of novel Fe, Co and Ni carbide MXenes

Y. Hu a, X. Y. Liu b, Z. H. Shen a, Z. F. Luo a, Z. G. Chen a and X. L. Fan *a
aState Key Laboratory of Solidification Processing, Center for Advanced Lubrication and Seal Materials, School of Material Science and Engineering, Northwestern Polytechnical University, 127 YouYi Western Road, Xi'an, Shaanxi 710072, China. E-mail: xlfan@nwpu.edu.cn
bQueen Mary University of London Engineering School, Northwestern Polytechnical University, 127 YouYi Western Road, Xi'an, Shaanxi 710072, China

Received 29th December 2019 , Accepted 27th April 2020

First published on 29th April 2020


Abstract

Two-dimensional (2D) magnets with room temperature ferromagnetism and semiconductors with moderate band gap and high carrier mobility are highly desired for applications in nanoscale electronics and spintronics. By performing the first-principles calculations, we investigate novel Fe, Co, Ni carbide based pristine (M2C) and functionalized (M2CT2, T: F, O, OH) MXenes. Our calculations show that Fe2C, Co2C, Ni2C, Fe2CF2, Fe2CO2, Fe2C(OH)2, Co2CF2, Co2C(OH)2 and Ni2CF2 are dynamically and mechanically stable. More importantly, Fe2C, Co2C, Fe2CF2 and Fe2C(OH)2 exhibit intrinsic ferromagnetism (magnetic moments 2–5μB per unit cell). Monte Carlo simulations suggest high Curie temperatures of 590 and 920 K for Fe2C and Fe2CF2, respectively, at the HSE06 level owing to the large spin magnetic moments and strong ferromagnetic coupling. Based on the deformation potential theory, we predict high and anisotropic hole mobility (0.2–1.4 × 104 cm2 V−1 s−1) for semiconducting Fe2CO2 and Co2C(OH)2. Additionally, Ni2CF2 demonstrates highly anisotropic electron mobility together with a direct band gap. Our results further show the effectiveness of surface functionalization in modulating the electronic and magnetic properties and broadening the properties of MXenes to achieve long-range intrinsic ferromagnetism well above room temperature and high carrier mobility.


Introduction

Two-dimensional (2D) materials have bright prospect in various applications, such as in electronic devices,1–4 catalysts,5–7 and energy storage and conversion.8–10 In particular, 2D ferromagnetic (FM) materials are greatly needed for nanoscale spintronic devices.11–15 Inducing magnetism into 2D non-magnetic materials via defect-engineering,16 doping17 and external electric-field18 has gained much attention recently, but the induced magnetism is localized and the precise control of the defect generation and dopant distributions remains a challenge.19,20 More recently, atomic-thin 2D intrinsic magnets, such as monolayer CrI3,21 bilayer Cr2Ge2Te6,22,23 half unit-cell thin nanosheets Co9Se8[thin space (1/6-em)]24 and α-Fe2O3[thin space (1/6-em)]25 have been realized. These results demonstrate long-range FM ordering in 2D materials and inspire further research on 2D intrinsic ferromagnetism.

Atomically thin nanosheets of nonlayered materials Co9Se8[thin space (1/6-em)]24 and α-Fe2O3[thin space (1/6-em)]25 have been successfully synthesized via a 2D oriented attachment and template-assisted oriented growth strategy, respectively, and they both show room temperature ferromagnetism.24,25 Besides, 2D monolayers including CoH2,26 ScH2,26 ScCl,27 CrOCl,28 CrOBr,28 MX2 (M = Fe, Co, Ni; X = Cl, Br, I)29 and some MXenes30–33 were predicted to be intrinsic magnets by density functional theory methods. More recently, Xu et al. and Zhang et al. concurrently reported 2D ferromagnets, CrI3[thin space (1/6-em)]21 and Cr2Ge2Te6,22,23 which were exfoliated from the corresponding layered bulk crystals. Unfortunately, the measured Curie temperatures of monolayer CrI3 (45 K)21 and bilayer Cr2Ge2Te6 (28 K)22 are far below room temperature.

Magnetic ions couple via direct-exchange interactions and indirect-exchange interactions mediated by one or two different anions. An indirect-exchange interaction between two metal atoms with the same valence is called super-exchange interaction. It is a double-exchange interaction if one of the coupled metal atoms have one electron more than the other. Super-exchange interactions usually involve virtual hopping and are weak. Correspondingly, the Curie temperatures of the recently found 2D magnets,21,22,26–29 such as CrI3 and Cr2Ge2Te6 in which the magnetic ions couple with each other via FM super-exchange, are low. In contrast, the Fe and Cr atoms of 2D ferromagnets, α-Fe2O3[thin space (1/6-em)]25 and Cr3X4 (X = S, Se, Te),34 exist in two oxidation states, the ferromagnetic double-exchange interaction involving strong real hopping is dominated, resulting in higher Curie temperature.

In the last few years, more than 40 MXenes35–50 have been realized experimentally. This new family of 2D materials hold promising potential in the fields of nano-electronic and optoelectronic devices49–53 as well as energy storage and conversion.35,37–40,42 Recent experimental studies found that the termination groups remaining on the surface of MXenes during the etching process can be eliminated via heat treatment.54 Meanwhile, pristine MXenes V2N and W2N have been synthesized via the salt-templated method and reduction of transition-metal oxides.55 Additionally, semiconducting MXenes Ti2CO2, Zr2CO2, Hf2CO2, Sc2CF2, Sc2CCl2 and Sc2C(OH)2 demonstrate high carrier mobility owing to their intriguing mechanical properties.51,52,56–58 In particular, the hole mobility of Ti2CO2 (7.4 × 104 cm2 V−1 s−1)56 is higher than that of phosphorene (2.4 × 104 cm2 V−1 s−1).59 High carrier mobility along with suitable band gap are the key properties for the next generation of high-speed electronics, which are unfortunately wanting in the two most studied 2D materials, graphene60 and MoS2.61,62 Moreover, MXenes, Mn2XT2, Ni2NT2, Cr2C, Cr2NO2 and Fe2NT2, are predicted to be ferromagnetic with a high Curie temperature above room temperature (460 K–3300 K).30–33

In this work, by performing a comprehensive computational study via the first-principles method, we investigated Fe, Co, and Ni carbide MXenes to explore the correlation between the extra super-exchange and magnetic coupling. We studied the Fe, Co, and Ni carbide in both the pristine (M2C) and functionalized (M2CT2, T: F, O, OH) forms. We first calculated the atomic structures and evaluated their stability, and then studied the electronic structures, long-range magnetic ordering and carrier mobility. We found two FM MXenes with Curie temperature well above room temperature, which are Fe2C and Fe2CF2. Moreover, we predict that Fe2CO2, Co2C(OH)2 and Ni2CF2 are semiconductors with high and anisotropic carrier mobility.

Computational methods

All the calculations in the present study were performed by adopting a spin-polarized density functional theory (DFT) method as implemented in the Vienna ab initio simulation package (VASP).63 Interactions between electrons and nuclei were described by the projector augmented wave (PAW) method,64,65 and the electronic exchange–correlation interactions were described by the Perdew–Burke–Ernzerhof (PBE) functional within the generalized gradient approximation (GGA)66 method. In particular, the more accurate Heyd–Scuseria–Ernzerhof (HSE06) method67,68 was adopted to calculate the electronic band structures and density of states, and the screening parameter in HSE06 was fixed at a value of 0.2 Å−1. The Brillouin zone integration was carried out by 9 × 9 × 1 k-mesh based on the Monkhorst–Pack scheme.69 The phonon spectra were calculated using the Phonopy code70 which is implemented within the VASP package. A vacuum space of 20 Å was added along the direction perpendicular to the surface of the monolayer to avoid the interaction between the adjacent layers. The cutoff energy for the plane wave basis set was set as 500 eV. The convergence criteria for the total energy and force are set as 1 × 10−6 eV and 0.01 eV Å−1, respectively.

Results and discussion

Structural properties and stability

Fig. 1 shows the atomic structures of MXenes M2C and M2CT2 (M = Fe, Co, Ni; T = F, O, OH). As shown in Fig. 1a and b, pristine M2C has one atomic layer of C atoms embedded by two atomic layers of M atoms. There are two possible absorption sites for the termination T-groups on the surface of M2C, above the bottom M atoms (A site) and above the C atoms (B site). Thus, there are three probable configurations for the functionalized MXenes M2CT2, namely, AA, BB and AB. AA/BB configuration has T-groups located on the A/B sites on the two surfaces. In the AB configuration, T-groups adsorb onto the A sites on one surface and the B sites on the other surface. Except Fe2CO2 which energetically prefers the AB configuration, configuration AA is most stable for the other M2CT2 because the T-groups are more likely to hybridize with the M atoms.
image file: c9nr10927g-f1.tif
Fig. 1 (a) Side and (b) top views of the atomic structures of MXenes M2C (M = Fe, Co, Ni). (c) AA, (d) BB and (e) AB configurations of MXenes M2CT2 (T = F, O, OH). A and B represent the two possible absorption sites for the termination groups T. The hexagonal primitive cell and orthogonal primitive cell are circled in orange and red dashed lines.

As shown in Fig. 2a–d, we considered five magnetic configurations including ferromagnetic (FM), anti-ferromagnetic (AFM-1, AFM-2, AFM-3) and non-magnetic (NM) configurations for each pristine MXene M2C and functionalized MXene M2CT2, which were simulated by the 2 × 1 × 1 supercell. A primitive cell only contains the nearest neighboring M atoms that can simulate the FM and one AFM configurations. In contrast, the 2 × 1 × 1 supercell is big enough to include the nearest neighboring (NN), second NN and third NN magnetic coupling M atoms, and to simulate three AFM configurations as shown in Fig. 2. As summarized in Table 1, our calculations show that the ground states of Fe2C, Co2C, Fe2CF2 and Fe2C(OH)2 are FM. While Fe2CO2 is most stable in the AFM-2 state, the remaining MXenes are most stable in the NM state.


image file: c9nr10927g-f2.tif
Fig. 2 Top and side views of the schematic diagrams of (a) ferromagnetic (FM), (b) anti-ferromagnetic (AFM-1), (c) AFM-2, and (d) AFM-3 states, and (e) the nearest neighboring (NN), second NN and third NN magnetic coupling interactions of MXenes M2C and M2CT2 (M = Fe, Co, Ni; T = F, O, OH). J1, J2 and J3 represent the NN, second NN and third NN magnetic coupling parameters. The yellow and blue arrows represent spin-up and spin-down states of M atoms, respectively.
Table 1 The calculated energy differences between the ferromagnetic state and anti-ferromagnetic states (ΔEAFM1-FM, ΔEAFM2-FM and ΔEAFM3-FM), and non-magnetic state (ΔENM-FM), total magnetic moment (Mtot), atomic magnetic moment of the M atom (MM), band gap (EHSEg), half-metallic gap (δ), nearest neighboring (NN), second NN and third NN magnetic coupling parameters (J1, J2 and J3), and the Curie temperature/Néel temperature (TMCC/N) of MXenes M2C and M2CT2 (M = Fe, Co, Ni; T = F, O, OH)
  ΔEAFM1-FM (meV) ΔEAFM2-FM (meV) ΔEAFM3-FM (meV) ΔENM-FM (meV) M tot (μB) M M (μB) E HSEg (eV) δ (eV) J 1 (meV) J 2 (meV) J 3 (meV) T MCC/N (K)
a Energy gap of the semiconducting spin-channel of half-metal.
Fe2C 148.08 231.76 274.72 721.51 4.11 2.19 Metal 5.97 5.60 0.20 530
Co2C 73.44 52.72 76.96 78.60 2.00 1.07 Metal 12.21 3.52 0.03 130
Fe2CF2 485.04 363.60 514.40 430.05 5.00 2.44 1.40a 0.66 19.87 6.14 0.34 910
Fe2CO2 146.60 −74.16 −21.16 29.83 0.00 1.37 0.66 24.70 −15.07 −0.60 40
Fe2C(OH)2 86.88 119.84 140.00 236.85 5.00 2.50 1.91a 1.22 3.35 2.70 0.28 220
Co2CF2 4.47 −27.60 42.67 −33.65 0.00 0.00 1.53
Co2C(OH)2 −2.00 −0.50 39.75 −12.00 0.00 0.00 1.12
Ni2C −20.06 −5.00 60.10 −50.04 0.00 0.00 Metal
Ni2CF2 −33.00 2.70 −40.95 −113.05 0.00 0.00 0.51


The phonon spectra and 2D elastic constants were calculated to study the dynamical and mechanical stability of MXenes M2C and M2CT2. As listed in Table S1, the 2D elastic constants of these MXenes all meet the Born–Huang criteria of C11 > 0, C11C22C122 > 0 and C66 > 0, indicating their mechanical stability.71 Fig. S1 shows that the studied M2C and M2CT2 are dynamically stable except for Co2CO2, Ni2CO2 and Ni2C(OH)2 whose phonon spectra have imaginary frequencies. The following study focuses on the dynamically and mechanically stable M2C (Fe2C, Co2C, Ni2C) and M2CT2 (Fe2CF2, Fe2CO2, Fe2C(OH)2, Co2CF2, Co2C(OH)2 and Ni2CF2), whose structural parameters are summarized in Table S2.

To further evaluate the feasibility of forming these MXenes, we calculated the formation energies for M2C via

 
Eform-M2C = E(M2C) − μC − 2μM(1-1)
where E(M2C) is the total energy of M2C and μC and μM are the chemical potentials of C and M atoms, respectively. μC/μM ranges from the energy of the C/M atom in the MXene structure (poor conditions) to the energy of the C/M atom in the element C/M (rich conditions), which can be expressed as:
 
E(M2C) − E(M2\_M2C) ≤ μCE(C)(1-2)
 
image file: c9nr10927g-t1.tif(1-3)
where E(C)/E(M) is the energy of the C/M atom in the element C/M and E(M2_M2C)/E(C_M2C) is the total energy of M2C with C/M atoms removed. Additionally, the adsorption energies of the T-groups on M2C are calculated via
 
Eadsor-T = E(M2CT2) − E(M2C) − E(T2) − 2Δμ(1-4)
where E(M2CT2) is the total energy of M2CT2 and E(T2) is the energy of the F2, O2 and H2 molecules in the gas phase. Δμ = μ − (1/2)E(T2), where μ is the chemical potential of the F, O and H atoms, which varies with pressure and temperature.

Table S2 lists the calculated formation energies of pristine MXenes as well as the adsorption energies of F on Fe2C, Co2C and Ni2C, O on Fe2C, and OH on Fe2C and Co2C by adopting Δμ = 0.0 eV as constant, which are all negative, indicating the exothermic feature. Additionally, the adsorption energies of the OH group on Fe2C(OH)2 and Co2C(OH)2 are comparable with those on Ti2C(OH)2, V2C(OH)2 and Nb2C(OH)2.72 We also examined the formation of the T-groups on pristine M2C at different coverages. The adsorption of 2, 4, 6, and 8 T-groups on the 2 × 2 × 1 supercell of M2C corresponds to 25%, 50%, 75% and 100% T-coverage, respectively. More than 72 structures with symmetrically distributed T-groups were calculated to find the most energetically favorable configurations at each coverage. Meanwhile, we considered the effect of temperature on the chemical potential. At temperatures ranging from 0 to 300 K, Δμ for F and O atoms are 0.0 to −0.32 eV, and those for the H atom are 0.0 to −0.2 eV.73 Fig. S2 summarizes the adsorption energies of F, O and OH on M2C at 25%, 50%, 75% and 100% coverage. It is noticed that the full coverage configurations are energetically more preferable compared with the partial coverage configurations at room temperature.

Electronic and magnetic properties

Our calculations show that Fe2C, Co2C, Fe2CF2 and Fe2C(OH)2 are most stable in the FM state. Their total magnetic moments are 4.0, 2.0, 5.0 and 5.0μB per unit cell, respectively, mainly attributed to the M atoms as exhibited by the spin-resolved charge density (SCD) shown in Fig. S3. The electronic band structures shown in Fig. 3 further demonstrate that Fe2C and Co2C are FM metals, while Fe2CF2 and Fe2C(OH)2 are FM half-metals with theoretically infinite magnetoresistance. Differently, Fe2CO2 is semiconducting and most stable in the AFM-2 state, while Co2CF2, Co2C(OH)2 and Ni2CF2 are non-magnetic semiconducting. The energy band gaps of semiconducting Fe2CO2, Co2CF2, Co2C(OH)2 and Ni2CF2 are 0.66, 1.53, 1.12 and 0.51 eV, respectively. In particular, Ni2CF2 is a direct band gap semiconductor with the valence band maximum (VBM) and the conduction band minimum (CBM) both located at the X point, and the other three are all indirect band gap semiconductors. In particular, the VBM of Co2CF2 locates at the Y point; its CBM is lower than the energy of the conduction band at the Y point by 0.02 eV, implying that Co2CF2 can be regarded as a direct band gap semiconductor. It is noted that Ni2C is a non-magnetic metal with the Dirac cone located above the Fermi level.
image file: c9nr10927g-f3.tif
Fig. 3 Spin-resolved electronic band structures of MXenes M2C and M2CT2 (M = Fe, Co, Ni; T = F, O, OH). All the results are obtained in the tetragonal primitive cell except for Fe2CO2 whose AFM-2 state is simulated by 2 × 1 × 1 supercell. The Fermi level is set as 0 eV.

Like other MXenes,33,74 the metallic features of Fe2C, Co2C and Ni2C subside following the termination of the surface by T-groups. As shown in Fig. S4, energy gaps arise for the electronic states of at least one spin channel at the Fermi level of M2CT2. In particular, Fe–F and Fe–OH interactions open the gap for the minority spin-states around the Fermi level, resulting in FM half-metal with higher magnetic moments. Additionally, Fe2CF2 and Fe2C(OH)2 have large half-metallic gaps of 0.7 and 1.2 eV, respectively, comparable to those of double perovskites, chalcogenides and similar materials,31,75,76 implying their stable half-metallicity. Moreover, Fig. S4 shows obvious overlap between the states of M and T atoms in the energy range of −6 to −2 eV, indicating strong hybridization which further strengthens the mechanical flexibility as shown in Table S1.

To understand the magnetism of Fe2C, Co2C, Fe2CF2, Fe2CO2 and Fe2C(OH)2, we plot the projected density of states (PDOS) for the M atoms in Fig. 4. Under the C3v symmetry, the 3d orbitals split into three groups, e1(dxz + dyz), a(dz2) and e2(dxz + dx2+y2). As shown in Fig. 4, the e1, a and e2 orbitals overlap with each other. The 3d electrons of Fe and Co ions occupy two spin channels concurrently because their exchange splitting (ΔEex) is weaker than their crystal field splitting (ΔEcf), resulting in a low spin state. In addition, the exchange splitting of Co2C and Fe2CO2 is smaller compared with those of Fe2C, Fe2CF2 and Fe2C(OH)2. Correspondingly, the magnetic moments of Co2C and Fe2CO2 are smaller. More specifically, four 3d electrons of Fe2+ ions in Fe2C occupy the e1 and e2 orbitals in the two spin-channel, leaving one electron occupying the spin-up channel of the a orbital and one electron occupying the spin-up channel of the e1 and e2 orbitals. In contrast, the a orbital and two e1 and e2 orbitals of Co2+ ions in Co2C are occupied in the two spin-channels, and four electrons occupy the two spin-channels of the a orbital, and one e1 and e2 orbital of the Fe3+ ions from Fe2CO2, which leaves one electron occupying the e1 and e2 orbitals in the one spin-channel for both cases of Co2C and Fe2CO2.


image file: c9nr10927g-f4.tif
Fig. 4 Projected density of states (PDOS) for M-d orbitals of MXenes M2C and M2CT2 (M = Fe, Co, Ni; T = F, O, OH). The Fermi level is set as 0 eV. ΔEex and ΔEcf represent the exchange splitting and the crystal field.

The magnetic ground states of M2C and M2CT2 depend on the magnetic coupling between the M atoms. Fig. 5a and b exhibit the direct-exchange interaction and super-exchange interaction mediated by the p states of the oxidized ions (C and T atoms). According to the Goodenough–Kanamori–Anderson (GKA) rules, the super-exchange interaction between the M atoms of M2C is FM as the M–C–M angles are around 90°.77 The two neighboring M atoms overlap with different p orbitals as shown in Fig. 5c. As for M2CT2, besides the super-exchange interactions mediated by the C atoms, there are also intralayer super-exchange interactions mediated by the T atoms. Taking Fe2C and Fe2CF2 as examples, Fig. S3a and c illustrate the super-exchange interactions mediated by the C-p and F-p states. This shows that Fe–C–Fe and Fe–F–Fe angles are around 90°, indicating that the FM Fe–Fe super-exchange interactions are mediated via the coupling between the Fe-d and C-p states and between the Fe-d and F-p states, as shown in Fig. S4.


image file: c9nr10927g-f5.tif
Fig. 5 (a) Illustration of the direct-exchange and (b) super-exchange interactions between two M atoms of MXenes, as well as (c) the ferromagnetic super-exchange interaction according to the Goodenough–Kanamori–Anderson rule. (d) The nearest neighboring (NN) and second NN magnetic coupling parameters (J1 and J2) of Co2C as a function of hole doping concentration. The calculated band structure at hole doping of −0.4e per unit are presented in the inset. (e) The specific heat (CV) as a function of temperature for Fe2C, Co2C, Fe2CF2, Fe2CO2, and Fe2C(OH)2.

We have tried to tune the electronic properties via charge doping as the carrier density is closely associated with the electronic and magnetic structures. In particular, hole doping usually lowers the Fermi level. As shown in Fig. 3e for the electronic band structure of Co2C, the bottom conduction bands of the majority spin-states and the top valence bands of the minority spin-states both slightly cross the Fermi level. Thus, the hole doping at small concentrations up to −0.4e per unit cell was adopted to slightly lower the Fermi level. As shown in Fig. 5d, Co2C converts from metal to half-metal at −0.4e per unit cell hole doping. Moreover, hole doping enhances the interlayer FM coupling but weakens the intralayer FM coupling slightly.

Curie temperature

The Curie temperature (TC) of the FM Fe2C, Co2C, Fe2CF2 and Fe2C(OH)2 and the Néel temperature (TN) of AFM Fe2CO2 were investigated by performing the classical Metropolis Monte Carlo (MC) simulations.78 We use the Heisenberg model to describe magnetic exchange interactions, including the interlayer (NN), intralayer (second NN), and next-nearest interlayer (third NN) coupling. The spin Hamiltonian is
 
image file: c9nr10927g-t2.tif(3-1)
where J1, J2 and J3 are NN, second NN and third NN magnetic coupling parameters, M is the net magnetic moment of M atoms, and i and j (k and l, m and n) stand for the NN (second NN, third NN) pair of M atoms. Correspondingly, the total energies of the FM, AFM-1, AFM-2 and AFM-3 states can be expressed as:
 
EFM = E0 − 6J1M2 − 12J2M2 − 6J3M2(3-2)
 
EAFM1 = E0 + 6J1M2 − 12J2M2 + 6J3M2(3-3)
 
EAFM2 = E0 − 2J1M2 + 4J2M2 + 6J3M2(3-4)
 
EAFM3 = E0 + 2J1M2 + 4J2M2 − 6J3M2(3-5)

In this context, the magnetic coupling parameters J1, J2 and J3 are calculated via the energy difference between the FM and AFM states as:

 
image file: c9nr10927g-t3.tif(3-6)
 
image file: c9nr10927g-t4.tif(3-7)
and
 
image file: c9nr10927g-t5.tif(3-8)

The calculated J1, J2 and J3 are listed in Table 1. The positive/negative values of J indicate the preference for FM/AFM coupling. It shows that the FM interlayer super-exchange interaction competes over the AFM direct-exchange interactions, resulting in FM interlayer exchange interactions for Fe2C, Co2C, Fe2CF2, Fe2CO2 and Fe2C(OH)2. This is also true for the intralayer exchange interactions except for Fe2CO2, in which the AFM intralayer direct-exchange interactions dominate over the FM intralayer super-exchange interactions. These results explain the magnetic ground states of Fe2C, Co2C, Fe2CF2, Fe2CO2 and Fe2C(OH)2. The small values of J3 are consistent with the long distances between the third NN magnetic coupling pair shown in Table S2.

The 100 × 100 × 1 supercell containing 20[thin space (1/6-em)]000 magnetic moment vectors was adopted to perform the MC simulations. Each spin on the magnetic site is rotated randomly in all directions, and the simulation for each MXene lasts for 105 steps at each temperature. Fig. 5e shows the evolution of specific heat defined as CV = (〈E2〉 − 〈E2)/KBT2 with temperature, from which we have obtained TC and TN by locating the peak position of CV. Meanwhile, the evolution of spin magnetic moments of M atoms with temperature (Fig. S5) also gives TC, agreeing with those values obtained from the specific heat. As listed in Table 1, the TN of Fe2CO2 is 40 K. The TC value of Fe2C(OH)2 is 220 K, higher than the TC values of MnPc (150 K),79 Co-based binary compounds CoCl2 (85 K) and CoBr2 (23 K),29 in which there are no extra interlayer super-exchange interactions. By comparison, the TC values of Fe2C and Fe2CF2 are much higher owing to their large magnetic exchange energy. In particular, Fe2CF2 has a high TC value of 910 K. On the other hand, the weak magnetic coupling in Co2C and Fe2C(OH)2 is due to small magnetic moments and weak interlayer super-exchange interactions, respectively. High TC and large magnetic moments (2–5μB per unit cell) make these MXenes attractive candidate materials for spintronics. Additionally, the estimated TC value of CrI3 is 42 K (Fig. S6), agreeing well with the experimental measured value21 and previous calculation results.26,27,80,81 Our results show that the termination groups are effective at tuning the TC value of MXene monolayers.

The magnetic coupling parameters were recalculated by adopting the HSE06 method, and the results are listed in Table S3, which are very close to the PBE results listed in Table 1. Not surprisingly, the recalculated TC and TN values (Table S3 and Fig. S7) based on the magnetic coupling parameters obtained via the HSE06 method are close to the PBE results. Specifically, the recalculated TC values of Fe2C, Co2C, Fe2CF2 and Fe2C(OH)2 are 590, 170, 920 and 270 K, increased by 0–70 K compared with the results at the PBE level. The higher-order three (four) spin interactions are generally small but sometimes key to the contradictions between experimental observations and theoretical results.82–85 Hence, we further calculated three-spin coupling parameters by including the three-spin interactions into the spin Hamiltonian, and the calculation details are presented (Fig. S8 and S9) in the ESI where the third NN magnetic coupling interactions are ignored. Table S4 lists the calculated magnetic coupling parameters at the HSE06 level, and the TC and TN obtained via MC simulations based on the extented Heisenberg model. Compared with the results obtained from the Heisenberg model, the NN exchange constants hardly change, but the second NN exchange constants of Co2C and Fe2CF2 decrease greatly. Meanwhile, the interlayer NN three-spin coupling constants may not be ignored. Nevertheless, the ferromagnetic states maintain to be the ground magnetic states for Fe2C, Co2C, Fe2CF2, and Fe2C(OH)2.

Moreover, the magnetocrystalline anisotropic energies (MAEs) were calculated by taking the spin–orbit coupling (SOC) into account at the PBE level, and are −0.375, −0.05, −0.141, −0.125 and 0.275 meV per M atom for Fe2C, Co2C, Fe2CF2, Fe2CO2 and Fe2C(OH)2, respectively. The positive (negative) values of MAE indicate that the easy magnetization axes are along the out-of-plane (in-plane) direction. All these values are much larger than those of bulk Fe (0.001 meV per atom) and Ni (0.003 meV per atom),86 and comparable to the experimental values of the Fe monolayer on Rh (111) (0.08 meV per atom)87 suggesting their potential applications in spintronic devices.

Carrier mobility

According to the deformation potential theory,88 the carrier mobility of 2D intrinsic semiconductors can be described as58,59,89
 
image file: c9nr10927g-t6.tif(4-1)
where KB is the Boltzmann constant, T is the temperature (300 K), and ħ is the reduced Planck constant. E1 is the deformation potential constant of the carrier and calculated as E1 = ∂Eedge/∂ε, where Eedge is the edge position of the VBM/CBM for holes/electrons and ε represents the uniaxial strain. C2D is the 2D elastic module and defined as EE0/S0 = (C2D/2)(Δl/l0)2, EE0 and Δl are the changes in the total energy and lattice constant under the applied uniaxial strain, and S0 and l0 represent the area and lattice constant at the equilibrium state, respectively. C2D is obtained via calculating the total energy change under the applied uniaxial strain as EE0 = (C2D/2)S0ε2. image file: c9nr10927g-t7.tif (image file: c9nr10927g-t8.tif and image file: c9nr10927g-t9.tif are the effective mass along the two primary axes) and m* is the effective mass along one of the primary axes. In the present study, the hole and electron mobilities of the semiconducting MXenes were calculated along the armchair (AC) and zigzag (ZZ) directions as shown in Fig. 1b.

By studying Fe2CO2, Co2CF2, Co2C(OH)2 and Ni2CF2 under the applied uniaxial strain ranging from −1% to 1% along the AC and ZZ directions, we plotted the changes in the total energy and the shift of the VBM/CBM as functions of the applied uniaxial strain (Fig. S10 and S11). Correspondingly, the elastic modules C2D, deformation potential constant E1 and effective mass m* are obtained and listed in Table 2. The C2D along the AC and ZZ directions are different because of these two directions are anisotropic. For Fe2CO2, the m* and E1 of the electrons along the AC/ZZ directions are 10.59/2.23 and 1.27/0.69 times those of the holes, respectively. Consequently, the electron mobility is much lower than the hole mobility along both directions of AC and ZZ, implying its potential applications in separating electrons and holes. Similarly, the electron mobilities of Co2CF2 and Co2C(OH)2 are much lower than their hole mobilities. In particular, both the electron and hole mobilities of Co2CF2 are much lower (<250 cm2 V−1 s−1) due to the larger E1. The big difference between the E1 of Fe2CO2 and Co2CF2 can be explained by the charge density difference between them at their band edges shown in Fig. 6. The larger charge densities at the VBM and CBM of Co2CF2 imply that the shifts of VBM and CBM are more sensitive to the applied strain.


image file: c9nr10927g-f6.tif
Fig. 6 Side views of the charge densties on the valence band maximum (VBM) and conduction band minimum (CBM) of Fe2CO2 and Co2CF2. The isosurface value is 0.02 e Å−3.
Table 2 The calculated effective mass (m*), elastic modules (C2D), deformation potential constant (E1), and electron and hole mobility (μ2D) along the armchair (AC) and zigzag (ZZ) directions of the semiconducting MXenes Fe2CO2, Co2CF2, Co2C(OH)2 and Ni2CF2 at 300 K
  Carrier (direction) m*/m0 C 2D (J m−2) E 1 (eV) μ 2D (cm2 V−1 s−1)
Fe2CO2 e (AC) 6.99 211.41 1.63 53.23
h (AC) 0.66 1.28 4455.42
e (ZZ) 2.45 214.09 1.04 378.80
h (ZZ) 1.10 1.50 1975.94
Co2CF2 e (AC) 1.06 168.89 6.94 22.69
h (AC) 0.64 4.52 238.61
e (ZZ) 7.54 169.29 4.08 69.67
h (ZZ) 1.72 3.97 115.39
Co2C(OH)2 e (AC) 2.01 185.99 2.30 184.06
h (AC) 0.59 2.73 3573.28
e (ZZ) 1.69 189.86 2.22 240.17
h (ZZ) 0.39 1.19 13[thin space (1/6-em)]891.38
Ni2CF2 e (AC) 0.34 137.76 1.77 2192.84
h (AC) 0.30 3.78 853.88
e (ZZ) 3.85 138.86 3.08 64.43
h (ZZ) 1.78 2.61 304.63


The hole mobility of Co2C(OH)2 is high and anisotropic. It is 1.4 × 104 cm2 V−1 s−1 along the ZZ direction, about an order of magnitude higher compared with that of SnSe,90 YN,91 janus MoSSe92 and Zr2CO2.56 The hole mobility of Ni2CF2 is also direction-dependent. In addition, both electrons and holes are transported quickly along the AC direction, and the electrons are transported 34 times faster along the AC direction than along the ZZ direction. Such a unique property was also exhibited by the Al2C monolayer,93 which can be exploited in applications related to p–n junctions. Additionally, its direct band gap of 0.51 eV facilitates efficient light emission and holds potential applications in optoelectronic devices.

Conclusions

In summary, we performed a comprehensive study on the structural, electronic and magnetic properties of Fe, Co, and Ni carbide MXenes in M2C and M2CT2 (T = F, O, OH) forms. Among them, Fe2C, Co2C, Ni2C, Fe2CF2, Fe2CO2, Fe2C(OH)2, Co2CF2, Co2C(OH)2 and Ni2CF2 are both mechanically and dynamically stable. Our calculations show that Fe2C and Co2C are FM metals, while Fe2CF2 and Fe2C(OH)2 are FM half-metals, which also have large magnetic moments of 2–5μB per unit cell. More importantly, we find that the termination groups are effective at tailoring the Curie temperatures and opening the energy gaps. In particular, the respective Curie temperatures of Fe2C, Fe2CF2 and Fe2C(OH)2 are 590 K, 920 K and 290 K at the HSE06 level based on the Monte Carlo simulations, which decrease (less than 40 K) with considering the higher-order magnetic interactions (tree-spin interactions). Additionally, Fe2CO2, Co2CF2, Co2C(OH)2 and Ni2CF2 exhibit semiconducting features while their corresponding pristine forms are metallic. The hole mobility of Co2C(OH)2 is high along the ZZ direction (1.4 × 104 cm2 V−1 s−1), suggesting its promising applications in hole-transport materials. Moreover, direct band gap together with highly anisotropic mobility make Ni2CF2 excellent candidate materials in the fields of optoelectronics and nanoelectronics.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the National Key R&D Program of China (2018YFB0703800) and the Natural Science Fund of Shaanxi Province for Distinguished Young Scholars (2019JC-10).

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Footnote

Electronic supplementary information (ESI) available. See DOI: 10.1039/c9nr10927g

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