Cr₂TiC₂-based double MXenes: novel 2D bipolar antiferromagnetic semiconductor with gate-controllable spin orientation toward antiferromagnetic spintronics

Abstract

Antiferromagnetic (AF) spin devices could be one of the representative components for applications of spintronics thanks to the numerous advantages such as resistance to magnetic field perturbation, stray field-free operation, and ultrahigh device operation speed. However, detecting and manipulating the spin of AF materials is still a major challenge due to the absence of a net magnetic moment and spin degeneracy in the band structure. Bipolar antiferromagnetic semiconductors are promising solutions to these problems. Herein, using density functional theory calculations, we present asymmetrical functionalized double MXenes (Cr₂TiC₂FCl) that behave as a novel bipolar antiferromagnetic semiconductor (BAFS) with vanishing magnetism, in which the valence band and conduction band around the Fermi level exhibit opposite spin directions. Remarkably, gate voltage can manipulate the spin orientation of the AF Cr₂TiC₂FCl and lead to a transition from BAFS to half-metal antiferromagnets (HMAF). Moreover, the mixed functionalized double MXenes with various F/Cl concentrations show the BAFS feature due to the different chemical environment for the Cr atom. Our results presented herein open a new strategy towards AF spintronics and the realization of the AF spin field effect transistor.

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1. Introduction

Spintronics, which employs the spin degree of freedom of electrons for information storage, transportation and processing, is one of the most promising technologies for next-generation information engineering.¹ The development of spintronic devices relies on finding new materials with specific magnetic properties. Generally, the magnetic order in materials can be manipulated by the magnetic field approach,² while materials with considerable spin-orbital coupling can be controlled by the electric field.³ 2D materials have attracted extensive research interest due to their many intriguing physical and chemical properties. In particular, 2D magnetic materials are predicted to have high spin-polarization and room-temperature magnetic order, which are of great advantage for spintronic applications. Recently, some 2D magnetic materials with intrinsic ferromagnetism and high spin-polarization have been extensively studied, such as transition-metal (TM) halides,^4–7 MXenes,^8–10 CrATe₃ (A = Si, Ge and Sn),^11,12 TM dihydride¹³ and Janus TMDs,¹⁴ which show promising applications in spintronic devices. Particularly, 2D ferromagnetism has been discovered experimentally in atom-thick CrI₃ and CrGeTe₃ crystals.^15,16 Subsequently, room-temperature ferromagnetism characteristics were found in 2D VSe₂/MoS₂ van der Waals heterostructures and epitaxial MnSe₂ films.^17,18 These experimental achievements of intrinsic 2D magnetic materials have attracted huge interest for the exploration of new physical properties and phenomena. For instance, numerous studies have been devoted to electrically and magnetically manipulate spin-related properties, e.g., Dzyaloshinskii–Moriya interaction, interlayer spin–flip and magnetic anisotropy.^19–24 Furthermore, 2D magnetic materials exhibit intriguing physical properties, such as multiferroics,^25,26 thermoelectrics,²⁷ quantum anomalous Hall effect⁷ and valleytronics.²⁸

However, so far, most of the theoretical and experimental studies focused on ferromagnetic (FM) order. The existence of stray magnetic fields in FM materials will unavoidably limit the generation and complete manipulation of spin-polarized carriers.²⁹ In principle, antiferromagnetic (AF) materials possess intrinsic advantages, including robustness against magnetic field perturbation, no stray fields, and ultrahigh speed of device operation, which have attracted significant attention due to their great potential in AF spintronics.³⁰ Until now, however, manipulating and detecting the spin structure in AF materials has been proved challenging due to the absence of a net magnetic moment and spin degeneracy in the band structure.

To overcome these bottlenecks, Van Leuken and de Groot³¹ proposed the concept of half-metallic antiferromagnets (HMAF) using CrMnSb Heusler compounds as examples. Such HMAF materials combined with high spin-polarization and AF order, offer new opportunities to manipulate and detect the spin in AF materials. Particularly, the HMAF properties in the Half-Heusler Mn₂Ru_xGa and Mn₂Pt_xGa alloys have been confirmed experimentally.^32,33 However, to date, only a few 2D AF systems have been predicted to have high spin-polarization, e.g., TM co-doped 2D semiconductor.^10,34,35 The transition metal carbides/nitrides, known as MXenes, are a family of 2D materials, which have been synthesized experimentally by the chemical exfoliation technique.^36,37 However, the magnetism and spin-polarization of MXenes generally disappear when their surfaces are functionalized, as reported in Cr₂CT₂, V₂CT₂ and Cr₂TiC₂T₂ (T = F, OH) MXenes.^8,38,39

In this paper, using first-principles calculations, we propose that a bipolar antiferromagnetic semiconductor with vanishing magnetism can be achieved in double MXenes Cr₂TiC₂ by using F and Cl atoms asymmetrically with mixed functionalization. The application of gate voltage can easily manipulate the spin direction, leading to the transition from BAFS to half-metal antiferromagnets. The underlying mechanisms are explained based on the band structure analysis.

2. Computational method and details

We performed first-principles calculations within the density functional theory (DFT) using the projector augmented wave method as implemented in the plane-wave code VASP (version 5.4.1) with the Perdew–Burke–Ernzerhof (PBE) exchange–correlation functional.^40–42 The criteria of energy and atom force convergence were set to be 10⁻⁵ eV per unit cell and 0.01 eV Å⁻¹, respectively. The Brillouin zone (BZ) was sampled using 15 × 15 × 1 and 21 × 21 × 1 Gamma-centered Monkhorst–Pack grids for the structural relaxation and electronic structure calculations, respectively. For the magnetic properties calculation, the Hubbard “U” correction was employed within the rotationally invariant DFT+U approach proposed by Dudarev et al.⁴³ A correction of U = 3 eV was employed based on the relevant previous reports.¹⁰ The band structure calculations for symmetrical and asymmetrical functionalization of Cr₂TiC₂ were performed using the screened-nonlocal exchange Heyd–Scuseria–Ernzerhof (HSE06) functional of the generalized Kohn–Sham scheme. The phonon frequencies were calculated using a supercell approach as implemented in the PHONOPY code.^44,45

3. Results and discussion

3.1 Symmetrical functionalization of Cr₂TiC₂

Before presenting the results for asymmetrically functionalized Cr₂TiC₂, we firstly discuss the structure, electronic and magnetic properties of symmetrically functionalized MXenes, including Cr₂TiC₂F₂ and Cr₂TiC₂Cl₂ sheets. The calculated lattice constants for Cr₂TiC₂F₂ and Cr₂TiC₂Cl₂ sheets are 3.03 Å and 3.14 Å, respectively, which are in good agreement with previous calculations.³⁹ The band structure (see Fig. S1†) shows that both the Cr₂TiC₂F₂ and Cr₂TiC₂Cl₂ sheets are semiconductors with band gap of 1.26 eV and 1.04 eV, respectively, without spin polarization. Although each Cr atom is spin-polarized with a large local magnetic moment, they do not contribute to the net spin-polarization of the Cr₂TiC₂F₂/Cr₂TiC₂Cl₂ sheets due to the equivalent chemical environment and the compensated AF order. The partial density of state (PDOS) for the d orbital of the Cr atoms in the upper and lower layers is shown in Fig. S1.† Clearly, the spin-up and spin-down d orbitals on the Cl-bonded and F-bonded Cr atoms (denoted as Cr₁ and Cr₂) in symmetrically functionalized Cr₂TiC₂ have a perfectly symmetrical distribution because the two Cr atoms have equivalent chemical environments. For the Cr₂TiC₂F₂ and Cr₂TiC₂Cl₂ monolayer, the iso-electronic F/Cl atom functionalization produces the same local magnetic moment for Cr atoms with distinct chemical environments. Therefore, Cr atoms in the crystal field made up by F and Cl atoms exhibit different exchange splitting, and the distinct crystal splitting between the upper-surface Cr atoms and lower-surface Cr atoms cause the Fermi level shift between the spin-up and spin-down channels. As chemically functionalized graphene with asymmetrical upper and lower surfaces (Janus graphene, asymmetrically functionalized by fluorine and hydrogen) have been synthesized experimentally,^46,47 it is natural to raise the following question: what is the impact of asymmetrical functionalization on the electronic and magnetic properties of monolayer Cr₂TiC₂?

3.2 Electronic and magnetic properties of Cr₂TiC₂FCl

To explore this aforementioned concept further, we constructed Cr₂TiC₂FCl, as shown in Fig. 1d. The lattice constant of 2D Cr₂TiC₂FCl double MXenes is 3.10 Å, which is just between the lattice constants of the Cr₂TiC₂F₂ and Cr₂TiC₂Cl₂ monolayer. To evaluate the stability of Cr₂TiCFCl monolayer, the formation energy, E_form, was calculated as follows:where E_tot(Cr₂TiC₂) and E_tot(Cr₂TiC₂FCl) stand for the total energies of pristine and functionalized MXenes, respectively. Energies of F₂ and Cl₂ in the gas phase were taken for the energies of E_tot(F) and E_tot (Cl), respectively. Similarly, the formation energy for the Cr₂TiC₂F₂ and Cr₂TiC₂Cl₂ monolayers also can be defined as follows:

E_form = E_tot(Cr₂TiC₂T₂) − E_tot(Cr₂TiC₂) − E_tot(T₂) (2)

where T represents F/Cl atoms. The calculated formation energy for Cr₂TiC₂FCl, Cr₂TiC₂F₂ and Cr₂TiC₂Cl₂ are shown in Fig. 2a. It is clear that the formation energies for these structures are all negative and much lower than that of the pristine Cr₂TiC₂ monolayer, which indicates the formation of strong chemical bonds between the Cr atoms and F/Cl atoms. The formation energy for asymmetrically functionalized Cr₂TiC₂FCl is just in between the formation energies of the corresponding symmetrically functionalized Cr₂TiC₂F₂ and Cr₂TiC₂Cl₂. To confirm the dynamic stability of the Cr₂TiC₂FCl MXenes, we investigated the phonon spectra, as shown in Fig. 2b. We note that the phonon spectrum has quite small imaginary frequencies (∼0.12 THz) in the vicinity of the Γ point, suggesting that the monolayer Cr₂TiC₂FCl is unstable to long wavelength periodic distortions. A similar phenomenon is also observed in other 2D materials, such as the well-studied graphene.^48,49 Such long-wavelength instability may induce ripples in the structure, but is not expected to significantly affect the overall structural stability of the 2D sheet.^50,51 In principle, this instability can be suppressed by support from a proper substrate. These results indicate that the Cr₂TiC₂FCl MXenes monolayer is dynamically stable and can exist as a free-standing 2D monolayer.

Fig. 1 (a) Top view for Cr₂TiC₂ double MXenes. The side view for (b) Cr₂TiC₂F₂, (c) Cr₂TiC₂Cl₂ and (d) Cr₂TiC₂FCl. The color scheme for Cr, C, Ti, F and Cl atoms is described in the figure. The Cr₁ and Cr₂ represent the Cl-bonded and F-bonded Cr atoms, respectively.

Fig. 2 (a) Formation energy (E_form) for symmetrical and asymmetrical double MXenes with respect to pristine Cr₂TiC₂. (b) Phonon dispersion curves for the Cr₂TiC₂FCl monolayer.

Next, we explored the electronic and magnetic properties of Cr₂TiC₂FCl. The FM states of the Cr₂TiC₂FCl monolayer have a total magnetic moment of 5.86μ_B (per unit cell), which is mainly contributed by Cr atoms. To determine the preferred magnetic ground state structures of the Cr₂TiC₂FCl sheets, the collinear FM, AFM-a, AFM-b and AFM-c states were considered, as shown in Fig. 3(a–d). It was found that the AFM-c magnetic configuration has the lowest energy, which was set as the reference energy. The FM, AFM-a, and AFM-b configurations have energies of 210 meV, 717 meV, 618 meV, respectively, with respect to the AFM-c configuration considering a 2 × 1 supercell. Moreover, including spin-orbital coupling, the non-collinear AFM (NCAFM) configuration with the 120° spin vectors and magnetic anisotropy were considered (see ESI†). These results clearly demonstrate that the AFM-c configuration of the Cr₂TiC₂FCl monolayer is the magnetic ground state with high magnetic stability. As shown in Fig. 3, the Cr layers in the upper-surface and lower-surface are separated by Ti₂C with a vertical distance of 4.76 Å; therefore, the AFM-c ground state configuration has both intra-plane and inter-plane magnetic coupling.

Fig. 3 The top and side views of possible magnetic configurations of the Cr₂TiC₂FCl MXene: FM (a), AFM-a (b), AFM-b (c), and AFM-c (d). Red and black balls represent Cr atoms with spin up and spin down electron configurations. The spin exchange parameter of the top view (e) and side view (f) for J_‖, J_⊥ and J_⊥′ are also marked, respectively.

To describe quantitatively the magnetic properties of the Cr₂TiC₂FCl monolayer, the intra-plane magnetic exchange coupling constant (J_||), and the inter-plane magnetic exchange coupling constant (J_⊥ and J_⊥′) were studied. The classical Heisenberg model with respect to J_‖, J_⊥ and J_⊥′ exchange coupling parameters can be expressed as follows:

where S is the net magnetic moment (3μ_B) at the Cr site i, and (i, j), (k, l) and (m, n) run over the nearest, next-nearest and next-next-nearest Cr atoms, respectively. By mapping the DFT total energies of the Cr₂TiC₂FCl of different magnetic structures (FM, AFM-a, AFM-b, and AFM-c) to the Heisenberg model, the exchange coupling parameters (J_‖, J_⊥ and J_⊥′) can be expressed by the following equations:

Thus, the magnetic exchange coupling parameters J_‖, J_⊥ and J_⊥′ are 62.52 meV, −12.28 meV and −18.80 meV, respectively. These results demonstrate that the intra-plane coupling between the Cr atoms in the upper-surface and lower-surface has a strong ferromagnetic nature, while the inter-plane interaction maintains antiferromagnetic coupling. Furthermore, from the mean-field approximation, the Néel temperature can be evaluated as ;⁵² thus, a high Néel temperature of 901 K is realized, suggesting potential applications for room-temperature spintronic devices.

3.3 Gate-controllable spin orientation

As AFM-c is the most stable magnetic state; in this section, we focus on its electronic and magnetic properties. The band structure of Cr₂TiC₂FCl shows that both the spin up and spin down states possess semiconducting features, with an indirect band gap of 0.91 eV, as shown in Fig. 4. Intriguingly, the valence band maximum (VBM) and the conduction band minimum (CBM) of Cr₂TiC₂FCl are derived from the opposite spin channels. Thus, the Cr₂TiC₂FCl sheet behaves as a novel bipolar antiferromagnetic semiconductor (BAFS). Unlike the bipolar magnetic semiconductor (BMS) proposed by Li et al.,⁵³ Cr₂TiC₂FCl is a ferromagnetic material. Because of the opposite spin channels at the VBM and CBM, its spin-polarization direction can be controlled simply by applying a gate voltage. Recently, such gate-controllable magnetic states have been realized experimentally in few-layer Cr₂Ge₂Te₆.⁵⁴ Similar to the BMS materials, the BAFS feature of Cr₂TiC₂FCl also can be described by three energy gaps (Δ1, Δ2 and Δ3), as shown in Fig. 4d. The Δ1 gap is defined as a spin–flip gap with opposite spin polarization between the VBM and CBM, while (Δ1 + Δ2) and (Δ1 + Δ3) are defined as spin-conserved gaps. For practical applications of bipolar semiconductor, Δ1 should be small enough to moderately shift the Fermi level to spin-up/spin-down channels by the gate voltage. Moreover, Δ2 and Δ3 are expected to be large enough to guarantee the half-metallic gap. It is worth emphasizing that the values of Δ1, Δ2 and Δ3 are 0.91 eV, 0.31 eV, and 0.27 eV, respectively. These values fit the criteria of BMS very well, indicating that Cr₂TiC₂FCl sheet is a promising 2D material for AF spintronics applications.

Fig. 4 Band structure for Cr₂TiC₂FCl double MXenes under gate voltage hole doping (a), neutral (b), and electron (c) with a carrier concentration of 0.1 electrons or holes per unit cell. The spin up and spin down channels are depicted in blue and pink, respectively. (d) The schematic plot of transformation between the bipolar HMAF and BAFS states under gate voltages of V_G > 0, V_G = 0, and V_G < 0, respectively. Spin–flip gaps and spin-conserved gaps (Δ1, Δ2 and Δ3) are marked. (e) Schematic plot of antiferromagnetic spintronics device based on BAFS materials, together with the I–V_G relationship under positive and negative gate voltage. The switching of the spin up and spin down current can be manipulated by the gate voltage.

As shown in Fig. 4a & c, there is a remarkable influence on the band structure of Cr₂TiC₂FCl for hole or electron doping. The doping electron and hole shift the Fermi level to different spin-polarized VBM and CBM regions, resulting in a tunable carrier spin orientation and transition from BAFS to HFAF. For low density electron doping, Cr₂TiC₂FCl changes from BMSAF to HMAF state with spin-down polarization, while a spin-up polarized HMAF state is obtained in the case of hole doping. Thus, completely spin-polarized currents with tunable spin orientation of the carriers and HMAF properties can be realized easily by a given doping type.

The novel BAFS materials combined with antiferromagnetic order and bipolar semiconducting character have potential applications for generating, manipulating, and detecting spin-polarized carriers in AF spintronics. Hence, in analogy to conventional semiconductor field effect transistors (FET), the gate voltage can switch the half-metallicity as well as control its spin polarized orientation. We briefly demonstrate a typical BAFS-based AF spin FET. As illustrated in Fig. 4(e), electron and hole doping was applied to tenably shift the Fermi level into the VB or CB in the BAFS materials. For instance, for hole doping, the Fermi level will shift into VB, resulting in a 100% spin-up polarized current (see Fig. 4e). Likewise, for electron doping, the Fermi level is conversely shifted into the CB; thus, a 100% spin-down polarized current is realized. Electron and hole doping can be realized experimentally by simply applying a gate voltage, as shown in Fig. 4d & e. The field-induced doping enables to control the spin polarized orientation and enhance the conductivity in BAFS materials, which will be promising for AF spintronics. Recently, gate-controllable electronic and magnetic properties in 2D magnets have been extensively reported.^54–56 Particularly, the magnetic states of few-layer Cr₂Ge₂Te₆ were controlled experimentally by gate voltage because of its bipolar magnetic semiconducting feature.⁵⁴ When a practical gate voltage is applied, the electric field can induce charge transfer between 2D magnets and substrates, resulting in electron/hole doping. As shown in Fig. 4, the band structures were calculated by considering electron/hole doping. It is clear that doping shifts the Fermi level, and has a slight impact on the shape of the electronic band. However, for MXenes, the asymmetrical chemical adsorption induces a dipole in the z-direction. Our calculated dipole moment density is 0.034 eÅ (along z-axis direction) for monolayer Cr₂TiC₂FCl, which is comparable to that of other MXenes.⁵⁷ When the real gate voltage is applied, it may enhance or suppress this dipole moment density and change the shape of the electronic band. To obtain a deeper understanding of the effects of the vertical gate voltage on the magnetic properties of MXenes, further comprehensive investigations are deserved.

3.4 The origin of BAFS

To gain insight into the fascinating electronic properties for Cr₂TiC₂FCl, the partial electronic density of states (PDOS) of the Cr₁ (Cl-bonded Cr atom) and Cr₂ (F-bonded Cr atom) atoms were recorded, as shown in Fig. 5. According to the D_3d local symmetry of the crystal field on Cr₁ and Cr₂ atoms, the 3d orbitals split into a non-degenerate a (d_z²) orbital and two 2-fold degenerate e₁ (d_xz/d_yz) and e₂ (d_xy/d_x²−y²) orbitals (the z axis is along the normal direction of the sheet). The VBM and CBM states of Cr₂TiC₂FCl are mainly derived from the Cr₂-a and mixed Cr₁-e₁/Cr₁-e₂ states, respectively. According to Griffith's crystal field theory,⁵⁸ the distribution of the d states of the TM ions reveal the crystal field splitting (Δ_cf) and exchange splitting (Δ_ex) due to the crystal field interactions and on-site coulombic interaction, respectively.^59,60 Clearly, the crystal field and exchange splitting of Cr₁-d and Cr₂-d are different, as shown in Fig. 5, because the Cr ions are located in a different chemical environment. Thus, the distinction of spin splitting between upper and lower Cr atoms is the dominant reason for the emergence of the BAFS feature in the Cr₂TiC₂FCl monolayer. Schematics of the Cr₁ (upper Cr atoms) and Cr₂ (lower Cr atom) spin exchange splitting in symmetrically and asymmetrically functionalized surfaces are shown in Fig. 5c & d. Although the individual Cr₁ and Cr₂ atoms are spin-polarized, they do not contribute to any net spin-polarization in the Cr₂TiC₂F₂ and Cr₂TiC₂Cl₂ system due to the equivalent chemical environment and the antiferromagnetic order. Nevertheless, for asymmetrical Cr₂TiC₂FCl MXenes, the different chemical environments in the upper and the lower surface induces a mismatch of d states for the Cr₁ and Cr₂ atoms, and consequently results in the BAFS feature.

Fig. 5 PDOS of d states for Cl-bonded Cr₁ (a) and F-bonded Cr₂ (b) calculated for Cr₂TiC₂FCl. The insets show the local structure of the Cr atoms with F and Cl functionalization, respectively. The Fermi level is set to zero. Schematic diagrams of the Cr spin exchange splitting in symmetrically and asymmetrically functionalized surfaces are shown in (c) and (d), respectively. α and β represent the spin-up and spin down, respectively, and the Cr₁ and Cr₂ denote the upper and lower Cr atoms.

3.5 The mixed functionalization of double MXenes

The double MXenes Cr₂TiC₂FCl, with the perfectly asymmetrical F/Cl atom functionalization, is an ideal model. Generally, MXenes are obtained by exfoliation in a hydrogen fluoride solution where both surfaces have a mixed functionalization with H, OH and F atoms.^61,62 It is therefore crucial to study the electronic properties for double MXenes with mixed functionalization. Next, we considered several typical mixed functionalization models (Cr₂TiC₂F_xCl_2−x, x = 0.25, 0.75, 1.25, 1.75) and calculated their magnetic and electronic properties, as shown in Fig. S3† and Fig. 6, respectively. These results show that the mixed functionalization double MXenes remain as a BAFS with interlayer AF ground states, as shown in Fig. 6. Thus, even an imperfect asymmetrical functionalization of Cr₂TiC₂ is sufficient to affect the chemical environment of the Cr atoms in the upper and lower surfaces to observe BAFS feature. In addition, the varying concentration of F/Cl on one of the surfaces provides an effective way to control the AF spin-polarization.

Fig. 6 DOS for various Cr₂TiC₂F_xCl_2−x systems, x = 0.25 (a), 0.75 (b), 1.25 (c), 1.75 (d). The pink and blue colors represent the spin up and spin down polarizations, respectively. The Fermi level is set to zero.

4. Summary

A new 2D bipolar antiferromagnetic semiconductor (BAFS) is reported for asymmetrical and mixed functionalization of Cr₂TiC₂ double MXenes using DFT at the HSE06 level. The valence and conduction bands in the BAFS materials are made up of opposite spin channels in a compensated AF order. We found that the application of electron and hole doping can easily manipulate the spin carrier orientation, leading to the transition from BAFS to half-metal antiferromagnets (HMAF), which could be realized experimentally via gate voltage. We also found that the BAFS characteristics are present even in Cr₂TiC₂F_xCl_2−x systems with mixed functionalization of the upper and lower surfaces. Our results presented herein open a new road for AF spintronics and the realization of AF spin field effect transistors.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

J. H., Q. D., and C. Z. acknowledge financial support provided by National Natural Science Foundation of China (Grant No. 11804041, 11804040 and 11804039).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c8nr07692h

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