Tunable Magnetism and Transport Properties in Nitride MXenes Hemant Kumar,† Nathan C. Frey,† Liang Dong,† Babak Anasori,‡ Yury Gogotsi,‡ and Vivek B. Shenoy*,† †
Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States Department of Materials Science and Engineering and A.J. Drexel Nanomaterials Institute, Drexel University, Philadelphia, Pennsylvania 19104, United States
‡
S Supporting Information *
ABSTRACT: Two-dimensional materials with intrinsic and robust ferromagnetism and half-metallicity are of great interest to explore the exciting physics and applications of nanoscale spintronic devices, but no such materials have been experimentally realized. In this study, we predict several M2NTx nitride MXene structures that display these characteristics based on a comprehensive study using a crystal field theory model and first-principles simulations. We demonstrate intrinsic ferromagnetism in Mn2NTx with different surface terminations (T = O, OH, and F), as well as in Ti2NO2 and Cr2NO2. High magnetic moments (up to 9 μB per unit cell), high Curie temperatures (1877 to 566 K), robust ferromagnetism, and intrinsic half-metallic transport behavior of these MXenes suggest that they are promising candidates for spintronic applications, which should stimulate interest in their synthesis. KEYWORDS: 2D materials, MXenes, half-metals, ferromagnetism, DFT, spintronics
F
Mn+1XnTx (M = transition metals, X = C and/or N, T = O, OH, F, n = 1−3), provide opportunities to achieve intrinsic 2D magnetism and half-metallicity as a few MXenes (such as Cr2C and Mn 2 C) have been predicted to be intrinsically magnetic. 13−17 Recent success in synthesizing ordered double-transition-metal (M 2 M′ n X n+1 T 2 , n = 1−2; e.g., Mo2TiC2T2) MXenes adds to the diversity of the MXene family.18 As a result, more than 20 types of MXenes with different transition metals and differing atomic layers (including Ti2CTx, V2CTx, Nb2CTx, Ti3C2Tx, Ti4N3Tx, Mo2TiC2Tx) have already been synthesized, and approximately 70 different MXenes have been proposed theoretically,19 not counting millions of solid solutions possible in various M−X systems. Among these, only one nitride MXene (Ti4N3Tx) has been reported.20 Very recently, by using a salt-templated method and reduction of transition-metal oxides, 2D sheets of MoN, V2N, and W2N have been synthesized, which further adds to the family of possible 2D transition-metal carbides and nitrides.21 Due to such diverse chemical compositions, a wide range of magnetic properties should be expected, and MXenes with any desired magnetic property can potentially be achieved with proper combinations of transition-metal elements and surface termination groups.
ollowing the discovery of graphene, different types of two-dimensional (2D) materials such as transition-metal dichalcogenides (TMDs), silicene, and phosphorene have been synthesized.1−3 These materials exhibit a wide range of physical properties that are being actively sought to fabricate high-performance electronic devices. While efforts in this area have been focused on the investigation of 2D semiconductors and optoelectronic materials, 2D magnetic materials remain largely unexplored. Robust and tunable magnetic properties in 2D materials can be valuable in quantum computation, logic and memory operations, spintronics, and other electronic devices where the spin degree of freedom of the carriers is manipulated.4−7 Most of the 2D materials synthesized so far are intrinsically nonmagnetic. Several experimental approaches to induce magnetism in these materials, such as doping, quantum confinement, and surface functionalization, have been demonstrated recently.8−10 For example, weak magnetism can be induced in graphene by doping it with nitrogen; zigzag edges of graphene nanoribbons exhibit half-metallic ferromagnetism in the presence of a strong electric field.9,11 Similarly, edges/grain boundaries of TMDs have been shown to exhibit spin polarization.12 However, such systems have very limited practical applications considering that inducing magnetism in a controllable manner in these materials systems remains a challenge, and the induced magnetism is usually not robust.12 Fortunately, 2D transition-metal carbides, nitrides, and carbonitrides, known as MXenes, with a general formula of © 2017 American Chemical Society
Received: April 13, 2017 Accepted: May 30, 2017 Published: May 30, 2017 7648
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Figure 1. Schematic to explain the local magnetic moment of M2NT2 MXenes with different transition-metal groups. (a) Side views of the crystal structure of the MXenes with the unit cell highlighted. (b) Top view of a monolayer MXene, with octahedral coordination. (c) Simplified density of states assumed in the model. (d) Arrangement of the electrons localized on the transition-metal centers for groups IV to VII of the periodic table. Dotted spin indicates electron occupation is equally probable in the states corresponding to either the top (T) or the bottom (B) layer.
Khazaei et al. first reported that Cr2C and Cr2N MXenes have lower ground-state energy for ferromagnetic configurations compared to nonmagnetic configurations.2 Recently, Si et al. have shown that unterminated Cr2C MXene is a ferromagnetic half-metal, whereas both ferromagnetism and half-metallicity disappear in their surface-terminated structures: the ground states of F-, OH-, H-, and Cl-terminated Cr2CTx MXenes are antiferromagnetic (AFM) semiconductors.13 Recent density functional theory (DFT) studies have predicted that MXenes such as Cr2CFCl, Mn2CTx, Mn2C, V2C, and Cr2N also demonstrate different magnetic ordering (predominately AFM).2,22,23 Although the aforementioned magnetic MXenes have been identified theoretically, a systematic study identifying the fundamental mechanism for the magnetic behavior in MXenes has not yet been conducted. We carry out a comprehensive theoretical study, based on DFT simulations, on the magnetic properties of nitride MXenes with a general formula of M2NT2 (M = Ti, V, Cr, Mn; T = F, OH, O) and identify several MXenes with halfmetallic transport and a stable ferromagnetic ground state, including Mn2NTx, which is robust against surface termination and oxygen-terminated Ti2NT2 and Cr2NT2. The main objectives of this article are to (1) present a generalized framework to predict the magnetic behaviors of MXenes and (2) identify MXenes with intrinsic ferromagnetic (FM) ground states that are stable with respect to surface terminations and thermal fluctuations at room temperature. In this paper, we primarily focus on nitride MXenes because each N in M2NT2 contains an additional electron compared to the transition-metal carbides M2CT2, leading to excess density of states (DOS) near the Fermi level. Such excess DOS provides higher conductivities (compared to the corresponding carbide MXenes) desirable in device applications and stabilizes the ferromagnetic phase according to the Stoner criterion.24 Additionally, the excess electron may potentially result in the
coexistence of two oxidation states of transition-metal M atoms and hence a dominant double-exchange interaction in the system (detailed in the discussion later). We note that 2D sheets of V2NTx and W2NTx have recently been synthesized. Therefore, it is expected that M2NT2 MXenes predicted here with other transition-metal elements can be synthesized using similar approaches.20,21
RESULTS Before presenting detailed results of our DFT simulations, we discuss a simple model to predict the magnetic behavior of M2NT2 MXenes (Figure 1a,b), based on the analysis of the crystal field that splits the transition-metal d-orbitals. The electronic structure of MXenes is strongly influenced by the coordination environment of the transition-metal atoms and the number of their d-electrons. Similar to TMDs, the nonbonding d-orbitals of the MXenes are positioned between bonding (σ) and antibonding (σ*) states of M−-X and M−T bonds (Figure 1c).25 Assuming that all constituent elements of the MXenes are in their nominal oxidation states (C4−, N3−, O2−, F−, and OH−), the M−X and M−T bonding states are filled, while their antibonding states remain empty. Hence, only electrons occupying the nonbonding d-orbitals can be assumed to contribute to magnetism. In the equilibrium structure, each transition-metal ion is subjected to an octahedral crystal field from the nearest-neighbor N and T (O, OH, F) atoms/groups (Figure 1b), which splits the d-orbitals into the lower energy t2g (dxy, dyz, and dxz) states and higher energy eg (dx2 −y2 and dz2) states (Figure 1c). Different filling configurations of these dbands based on the available number of electrons give rise to a large array of magnetic behaviors of these MXenes. A similar description based on symmetries in transition-metal coordination has been used to identify transition-metal oxides with optimal transport properties.26 7649
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Figure 2. Spin-polarized charge density distribution for different magnetic ordering configurations in F-terminated Mn2N. (a, d) Ferromagnetic, (b, e) antiferromagnetic-1, (c, f) antiferromagnetic-2. Red and blue isosurfaces represent spin-up and spin-down densities.
To demonstrate the validity of our physical model, we first apply it to analyze the electronic structure of Cr2CF2, one of the well-studied magnetic carbide MXenes. The nominal oxidation state of Cr in Cr2CF2 is +3 after donating two electrons to the neighboring C4− and one electron to neighboring F−. Following Hund’s rule, the remaining three d-electrons of Cr3+ half-fill the t2g band, which gives rise to a local magnetic moment of 3 μB per Cr atom due to the aligned spins of the three electrons. Such a strong local magnetic moment completely splits the t2g orbitals into fully occupied bands for the majority spin and open bands for the minority spin, resulting in a semiconducting behavior. Both the magnitude of the local magnetic moment and the transport behavior predicted by our model agree with the conclusions of DFT calculations by Si et al. obtained using the hybrid Heyd−Scuseria−Ernzerhof screened functional.13 A similar electronic filling configuration can be found in oxygenterminated Mn2CO2, where each Mn atom donates four electrons to the neighboring atoms (2e to carbon and 2e to oxygen), leaving three d-electrons and hence a local magnetic moment of 3 μB per Mn atom. Similarly, for the F/OH termination of this MXene, the oxidation state of Mn atoms (F and OH are isoelectronic and accept one electron from Mn) is +3, and four unpaired electrons arrange in t3e1 (4 μB) electronic configurations. This leads to the high-spin configuration with a magnetic moment of 4 μB and a partially filled eg-band, causing metallic conductivity for the majority spins. This is consistent with the DFT+U study by He et al., who calculated a local magnetic moment of ∼3 μB and 4.1 μB per Mn atom for O and F termination, respectively.14 This demonstrates that the predictions from our simplified model are consistent with rigorous DFT simulations and are applicable to different transition metals and surface terminations. After establishing the validity of our model, we use this model to predict magnetic properties of nitride MXenes. The only difference between a carbide and the corresponding nitride MXenes is the presence of an extra electron per unit cell introduced by nitrogen, which leads to a higher magnetic moment per unit cell and generates interesting magnetic behaviors. Each nitrogen atom gains three electrons either by accepting two electrons from the transition-metal atom in the top layer and one electron from the bottom layer M atom or vice versa, which are equally energetically favorable due to the lattice symmetry. This leads to the coexistence of two different oxidation states (such as +2/+3 for group IV and +3/+4 for group V atoms in Figure 1d) of the two transition-metal atoms for a given surface termination. Another possibility is that the two M atoms share a d-electron and both have the same halfinteger nominal oxidation state (such as +2.5/+2.5 or +3.5/
+3.5 for F and O terminations, respectively, in Figure 1d). In the FM configurations where both top and bottom transitionmetal atoms have the same spin orientation, the unpaired electron has equal probability to localize near either transitionmetal atom, and hence the latter case is preferred. However, AFM configurations have opposite spin orientations with nearest-neighbor transition-metal atoms, leading to the localization of the unpaired electron near one transition-metal atom, as this electron must flip its spin orientation to hop to a neighboring transition-metal atom. This is the reason that the MXenes with mixed oxidation states of transition-metal atoms are preferred for AFM configurations. On the basis of these simple considerations, we can predict the magnetic moment for a variety of MXenes. Although we limit applying our model to the M2NT2 MXenes with third-row transition-metals (3d) M elements for the rest of this paper, magnetic properties predicted here should be applicable for higher rows (4d and 5d M elements) as well. However, as we go to 4d and 5d transition metal elements, valence electrons are more likely to be delocalized, which in turn may lead to nonmagnetic ground states. On the other hand, their atomic radii increase with an increasing atomic number, which causes a larger bond distance with adjacent N and T atoms and hence reduces hybridization. Next, we present DFT results for different MXenes and show that predictions made by our model are indeed consistent with electronic structure simulations (Table S1 in the SI). We noticed small differences in the magnitudes of the magnetic moment in some MXenes, which are due to a small degree of delocalization of electrons in the 2D crystals as opposed to the simplified isolated atom picture used in our model. Since both FM and AFM ground states are possible with appropriate selection of transition-metal elements and surface terminations, we classify MXenes based on their magnetic ground state and discuss different characteristics of these MXenes. Ferromagnetic MXenes. The ferromagnetic ground state is one of the most sought-after phases for 2D magnetic materials. In the quest for FM MXenes, we have identified five different nitride MXenes (Mn2NF2, Mn2NO2, Mn2N(OH)2, Ti2NO2, and Cr2NO2) with robust FM ground states (Table 1). The ground-state energy of Mn2NF2 for the nonmagnetic phase is 7.1 eV higher compared to the spin-polarized FM phase, which suggests that the magnetically ordered phase of Mn2NF2 is very stable. The distribution of the electron density for the FM state is shown in Figure 2a. The magnitude of the total magnetic moment per formula unit is ∼9.0 μB from both our model and DFT calculations, which mostly derives from the localized spin density near the transition-metal atoms, as 7650
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Figure 3. Electronic band structure and density of states of Mn2NT, showing robust half-metallicity for all possible surface terminations. Large dispersion in band energies indicates itinerant character of electrons and good metallic conductivity. DFT-calculated site-projected DOS of (a) Mn2NF2, (c) Mn2NO2, and (e) Mn2N(OH)2 showing large exchange splitting for minority spin and delocalized fluorine p-states below the Fermi level. Ferromagnetism and half-metallicity with metallic conduction for majority (up-) spin and wide band gap (>3 eV) semiconducting transport for minority (down-) spin channels are illustrated in band structure plots for (b) Mn2NF2, (d) (Mn2NO2, and (f) Mn2N(OH)2 (red and blue solid lines represent majority and minority spins, respectively).
shown in Figure 2. The magnitude of the magnetic moment can be rationalized within the framework of the model discussed above. The electronic configuration of an isolated Mn atom is [Ar][4s2, 3d5]. As discussed above, each Mn atom donates one electron to the surface fluorine atoms, and each nitrogen atom accepts three electrons from both Mn atoms, leaving nine delectrons (d4 and d5 for each Mn atom) per unit cell distributed over both Mn atoms. Due to the large magnetic exchange interactions of the localized majority spins, spin degeneracy in the t2g band is broken and the majority spin t2g is pushed below the Fermi level, while the minority spin band is pushed above the Fermi level (Figure 3), which makes electron pairing in the t2g band energetically unfavorable. For this reason, a high magnetic moment state (t3e1/t3e2) is energetically preferred in the simulations. Since both F and OH termination groups are isoelectronic and accept one electron from each transitionmetal ion, the magnetic moment per unit cell for Mn2N(OH)2 is 8.8 μB from our DFT calculations. On the other hand, oxygen-terminated surfaces require the transfer of two electrons from each Mn atom, and hence, a magnetic moment of 7.0 μB per unit cell is predicted by our model and confirmed by DFT simulations. Next, to investigate the stability of FM ordering with respect to AFM ordering, we consider two different antiferromagnetic configurations: AFM1 and AFM2, as shown in Figure 2b and c. For the AFM1 configuration, we create an AFM arrangement of the in-plane spins while keeping the interlayer spin in FM configuration. For the AFM2 configuration, we keep in-plane FM coupling, while interlayer coupling is AFM. The computed spin-charge densities for all the magnetic configurations are shown in Figure 2. Ground-state energies for the F-termination (OH) in AFM1 and AFM2 states are 997.4 meV (917.6 meV) and 889.3 meV (842.4 meV), respectively, higher than those in the FM state. Similarly, for the O-termination, total energies for
both AFM configurations are higher than those of the FM state by 703.1 and 699.8 meV for the AFM1 and AFM2 states, respectively. Total energies of these magnetic configurations show that FM is the ground state for all three termination groups. The existence of an FM ground state for all the considered termination groups suggests that ferromagnetism in Mn2F2Tx MXenes is robust against variations in surface terminations and can therefore be readily realized with current synthesis methods without any postprocessing to eliminate a certain type of termination group. These MXenes are more suited for practical applications than their carbide counterpart Mn2C MXenes, which exhibit an FM ground state for F/OHterminations, but an AFM ground state for O-terminations.22 The difference between magnetic ground states for Oterminated carbide and nitride MXenes arises due to the extra electron from nitrogen. For the MXene carbide, each Mn has three d-electrons, which completely fill the t2g band, and to maximize electron hopping between the two transition metals, they arrange in an AFM spin configuration. On the other hand, for the nitride case, an extra electron resides in the e2g band, leading to a partially filled state, which allows electron hopping for FM configurations as well. Current synthesis methods produce MXene flakes with a combination of O, OH, and F surface terminations. From Table S1, other MXenes with FM ground states include Cr2NO2 and Ti2NO2. Cr has six valence electrons with the electronic shell configuration [Ar][3d4, 4s2]. On the basis of the discussion in the previous section, each unit cell will have five unpaired electrons distributed over two Cr ions after each Cr atom donates two electrons to oxygen and both Cr atoms together provide three electrons to the shared N atom. Accordingly, these electrons can reside in the t2g band, and an effective magnetic moment of ∼5 μB per unit cell is expected according to our model for Cr2NO2. In the FM state, the 7651
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Table 2. Exchange Parameter and Curie Temperature of Different MXenes Obtained from Ising Model MC Simulationsa
a
EAFM1 = E0 − 2J1μ2 + 4J2 μ2 EAFM2 = E0 + 6J1μ2 − 12J2 μ2
Here E0 represents the energy for the nonmagnetic part. By solving these equations for the exchange parameters J1 and J2, we obtain (EAFM2 − E FM) 12μ
2
, J2 =
(3EAFM1 − E FM) 24μ2
Calculated values of J1 and J2 for all FM MXenes are given in Table 2. For F-terminated Mn2NF2, both interlayer exchange parameter J1 (3.66 meV) and intralayer exchange parameter J2 (2.16 meV) are FM, which indicates that both interlayer and intralayer couplings are FM, leading to a robust FM order for Table 1. Lattice Parameters a of MXenes with FM Ground State for Different Magnetic Configurations a-lattice parameter (Å) MXene
FM
AFM1
AFM2
Mn2NF2 Mn2NO2 Mn2N(OH)2 Cr2NO2 Ti2NO2
3.1927 3.0315 3.2101 2.9907 3.0672
3.1659 3.0220 3.1191 3.0206 NA
3.1964 2.9884 3.2116 3.0031 NA
EAFM1 − EFM
EAFM2 − EFM
J1 (meV)
J2 (meV)
TC (K)
Mn2NF2 Mn2NO2 Mn2N(OH)2 Cr2NO2 Ti2NO2
997.4 703.1 917.6 332.5 NA
889.3 699.8 842.4 137.1 NA
3.66 4.76 3.47 1.83 NA
2.16 2.40 1.97 2.87 NA
1877 1379 1743 566 NA
All energies are in meV.
this MXene. The exchange parameters for O and OH surface terminations are also given in Table 2, which indicate the tendency for FM ordering for these terminations as well. To compute the Curie temperature, we carried out Monte Carlo (MC) simulations for a bilayer-triangular lattice with the computed exchange parameters. The average magnetic moment for a 30 × 30 lattice computed from MC simulations with increasing temperatures is shown in Figure S1 for all three terminations. On the basis of these MC simulations, Mn2NF2 remains FM until T = 1877 K. Exchange parameters, along with the computed Curie temperatures for all other FM MXenes, are also given in Table 2. Both exchange parameters are positive for all FM MXenes, indicating ferromagnetic coupling between both intralayer nearest neighbors and interlayer nearest neighbors (next-nearest neighbors). Curie temperatures computed from MC simulations range from 1877 to 566 K. High Curie temperatures along with large magnetic moments (ranging from 1.0 μB to 9.0 μB per unit cell) makes these MXenes very attractive for 2D spintronics applications. Half-Metallicity in the FM MXenes. The calculated density of states reveals that FM MXenes are characterized by the existence of metallic transport behavior for one spin channel and insulating behavior for the other (Figures 3, 4). A large local magnetic moment creates a strong local magnetic exchange field, which pushes minority spin states above the Fermi energy, causing gap opening. Such half-metallicity with a large band gap for minority spin (1.0−2.1 eV, defined as the energy gap between the valence-band maximum for minority spin and Fermi energy) leads to 100% spin polarization for the conduction electrons, and the conductivity is dominated by single spin charge carriers. Materials with such a transport behavior are highly desired for next-generation spintronic devices such as spin filters, spin-polarized FET, spin injectors, and magnetic sensors.4,28 Most of the known half-metals, e.g., La0.7Sr0.3MnO3, CrO2, and Heusler compounds, have a small band gap (∼100 meV) for minority carriers, which gives rise to only partial spin polarizations.27−30 Son et al. predicted that zigzag graphene nanoribbons can also exhibit half-metallicity in the presence of an electric field.11 However, the magnitude of the electric field required to observe half-metallicity is extremely high. Recently, half-metallicity was also predicted in carbide MXenes (Cr2CTx and Mn2CTx); however, these materials show half-metallicity either for unterminated surfaces (Cr2C) or only with a certain surface termination group (Mn2CF2).13,22 In contrast, the Mn2N MXene investigated here exhibits robust intrinsic half-metallicity, and a wide band gap is predicted for the minority spin of all three surface terminations. This indicates that half-metallicity can be observed in these MXenes if they are obtained from current synthesis methods, which usually produce mixed surface termination groups.
E FM = E0 − 6J1μ2 − 12J2 μ2
J1 =
MXene
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Figure 4. Total density of states per supercell (black) for four 3d transition metal MXenes (Mn, Cr, V, and Ti). The left column represents the F-terminated and right column is O-terminated MXenes. The site-projected density of states for the d-orbital of the transition-metal atoms (blue) and the p-orbitals of N (green) and surface termination O/F (magenta) in FM configurations. Localized DOS for F and delocalized nature of O DOS is demonstrated.
Antiferromagnetic MXenes. Antiferromagnetic ordering is the most prevalent type of magnetic ground states in MXenes. In fact, most of the surface-terminated MXenes studied so far have been predicted to have AFM ground states. We have identified several nitride MXenes with robust AFM ordering. Among the 12 different MXenes investigated in this study, we have identified seven different MXenes with either AFM1 or AFM2 ground states. Lattice constants along with total energy for different MXenes are given in Table S1. Ti2NF2, Ti2N(OH)2, V2NF2, V2NO2, V2N(OH)2, Cr2NF2, and Cr2N(OH)2 are MXenes with an AFM1 ground state, i.e., magnetic ordering with intralayer AFM coupling and interlayer FM coupling. Significantly lower energies of AFM states compared to the nonmagnetic phase suggest that magnetic exchange interactions are strong in these materials, and any long-range order arising due to these exchange interactions should prevail above room temperature. Next, we rationalize the different exchange couplings observed in the DFT simulations. The metal−metal distance for all MXenes studied here is approximately 3 Å, which precludes any direct exchange interaction between the metal ions. The underlying reason for the FM and AFM1 ground states can be understood by studying the relative strengths of the superexchange and the double-exchange interactions, which are the consequences of orbital occupancies and overlaps allowed by crystal symmetry. Goodenough−Kanamori rules for ligand-mediated superexchange interactions dictate that if two cations with half-filled orbitals overlap with the same p-orbital
of a ligand, superexchange interaction between them is AFM. On the other hand, superexchange interaction between cations with partially occupied or empty orbitals can be either FM or AFM depending upon the direct exchanges between ligand− metal ions. Double-exchange interaction is FM, as hopping between partially occupied orbitals is maximized if electrons do not have to flip their spin. A closer look at the partial DOS (PDOS) plotted in Figure 4 suggests that the fluorine DOSs (the left column in Figure 4) are mostly distributed over a narrow energy range of 2 eV and appear deep inside the valence band (−8 to −6 eV below the Fermi level) for all MXenes except Mn2NF2 (Figure 4a). OHterminated MXenes have similar DOS characteristics because of being isoelectronic to F-terminations and thus are not shown in Figure 4. On the other hand, DOSs corresponding to oxygen atoms have broad peaks distributed over a large energy range (−6 to 0 eV below the Fermi level), which means the electrons are delocalized (Figure 4 right column). These observations suggest that electrons in oxygen-terminated MXenes have considerable itinerant character, which in turn leads to dominant double-exchange interaction, stabilizing FM ordering. This is indeed reflected in our DFT simulations: all oxygenterminated MXenes, except V2NO2, have FM ground states. For fluorine-terminated MXenes, electrons are localized, double-exchange interactions are weak, and the magnetic ground state is determined by superexchange interactions. Starting from Ti to Cr, orbital occupancy varies from t1e0 to t3e0, and electrons on both sides of the anion overlap with the 7653
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remains the same for all U values with a systematic change in the exchange energy (see SI, Figure S2). A Γ-centered K-point mesh of 12 × 12 × 1 in the first Brillouin zone is found to yield well-converged results during structure optimization. For the density of states calculations, a denser K-point mesh of 32 × 32 × 1 was used. A vacuum space of 2 nm thickness is used to prevent any interactions between the adjacent periodic images of MXene. The atomic positions of this structure are optimized until all components of the forces on each atom are reduced to values below 10−2 eV/Å. Structure optimizations were performed for all magnetic configurations separately.
same symmetry orbital. In this scenario, superexchange interaction is strongly AFM, leading to the AFM1 ground state. However, this simple explanation has two exceptions: (1) Mn2NF2 has an FM ground state, but the rule suggests that the ground state should be AFM; (2) V2NO2 shows an AFM1 ground state, while the rule suggests it should be FM. Mn atoms in Mn2NF2 MXene have an electronic configuration of t3e1/t3e2, which means the highest occupancy electrons are placed in dx2−y2- and dz2-orbitals. For structures with octahedral symmetry, these orbitals have stronger overlap with anion porbitals, as they can form a pσ bond. Such orbital overlap will lead to itinerant electrons, as indicated by the broad peak of fluorine DOS shown in Figure 4, left column. Therefore, the FM ground state is stabilized in Mn2NF2 due to itinerant electrons increasing double-exchange interactions. The AFM1 ground state of V2NO2 (despite delocalized electrons) can be understood from the dominant superexchange interaction. The above discussion suggests that the oxygen termination is preferred to achieve a robust FM ground state in nitride MXenes. Due to intralayer trigonal lattice symmetry of the transitionmetal atoms, ground states with AFM exchange coupling are unlikely to have any spin ordering, and only frustrated spin configurations will prevail at all temperatures. However, such frustrated spin configurations exhibit many interesting spin phenomena such as spin glass, chiral correlations, and some nontrivial spin textures. Moreover, because of the two atomic layers with competing exchange interactions, further complexity is added to the magnetic behavior. Detailed studies focusing on these aspects might reveal some interesting physics.
ASSOCIATED CONTENT S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsnano.7b02578. Lattice parameters, ground-state energies, and the magnitude of localized magnetic moments for all simulated MXenes from DFT+U simulations in Table S1, variation of exchange energy with varying U parameter and results from MC simulations of Ising model in Figures S1 and S2, respectively (PDF)
AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. ORCID
Hemant Kumar: 0000-0003-4339-5711 Nathan C. Frey: 0000-0001-5291-6131 Liang Dong: 0000-0002-3916-1720 Yury Gogotsi: 0000-0001-9423-4032
CONCLUSIONS A systematic study on the magnetic properties for a series of M2NTx nitride MXenes has been conducted to develop a comprehensive understanding of their electronic and magnetic properties. A crystal field theory based model has been developed to understand the magnetic properties of existing MXenes and to predict several FM MXenes. We find that Mn2NTx has a highly desirable ferromagnetic ground state regardless of surface terminations, and Curie temperatures for all terminations are well above the room temperature. In addition, intrinsic half-metallic transport behavior with a wide band gap for a minority spin carrier, which is crucial for 100% spin polarization of conduction electrons, has been demonstrated for Mn2NF2, Mn2NO2, Mn2N(OH)2, Ti2NO2, and Cr2NO2. These results suggest that 2D nitride MXenes are a promising material class for spintronics. This study will be helpful in guiding the synthesis of magnetic MXenes for device applications.
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS This work is supported primarily by contract W911NF-16-10447 from the Army Research Office (V.B.S.) and also by grants EFMA-542879 (H.K.) and CMMI-1363203 (L.D.) from the U.S. National Science Foundation. N.C.F. was supported by the Department of Defense through the National Defense Science & Engineering Graduate Fellowship program. REFERENCES (1) Butler, S. Z.; Hollen, S. M.; Cao, L.; Cui, Y.; Gupta, J. a.; Gutierrez, H. R.; Heinz, T. F.; Hong, S. S.; Huang, J.; Ismach, A. F.; Johnston-Halperin, E.; Kuno, M.; Plashnitsa, V. V.; Robinson, R. D.; Ruoff, R. S.; Salahuddin, S.; Shan, J.; Shi, L.; Spencer, M. G.; Terrones, M.; et al. Progress, Challenges, and Opportunities in Two-Dimensional Materials Beyond Graphene. ACS Nano 2013, 7, 2898−2926. (2) Khazaei, M.; Arai, M.; Sasaki, T.; Chung, C.-Y.; Venkataramanan, N. S.; Estili, M.; Sakka, Y.; Kawazoe, Y. Novel Electronic and Magnetic Properties of Two-Dimensional Transition Metal Carbides and Nitrides. Adv. Funct. Mater. 2013, 23, 2185−2192. (3) Wang, H.; Yuan, H.; Sae Hong, S.; Li, Y.; Cui, Y. Physical and Chemical Tuning of Two-Dimensional Transition Metal Dichalcogenides. Chem. Soc. Rev. 2015, 44, 2664−2680. (4) Wolf, S. A.; Awschalom, D. D.; Buhrman, R. A.; Daughton, J. M.; von Molnár, S.; Roukes, M. L.; Chtchelkanova, A. Y.; Treger, D. M. Spintronics: A Spin-Based Electronics Vision for the Future. Science 2001, 294, 1488−1495. (5) Sakai, S.; Majumdar, S.; Popov, Z. I.; Avramov, P. V.; Entani, S.; Hasegawa, Y.; Yamada, Y.; Huhtinen, H.; Naramoto, H.; Sorokin, P. B.; Yamauchi, Y. Proximity-Induced Spin Polarization of Graphene in
METHODS All calculations were performed using first-principles calculations based on density functional theory as implemented in the Vienna ab initio simulation (VASP) code.31,32 Projector augmented wave (PAW) pseudopotentials are used with a cutoff energy of 400 eV for planewave expansions.33 The exchange−correlation functional is treated within the Perdew−Burke−Ernzerhof generalized gradient approximations (GGA).34 To describe the strong-correlation effects in transition-metal atoms, on-site Coulomb interactions were introduced using Dudarev’s GGA+U approach.35 U values for different transitionmetal atoms were selected from previous studies and are 4, 3, 4, and 4 eV for Ti, V, Cr, and Mn, respectively. The impact of U values on magnetic ground states was studied by changing U values from 0 eV to 7 eV for Mn2NF2, which demonstrates the magnetic ground state 7654
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