Surface-Engineered MXenes: Electric Field Control of Magnetism and

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Surface Engineered MXenes: Electric Field Control of Magnetism and Enhanced Magnetic Anisotropy Nathan C. Frey, Arkamita Bandyopadhyay, Hemant Kumar, Babak Anasori, Yury Gogotsi, and Vivek B. Shenoy ACS Nano, Just Accepted Manuscript • Publication Date (Web): 17 Jan 2019 Downloaded from http://pubs.acs.org on January 17, 2019

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Surface Engineered MXenes: Electric Field Control of Magnetism and Enhanced Magnetic Anisotropy Nathan C. Frey,† Arkamita Bandyopadhyay,† Hemant Kumar,† Babak Anasori,‡ Yury Gogotsi,‡ and Vivek B. Shenoy*, † †Department

of Materials Science and Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

‡Department

of Materials Science and Engineering, and A.J. Drexel Nanomaterials Institute, Drexel University, Philadelphia, Pennsylvania 19104, USA

* Corresponding Author, Email: [email protected]

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Abstract Controlling magnetism in two-dimensional (2D) materials via electric fields and doping enables robust long-range order by providing an external mechanism to modulate magnetic exchange interactions and anisotropy. In this report, we predict that transition metal carbide and nitride MXenes are promising candidates for controllable magnetic 2D materials. The surface terminations introduced during synthesis act as chemical dopants that influence the electronic structure, enabling controllable magnetic order. We show ground state magnetic ordering in Janus M2XOxF2-x (M is an early transition metal, X is carbon or nitrogen, and x = 0.5, 1, or 1.5) with asymmetric surface functionalization, where local structural and chemical disorder induces magnetic ordering in some systems that are non-magnetic or weakly magnetic in their pristine form. The resulting magnetic states of these noncentrosymmetric structures can be robustly switched and stabilized by tuning the interlayer exchange couplings with small applied electric fields. Furthermore, bond directionality is enhanced by Janus functionalization, resulting in improved magnetic anisotropy, which is essential to stable 2D magnetic ordering. The mixed terminationinduced anisotropy leads to robust Ising ferromagnetism with an out-of-plane easy axis over the full range of relevant termination compositions for Janus Mn2N. Janus Cr2C, V2C, and Ti2C were found to be robustly antiferromagnetic. Our results provide a strategy for exploiting asymmetric surface functionalization to achieve room-temperature nanoscale magnetism under ambient conditions in MXenes with currently available synthesis techniques.


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KEYWORDS: 2D materials, MXene, ferromagnetism, magnetic anisotropy, electrical control, Janus, DFT With the advent of nanoscale magnetism in 2D crystals,1–3 attention has turned to control of magnetization in these materials via external means, which may represent a significant breakthrough in rapid switching of magnetic ordering.4 Recent reports have shown that electrostatic doping and external electric fields can be used to tune the exchange mechanisms in bilayer CrI3 to both change the magnetization direction and induce magnetic behavior.5,6 However, with the advantages inherent to 2D magnetic systems comes the requirement of significant anisotropy to protect magnetic ordering against thermal disorder.7 Strategies are therefore needed to enable both rapid switching of magnetic states and enhance magnetic anisotropy. Applied fields, which are effective for modifying magnetic behavior in noncentrosymmetric materials,4,8–11 and the more general method of doping, are of great interest in achieving these goals and realizing controllable, room-temperature nanoscale magnetism for voltage-controlled spintronic devices. Theoretical predictions12 and the recent report of magnetism in Ti3C213 have advanced the family of 2D transition metal carbides and nitrides named “MXenes”14,15 as promising 2D magnetic materials. Studies of asymmetrically functionalized MXenes have predicted that Janus Cr2C behaves as a bipolar antiferromagnetic semiconductor (BAFS) with zero magnetization and high Néel temperatures,16 and the BAFS Janus Cr2TiC2FCl can be switched to a half-metallic antiferromagnet (HMAFM) via a gate voltage.17 Unlike current 2D magnets, MXenes are stable under ambient conditions and are robust to oxygen exposure and moisture. With the general formula Mn+1XnTx (M = early transition metal, X = C/N, T = O, OH, F, n = 1-3), MXenes have been predicted to exhibit diverse magnetic behavior based on their composition and thickness.12,18– 21

In particular, we predicted that manipulating the chemical degrees of freedom inherent to these


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materials enables a rich variety of collinear and noncollinear 2D magnetic ordering in nitride MXenes.22,23 That approach, in addition to the success of electrostatic doping for control of 2D magnetism, suggests that the surface functionalization introduced during MXene synthesis24 represents not only a challenge, but a promising opportunity, for manipulating 2D spin states. MXene surface terminations can be modified by thermal annealing15 to tune electronic properties and induce charge asymmetry,25,26 such that magnetism in these materials is particularly wellsuited to fine-tuned external control via the methods described above. This motivates the study of the effects of mixed surface termination on magnetic ordering, anisotropy, and electric field control. In this work we propose a general strategy for exploiting the mixed surface functionalization in MXenes to enable electrical control of magnetic ordering and enhanced spin anisotropy. Using applied electric fields in MXenes, where spatial inversion symmetry is broken by surface termination, the exchange couplings are tuned to achieve switching of magnetic order. Moreover, the symmetry breaking and intrinsic charge distribution asymmetry induced by local disorder in surface functionalization increases magnetic anisotropy, stabilizing out-of-plane spin orientation. Throughout this paper, we use the term “Janus” in a general sense, referring to MXenes in which there is some substantial composition and/or structural asymmetry between the top and bottom faces because of a mixture of different termination species. We construct several models of asymmetric surface functionalization to sample the range of possible compositions of the dominant terminations introduced during chemical etching, O and F.24 To capture the most interesting magnetic behavior in MXenes, we consider both MXenes that are predicted to have robust, highly desirable magnetic properties (Mn2N and Cr2C),18,23 and MXenes that can be experimentally synthesized (Ti2C and V2C),15 which are therefore of immediate interest for experimental realization of 2D magnetism.


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Using first-principles density functional theory (DFT) and Monte Carlo calculations, we study the effects of mixed termination and characterize a wide variety of magnetic and transport behavior in Janus M2X MXenes. Our findings are then rationalized based on our crystal field model23,27 and the Goodenough-Kanamori rules. Janus Mn2N is found to be robustly ferromagnetic (FM) regardless of surface termination structure and composition. While Janus carbide MXenes are found to prefer antiferromagnetic (AFM) or weakly ferrimagnetic ordering, we present a simple physical model to elucidate how external electric fields enable switching of the magnetic order in an analogous way to applied strain.28–30 Noncollinear calculations including spin-orbit coupling (SOC) reveal that the Ising ferromagnetism previously predicted in Mn2NTx (T = O, OH)22,23 persists over the full composition range of mixed surface terminations, and the magnetic easy axis remains in the out-of-plane direction. Surprisingly, Janus functionalization also induces magnetic ordering in some systems that are predicted to be non-magnetic or weakly magnetic with bare (no surface termination) and pure surface termination. These results show that asymmetric functionalization in 2D materials is a promising approach for inducing magnetism, enabling electrical control, and enhancing magnetic anisotropy. In particular, this work completes our understanding of the basic physical processes underlying exchange mechanisms in magnetic MXenes, and provides pathways for achieving robust nanoscale magnetism in currently available 2D materials.


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Results

Figure 1. M2XOxF2-x MXene models of Janus functionalization and collinear magnetic ordering. (a) Side, top, and bottom views of the supercell with the four termination sites labeled. (b) Side views of the x = 1, x = 0.5, and x = 1.5 models. The space groups and termination species compositions are labeled in each model. The site occupancies for each model are given in Table 1. (c) Collinear ferromagnetic (FM), intralayer antiferromagnetic (AFM1) and interlayer antiferromagnetic (AFM2) ordering configurations are shown with spin up (spin down) in yellow (blue). Five models were constructed to represent the full range of mixed surface termination compositions and ordering in the M2XTxT’2-x structure. Using a 2 x 1 x 1 supercell, we are able to sample compositions for two surface termination species, O and F, of x = 0.5, 1, and 1.5. In this minimal supercell, there are four sites occupied by termination species, labeled 1-4 in the unit cell shown in Figure 1a. For convenience, the site occupancies for each model are given in Table 1. 6 ACS Paragon Plus Environment

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The mixed surface termination models are shown in Figure 1b. The models are labeled according to the composition of the surface functionalization groups, e.g. O0.5F1.5 for x = 0.5. Because of the four available termination sites, there are three distinct orderings for O and F when x = 1. These models are distinguished by composition labels with a superscript indicating the structural symmetry. As an example, in the OF(3) model, the top surface is purely terminated by O and the bottom surface is purely terminated by F, so the structure retains a three-fold rotation symmetry. Similarly, the OF(21)and OF(2) models are distinguished by their 21 screw and two-fold rotation axis, respectively. As discussed below, the symmetry breaking introduced by increasing chemical and structural disorder has drastic consequences for the magnetic ordering and spin anisotropy. The collinear magnetic orderings are shown in Figure 1c; fully FM ordering, intralayer AFM coupling (AFM1) and interlayer AFM coupling (AFM2). Table 1. Site occupancies for mixed termination models. Model OF(3) (2 ) OF 1 OF(2) O0.5F1.5 O1.5F0.5

1 O O O F O

2 O F F O F

3 F O F F O

4 F F O F O

Considering larger supercells would allow for accessing intermediary compositions and more realistic models of disorder in asymmetric surface functionalization. However, as we will demonstrate below, it is the crystal field environment (determined by crystal symmetry) and the transition metal oxidation states (determined by the termination composition) that most significantly influence the predicted magnetic ordering, and the possible ranges of both factors are well-described by the models considered here. Additionally, we restrict our calculations to the two most prevalent surface termination species in MXenes, O and F. While OH is introduced during


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the selective chemical etching process that yields MXenes, OH groups can be removed or transformed to O-termination via annealing,15 and we have previously shown that the magnetic behavior of isoelectronic F or OH terminated MXenes is similar.23

Figure 2. Schematic of local magnetic moments of Janus M2X systems and induced semiconductivity. (a) Mn2N remains strongly FM regardless of asymmetric functionalization, as predicted by the arrangement of electrons on the Mn atoms in the top and bottom layers. Semitransparent, dotted arrows indicate half-integer spin up electrons. (b, c) Non-magnetic, pure O terminated Ti2C and weakly AFM V2C become robustly AFM under all considered mixtures of O and F termination. (d) Band structure of semiconducting, FM Mn2NOF(3). (e, f) Band structures of semiconducting, AFM Ti2COF(3) and V2COF(3). The isosurface values for the spin density plots of Janus Mn2N, Ti2C, and V2C are 0.09, 0.01, and 0.03 𝜇𝐵/Å3, respectively. We first performed exhaustive DFT calculations on the four model MXene systems listed above, considering the five mixed termination models for each MXene to determine how the mixed termination affects magnetic ordering. The calculations show that Mn2N has a robust FM ground state for all surface functionalization models. The large exchange splittings, EAFM1-FM and EAFM2FM

(from 407 to 1291 meV), are reported in Table 2. Correspondingly large per-atom magnetic

moments ~4 𝜇𝐵 (Table 2) were found in each model system. Rather than destroying the FM 8 ACS Paragon Plus Environment

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ordering of the pristine systems, the magnetic ordering is preserved and even enhanced under asymmetric surface functionalization. These results are rationalized within the framework of our model for predicting magnetic ordering in MXenes. The details of this model can be found in Refs.23,27. Here, we extend the model to explain the magnetic behavior of Janus MXenes. Briefly, the origin of the ground state magnetic orderings is understood by first assuming nominal oxidation states of all constituent X and T atoms (C4-, N3-, O2-, and F-), and an approximately octahedral crystal field acting on the transition metal atoms by the surrounding X and T atoms. The crystal field breaks the d-orbital degeneracy into low energy t2g (dxy, dyz, and dxz) and higher energy eg (dx2-y2 and dz2) orbitals. We then determine the d-band fillings by simply counting the electrons left to each transition metal atom after the X and T atom oxidation. The resulting magnetic ordering is determined by the d-band filling configurations and the Goodenough-Kanamori rules. Partially (fully) filled t2g or eg bands favor FM (AFM) ordering to maximize hopping between transition metal atoms. There are slight distortions in the octahedral crystal fields for M atoms with M-T and M-T’ bonds, but this does not affect the overall validity of predictions based on the t2g-eg orbital analysis.27 As an illustrative example, we consider Mn2NOF(3). In this unit cell, all the top layer Mn atoms are bonded to three N and three O atoms. The Mn donates 2/3 of an electron to each O atom, and 1/2 of an electron to each N atom. Three electrons occupy the low-lying t2g orbitals, while any remaining electrons are forced into the eg. On the bottom layer, each Mn is bonded to three N and three F atoms. The Mn again donates 1/2 of an electron to each N atom, and 1/3 of an electron to each F. Between both Mn atoms in the unit cell, 6 electrons in total are donated, resulting in either two Mn3+ oxidation states, or an Mn4+/Mn2+ pair if one of the unpaired electrons preferentially localizes on one of the Mn atoms. In the former case, the eg level is partially filled in both layers,


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and there is an average local magnetic moment of 4 𝜇𝐵 per Mn atom. The partial filling promotes hopping of the majority spins and favors FM ordering, which is consistent with the DFT results. The electron filling diagrams for all Mn2N models (Figure 2a) show that the model predicts partial filling in the eg band of both layers regardless of surface termination, and the same reasoning can be applied to see that all the systems remains FM. Indeed, the predicted average magnetic moments per Mn atom of 4, 4, 4, 4.25, and 3.75 𝜇𝐵 for the OF(3), OF(21), OF(2), O0.5F1.5, and O1.5F0.5 configurations, respectively, agree with the DFT calculated per-atom magnetic moments (Table 2) to within 0.1 𝜇𝐵 for all surface termination models. Next, we repeat this treatment for Janus Cr2C, Ti2C, and V2C and find a trend of preferred AFM ordering that can be explained by understanding the competing exchange mechanisms in the Janus structures. As an example, we examine in detail the Cr2COF(2) model. DFT calculations show that the system has an AFM2 ground state, however, the crystal field model predicts partially occupied eg bands in both layers, which should lead to FM ordering. The calculated magnetic ground states for all carbide MXene mixed termination models similarly have AFM ordering (Table S1). This effect can be explained by the presence of carbon instead of nitrogen, and the AFM superexchange between interlayer Cr atoms, mediated by carbon. Generally, FM ordering is more robust in the nitrides because of the extra electron introduced by nitrogen compared to carbon, which leads to higher magnetic moments.23 Additionally, along the 180° Cr-C-Cr bond, the Cr atoms are indirectly coupled through the non-magnetic C atom, favoring an AFM exchange between the Cr atoms to avoid flipping spin orientations and maximize hopping. When the bond angle is closer to 90°, as in the intralayer Cr-C-Cr bonds, there is a competing FM superexchange. Because of the mixed transition metal oxidation states, some AFM configurations may exhibit weak ferrimagnetism (Table S2) rather than true antiferromagnetism. For example, Cr2CO1.5F0.5


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has an AFM1 spin configuration, but the unequal O and F compositions result in a net magnetization of 0.12 𝝁𝑩/atom. In other cases, e.g. the AFM1 Ti2COF(3) ground state, the spins within each layer are antiparallel (intralayer AFM ordering) and the oxidation states are the same within each layer, so the net magnetization is zero. The strength of these AFM interactions can be probed directly by straining the structure along the z-axis to extend the 180° Cr-C-Cr bond, reducing the AFM superexchange.31 As the outof-plane strain increases, both the AFM superexchange and the FM superexchange across the 90° Cr-C-Cr bond decrease. This first causes the exchange splitting EAFM1-FM to increase, as the FM superexchange contribution decreases more rapidly, but at sufficient strain (14%) the interlayer separation is large enough that the AFM superexchange no longer dominates, and the system recovers the expected FM ground state (Figure S1). Similarly, the model predictions for Ti2C and V2C must account for the strong AFM superexchange interactions in these systems. Ti2C and V2C are particularly interesting because they have already been synthesized, and bare Ti2C and V2C have been predicted to be magnetic.32,33 However, magnetic ordering is destroyed in Ti2C by oxygen functionalization,32 and V2C is AFM,33 but this state may be unstable because of the small exchange splittings and per-atom magnetic moments.21 Here we show that the asymmetry of Janus functionalization introduces free unpaired electrons into these systems and robust magnetic ordering is recovered (Figure 2b,c). Calculated exchange parameters for V2C are listed in Table 2 and discussed below. FM ordering is unstable for all mixed O and F terminations (Janus models) of Ti2C, so the exchange parameters are omitted.


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Figure 3. Scatter plot showing the diversity of transport (semiconducting (SC), half-metallic (HM), and metallic (M)) and magnetic behavior available in Janus MXenes. The density of states of a representative half-metallic antiferromagnet is shown in the inset. Some representative compounds are highlighted. Apart from the variety of magnetic ordering that can be achieved with mixed functionalization, the asymmetry also induces a range of transport behavior. In Mn2N MXene with OF(2) and O0.5F1.5 terminations, the local magnetic exchange field induced by the local magnetic moments is sufficiently strong to gap the majority and minority spin bands, causing FM halfmetallicity, as predicted in the Mn2N MXenes with pure surface termination.23 In many of the carbide structures, although there is no net magnetic moment (or weak ferrimagnetism), the mixed termination causes a symmetry breaking and two distinct sublattices with an exchange splitting between the spin channels. The result is either a half-metallic ferrimagnet or an HMAFM in the case of vanishing net magnetization, which is highly desirable (but difficult to construct) for spintronic applications requiring fully spin-polarized current without magnetic fields.34 Even more elusive are semiconducting FM and AFM states; the band structures of the OF(3) models of Mn2N, 12 ACS Paragon Plus Environment

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Ti2C, and V2C in Figure 2d-f show such behavior in the Janus systems. This rich diversity in physical properties is shown in Figure 3, where each point represents a Janus MXene and select examples are highlighted. The transport behavior of each MXene is listed in Table S3. The stability of the observed magnetic behavior was investigated by computing the magnetic exchange constants for each system and performing Monte Carlo simulations to estimate the corresponding critical temperatures. The Ising Hamiltonian with nearest (intralayer) and nextnearest (interlayer) neighbor interactions is given by 𝐻 = ― ∑𝑖,𝑗𝐽1𝜇𝑖𝜇𝑗 ― ∑𝑖,𝑘𝐽2𝜇𝑖𝜇𝑘, where 𝐽1 and 𝐽2 are the interlayer and intralayer exchange parameters, respectively. Mapping the various magnetic orderings to this Hamiltonian and solving for 𝐽1 and 𝐽2 from the DFT-computed exchange splittings, we obtain the parameters; the values for Mn2N, Cr2C, and V2C are listed in Table 2. FM ordering is unstable for all configurations of Ti2C, so exchange parameters are not reported. These values are only a mean field approximation, and the mixed oxidation states have the effect of modifying the 𝐽𝑖𝑗𝜇𝑖𝜇𝑗 terms, such that the local magnetic moments are spatially varying. To simplify the calculations and emphasize the underlying magnetic behavior, we have taken 𝜇 to be the average spin state in each system, ignoring local variation in the magnetic moments.17,35 For all Mn2N mixed termination models, both exchange parameters are positive and between 2 and 6 meV, indicating strong FM interlayer and intralayer coupling. This is reflected in the computed Curie temperatures, which range from 162 K to above room temperature. Still, the Curie temperatures are significantly suppressed compared to the structures with pure termination, and the computed Néel temperatures of AFM Janus MXenes are similarly suppressed. Because all synthesized MXenes have disordered surface functionalization, this may explain why magnetic ordering has not yet been observed in these systems in room temperature experiments.25


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Table 2. Exchange parameters, Curie (TC) temperatures for Mn2N, and Néel (TN) temperatures for Cr2C and V2C. J and TC values in parentheses are obtained with an applied electric field of 1.0 V/nm. All energies are in meV. Mn2N OF(3) (2 ) OF 1 OF(2) O0.5F1.5 O1.5F0.5 Cr2C OF(3) (2 ) OF 1 OF(2) O0.5F1.5 O1.5F0.5 V2C OF(3) (2 ) OF 1 OF(2) O0.5F1.5 O1.5F0.5

EAFM1EFM 714.2 714.0 1290.9 880.7 648.9

EAFM2EFM 651.3 406.6 1121.7 673.3 682.7

J1

J2

𝝁𝑩/atom

TC/TN

3.49 (4.38) 2.18 (2.19) 5.98 (6.86) 3.23 (37.1) 4.11 (2.46)

2.00 (2.13) 2.33 (6.79) 3.67 (3.84) 2.36 (3.04) 1.90 (-2.3)

3.94 3.94 3.95 4.17 3.72

173 (196) 163 (377) 310 (335) 187 (843) 180

-131.5 -1.7 -164.1 -146.6 -2536.0

-316.8 -6.5 -129.8 -410.4 -2472.7

-2.56 -0.06 -1.12 -3.15 -22.39

-0.16 0.00 -0.78 -0.06 -11.63

3.21 2.90 3.10 3.29 3.03

65 4 23 86 335

-369.6 -400.0 -255.1 285.2 -84.1

730.7 -546.1 -270.9 -69.6 -256.3

22.52 -16.92 -8.48 -1.64 -9.08

-14.17 -5.06 -3.87 5.46 0.04

1.64 1.64 1.63 1.88 1.53

347 62 128 83 281

The suppression of both FM ordering and critical temperature with mixed termination seems to suggest that observing 2D magnetism in MXenes will require careful control of surface chemistry. High-temperature annealing can be used to cause full desorption of OH and partial F desorption, but currently there are no available methods for creating pristine MXene surfaces with a single surface termination or avoiding surface termination altogether. This motivates the search for a different method, one that takes advantage of local disorder, requiring only the degree of control of surface termination that can be achieved with annealing. One such avenue is highlighted by the fact that out-of-plane stress reduces AFM superexchange and promote FM ordering, as discussed above. Although mechanically-induced out-of-plane strain may be difficult to apply experimentally, its theoretical utility in switching nanoscale magnetic states encourages us to pursue analogous means of external magnetic control. 14 ACS Paragon Plus Environment

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In the Janus systems there is a surface dipole moment induced by the charge asymmetry and finite separation of the M atom layers. To achieve an out-of-plane strain effect, we couple the surface dipole to an external electric field, which causes charge redistribution and changes bond lengths, effectively tuning the strength of the magnetic exchange interactions in the system. We relax each structure and compute the changes in bond lengths and energy for each magnetic phase while applying small fields between 0.1 and 1.0 V/nm. Calculating the zone centered (Γ-point) phonon frequencies as a function of electric field for Mn2NOF(3) and Cr2CO1.5F0.5 (Table S4), we find no negative frequencies, confirming the dynamical stability of the structures under an applied field. In the simplest case, applying a small electric field of the order 1.0 V/nm to Janus Mn2N further destabilizes the AFM phases and increases the exchange splitting, commensurate with the asymmetry present in the system. The exchange parameters and TC values under an applied field are given in parentheses in Table 2. Strong coupling in the OF(21) and O0.5F1.5 configurations leads to TC values enhanced from below room temperature (163 and 187 K) to well above room temperature (377 and 843 K). These results indicate that robust FM states can be achieved in Mn2N via electrostatic gating without requiring pristinely terminated surfaces. Beyond stabilizing 2D magnetic ordering, electric fields can be used to rapidly switch between magnetic states. There has been recent success in using applied electric fields for magnetic switching of bilayer CrI3, which is AFM in bilayer form,36 back to the FM state observed in the monolayer.5 In an analogous manner to the electrostatic gating that induces FM coupling in bilayer CrI3, small electric fields enable magnetic switching of AFM Cr2COxF2-x. Extremely small fields, below 1.0 V/nm, were sufficient to induce an FM ground state (Figure 4a) by altering the 180° CrC-Cr bonds and reducing the AFM superexchange.


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Figure 4. Electrical control of magnetic ordering in Cr2CO1.5F0.5. a) An applied electric field increases the Cr-C-Cr bond length, b, reduces AFM superexchange, and causes a transition from AFM to FM phase. The out-of-plane deformation is exaggerated for visual clarity to emphasize the structural change. b) Linear relationship between strain and dipole moment (eÅ) and electric field (V/nm). c) PDOS before (left) and after (right) application of an electric field.


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To explain the origins of the magnetic stabilization and switching, we propose a simple macroscopic model and microscopic understanding from analyzing the electronic structures. As the field strength is increased, we compute the change in the M-X-M bond length (strain) and the corresponding change in the dipole moment. Figure 4b shows the relationship between induced strain and dipole moment as a function of applied electric field in Cr2CO1.5F0.5. Over the whole range of applied electric fields, between 0.1 and 1.0 V/nm, the structure transitions from an AFM ground state to FM. The strain is measured compared to the zero-field relaxed ground state, and the surface dipole moment is estimated by multiplying the interlayer separation by the interlayer charge difference (obtained from Bader charge analysis). In the O1.5F0.5 structure there is significant charge separation because of the mixed average oxidation states in the upper layer (Cr3.5+) and the bottom layer (Cr4+), and the commensurate strain-electric field coupling is strong. The linear relationships in Figure 4b can be easily understood in a simple macroscopic picture. We consider the strain energy corresponding to the dipole potential energy and assume that the dipole moment increases linearly with strain under small fields. The strain energy and 1

dipole potential energy are 2𝜇𝜀2 and 𝛽𝑝 ⋅ 𝐸, respectively, where 𝜇 and 𝛽 are constants, 𝜀 is the strain, 𝑝 is the strain-dependent dipole moment, and 𝐸 is the electric field. The change in the dipole moment with strain leads to 𝑝 ⋅ 𝐸 = (𝑝0 + 𝜒𝜀)𝐸, where 𝜒 is a constant and 𝑝0 is the magnitude of the zero-field dipole moment. Equating the strain energy and dipole potential energy and ignoring trivial constants then gives 𝜀~

2𝜒𝛽 𝜇

and we define the coefficient 𝛼 =

𝐸 for small fields and correspondingly small strains (𝜀 < 2%),

2𝜒𝛽 𝜇

. This macroscopic picture describes the induced strain under

applied fields, and fitting the DFT data to this model (blue dashed line in Figure 4b) gives 𝛼 = 1.12 nm/V for Cr2CO1.5F0.5. The magnitude of 𝛼 quantifies the degree of asymmetry in a system as a function of the electric field response. Additionally, plotting the dipole moment as a function 17 ACS Paragon Plus Environment

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of applied field (red triangles in Figure 4b) for the O1.5F0.5 configuration reaffirms that the assumption of linear behavior is valid for the small field strengths considered. Examining the electronic structure evolution with applied fields provides a deeper, microscopic understanding of the magnetic state switching. Because of the broken inversion symmetry and intrinsic charge asymmetry in the Janus MXenes, the out-of-plane external field causes further charge redistribution, raising the energy of the dz2 orbitals and weakening the bonds. The applied potentials on both sides of the monolayer tune the energy of the highly localized d states and the resulting bond elongation weakens AFM superexchange, driving the AFM to FM transition. Just as in the intrinsically FM MXenes, the induced FM transition leads to a strong magnetic exchange field that promotes exchange splitting between the majority and minority bands and half-metallic transport. The shift in the d state energies and the resultant half-metallicity can be seen in the partial density of states (PDOS) before (Figure 4c, left) and after (Figure 4c, right) applying an electric field. Because of the generality of this result, we expect this strategy can be used for electrical control of magnetism in any asymmetric magnetic MXene. Further, electric fields can be combined with in-plane stress21,37 to achieve even finer control of magnetic ordering and to enhance local magnetic moments. Practical electrical control of magnetic ordering is not the only advantage inherent to magnetic Janus MXenes. We have previously shown that tuning electron localization through pure surface terminations in Mn2N can promote robust Ising ferromagnetism or introduce a noncollinear XY spin structure.22 Since the SOC and electron localization that govern noncollinear magnetism can be controlled to produce strong magnetic anisotropy in pristine MXene systems, it is of great interest to consider the effects of asymmetric functionalization on the anisotropy, which enables long-range magnetic ordering at finite temperatures in 2D.7 In pristine Mn2NO2, the magnetic


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anisotropy energy (MAE) is greater than 60 𝜇eV/atom, while pristine Mn2NF2 has MAE less than 2 𝜇eV/atom and no in-plane MAE, resulting in a continuous XY spin symmetry and no out-ofplane Ising ferromagnetism. In a realistic experimental setting then, the mixture of F and O surface functionalization might be expected to destroy long-range order. However, there is also structural symmetry breaking that may contribute to anisotropy. Surprisingly, we find that for all mixed termination models, Mn2N remains a strong Ising ferromagnet with an out-of-plane easy axis, robust to both thermal and chemical disorder. We performed DFT calculations with SOC to calculate the total energies for each structure with the spin quantization axis along the high symmetry directions: out-of-plane (001), in-plane (100), (110), and (010), and canted out-of-plane (111). After confirming that the (001) direction is the easy axis for all structures (Table S5), we then calculated the MAE between the (001) direction and in-plane directions, sampling the entire xy plane from 0° to 360° at intervals of 12°. The MAE between the (001) direction and an in-plane orientation (xy0) at an angle 𝜙 is given by 𝐸(𝑆𝑥𝑦0) ―𝐸

(𝑆001). The MAE as a function of 𝜙 is plotted for each Mn2N model in Figure 5.


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Figure 5. MAE (𝜇eV/atom) as a function of in-plane angle 𝜙 (degrees) for mixed termination models of Mn2N. Starting from the O1.5F0.5 configuration (Figure 5, yellow points), which has 75% O and 25% F termination, we see that the MAE is in fact not at all reduced by the presence of F termination. It remains above 60 𝜇eV/atom, as in the case of pure O termination, suggesting that the structural asymmetry compensates for the increased electron localization (isotropic bonding) from the F termination. When the compositions are switched to 25% O and 75% F as in the O0.5F1.5 model (purple points), the MAE is reduced to between 20 and 40 𝜇eV/atom, but the presence of O ensures that the MAE is still an order of magnitude larger than that of pristine F terminated Mn2N. The substantial 𝜙 dependence of the MAE can be understood by recognizing that the peaks occur at 30° and 210° (identical due to two-fold rotation symmetry), the orientations that align spins with the highly directional, covalent Mn-O bond. The 𝜙 dependence is similarly pronounced in 20 ACS Paragon Plus Environment

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structures with significant asymmetry in the xy plane, e.g. OF(21). At intermediary composition (50% O and 50% F) in models OF(3) and OF(2) (blue and red points), the MAE is between that of O0.5F1.5 and O1.5F0.5, and shows little to no angular dependence because of the in-plane symmetry of these structures. The OF(21) model, despite having the same 1:1 composition, exhibits stronger anisotropy than even the pure O terminated structure. It reaches values above 100 𝜇eV/atom and the two-fold rotation symmetry is strongly apparent in the angular variation of the MAE. This is because the OF(21) configuration uniquely breaks the structural symmetry, distorting the Mn-NMn bond angle, introducing significant anisotropy. Two powerful conclusions can be drawn from these results: 1) Ising ferromagnetism persists with surface impurities, such that observable 2D magnetism is robust to both thermal and chemical disorder; and 2) rather than undermining the magnetic ordering, local disorder and induced structural symmetry breaking can be used to enhance the magnetic anisotropy. Conclusions In this work, we investigated with DFT calculations the effects of disordered surface termination on the magnetic properties of nitride and carbide MXenes. Ground state FM ordering is preserved in Janus Mn2N for all models of mixed termination, and Janus Cr2C, V2C, and Ti2C were found to be robustly AFM. Surprisingly, asymmetric surface functionalization also induces or stabilizes magnetic ground states in systems that are predicted to be non-magnetic or weakly magnetic in their pristine states. Janus MXenes exhibit a diverse range of magnetic and transport behavior, including semiconducting ferromagnets and half-metallic antiferromagnets. The predicted properties were rationalized within the framework of our crystal field model. Beyond their interesting intrinsic behavior, the structural, chemical, and charge asymmetries in Janus MXenes enable external control of their magnetic states. Small applied electric fields tune the


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magnetic exchange parameters to achieve both enhanced Curie temperatures and switching from AFM to FM states. Moreover, the enhanced bond directionality in Janus Mn2N promotes an Isinglike out-of-plane spin orientation and increased magnetic anisotropy compared to pristine Mn2NO2. This study provides insight into obtaining robust, electrically controllable nanoscale magnetism and strong anisotropy in MXenes with realistic surface functionalization. Methods DFT calculations used the Vienna Ab-Initio Simulation Package (VASP)38,39 with projector augmented wave (PAW)40 pseudopotentials and the Perdew-Burke-Ernzerhof (PBE)41 exchangecorrelation functional. Spin-orbit coupling was included in calculations of the magnetic anisotropy energies, and the spin-polarized DFT+U correction42,43 was applied to strongly correlated Ti, Cr, V, and Mn atoms with the typical U = 4 eV value. The specific U value does not change the predicted magnetic ordering, nor the easy axis determination.22,23 For determining the magnetic ground states, a plane-wave basis set energy cutoff of 400 eV was used, forces on each atom were converged to within 10-2 eV/Å, and total energy changes were converged to below 10-8 eV. A Γcentered k-point mesh of 9 x 18 x 1 was used. For calculations including spin-orbit coupling, the plane-wave energy cutoff was increased to 520 eV, the k-mesh was increased to 11 x 21 x 1, and the total energy convergence criteria was also set to 10-8 eV. Critical temperatures were computed using Monte Carlo simulations on a 40 x 40 bilayer-triangular lattice. Supporting Information Strain-induced magnetic switching in Cr2COF(2) in Figure S1, all calculated magnetic ground states in Table S1, net magnetic moments of ground states of Janus Cr2C, Ti2C, and V2C in Table S2, all calculated transport behavior in Table S3, lowest energy zone centered phonon frequencies of Mn2NOF(3) and Cr2CO1.5F0.5 as a function of applied electric field in Table S4, and MAE values


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for high symmetry directions of Mn2N models in Table S5. This material is available free of charge via the Internet at http://pubs.acs.org. Acknowledgments: This work is supported primarily by contract W911NF-16-1-0447 from the Army Research Office (V.B.S.) and also by grants EFMA-542879 and CMMI-1363203 (H.K.) from the U.S. National Science Foundation. N.C.F. was supported by the Department of Defense (DoD) through the National Defense Science & Engineering Graduate Fellowship (NDSEG) Program. B.A. and Y.G. acknowledge funding from the U.S. Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences, grant #DE-SC0018618. References (1)

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Surface-Engineered MXenes: Electric Field Control of Magnetism and

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