Tuning Noncollinear Spin Structure and Anisotropy in Ferromagnetic

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Tuning Noncollinear Spin Structure and Anisotropy in Ferromagnetic Nitride MXenes Nathan C. Frey, Hemant Kumar, Babak Anasori, Yury Gogotsi, and Vivek B. Shenoy ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.8b03472 • Publication Date (Web): 08 Jun 2018 Downloaded from http://pubs.acs.org on June 9, 2018

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Tuning Noncollinear Spin Structure and Anisotropy in Ferromagnetic Nitride MXenes Nathan C. Frey,† 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 Recent experimental success in the realization of two-dimensional magnetism has invigorated the search for low-dimensional material systems with tunable magnetic anisotropy that exhibit intrinsic long-range ferromagnetic order. Here we report that modifying the surface termination and transition metal in monolayer M2NTx nitride MXenes gives rise to a rich diversity of noncollinear spin structures and finely tunable magnetocrystalline anisotropy. Based on firstprinciples simulations, we predict that manipulating the strength of the spin-orbit interaction and electron localization via the chemical degrees of freedom can induce sufficient anisotropy to counteract thermal fluctuations that suppress long-range magnetic order. We find that Ti2NO2 and Mn2NF2 MXenes have continuous O(3) and O(2) spin symmetries, respectively, that may be broken by an applied field, while Cr2NO2 and Mn2NO2 are intrinsic Ising ferromagnets with outof-plane easy axes and magnetic anisotropy energies up to 63 eV/atom. These systems also exhibit both gapped and gapless Dirac points near the Fermi level. Our study suggests that nitride MXenes offer a promising avenue for achieving both practical spintronic devices and investigating fundamental spin processes in two-dimensional materials. KEYWORDS: 2D materials, MXenes, magnetic anisotropy, noncollinear magnetism, DFT, spintronics

Magnetism in two-dimensional (2D) materials has received increasing attention with the recent discoveries of Ising ferromagnetism in monolayer chromium triiodide,1 intrinsic longrange ferromagnetic order in atomic layers of Cr2Ge2Te6,2 and room-temperature ferromagnetism 2 ACS Paragon Plus Environment

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(FM) in VSe2 monolayers on van der Waals substrates.3 These recent successes have shown that in order to guide further experimental efforts, understanding how spin-orbit interactions govern magnetic behavior in 2D systems is essential. Noncollinear spin structures and spin anisotropy remain relatively unexplored in 2D materials, despite the potential applications of 2D magnetism in quantum computation, spintronics, magnetoelectrics and magneto-optics.4–9 In addition to exploiting the carrier spin degree of freedom in devices, the search for intrinsically magnetic 2D materials is also of fundamental interest in understanding the basic physics of spin processes. One promising candidate for achieving robust, tunable, intrinsic monolayer magnetism is the large family of 2D transition-metal carbides, nitrides, and carbonitrides, called MXenes. MXenes have the general formula Mn+1XnTx (M = early transition metal, X = C/N, T = O, OH, F, n = 1-3), and the many degrees of freedom available in transition metal atom, layer thickness, and surface functionalization enable fine-tuning of desirable magnetic properties and anisotropy.10–12 Bare MXenes (i.e., with no surface functionalization) like Cr2C and Mn2C, as well as some functionalized MXenes, have been predicted to be intrinsically magnetic.13–16 Recently, we developed a general framework to predict magnetic ground states in MXenes, and identified several promising nitride MXenes that exhibit intrinsic ferromagnetic ordering robust to surface termination and thermal fluctuations.17 However, long-range magnetic ordering at finite temperatures in two dimensions is, in principle, prohibited in systems with continuous spin symmetries due to divergent contributions from gapless spin waves.18 In order to lift the restriction on spontaneous symmetry breaking of a continuous spin symmetry, some amount of magnetic anisotropy is required. Therefore, to provide insight into the synthesis and characterization of magnetic MXenes, a thorough study of magnetic anisotropy is needed. Recent reports include calculated magnetic anisotropy energies (MAE) for the antiferromagnetic bare


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and ferromagnetic functionalized Mn2C MXene, finding values comparable to Fe or Co.14,19 While these studies illustrate the importance of investigating spin anisotropy in MXenes, a fundamental understanding and demonstration of fine-tuned control of noncollinear spin structures is still needed. In this paper, we investigate the impact of spin-orbit coupling (SOC) and electron localization via surface functionalization on the magnetic properties of nitride MXenes. While more than 20 carbide MXenes have been created experimentally,11 only a few 2D nitrides have been synthesized so far.20,21 Therefore, theoretical analysis and identification of nitrides with potentially interesting and important physical properties is needed to steer experimental efforts towards the most attractive nitride MXene compositions. We find that, owing to the diversity of available chemical compositions of nitride MXenes, any desired spin symmetry can be achieved. In particular, surface functionalization can induce a change from continuous O(2) spin symmetry in an XY ferromagnet to anisotropic Ising ferromagnetism, and increasing atomic number of the transition metal leads to a similarly pronounced transition from a continuous Heisenberg magnet to Ising ferromagnetism. We perform density functional theory (DFT) calculations with SOC to account for the effects of noncollinearity in the spin structures. In doing so, a trend in the evolution of spin anisotropy emerges that can be easily understood in terms of the strength of the spin-orbit interaction and the directionality of the surface termination bonding. We show how this understanding can then be exploited to modify the spin structure and tune the magnetic anisotropy. This tunability enables a wide variety of applications, from careful probing of fundamental spin behavior in XY and Heisenberg ferromagnets, to stable intrinsic Ising ferromagnetism for spintronics and magnetoelectronics.


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Results We investigate the effects of spin anisotropy in monolayer MXenes that we have predicted to be 2D ferromagnets with Curie temperatures above room temperature. FM ordering in 2D crystals is determined by magnetic anisotropy. In order to understand the nature of FM ordering in these materials, we consider the SOC induced changes to system energy as TM spins are rotated. Figure 1 shows the top (Figure 1a) and side (Figure 1b) views of the M2XT2 MXenes considered in this work. In the hexagonal unit cell, the high symmetry directions are along the inplane a (100) axis, b (010) axis, a + b (110) axis, and the out-of-plane c (001) axis and (111) axis. These directions are highlighted in the crystal systems in Figure 1.

Figure 1. Schematic of M2XT2 MXenes highlighting high-symmetry axes. (a) Top view of the crystal structure highlighting in-plane (100), (110), and (010) high-symmetry axes. (b) Side view highlighting out-of-plane (001) and (111) high-symmetry axes.

We first consider the surface functionalized nitride MXenes Mn2NT2 and Cr2NT2, which were previously reported to be intrinsic half-metals with robust ferromagnetism. Based on previous findings suggesting that O-functionalized MXenes generally exhibit the most robust magnetic ordering, compared to other common surface functionalizations F and OH, we anticipate that Mn2NO2 and Cr2NO2 are strong candidates in the search for Ising-like 2D ferromagnets. Figure 2a shows the angular dependence of the magnetocrystalline anisotropy


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energy of Mn2NO2, as the spin axis is rotated through the ac plane. The MAE is defined as the difference in energy between the system with a given spin orientation, ̂ (, ) (where is the azimuthal angle and is the polar angle), and the system with spins parallel to the magnetic easy-axis. The electron localization function (ELF) is also plotted to provide an illustration of the directionality of bonding. The easy-axis is found to be the out-of-plane (001) direction, and the energy of the system with spins oriented along this direction is set to zero. The MAE evolves in the characteristic way for an Ising ferromagnet, showing nearly perfect agreement when fit to the usual equation for the uniaxial anisotropy in a system with sixfold rotation symmetry,

= sin + sin

(1)

where and are system-dependent anisotropy constants, and is the azimuthal angle of rotation. Positive values of and indicate strong Ising-like ferromagnetism with an out-ofplane easy axis, whereas > 0 and < 0 suggests a weak tendency towards disorder. However, in general for the systems considered here,

≪ 1, and the higher-order contribution

is negligible. From fits of the angular dependence of the MAE, both and are found to be positive for Mn2NO2. Additionally, the dimensionless magnetic anisotropy parameter is calculated according to the definition =

∥ (! "! )

, where J1 and J2 are the interlayer (next

nearest-neighbor) and intralayer (nearest-neighbor) ferromagnetic exchange coupling constants, and #∥ and #$ are the energies with the spin quantization axis oriented parallel or perpendicular to the 2D plane of the MXene monolayer, respectively. These results are summarized in Table 1. The MAE reaches a maximum value of 63 μeV/TM at = 90°, corresponding to an in-plane spin orientation. Figure 2b illustrates the evolution of the MAE as the spin axis rotates through


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all space. Clearly, the MAE exhibits a strong dependence on the azimuthal angle , and a much weaker dependence on the polar angle . Similar angular dependence is seen in Figure S1a, in the OH-terminated Mn2N MXene, although the MAE is significantly lower: 1.3 μeV/TM. In addition to the reduced absolute value, the MAE shows a much stronger polar dependence in Mn2N(OH)2, as shown in Figure S1b. For this reason, the three-fold symmetry of the MAE is especially apparent for Mn2N(OH)2, although it is present in all of the Ising-like systems. While the maximum MAE is achieved in the in-plane a (100) direction, the MAE is reduced by 0.1 eV in the (110) orientation.

Figure 2. Magnetocrystalline anisotropy in the Ising ferromagnet Mn2NO2. (a) Angular dependence of the MAE of Mn2NO2 with the spin axis in the ac plane. The MAE is set to zero in the magnetic easy axis, which is the out-of-plane (001) direction. (b) Spherical plot indicating the increase in energy (lighter coloration and radial distance) due to rotating the spin axis away from the easy axis in Mn2NO2. (c) The electron localization function plotted at an isosurface value of 0.05.

Similarly, Cr2NO2 exhibits an out-of-plane easy axis and strong angular dependence of the MAE, characteristic of an Ising ferromagnet. Figure S1c shows the dependence of the MAE on the azimuthal angle, and the fit to Eq. 1. The maximum of the MAE is 22 μeV/TM, at = 90°. The anisotropy constants are such that > 0 and > 2 , consistent with an (001) easy axis. Figure S1d shows a trend for the MAE of Cr2NO2 similar to that for Mn2NO2, with a strong dependence and weak dependence. 7 ACS Paragon Plus Environment

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For the two strong Ising systems, Mn2NO2 and Cr2NO2, the anisotropy parameters are 2 ∗ 10 and 1 ∗ 10 , respectively. Meanwhile, of Mn2N(OH)2 is two orders of magnitude smaller, at 6 ∗ 104 . To estimate the Curie temperatures of these materials, we use the result obtained from Monte Carlo simulations22 for the anisotropic Heisenberg model with the Hamiltonian > >

5 = 26 ∑B;=C8(1 2 )9:;< :=< + :; := ? + :;@ :=@ A

(2)

where J is the magnetic exchange constant, is the previously defined anisotropy parameter, and >

the sum < DE > is over nearest-neighbor spins, G:GHF = (:;< , :; , :;@ ). This model incorporates finite exchange anisotropy for 0 < < 1, and the classical Ising model, or Heisenberg model, is recovered in the limit = 1, or = 0, respectively. This model does not uniquely represent finite magnetic anisotropy, but for small values of 0.001 < < 0.1, the estimated TC is found to be nearly identical whether magnetic anisotropy is incorporated via exchange anisotropy or uniaxial single-ion anisotropy. In agreement with previous findings that even small amounts of anisotropy can yield a stable FM ground state at non-zero temperature, we find a TC of 53 K and 67 K for Cr2NO2 and Mn2NO2, respectively. For Mn2N(OH)2, which has a of the order 10-5, the magnetic anisotropy is not sufficient to stabilize FM ordering against thermal fluctuations. We note that the Monte Carlo simulations referenced above assume a square lattice with four nearest neighbors and neglect next nearest-neighbor interactions, whereas in a single MXene flake transition-metal atoms form a bilayer-triangular lattice, with six (intralayer) nearest neighbors and three (interlayer) next-nearest neighbors. TC is underestimated here due to the larger number of nearest neighbors in the bilayer-triangular lattice, and neglecting the interlayer exchange coupling, which is also strongly ferromagnetic for all the systems considered here.


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However, we expect the estimates presented in Table 1 to be reasonable order of magnitude approximations and most importantly, the magnetic anisotropy is sufficient to result in a finite TC.

Table 1. Magnetic anisotropy energies defined as the energy difference with the spin quantization axis parallel and perpendicular to the magnetic easy axis, anisotropy constants, anisotropy exchange parameters, and Curie temperatures estimated from Monte Carlo results for the anisotropic Heisenberg and *XY models. MXene

MAE [IeV]

K1 [µeV]

K2 [µeV]

Gamma

Tc [K]

Mn2NO2

63

63

0.004

2 ∗ 10

67

Mn2N(OH)2

1.3

1.7

-0.05

6 ∗ 104

N/A

Mn2NF2

2.0

2.9

-1.4

8 ∗ 104

1148*

Cr2NO2

22

23

-0.05

1 ∗ 10

53

Ti2NO2

0.78

0.09

-0.03

N/A

N/A

Motivated by the prediction of intrinsic Ising-like ferromagnetism at finite temperature stabilized by anisotropic spin-orbit interactions in Mn2NO2, we next turn to exploiting the freedom in surface functionalization to tune the noncollinear spin behavior. In sharp contrast to the O-functionalized Mn2N, we find that upon F-termination, Mn2NF2 exhibits an easy magnetization plane, such that there is no energetic barrier to rotation of spins within the plane of the single-layer MXene sheet. Figure 3a shows the angular dependence of the MAE in Mn2NF2, which is zero in-plane ( = 90°), and reaches a maximum of 20 μeV/TM perpendicular to the plane. The heatmap in Figure 3b illustrates the in-plane MAE, which is zero for all polar angles in-plane, and is only weakly dependent on in the out-of-plane orientations. Based on the continuous O(2) spin symmetry in the plane, we conclude that there is no ferromagnetic order at


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finite-temperature in Mn2NF2, according to the Mermin-Wagner theorem which prohibits spontaneous

symmetry

breaking

in

systems

with

dimension

K

2.

Instead,

a

Berezinskii−Kosterlitz−Thouless (BKT) transition to a quasi-long-range ordered phase is allowed at low temperatures.

Figure 3. Magnetocrystalline anisotropy in the XY-like Mn2NF2 MXene. (a) Angular dependence of the MAE of Mn2NF2. The MAE is zero for all in-plane orientations. (b) Heat map of the spherical in-plane polar () and out-of-plane azimuthal () dependence of the MAE. (c) The electron localization function plotted at an isosurface value of 0.05.

For the XY magnet Mn2NF2, the critical temperature of the BKT transition can be estimated according to the well-known result from Monte Carlo simulations of the XY model,23,24 which gives LM =

N.OP OQR

(#ST 2 #UST )

(3)

where VW is Boltzmann’s constant, and #ST and #UST are the energies of the collinear FM and antiferromagnetic (AFM) configurations, respectively. The energy difference is #ST 2 #UST = 889.3 meV/TM, which yields an estimated TC for the BKT transition of 1148 K. Next, we investigate the predicted ferromagnetic half-metal with the lightest transition metal atom, Ti2NO2. Based on the strength of the spin-orbit interaction going as Y , where Z is the atomic number of the M atom, we expect that SOI-induced anisotropy will be weakest for


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MXenes with M = Ti. Indeed, Figure 4 illustrates the very nearly uniform MAE, which is almost independent of spin orientation. Setting the in-plane orientations to zero, the MAE reaches a maximum of only 0.78 μeV/TM when the spin axis is perpendicular to the plane. This value is one to two orders of magnitude smaller than that for conventional 3D ferromagnets,25 and nearly two orders of magnitude smaller than the values reported above for the Ising-like FM systems. Interestingly, collinear AFM states are unstable for Ti2NO2; the optimized structure relaxes only to FM ordering, so it is not possible to estimate the anisotropy parameter, or TC, though it is certainly very near to zero, due to the almost nonexistent magnetocrystalline anisotropy. We conclude that Ti2NO2 is best described as a 2D Heisenberg magnet, where a magnetic easy axis could be preferentially selected via the application of an external magnetic field. In particular, an applied field can open a spin-wave excitation gap and be used to fine tune the transition temperature, as recently observed in experiments on atomic layers of Cr2Ge2Te6.2

Figure 4. Magnetocrystalline anisotropy in the Heisenberg-like Ti2NO2 MXene. Lighter coloration and radial distance indicate increase in MAE. The MAE is less than 1 μeV/TM for all spin orientations.

Having shown the rich variety of spin-orbit coupling induced behavior available in single flake MXenes through manipulating the M, X, and T degrees of freedom, we next provide a simple physical picture to explain these results. To understand the observed trends in


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magnetocrystalline anisotropy, it is sufficient to consider the size of the transition metal atom, and the directionality of bonding due to surface functionalization.

Figure 5. Schematic of spin symmetries accessible via tuning of spin-orbit interaction and electron localization. Increasing the TM atomic number increases the spin-orbit interaction, while increasing the electronegativity of the surface termination group increases the electron localization.

The most dominant effect is, of course, the strength of the spin-orbit interaction. The clear trend of increasing MAE in Ti2NO2, Cr2NO2, and Mn2NO2 follows from the increasing atomic number of the transition metal Z = 22, 24, and 25, respectively. The z-components of the spin and orbital moments for the M atoms of each system with the spin axis oriented along the zdirection are reported in Table S1. Due to the octahedral symmetry which lifts the d-orbital degeneracy, the orbital moments are nearly completely quenched in all cases (Table S1), indicating that the dominant contribution to the MAE is exchange anisotropy rather than single12 ACS Paragon Plus Environment

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ion anisotropy. The SOC contribution to the total energies of each system also decreases from 7.0 meV/unit cell to 5.2 meV/unit cell and 4.5 meV/unit cell for Mn2NO2, Cr2NO2, and Ti2NO2, respectively (Table S1). As expected, the heavier M atoms induce a stronger SOC effect. Further tuning of the spin anisotropy can be achieved via the surface functionalization. The three most common surface terminations introduced during MXene synthesis, in increasing order of electronegativity, are O, OH, and F. The increased localization of electrons introduced by OHand F-termination (seen in the ELF plotted for Mn2NF2 in Figure 3c), which involves bonding of higher ionic character, decreases the anisotropy and decreases the MAE. Conversely, diminished electron localization in O-terminated MXenes (seen in the ELF plotted for Mn2NO2 in Figure 2c), caused by highly directional covalent bonding, increases the anisotropy, as seen in the trend of Mn2NT2 (T = O, OH, F) from a robust Ising ferromagnet (MAE > 10 μeV/TM) to a weak one (MAE ~ 1 μeV/TM), and finally an XY magnet. This effect is clearly illustrated in the siteprojected density of states (DOS) with SOC shown in Figure S3. In the strongly Ising-like Mn2NO2 and Cr2NO2 systems, there is substantial overlap between the M atom d orbitals and the O atom p orbitals, particularly the pZ orbital, near the Fermi level, indicating the covalent, anisotropic nature of the bonding. In contrast, the more isotropic Mn2N(OH)2 and Mn2NF2 systems show a negligible contribution to the DOS near the Fermi level from the O and F atom orbitals. We further examine the effects of electron localization by systematically calculating the magnetic moment per atom and the MAE between the (001) out-of-plane easy-axis and the (100) in-plane direction as a function of the Hubbard U parameter for the Ising-like Mn2NO2 MXene. As the U parameter is increased from 0 eV to 7 eV, the electron localization increases and the magnetic moment monotonically increases from 2.4 W to 4.2 W (Figure S4). Consistent with the picture presented above, over the same U parameter interval the MAE monotonically


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decreases (Figure S4) from 216 eV/atom to 15.4 eV/atom, as the electrons become increasingly localized.

Figure 6. Electronic band structure with spin-orbit coupling, showing the appearance of Dirac points near the Fermi level in (a) Cr2NO2, (b) Mn2N(OH)2, and (c) Mn2NF2.


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Finally, we consider the possibility of SOC-induced nontrivial band topology in these ferromagnetic MXenes. There have been multiple reports of Dirac points and nontrivial band topology in calculated band structures of single flake MXenes,26–29 although there has been no experimental verification as of yet. Due to the inversion symmetry present in these monolayer MXenes, we expect conical bands may appear both at high-symmetry points and accidental points in the Brillouin zone.30 Here, we show the presence of both gapped and gapless Dirac points near the Fermi level in Cr2NO2, Mn2N(OH)2, and Mn2NF2 (Figure 6). Band structures with spin-orbit coupling are shown for the other MXenes in Figure S2. As expected, there are essential Dirac points at the high-symmetry K points in the hexagonal Brillouin zone. We also find bands with linear dispersion at low-symmetry points along the high-symmetry [ 2 \ 2 2 [ line. These points exist below the Fermi level, but the chemical potential may be modified by doping or applying an electric field.

Conclusions In summary, we have shown that the diversity of chemical compositions in nitride MXenes allows for fine-tuning of the spin-orbit interaction and bond directionality to achieve tunable magnetic anisotropy and any desired spin symmetry. Ti2NO2 was predicted to be a 2D isotropic Heisenberg magnet with continuous O(3) spin symmetry, with magnetic anisotropy less than 1 eV/TM for all spin orientations. F-functionalized Mn2N has no in-plane anisotropy, but does possess appreciable out-of-plane anisotropy, yielding an XY system expected to have a BKT transition to a quasi-long-range ordered configuration. Mn2NO2, Mn2N(OH)2, and Cr2NO2 are 2D Ising ferromagnets, due to the interplay of sufficiently strong spin-orbit coupling and bond anisotropy. Furthermore, we estimate the transition temperatures based on established


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results from Monte Carlo simulations for the XY model and the anisotropic Heisenberg model. We also show the existence of both gapped and gapless Dirac points below the Fermi level in these systems, where the gaps and Fermi level may be tuned via applied strain and a gate voltage, respectively. This study elucidates the nature of noncollinear spin structures in nitride MXenes, a promising family of magnetic 2D materials, and provides insight into tuning magnetic anisotropy in 2D systems for practical device applications.

Methods Our DFT calculations were performed with the Vienna Ab-Initio Simulation Package (VASP).31,32 Projector augmented wave (PAW) pseudopotentials33 were used with an energy cutoff of 520 eV for plane-wave expansions. The Perdew-Burke-Ernzerhof (PBE) generalized gradient

approximation

(GGA)

to

the

exchange-correlation

functional

was

used.34

Magnetocrystalline anisotropy energies were calculated by including spin-orbit coupling. To account for the strongly-correlated Ti, Cr, and Mn transition metals, all electronic structure calculations and geometry relaxations were done with the spin polarized DFT+U correction.35,36 A U value of 4 eV was used for Ti, Cr, and Mn, as is typical in the literature, for the on-site Coulombic repulsion. U values from 0 eV to 7 eV were used to evaluate the MAE for Mn2NO2 (Figure S4), confirming that the system remains an Ising-like ferromagnet with an out-of-plane easy axis for all values of U. A Γ-centered k-point mesh of 10 x 10 x 1 in the first Brillouin zone was used for structural relaxations of the unit cell. Atomic positions within unit cells and supercells were optimized to within 0.01 eV/ Å force on each atom, and total energy changes were converged to within 10-6 eV. For all static electronic structure calculations including spinorbit interactions, the Γ-centered k-point mesh was increased to 21 x 21 x 1 and total energy


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changes were converged to within 10-8 eV to ensure accurate calculations of the MAE on the order of μeV. We compute the anisotropy parameter, , considering both intralayer (nearestneighbor) and interlayer (next nearest-neighbor) coupling, as the coupling constants were previously shown to be of the same order of magnitude in these nitride MXene systems.17 Computing by averaging the coupling constants, or neglecting next nearest-neighbor coupling, does not significantly change the results for the strong Ising-like systems, and therefore the estimated TC values remain the same order of magnitude, regardless of the definition of . 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. Supporting Information. Magnetic anisotropy of the Ising-like Mn2N(OH)2 and Cr2NO2 MXenes in Figure S1, band structures with SOC of Mn2NO2 and (b) Ti2NO2 in Figure S2, site-projected DOS for all simulated MXenes in Figure S3, variation of MAE with varying U parameter for Mn2NO2 in Figure S4, spin and orbital moments and SOC energies in Table S1. This material is available free of charge via the Internet at http://pubs.acs.org. References (1)

Huang, B.; Clark, G.; Navarro-Moratalla, E.; Klein, D. R.; Cheng, R.; Seyler, K. L.; Zhong, D.; Schmidgall, E.; McGuire, M. A.; Cobden, D. H.; Yao, W.; Xiao, D.; Jarillo-


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