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Letter

Rational Design of 2-Dimensional Metallic and Semiconducting Spintronic Materials Based on Ordered Double-Transition-Metal MXenes Liang Dong, Hemant Kumar, Babak Anasori, Yury Gogotsi, and Vivek B. Shenoy J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.6b02751 • Publication Date (Web): 30 Dec 2016 Downloaded from http://pubs.acs.org on December 31, 2016

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The Journal of Physical Chemistry Letters

Rational Design of 2-Dimensional Metallic and Semiconducting Spintronic Materials Based on Ordered Double-Transition-Metal MXenes Liang Dong†, 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 & Engineering, and A.J. Drexel Nanomaterials Institute, Drexel University, Philadelphia, Pennsylvania 19104, USA

* Corresponding Author, Email: [email protected]

Abstract 2-Dimensional materials that display robust ferromagnetism have been pursued intensively for nanoscale spintronic applications, but suitable candidates have not been identified. Here we present theoretical predictions on the design of ordered double-transition-metal MXene structures to achieve such a goal. Based on the analysis of electron filling in transition metal cations and first principles simulations, we demonstrate robust ferromagnetism in Ti2MnC2Tx monolayers regardless of the surface terminations (T=O, OH, and F), as well as in Hf2MnC2O2 and Hf2VC2O2 monolayers. The high magnetic moments (3-4 µB/unit cell) and high Curie temperatures (495 K-1133 K) of these MXenes are superior to those of existing 2D ferromagnetic materials. Furthermore, semimetal to semiconductor and ferromagnetic to antiferromagnetic phase transitions are predicted to occur in these materials in the presence of small or moderate tensile in-plane strains (0-3 %), which can be externally applied by mechanically or internally induced by the choice of transition metals.

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2-Dimensional (2D) ferromagnetic materials have been actively sought out since the discovery of graphene, as their spin-dependent transport properties are very attractive for nanoscale memory and transistor devices.1-3 When these materials are coupled to other 2D or 3D materials (such as topological insulators), novel applications in quantum computing and spintronics can be achieved.3-5 Previous research efforts on 2D ferromagnetic materials have been mainly focused on graphene and transition metal dichalcogenides (TMDs). Experimentally identified ferromagnetic 2D materials include stretched graphene nanobubbles (pseudo– magnetic),6 graphene with point defects (adatoms and vacancies),7-8 and zig-zag edges at the grain boundaries of TMD nanosheets,9 wherein ferromagnetism originates from the unsaturated p orbitals. These materials, however, suffer from severe problems such as poor carrier transport (because of the presence of defects) and the lack of a stable long-range magnetic order at room temperature (since pristine graphene and TMDs are not spin polarized). Therefore, high-crystalquality large-area 2D ferromagnetic materials are highly desired for device applications. Fortunately, novel types of layered materials are emerging in recent years, providing new opportunities to realize this goal. This is the topic of this Letter, where we present a theoretical study on the rational design of 2D MXene monolayers to achieve robust ferromagnetism and tunable transport properties (transitions between metallic and semiconducting states). MXenes are 2D transitional metal carbides and nitrides with a general formula Mn+1XnTx, where M, X and T represent the transition metal element(s), carbon and/or nitrogen, and surface termination groups (mostly O, OH, and F), respectively, and n=1, 2, or 3.10 These materials have been of great interest primarily due to their great potential in energy storage applications such as Li-ion batteries11-13 and supercapacitors,14 as well as electromagnetic interference shielding,15 optics and plasmonics.16 There have been many types of MXenes with a single M element (M=Ti,



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V, Zr, Nb, and Ta, etc.) synthesized so far.10, 14, 17-19. Very recently, ordered double-transitionmetal MXene structures such as Mo2TiC2Tx, Mo2Ti2C3Tx, and Cr2TiC2Tx have been experimentally realized, and about twenty more are theoretically predicted.20-21 In these MXenes, one or two layers of a transition metal (e.g., Ti) are sandwiched between the layers of another one (e.g., Mo or Cr) in a 2D carbide structure. It is thus expected that many more doubletransition-metal MXenes will become available soon, whose electronic, magnetic, and chemical properties can be tuned by incorporating different transition metal elements. For example, –F and –OH terminated Mo2TiC2Tx has been found to be antiferromagnetic semiconductors.21 Although attempts have been made to design ferromagnetic materials,22-24 robust ferromagnetism that is not sensitive to the nature of the surface terminations has not been achieved. In this Letter, we first demonstrate a rational framework to predict magnetism in new ordered Ti2MnC2Tx, Hf2MnC2Tx, and Hf2VC2Tx (T=F, OH, and O) MXene monolayers. We then confirm, using density functional theory (DFT) calculations, that Ti2MnC2Tx monolayers possess ferromagnetic semi-metallic/metallic ground states regardless of the surface terminations (T=F, OH, and O), while Hf2MnC2O2 and Hf2VC2O2 monolayers are ferromagnetic semiconductors in their ground states. These MXene structures are intrinsically ferromagnetic without any chemical or structural modifications, and therefore can potentially be synthesized in crystalline state. Their estimated Curie temperatures are well above the room temperature, which is promising from the point of view of applications. Furthermore, small to moderate in-plane strains induce a semimetal to semiconductor transition in the ferromagnetic Ti2MnC2O2 monolayer, and a ferromagnetic to antiferromagnetic transition in Ti2MnC2(OH)2 and Ti2MnC2F2 monolayers. As such, we expect these MXene materials to play an important role in next generation spintronic devices.


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The crystal structures of Ti2MnC2Tx, Hf2MnC2Tx, and Hf2VC2Tx are shown in Fig. 1. In this monolayer, Ti/Hf atoms are in the outer layers, and Mn/V atoms reside in the middle layer. For each given MXene structure, we treat the O, OH, and F surface termination groups separately, and set x=2 as in the 100% termination case. In the ground state relaxed structure, each of the transition metal atoms is surrounded by six nearest-neighboring C and T atoms/groups, which almost form an octahedron. Therefore, their local chemical environment is close to the transition metal atoms in the octahedrally coordinated 1T phase of 2D TMDs.25 Here, we propose a simple analysis that counts the number of d electrons in the unit cell to qualitatively analyze the electronic structure of these MXenes around the Fermi level (EF). Let us take Ti2MnC2O2 as an example to explain this approach. First, we assume that each Ti or Mn atom contributes two 4s electrons and two 3d electrons to the surrounding C and O atoms, leaving all the elements in their nominal oxidation states, i.e., Ti4+, Mn4+, C4-, and O2- [Fig. 1(a)]. As a result, the bonding (σ) states between Ti4+/Mn4+ and C4-/O2- are filled, while the antibonding (σ*) states between them remain empty [Fig. 2(a)]. In other words, these states have little effect on the electronic or magnetic properties of the entire MXene structure. Therefore, the only energy states that need to be considered are the partially occupied non-bonding d orbitals of the transition metal ions, whose energies reside between the energies of the σ and σ* states. We note that such a simplified electronic band diagram was also applied to describe the electronic structure of the 1T phase of 2D TMDs.25 Next we consider the octahedral crystal field from the six C4- and O2- surrounding each Ti4+ and Mn4+, which breaks the d-orbital degeneracy under a trigonal-antiprismatic D3d symmetry and splits the d orbitals into two categories: the low lying , , and (t2g) states and the higher energy and (eg) states [Fig. 2(a)]. (Note that the z-direction here is 5 ACS Paragon Plus Environment


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defined as the long axis of the octahedron, which is tilted from the out-of-plane [0001] direction of the crystal.) The number of electrons at the t2g states plays a key role in the electronic and magnetic properties of Ti2MnC2O2. Since the electronic configurations of Ti4+ and Mn4+ are [Ar]3d0 and [Ar]3d3, respectively, no electrons occupy any t2g states of Ti4+ while three electrons half occupy each of the t2g states of Mn4+. Therefore, in the absence of spin polarization, EF of Ti2MnC2O2 penetrates the t2g states of Mn4+, leaving the entire system metallic. However, the spin alignment of the three Mn4+ d electrons can further reduce the ground state energy of this MXene, and give rise to a spontaneous magnetic moment of µ=3 µB/unit cell. Now we proceed to carry out DFT simulations to verify this analysis. Our DFT simulations are carried out using the Vienna ab-initio simulation package (VASP).26 Projector augmented wave pseudopotentials27 are used with a cutoff energy of 600 eV for plane-wave expansions. The exchange-correlation functional is treated within the Perdew–Burke–Ernzerhof (PBE) generalized gradient approximations (GGA).28 Considering the strong correlation effects in transition metals, the structural relaxations and electronic structure calculations are performed with spin polarized GGA+U calculations29 throughout the study. The on-site Coulomb term U for Ti, V, Mn, and Hf is chosen to be 4 eV,30 3 eV,31 4 eV,31 and 2 eV, respectively. For the MXene monolayers, a Γ-centered k-point mesh of 12×12×1 in the first Brillouin zone is found to yield well-converged results for the unit cell during the structural relaxations. A denser k-point mesh of 24×24×1 is used to calculate the energy and electronic structure of the unit cell. The ferromagnetic phase is simulated using a 2×1 supercell (Fig. S1 in Supporting Information), with a k-point mesh of 12×24×1 for the energy and electronic structure calculations. For the MXene structures we consider here, this supercell is equivalent to other commonly used 2×2 and 1×√3 supercells of the antiferromagnetic phase (see Sec. I in Supporting Information). The non6 ACS Paragon Plus Environment

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collinear antiferromagnetic phase is also considered using a √3×√3 supercell, but its energy is similar to the 2×1 antiferromagnetic phase (see Sec. I in Supporting Information). A 15 Å-thick vacuum space is found to be large enough to prevent any interactions between the adjacent periodic images of the monolayer. The atomic positions of the unit cells are optimized until all components of the forces on each atom are reduced to values below 0.01 eV/Å. The structural stability of these MXenes are confirmed by the fact that no negative frequencies appear in the phonon band structure calculated using the Phonopy package32 (Fig. S2 in Supporting Information). Our calculations also confirm that the fully ordered structures of these MXenes are energetically more stable than the alloy structures, i.e., with mixed Ti/Hf and Mn/V in the same atomic layer (see Fig. S3 in Supporting Information). The calculated partial density of states (DOS) for the non-magnetic and magnetic phases of the Ti2MnC2O2 monolayer are shown in Figs. 2(b) and (c), respectively. The Mn-3d (t2g) states dominate the energy bands around EF in the non-magnetic phase while the contributions from other elements are much smaller [Fig. 2(b)], agreeing with the schematic shown in Fig. 2(a). In the ferromagnetic phase [Fig. 2(c)], the majority (up-) spin and minority (down-) spin bands are split in energy by the magnetic exchange field. The effect of such a field is most significant for the half-occupied t2g states, pushing the corresponding bands far away from EF. The up-spin t2g states get lowered to 2-6 eV below EF while the down-spin t2g states are raised to 2-4 eV above EF, and all of the three t2g states (i.e., , , and ) contribute equally to the ferromagnetism (see Fig. S4 in Supporting Information). The calculated µ of the ferromagnetic phase of Ti2MnC2O2 monolayer is 2.97 µB/unit cell (Table 1), consistent with the value predicted by our model (3 µB/unit cell). The origin of µ can be clearly attributed to the spin polarization of Mn4+ d electrons in the middle layer of Ti2MnC2O2, based on the spin density map [Fig. 2(d)]. From Fig.



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2(d), we can also conclude that the Ti4+ cations do not contribute to the spontaneous magnetic moment in Ti2MnC2O2 monolayer, while the C4- anions are antiferromagnetically coupled to the Mn4+ cations but their contribution is much smaller than that of Mn4+ cations. Taken together, these results demonstrate the validity of the analysis shown in Fig. 2(a). To determine which phase is the ground state for Ti2MnC2O2 monolayer, we compare the energies of the ferromagnetic, antiferromagnetic, and non-magnetic phases (Efm, Eafm, and Enm, respectively). Our results show that the ground state of Ti2MnC2O2 monolayer is ferromagnetic, with Eafm-Efm=0.047 eV and Enm-Efm=2.272 eV (Table 1). The large differences between Efm/Eafm and Enm imply a stable magnetic ordering in this MXene monolayer. Such energy differences are accompanied by changes in the lattice size of Ti2MnC2O2: the in-plane lattice parameter a of the non-magnetic phase of Ti2MnC2O2 monolayer (3.015 Å) is reduced compared to that of the ferromagnetic/antiferromagnetic phases (3.063 Å), leading to a smaller distance l between the Mn4+ cations and the C4- anions (Table 2). As a consequence, the p-d interaction in the nonmagnetic phase is stronger, completely delocalizing the d electrons in the system and preventing the occurrence of spin polarization. On the contrary, the p-d interaction in the ferromagnetic/antiferromagnetic phases is weaker and the d electrons of Mn4+ remain localized. We note that the differences in energy and crystal structure between the non-magnetic and ferromagnetic/antiferromagnetic phases in general hold for all the MXenes studied here (Table 1). We also note that the ferromagnetic phase remains the ground state for Ti2MnC2O2 as the on-site Coulomb term U for Mn is varied between 2 eV and 6 eV, but Eafm-Efm is different (Fig. S5 in Supporting Information). However, our choice of U (4 eV) lies in a reasonable range, and is widely used to study the electronic and magnetic properties of other Mn-containing compound materials (see Sec. V in Supporting Information).


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With an understanding of the electronic and magnetic properties of Ti2MnC2O2 monolayer, we further extend the analysis to MXenes in the Ti2MnC2Tx family with other surface termination groups (–OH and –F). Our calculations show that these MXenes have a ferromagnetic ground state as well, and their spontaneous magnetic moments are even higher (Table 1). To rationalize this, we go back to our simplified model wherein the oxidation state of the Ti cations becomes 3+ (i.e., Ti3+: [Ar]3d1), but that of Mn remains 4+ [Fig. 2(e)]. The single d electron of Ti3+ cation couples to the d electrons of Mn4+ through the Ti-C-Mn bonds in two possible ways, depending on the magnetic state of the system. The first one is that the d electron of Ti3+ hops to the half-filled t2g states of Mn4+, which tends to reduce or eliminate the spin polarization in the system. This mechanism exists in the non-magnetic phase of Ti2MnC2(OH)2 (or Ti2MnC2F2), whose DOS profile [Fig. 2(f)] looks similar to that of Ti2MnC2O2 in the nonmagnetic phase [Fig. 2(b)], but with an elevated EF due to the additional d electrons from the two Ti3+ cations. The second possibility is that the d electron of Ti3+ couples to the eg states of Mn4+ and aligns in a ferromagnetic manner with the d electrons at the t2g states of Mn4+, leaving a state with large magnetization (µ=5 µB/unit cell). The actual ground state obtained from DFT calculations is in between the scenarios, with µ=3.90 µB/unit cell in the ferromagnetic phase of Ti2MnC2(OH)2 (Table 1). The contribution of Ti3+ to the total magnetic moment can be clearly visualized from the spin density map [Fig. 2(h)]. However, the amount of magnetic moment per Ti3+ (0.45 µB/unit cell) is much smaller than the value predicted by the model, implying that the d electron of Ti3+ couples to both t2g and eg states of Mn4+. As a result, the up-spin and down-spin bands derived from the Ti d electrons are not completely separated in energy, and are both partially occupied at EF [Fig. 2(g)].



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Based on the results presented so far, we can conclude that the family of Ti2MnC2Tx MXenes have a ferromagnetic ground state regardless of the surface termination groups, and are thereby suitable for device applications. In terms of electronic properties, Ti2MnC2Tx MXenes are all semi-metallic or metallic [Figs. 3(a) and (b)]. In the following, we show that their transport and/or magnetic properties can be carefully controlled by choosing proper transition metal elements and surface termination groups in the MXene structure. Specifically, a ferromagnetic or anti-ferromagnetic semiconducting ground can be achieved by replacing the Ti with Hf atoms in Ti2MnC2O2 and Ti2MnC2F2, respectively [Figs. 3(c) and (d)]. As Ti and Hf are isoelectronic elements, the analysis of the electronic and magnetic properties of Ti2MnC2Tx also applies to Hf2MnC2Tx. The magnetization µ obtained from DFT calculations is 3 µB/unit cell, 4.84 µB/unit cell, and 5 µB/unit cell for the ferromagnetic/antiferromagnetic phases of Hf2MnC2O2, Hf2MnC2(OH)2, and Hf2MnC2F2, respectively, closer to the values predicted by our model (Table 1). In other words, the isolated transition metal cation picture described by the simplified model in Figs. 2(a) and (c) fits Hf2MnC2Tx better than Ti2MnC2Tx. The reason is that the larger atomic size of Hf (compared to Ti) leads to an in-plane tensile strain that increases the in-plane lattice parameter a of Hf2MnC2Tx (Table 2). As a result, the Mn-C distance l in Hf2MnC2Tx is larger, the p-d interaction is reduced, and the Mn4+ d electrons are more localized. The ground state of Hf2MnC2O2 is ferromagnetic with Eafm-Efm=0.078 eV, analogous to the case of Ti2MnC2O2. Their electronic band structure looks similar as well, but the only difference is that Ti2MnC2O2 is a semi-metal [Fig. 3(a)] while Hf2MnC2O2 is a semiconductor with a small band gap Eg=0.238 eV from DFT calculations [Fig. 3(c)]. Considering the fact that DFT calculations usually underestimate the band gap energy even using GGA+U, the actual Eg of Hf2MnC2O2 might be somewhat larger, which is very promising for 2D spintronic transistor


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applications. On the other hand, Hf2MnC2(OH)2 is an antiferromagnetic metal and Hf2MnC2F2 is an antiferromagnetic semiconductor [Fig. 3(d), Eg=1.027 eV] in their respective ground states (Table 1). A possible reason for these ground states in Hf2MnC2(OH)2 and Hf2MnC2F2 is that the five d orbitals of Mn are all half-occupied by three electrons from Mn4+ and two electrons from Hf3+ in the outer layers, which possess the same spin direction (i.e., µ=5 µB/unit cell, see Table 1). So in these MXenes, electron hopping from one Mn to the adjacent Mn is forbidden in the ferromagnetically ordered regime, but is allowed in the antiferromagnetic state (Fig. S6 in Supporting Information). Therefore, the antiferromagnetic phase of these two terminations becomes lower in energy. This phenomenon does not appear in Ti2MnC2(OH)2 or Ti2MnC2F2, because their spontaneous magnetic moment is around 4 µB/unit cell. It is interesting to note that none of band structures shown in Fig. 3 display the threefold degeneracy of the t2g orbitals at the Γ point. The reason is that the t2g orbitals in these MXene monolayers further split into a dxy and a two-fold dxz, dyz orbitals (see Fig. S4 in Supporting Information) due to a small distortion of the octahedron surrounding the Mn atoms. In fact, such a phenomenon also occurs in the band structure of monolayer 1T TiS2, whereas bulk 1T TiS2 preserves the threefold degeneracy at the Γ point in the bands right above EF, which originate from the t2g orbitals of Ti.33 However, this phenomenon does not affect our predictions of the local magnetic moments of these MXenes using the t2g-eg orbital analysis as presented in Fig. 2, whose validity can be confirmed by comparing the predicted and calculated local magnetic moment in Table 1. Similar to Ti2MnC2Tx and Hf2MnC2Tx, Hf2VC2Tx monolayers are ferromagnetic or antiferromagnetic in their ground states as well, because the V4+ cations have one electron ([Ar]3d1) to occupy the t2g orbitals. Hf2VC2O2 is a ferromagnetic semiconductor, with a very 11 ACS Paragon Plus Environment


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small band gap Eg=0.055 eV (Fig. S7 in Supporting Information). The calculated spontaneous polarization is 1 µB/unit cell, consistent with the prediction of our model (Table 1). Hf2VC2(OH)2 and Hf2VC2O2 own a slightly larger µ (1.33 µB/unit cell and 1.27 µB/unit cell, respectively), but they have antiferromagnetic metallic ground states. Furthermore, we estimated the Curie temperatures (TC) of the ferromagnetic MXene structures discovered in this study (Ti2MnC2Tx, Hf2MnC2O2, and Hf2VC2O2). For these infinitely large 2D hexagonal lattice, = 3.642 / , where J is the nearest neighboring spin exchange parameter and kB is the Boltzmann constant.34 To calculate J, we apply the difference between Efm and Eafm of a given MXene structure to the 2D Ising model, where the Hamiltonian of the system is = − ∑, , with µi (µj) denoting the magnetic moment at site i (j). The calculated TC values of these MXenes are well above room temperature (495 to 1133 K, Table 1), which is very promising for device applications. The only exception is Hf2MnC2F2, whose TC is 108 K. However, the fluorine surface coverage can be reduced by using a lower fluorine concentration in the etching solution or by post-treatments, such as annealing.35-37 Finally, the differences in the electronic and magnetic properties of Ti2MnC2Tx and Hf2MnC2Tx inspired us to engineer these electronic and/or magnetic properties of Ti2MnC2Tx using biaxial in-plane strains ε. For example, strain-free Ti2MnC2O2 is a ferromagnetic semimetal in the ground state; while under a tensile strain of ε>0.5 %, this MXene becomes a ferromagnetic semiconductor, whose band gap varies almost linearly as ε varies between 0.5 % and 5 % [Fig. 4(a)]. Such a range of strains can be externally applied to the system via mechanical deformation, which should be sustainable for 2D materials. Alternatively, the strains can be internally induced via partially replacing Ti with Hf in Ti2MnC2O2 [i.e., (HfsTi1-s)2MnC2O2], with s=8.35 % corresponding to ε=0.5 % (roughly estimated using Vegard’s 12 ACS Paragon Plus Environment

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Law). It is also interesting to anticipate ferromagnetic to antiferromagnetic phase transitions to occur in Ti2MnC2(OH)2 and Ti2MnC2F2 under the tensile strains ε=2.8 % and ε=0.3 %, respectively [Fig. 4(b)]. These phase transitions in the electronic and magnetic properties should also be of potential interest in spintronic devices. In particular, antiferromagnetic spintronic devices have raised a growing attention in recent years, as antiferromagnets are more robust against disturbing magnetic fields and more suitable for high-frequency data storage as compared to ferromagnets.38 We note that there have been some predictions on ferromagnetic ground states in unterminated (i.e., bare) MXenes, such as Ti2C, Zr2C, and Cr2C.23-24 Such bare MXenes, however, are very difficult to achieve since the dangling bonds of the transition metal atoms in the outer layers are immediately passivated by the surface terminations in solution-based synthesis conditions or after exposure to air. High-quality neutron total scattering and nuclear magnetic resonance (NMR) measurements showed that synthesized MXenes have a mix of –OH, –F and =O terminations,35-36 which drastically affect their magnetic properties. In fact, magnetism is suppressed in terminated Ti2CTx and Zr2CTx MXene. We also notice that an earlier DFT study in 2013 predicted that –OH or –F terminated Cr2CTx and Cr2NTx MXenes are ferromagnetic. 22 Such a conclusion, however, is incorrect as the authors completely ignored the antiferromagnetic phase in their study. More recent first principles simulations have shown that the ground states of –OH or –F terminated Cr2CTx and Cr2NTx are instead antiferromagnetic.24, 39 During the preparation of this paper, another Mn-based ferromagnetic MXene structure was reported using a DFT study with the chemical formula Mn2CT2 (T=F and OH).40 However, the Mn2CT2 MXene turns to antiferromagnetic if terminated by =O,40 implying the instability of their ferromagnetic ground states when exposed to air. On the other hand, Ti2MnC2T2 we



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identify here is the first ferromagnetic MXene ferromagnetic MXene structure that can retain its ferromagnetic ground state with mixed terminations of –F, –OH, and =O. Their ferromagnetic properties are robust, in terms of high magnetic moments (3-4 µB/unit cell) and high Curie temperatures (495 - 1133 K), which are superior to the existing 2D ferromagnetic materials. In summary, we have determined that Ti2MnC2Tx MXenes are ferromagnetic 2D metals or semi-metals in the ground states, regardless of their surface terminations. On the other hand, only =O terminated Hf2MnC2Tx and Hf2VC2Tx (i.e., Hf2MnC2O2 and Hf2VC2O2) are ferromagnetic semiconductors, while the –OH or –F surface termination groups in these MXene families result in antiferromagnetic ground states. The Curie temperature values of the ferromagnetic MXenes identified here are well above the room temperature (495 to 1133 K), except for Ti2MnC2F2. In addition, small or moderate tensile in-plane strains can result in a ferromagnetic semi-metal to ferromagnetic semiconductor phase transition in Ti2MnC2O2, and ferromagnetic to antiferromagnetic phase transitions in Ti2MnC2(OH)2 or Ti2MnC2F2. The synthesis of the MXenes we study here relies on the realization of their precursors – the MAX phase of carbides, which is possible as a few types of Mn- and V-containing MAX phase of carbides have become available41-42 and more will emerge in the future (Sec. VIII in Supporting Information). These results can be used to guide the selection of transition metals and surface termination groups through synthesis and post-synthesis treatments to produce robust 2D ferromagnetic metals and semiconductors for future spintronic applications.


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Acknowledgements This work is supported by the grant W911NF-16-1-0447 from the Army Research Office. Part of this work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1053575. L.D. thanks Dr. Junwen Li at National Institute of Standards and Technology for valuable discussions. B.A. was supported by King Abdullah University of Science and Technology under the KAUST-Drexel University Competitive Research Grant.

Supporting Information (I) Supercell structures for antiferromagnetic phases of the MXenes, (II) phonon band structures of the MXenes, (III) relative stability of the fully ordered and alloyed structures of the MXenes, (IV) detailed density of states analysis for the ferromagnetic phase of Ti2MnC2O2, (V) effects of on-site Coulomb term U on the magnetic properties of Ti2MnC2O2, (VI) mechanism of the antiferromagnetic phases of the MXenes, (VII) electronic band structure of Hf2VC2O2 monolayer in the ferromagnetic ground state, and (VIII) Mn- and V-Containing Carbides in the MAX Phases.

Note The authors declare no competing financial interest.



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Table 1. The energies of ferromagnetic (Efm), antiferromagnetic (Eafm), and non-magnetic (Enm) states for the MXene monolayers (unit: eV) and the spontaneous magnetic moment µ (unit: µB) per unit cell. Efm is set to be 0 eV as a reference, and the energy marked in red represents the ground state energy. The Curie temperatures TC (unit: K) for the MXenes with ferromagnetic ground states are given as well. Efm

Eafm

Enm

µ(DFT)

µ(model)

TC

Ti2MnC2O2

0

0.047

2.272

2.97

3

495

Ti2MnC2(OH)2

0

0.104

1.868

3.90

5

1103

Ti2MnC2F2

0

0.010

1.908

4.24

5

109

Hf2MnC2O2

0

0.078

2.588

3

3

829

Hf2MnC2(OH)2

0

-0.085

1.846

4.84

5

/

Hf2MnC2F2

0

-0.084

1.971

5

5

/

Hf2VC2O2

0

*

0.080

1

1

1133

Hf2VC2(OH)2

0

-0.150

0.115

1.33

3

/

Hf2VC2F2

0

-0.177

0.105

1.27

3

/

*: Eafm of Hf2VC2O2 is not available because DFT calculations always yield a non-magnetic state for this MXene. So, TC for this material is estimated using the difference between Efm and Enm.



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Table 2. The lattice parameter a and Mn-C distance l in the magnetic (ferromagnetic/antiferromagnetic) and non-magnetic phases of the MXene monolayers (unit: Å) Magnetic

Non-magnetic

a

l

a

l

Ti2MnC2O2

3.063

2.122

3.015

2.047

Ti2MnC2(OH)2

3.151

2.265

3.131

2.099

Ti2MnC2F2

3.146

2.289

3.124

2.100

Hf2MnC2O2

3.245

2.197

3.186

2.114

Hf2MnC2(OH)2

3.348

2.438

3.298

2.171

Hf2MnC2F2

3.354

2.462

3.300

2.178

Hf2VC2O2

3.226

2.205

3.194

2.189

Hf2VC2(OH)2

3.284

2.260

3.259

2.221

Hf2VC2F2

3.281

2.264

3.264

2.257


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Figure 1

(a) Side view and (b) top view of the Ti2MnC2Tx, Hf2MnC2Tx, and Hf2VC2Tx

monolayer structures, using Ti2MnC2O2 as an example. The unit cell is outlined by the dotted lines in part (b). The in-plane lattice parameter a and Mn-C bond length l are shown in the figure as well. Grey, purple, cyan and red circles represent Ti, Mn, C, and O, respectively.



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Figure 2

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Predicted electronic and magnetic properties of MXenes. (a) A simplified band

diagram that explains the electronic band structure of Ti2MnC2O2 monolayer around the Fermi level (EF). (b) The DFT calculated partial density of states (DOS) of Ti2MnC2O2 monolayer in the non-magnetic phase. (c) Partial DOS of Ti2MnC2O2 monolayer in the ferromagnetic phases. (d) The magnetic spin density of Ti2MnC2O2 monolayer in the ferromagnetic phase, with the positive and negative values plotted in red and blue, respectively. (e) The simplified band diagram for Ti2MnC2(OH)2 monolayer around EF. (f) Partial DOS of Ti2MnC2(OH)2 monolayer in the non-magnetic phases. (g) Partial DOS of Ti2MnC2(OH)2 monolayer in the ferromagnetic phases. (h) The magnetic spin density of Ti2MnC2(OH)2 monolayer in the ferromagnetic phase. The magnetic moments in both materials are primarily localized around the Mn4+ in the middle layer. In panel (d), Ti4+ has no d electrons, and thereby does not contribute to magnetism; while in panel (h), Ti3+ contributes one d electron that is ferromagnetically coupled to Mn4+.


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Figure 3

The electronic band structure of MXene monolayers, showing that their transport

and magnetic properties can be controlled by choosing proper transition metal elements and surface termination groups. (a) Ti2MnC2(OH)2 is a ferromagnetic metal, (b) Ti2MnC2O2 is a ferromagnetic semi-metal, (c) Hf2MnC2O2 is a ferromagnetic semiconductor, and (d) Hf2MnC2F2 is an antiferromagnetic semiconductor. The bands for majority (up-) and minority (down-) spins are illustrated in red solid and blue dashed lines, respectively.



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Figure 4

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The effect of tensile in-plane strain (ε) on the band gap (Eg) and magnetic

properties of Ti2MnC2Tx: (a) a ferromagnetic semi-metal to ferromagnetic semiconductor phase transition occurs in Ti2MnC2O2 at around ε=0.5 %, (b) ferromagnetic to antiferromagnetic phase transitions occur in Ti2MnC2(OH)2 and Ti2MnC2F2 at around ε=2.8 % and ε=0.3 %, respectively. The positions of phase transitions are marked by the red arrows.


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TOC Graphic 38x29mm (300 x 300 DPI)

ACS Paragon Plus Environment


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Figure 1 (a) Side view and (b) top view of the Ti2MnC2Tx, Hf2MnC2Tx, and Hf2VC2Tx monolayer structures, using Ti2MnC2O2 as an example. The unit cell is outlined by the dotted lines in part (b). The in-plane lattice parameter a and Mn-C bond length l are shown in the figure as well. Grey, purple, cyan and red circles represent Ti, Mn, C, and O, respectively. 81x81mm (300 x 300 DPI)


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Figure 2 Predicted electronic and magnetic properties of MXenes. (a) A simplified band diagram that explains the electronic band structure of Ti2MnC2O2 monolayer around the Fermi level (EF). (b) The DFT calculated partial density of states (DOS) of Ti2MnC2O2 monolayer in the non-magnetic phase. (c) Partial DOS of Ti2MnC2O2 monolayer in the ferromagnetic phases. (d) The magnetic spin density of Ti2MnC2O2 monolayer in the ferromagnetic phase, with the positive and negative values plotted in red and blue, respectively. (e) The simplified band diagram for Ti2MnC2(OH)2 monolayer around EF. (f) Partial DOS of Ti2MnC2(OH)2 monolayer in the non-magnetic phases. (g) Partial DOS of Ti2MnC2(OH)2 monolayer in the ferromagnetic phases. (h) The magnetic spin density of Ti2MnC2(OH)2 monolayer in the ferromagnetic phase. The magnetic moments in both materials are primarily localized around the Mn4+ in the middle layer. In panel (d), Ti4+ has no d electrons, and thereby does not contribute to magnetism; while in panel (h), Ti3+ contributes one d electron that is ferromagnetically coupled to Mn4+. 87x47mm (300 x 300 DPI)



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Figure 3 The electronic band structure of MXene monolayers, showing that their transport and magnetic properties can be controlled by choosing proper transition metal elements and surface termination groups. (a) Ti2MnC2(OH)2 is a ferromagnetic metal, (b) Ti2MnC2O2 is a ferromagnetic semi-metal, (c) Hf2MnC2O2 is a ferromagnetic semiconductor, and (d) Hf2MnC2F2 is an antiferromagnetic semiconductor. The bands for majority (up-) and minority (down-) spins are illustrated in red solid and blue dashed lines, respectively. 68x26mm (300 x 300 DPI)


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Figure 4 The effect of tensile in-plane strain (ε) on the band gap (Eg) and magnetic properties of Ti2MnC2Tx: (a) a ferromagnetic semi-metal to ferromagnetic semiconductor phase transition occurs in Ti2MnC2O2 at around ε=0.5 %, (b) ferromagnetic to antiferromagnetic phase transitions occur in Ti2MnC2(OH)2 and Ti2MnC2F2 at around ε=2.8 % and ε=0.3 %, respectively. The positions of phase transitions are marked by the red arrows. 43x23mm (300 x 300 DPI)


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