First-Principles Prediction of Room-Temperature Ferromagnetic

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C: Physical Processes in Nanomaterials and Nanostructures

First-Principles Prediction of Room-Temperature Ferromagnetic Semiconductor MnS via Isovalent Alloying 2

Jintong Guan, Chengxi Huang, Kaiming Deng, and Erjun Kan J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b00763 • Publication Date (Web): 01 Apr 2019 Downloaded from http://pubs.acs.org on April 1, 2019

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The Journal of Physical Chemistry

First-Principles Prediction of Room-Temperature Ferromagnetic Semiconductor MnS2 via Isovalent Alloying Jintong Guan†, Chengxi Huang†,*, Kaiming Deng†, Erjun Kan†,*

† Department of Applied Physics and Institution of Energy and Microstructure, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, P. R. China

ACS Paragon Plus Environment

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Abstract

Although semiconducting ferromagnetism has been experimentally discovered in twodimensional (2D) crystals, the spin coupling is still quite weak, which leads to a rather low Curie temperature (TC). Thus, it is quite confused whether the ferromagnetism in semiconductors can survive under room temperature. Here, through isovalent alloying, we propose that the semiconducting ferromagnetism of 2D MnS2 can be significantly enhanced with TC improved higher than room temperature. Based on first-principles calculations, we systematically studied the properties of original MnS2 and the isovalent alloying systems MnxRe1-xS2. The spin coupling is significantly enhanced by introducing Mn-Re virtual bonds, and the highest TC of the system reaches 360 K. Besides, a tensile


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strain will further enhance the ferromagnetic couplings as well as the uniaxial magnetic anisotropy, which is important for the stabilization of long-range ferromagnetic order in a 2D system. Our results not only broaden the family of 2D ferromagnetic semiconductors, but also provide the direct clues to prepare such high-temperature magnetic materials for promising applications in spintronics.


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Introduction Owing to spontaneous net magnetization, moderate electrical resistivity at finite temperature, two-dimensional (2D) ferromagnetic (FM) semiconductors possess their unique potentials in spintronic applications and have attracted great research interests.19

Since the pioneering experimental works of exfoliated 2D FM Cr2Ge2Te6 and CrI3 layers

in 2017,10,11 plenty of new phenomena and 2D magnetic materials have been reported. However, their Curie temperatures (TC, 20 K and 45 K for Cr2Ge2Te6 and CrI3, respectively) are even lower than the liquid nitrogen temperature (77 K), which badly restricts their practical applications in spintronics. Thus, it is quite necessary to develop new 2D ferromagnetic crystals with robust long-range spin ordering, which can survive above room temperature. Previously, many theoretical works have been devoted to predicting ferromagnetism in 2D VDW crystals.12-22 For example, nonmagnetic 2D semiconductors, such as GaSe, αSnO and InP3 can be tuned into ferromagnets by carrier doping.23,24 However, high concentration of carrier doping may break the intrinsic semiconducting property. Besides, high-throughput is also a burgeoning method for searching 2D FM semiconducting


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materials.25,26 Generally, in intrinsic semiconductors, FM coupling is mainly driven by the super-exchange interactions.27-29 Although external manipulations, such as electric field and charge doping, may enhance the magnetic coupling, semiconductor-metal transitions cannot be avoided. Consequently, improving the strength of FM interactions in semiconductors is still very difficult. In our previous work, a simplified double-orbital model has been proposed that reducing the virtual exchange gap (Gex) between the occupied and empty spin-polarized orbitals will enhance the FM coupling between magnetic dipoles in a semiconductor.30 This method would guide us to develop new kinds of FM semiconductors and create opportunities for realistic spintronic applications. Based on the explored super-exchange mechanism, we still need to answer whether room-temperature ferromagnetism in 2D semiconductors can be realized by this method? In this paper, we explored that the robust ferromagnetism in MnS2 monolayer can survive above room temperature. Theoretical results have revealed that only 1T-phase is stable for single-layered MnS2.31 In this phase, MnS2 prefers an octahedral configuration in which each Mn ion is surrounded by six S ions, forming octahedral-shaped structure.


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Interestingly, this 1T-phase MnS2 monolayer shows semiconducting property and intrinsic ferromagnetic (FM) ordering with relatively high TC of 225K,32, but still below the roomtemperature. Here, by means of ab initio calculations, we demonstrated that by introducing rhenium (Re) atoms into MnS2 monolayer, an intrinsic FM semiconductor Mn2ReS6 with TC above room-temperature (~ 360 K) and well-preserved semiconducting features can be achieved. Results and Discussion Re is located at the same group (VIIB) with Mn, which suggests that Re ion may show the same valence state as Mn ion in a similar chemical and crystal environment. This will avoid unexpected carrier doping or charge transferring those may break the intrinsic semiconducting properties when we use Mn and Re ions to construct alloyed transition metal compounds. Compared with Mn in the monolayer, the introducing of Re atoms will provide a chance to introduce not only average on-site energy difference ∆o but also exchange-split difference ∆u which may reduce Gex. Intuitively, the concentration and distribution, namely the atomic order (AO) of the introduced Re atoms should directly


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affect the FM coupling. Thus, a systematical investigation at atomic scale is quite necessary.

Figure 1. The structural configurations of the MnS2 and MnxRe1-xS2 alloying compounds with different value of x. (a) MnReS4; (b) Mn2ReS6; (c) Mn3ReS8; (d) MnRe2S6; (e) MnRe3S8.

To address the above issues, we firstly focus on the geometric configurations with different concentration. Tons of possible alloying configurations are considered by performing extensive DFT calculations, and the optimal structures under different concentrations are presented in Figure 1. Table S1 summarized the basic properties of the optimized structures. Noted that there could be many possible structural


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configurations of MnxRe1-xS2 monolayers due to the different distribution patterns of Re and Mn sublattices. We focus on the ground state structures under each concentration in our following research, and the other meta-stable states are presented in the Supporting Information (SI). It should also be noted that ReS2 actually prefer to forming a distorted Td-type structure,33 and presenting non-magnetic property. But in order to better demonstrate

the

mechanism

of

the

relationships

between

FM

coupling

and

concentration/distribution of Re ions, here we consider a hypothetical MnS2-liked nondistorted 1T-phase of ReS2 as a comparison to other MnxRe1-xS2 systems (shown in SI). To study the magnetic properties of these 2D crystals, we carried out spin-polarized calculations to check the preferred spin ordering in the ground state. The magnetic couplings of MnxRe1-xS2 systems (shown in Figure S3 and S4) are severely affected by the geometric structures, and the ground states of MnReS4, Mn2ReS6 and Mn3ReS8 prefers FM coupling, while the other MnS2 analogue are antiferromagnetic (AFM). As we know, in monolayer MnS2, each magnetic site (Mn) is coordinated by 6 S atoms and crystallize in an octahedral field which leads to half occupied t2g orbitals and a formal magnetic moment of 3 μB/f.u.. Since Re ion has the same valent state as Mn, the magnetic


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moments of MnxRe1-xS2 systems are not expected to be changed. Consequently, the super-exchange interaction is response for the FM coupling. The total exchange energy (Eex = EAFM - EFM, positive values indicate FM couplings) are summarized in Table 1, where the normalization coefficient (number of magnetic sites N) is employed to normalize the exchange energy for comparison. As the concentration of Re ions increases, the FM coupling is enhanced firstly, and then weakened. Interestingly, the strongest ferromagnetism occurs in monolayer Mn2ReS6. Table 1. Summary of the normalized exchange energy of MnxRe1-xS2 monolayers. The calculated results of MnS2 is in agreement with previous report. 32

Symmetry NMetal

EFM (eV)

EAFM (eV)

Eex/N (meV)

MnS2

P-3m1

3

-48.928

-48.695

77.67

Mn3ReS8

P-3m1

4

-68.788

-68.439

87.25

Mn2ReS6

P-31m

3

-52.523

-52.241

94

MnReS4

P2-m

2

-36.013

-35.876*

68.5*

MnRe2S6

P-31m

3

-55.457

-55.478

-9

MnRe3S8

P-3m1

4

-74.876

-75.166

-72.5

meta-ReS2

P-3m1

2

-38.718

-39.003

-142.5


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*The exchange energy of MnReS4 are roughly estimated, because the initial AFM state of MnReS4 always converges into a ferrimagnetic state with unzero but small magnetization. To find out how the AO affect the magnetic coupling, we calculated the band dispersions for MnxRe1-xS2 under different Re concentrations. Since Mn2ReS6 shows the strongest ferromagnetism, we focus on Mn2ReS6 to explore how the AO affects the electronic and magnetic structures. In this structure, the transition metal atoms are located at the center of the octahedral crystal field, in which the d-orbitals split into two parts, namely, threefold t2g and twofold eg manifolds. To maintain the semiconducting property, the lower t2g orbitals are half occupied meanwhile the higher eg orbitals are empty, the upper-lifted Ret2g orbitals create an more efficient channel for super exchange. It can be seen from the calculated projected band structure and peaks of projected density of states (pDoS), a distinct energy level stagger between Mn-d↑ and Re-d↑ orbitals occurs near the Fermi level. Compared to intrinsic MnS2 32, the Re-d↑ energy levels insert into the splitting Mn-

d↑ orbitals and reduces the Gex. The reduced Gex directly strengthen the super-exchange and win the competition with AFM direct-exchange between Mn and Re ions. To concretely figure out the enhancement of FM couplings, we calculated the exchange


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parameters of virtual bonds (defined as interaction between two nearest neighboring transition metals) JMn-Mn and JMn-Re those are 4.0 and 16.8 meV in Mn2ReS6, respectively. Overall, we can conclude that in order to obtain the maximum FM coupling, it is indispensable to construct a MnxRe1-xS2 system with maximum density of Mn-Re virtual bonds.

Figure 2. The projected band structure of Mn2ReS6; Schematic diagrams of orbital evolution and the origin of energy level staggering of Mn and Re orbitals and the projected density of states. (The red and blue line represents Mn- and Re-contribution respectively)

To represent the relationship between AO and exchange energy, here, we use a parameter A to quantify the AO (defined as A 

1  ni , where ni represents the number 2N i


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of Mn-Re virtual bonds connected to the i site in the lattice. N represents the total number of transition metal sites. The summation subscript i runs over all the magnetic sites), which represents the density of the Mn-Re exchange path. Since the exchange paths cannot be identical with different Re concentration, we separate these data into Mn- and Redominant side. As shown in Figure 4, the exchange energy is almost linearly increased with the A, except for MnReS4. Because in MnReS4, there are not only Mn-Re virtual bonds, but also Re-Re virtual bonds. The latter ones prefer AFM coupling. Thus for Rerich side where the Re-Re virtual bonds become dominant, the systems turns into AFM. Nevertheless, the Eex is positively correlated to A at the Mn-rich side. The maximum A of the MnxRe1-xS2 monolayer is Mn2ReS6 which corresponds to the maximum Eex on both sides.


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Figure 3. The Eex numerical trend relative to the AO. The light (pink) and dark (blue) halves are Mn- and Re- dominate parts respectively. It could be seen that the exchange energy is almost monotonically increasing with A except for MnReS4.

Now we pay our attention to the ferromagnetically best Mn2ReS6 monolayer, which possesses the maximum Amax and the highest Eex among MnxRe1-xS2 system. Considering the practical spintronic application of the Mn2ReS6 monolayer, it is necessary to estimate the Curie temperature of ferromagnetism. Here we use the Heisenberg model in addition with a magnetic anisotropic term to describe the magnetic behavior of these


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systems under finite temperature (the in-plane anisotropy is omitted). The spin Hamiltonian Hˆ    JS i S j   D( S iz ) 2 i , j 

i 

where the summation runs over all nearest-neighboring Mn and Re sites. J is the exchange interaction parameter for Mn-Re virtual bonds (in Mn2ReS6, there are only MnRe virtual bonds), D is the single site magnetic anisotropy parameter, Siz represent components of S along z (out-of-plane) orientations, and |S| = 3/2 for both Mn and Re. The first term represents the magnetic exchange coupling and dominates the magnitude of TC in the system. A low tensile strain could reduce the nearest-neighbor dd direct exchange, which may improve the TC. Computational results show that the exchange energy is linearly increased with the external strain. Another key factor for the formation of long-range FM order in 2D materials, namely magnetic anisotropy, is also studied here. Same as MnS2 monolayer,34 Mn2ReS6 possesses an out-of-plane easy axis, which can be further stabilized by an external strain, as shown in Figure 4b.


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Figure 4. (a) Total exchange energy (Eex = EAFM - EFM, positive values indicate ferromagnetic couplings) and (b) magnetic anisotropic energy (MAE = Ein-plane - Eout-of-plane, positive values indicate easy out-of-plane magnetization axis) per unit-cell as a function of in-plane biaxial tensile strain (ε). (c) Magnetization per site as a function of temperature for MnS2, Mn2ReS6 monolayer, and Mn2ReS6 monolayer under 5% tensile strain from Monte Carlo simulations, where the dashed lines are the corresponding Curietemperature of the materials.


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Figure 5. (a)Phonon spectrum and total energy fluctuations with respect to molecular dynamics (MD) simulation step for Mn2ReS6 at 400 K. No imaginary part and no drastic fluctuation are found in the figure, from which we can infer that Mn2ReS6 monolayer is stable on both dynamic and thermodynamic. (b) Structures after MD simulations of 15 ps for Mn2ReS6 monolayer, no remarkable structural disruption is found in the structure. The

ab initio molecular dynamics simulations were performed by using a 4 × 4 × 1 supercell under a Nose-Hoover thermostat at 400 K.


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Since the predicted Curie temperature of Mn2ReS6 monolayer is as high as 360 K, it is essential to check out the stability for the possibilities of experimental synthesis and application. The stability is assessed to their phonon dispersion and molecular dynamic simulations. From the calculated phonon spectrum of the well-relaxed Mn2ReS6, no imaginary phonon modes are observed, which confirms the dynamic stability of this material. To further confirm the thermal stability of the ferromagnetism-intensified Mn2ReS6 semiconductor, we performed ab initio molecular dynamics (AIMD) simulations at 400K for 15 ps. Form the energy spectrum and AIMD snapshots (Figure 5), we can see this monolayer is well maintained within 15 ps, suggesting that semiconductor Mn2ReS4 is thermally stable. Besides during the AIMD simulations, all atoms in the cell vibrate near their equilibrium positions and no phase transition is observed, demonstrating the crystal is highly stable at room temperature. Conclusion In summary, based on first-principles calculations, we explored the existence of roomtemperature ferromagnetism in 2D semiconductors, which is realized through constructing alloy transition metal compounds.

Based on this strategy, we further


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proposed that atomic order directly influences the magnetic coupling in alloyed semiconductors. To verify this, a series of 2D MnxRe1-xS2 alloyed compounds were taken as examples to demonstrate the relationships between atomic order and the magnetic coupling. Besides, on this basis, we designed alloyed transition metal compound, Mn2ReS6 monolayer. Importantly, the Curie temperature of Mn2ReS6 monolayer is as high as 360 K, which is much higher than that of prototypical MnS2 monolayer (225 K). Thus, our findings provide an important way to synthesize high-temperature ferromagnetic semiconductors, which will benefit the development of spintronic in real devices. Method All of our first-principles calculations were performed based on density functional theory (DFT) implemented in the Vienna Ab initio Simulation Package (VASP).35 For exchangecorrelation functional, the generalized gradient approximation (GGA) given by Perdew, Burke, and Ernzerhof (PBE) was used.36 The effective Hubbard Ueff = 4 and 2 eV were added according to Dudarev’s method for the Mn-d and Re-d orbitals, respectively. Because Ueff of Mn in different systems are usually taken within the range of 2~4 eV and the Ueff difference of 2 eV between 3d and 5d elements (Ueff,3d - Ueff,5d = 2 eV) is


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reasonable.37-39 The projector augmented wave (PAW)40 method was used to treat the core electrons. HSE06 hybridized functional was also performed on the magnetic properties as a contract standard. The results are very similar to those from DFT+U calculations (Figure 2). 41 The plane wave cutoff energy was set to be 500 eV and the first Brillouin zone was sampled by using a Γ-centered 13×13×1 Monkhorst-Pack grid. A vacuum space of 25 Å along the z direction was adopted to model the 2D system. The spin-orbit coupling (SOC) was included in the electronic self-consistent calculations. The phonon calculations were performed by the PHONOPY code.42 The spin dynamical process is studied by the classical Metropolis Monte Carlo (MC) simulations.43 For Mn2ReS6 monolayer, a 30  30 2D monolayer spin lattice containing 1800 spin sites with the periodic boundary condition is used. During the simulation steps, each spin is rotated randomly in all directions. The average magnetization per site is taken after the system reaches the equilibrium (with at least 105 simulation steps) state at a given temperature. The Curie temperature (TC) is taken as the critical point of the specific heat, defined as CV = (-2)/kBT2. The estimated TC of CrI3 monolayer (~ 50 K) is very close to the experimental result (~ 45 K), suggesting the rationality of this method.


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ASSOCIATED CONTENT

Supporting Information. Structural properties of Mn2ReS6. Structural properties of MnxRe1-xS2 monolayers. Preferable magnetic order in 1T-phased ReS2. Preferable magnetic order on both Mn- and Re-dominate sides. Strain effect on Mn2ReS6.

AUTHOR INFORMATION Corresponding Authors * [email protected] * [email protected]

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval

to the final version of the manuscript. ACKNOWLEDGMENT


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The work is supported by the NSFC (51522206, 11774173, 11574151), the Fundamental Research Funds for the Central Universities (No.30915011203). C.H. and E.K. acknowledge the support from the Tianjing Supercomputer Centre and Shanghai Supercomputer Center.

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TOC Graphic


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First-Principles Prediction of Room-Temperature Ferromagnetic

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