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C: Physical Processes in Nanomaterials and Nanostructures

Two-Dimensional Manganese Nitride Monolayer With Room Temperature Rigid Ferromagnetism Upon Strain Zhenming Xu, and Hong Zhu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b02323 • Publication Date (Web): 06 Jun 2018 Downloaded from http://pubs.acs.org on June 6, 2018

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The Journal of Physical Chemistry

1

Two-Dimensional Manganese Nitride Monolayer with Room

2

Temperature Rigid Ferromagnetism upon Strain

3 Zhenming Xu, Hong Zhu*

4 5 6

University of Michigan–Shanghai Jiao Tong University Joint Institute,

7

Shanghai Jiao Tong University, 800, Dongchuan Road, Shanghai, 200240, China

8 9

Abstract: Developing low-dimensional spintronic materials with room temperature

10

magnetic ordering and large spin polarization is the key for the fabrication of practical

11

spintronic devices with high circuit integration density and speed. Here,

12

first-principles calculations were performed to systematically investigate a

13

two-dimensional hexagonal MnN monolayer with room temperature magnetic

14

ordering and 100% spin polarization. MnN monolayer is thermally, dynamically and

15

mechanically stable. MnN monolayer is intrinsically half-metallic with very wide

16

band gap. The Curie temperature of MnN monolayer is estimated to be ~368 K,

17

which is more than the room temperature and insensitive to strain. MnN monolayer

18

shows half-metallic and excellent magnetic stability upon external strains from -10%

19

to 10%. Our calculations indicate that MnN monolayer could be a promising material

20

for the room temperature spintronic devices.

21 22

Introduction

23 24

Graphene, discovered by Andre Geim and co-workers by a simple method of scotch

25

tape stripping in 2004, opens a new era of studying and applying two-dimensional

26

(2D) materials1-4. The reduction of material dimension gives rise to the novel physical

27

and chemical properties, which are quite different from that of the three-dimensional

28

(3D) structure5-6. 2D materials can be widely applied in many fields, such as

*

Corresponding author:

E-mail: [email protected]; University of Michigan–Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, 800, Dongchuan Road, Shanghai, 200240, China

1

ACS Paragon Plus Environment

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nanoelectronic and optical devices7-10, energy storage11-16, catalysis17-20 and chemical

2

sensors21-23.

3 4

Nanoelectronic devices, especially for spintronics, which are urgently needed for

5

developing the high speed and low energy consuming information technology, are

6

one of the most important application areas for 2D materials24. It is due to the fact that

7

fabricating spintronic devices at nanoscale based on the low-dimensional spintronic

8

materials can achieve high integration density and speed24. However, most 2D

9

materials like graphene1, 3, graphdiyne25-26, phosphorene27-28, h-BN29-30, borophene31,

10

etc. intrinsically show non-magnetic or weakly magnetic characteristics, which limit

11

their applications in spintronics. In general, a practical spintronic material should have

12

a sizable room temperature magnetic moment, which means that a large spin

13

polarization of electron state around the Fermi energy level is essential24. Among

14

many reported 2D materials, only a few 2D transition metal carbides, nitrides, sulfide

15

and trihalides show intrinsic ferromagnetisms, such as Ti2C32, Cr2C33, Mn2C34, FeC235,

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Ti2N32, CrN36, MoN237, MoS238-39, NbS240, and TMX2 transition metal dihalides (X =

17

Cl, Br and I) monolayer41-42, in which the unpaired d-electrons in transition metals

18

contribute to the formation of the spin-polarized electronic states. In addition, earlier

19

reports suggest that transition metal (TM) incorporation into metal-free 2D materials

20

such as graphene43-44 and carbon nitride45-46 could induce local magnetic moment and

21

also lead to half-metallicity.

22 23

Here, we report a room temperature ferromagnetic and half-metallic 2D hexagonal

24

manganese nitride with 100% spin polarization and high Curie temperature, which

25

may be synthesized by a spontaneous graphitic conversion from the ultrathin

26

(111)-oriented cubic MnN in the future experiments47. Similar spontaneous

27

graphitization of ultrathin cubic structures can be found in diamond, boron nitride,

28

and rock salt47. In this work, using first-principles calculations and ab-initio molecular

29

dynamics (AIMD) simulations based on density functional theory (DFT), we have

30

systematically investigated the hexagonal MnN monolayer to ascertain its potential

31

application for spintronic devices. Firstly, the thermal, dynamical, and mechanical

32

stability of MnN monolayer were confirmed by AIMD simulation, phonon dispersion

33

calculation, and mechanical parameter calculation. Then, the spin-polarized electronic 2


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1

structures, magnetic properties and Curie temperature of MnN monolayer with and

2

without strain are discussed in detail.

3 4

Computational methods

5 6

All atomic and electronic structure calculations were carried out by using the

7

projector augmented wave (PAW) method48 in the framework of DFT49, as

8

implemented in Vienna ab-initio Simulation Package (VASP). The generalized

9

gradient

10

approximation

(GGA)50 49

exchange-correlation functional 6

2

5

2

and

Perdew–Burke–Ernzerhof

(PBE)

is used. The electron configurations of Mn and N

3

11

atom are 3p 4s 3d and 2s 3p , respectively. To consider the strong correlation effects

12

of transition metal Mn element, structural optimizations were performed by using the

13

spin-dependent GGA plus Hubbard correction U (GGA+U) method51. The Hubbard U

14

parameter of Mn atom is set to 5.5 eV based on the previous study on manganese (III)

15

compound52. For more accurate descriptions of electronic structures, the hybrid

16

functional HSE0653-54 is employed for the band-structure and density of electron state

17

(DOS) calculations. A vacuum region of 15 Å is applied to avoid interactions between

18

the neighboring configurations. After convergence tests (see details in Supporting

19

Information, Table S1), the plane-wave energy cutoff is set to 520 eV. The

20

Monkhorst–Pack method55 with 11×11×1 and denser 25×25×1 k-point meshes are

21

mployed for the Brillouin zone sampling, respectively for the structural relaxations

22

and electronic structure calculations. The convergence criterions of energy and force

23

calculations are set to 10−5 eV and 0.01 eV Å−1, respectively. The phonon calculations

24

were performed with a 3×3×1 supercell based on the density functional perturbation

25

theory (DFPT)56, as implemented in the PHONOPY code57. In addition, ab-initio

26

molecular dynamics (AIMD) simulations based on the Born-Oppenheimer

27

approximation were performed at the room temperature of 300 K in a statistical

28

ensemble with fixed particle number, volume and temperature (NVT) by using a

29

3×3×1 supercell of MnN monolayer as initial structure. The time step is set to 3 fs,

30

and the supercell systems were simulated for 10000 steps, with a total of 30 ps. A

31

plane-wave energy cutoff of 350 eV, Gamma-point only k-point mesh and periodic

32

boundary condition were also used dor AIMD simulations.

33 3



1 2

Results and discussion

3

Geometry and stability

4 5

Our proposed graphene-like MnN monolayer belongs to the hexagonal honeycomb

6

structure, and the corresponding atomic structure is depicted in Figure 1. The

7

optimized lattice constant a of MnN monolayer is 3.388 Å, and the corresponding

8

Mn-N bond length is 1.956 Å. To confirm the dynamical stability of MnN monolayer,

9

its phonon dispersion was firstly calculated, as depicted in Figure 2a. All the

10

vibrational modes of our predicted MnN monolayer show positive frequencies,

11

indicating MnN monolayer is stable or at least structurally metastable. The vibrational

12

modes with lower frequencies (less than 450 cm−1) are composed of three acoustic

13

branches and one optical branch. Viewed from the total and partial density of phonon

14

states, Mn atom with greater atomic mass mainly devotes to the acoustic vibrational

15

modes with lower frequencies. While the high-frequency optical branches especially

16

for those above 800 cm-1 are mainly contributed by N atom with smaller atomic mass,

17

separated from the lower frequency optical vibrational modes by a phonon gap of 350

18

cm−1.

19 20

Then, AIMD simulations were performed by using a 3×3×1 supercell of MnN

21

monolayer at 300 K for 30 ps to examine its thermal stability. During the whole

22

AIMD simulation process, the total potential energies of MnN monolayer vibrate

23

around a constant of ~ -8.38 eV/atom, and the fluctuations of total potential energy

24

during the last 10 ps are ~20 meV/atom, as shown in Figure 2b. In addition, the

25

supercell structure after 30 ps AIMD simulations nearly maintains the initial

26

hexagonal honeycomb structure with some weak puckers, as illustrated in the inset of

27

Figure 2b, which indicates the thermal stability of MnN monolayer. The elastic

28

constants of MnN monolayer were also calculated to further verify its mechanical

29

stability58-59. According to the Born elastic theory60-61, the elastic constant constitutes a

30

symmetric 6 × 6 tensor matrix in the linear elastic range. Our calculated elastic

31

constants are C11 = 36.663 GPa, C22 = 36.663 GPa, C12 = 32.193 GPa, and C44 =

32

2.235 GPa, respectively (see details in Supporting Information, Table S2). All these

33

elastic constants comply well with the Born criteria for the 2D hexagonal crystal60-61, 4


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that is C11 > 0, C22 > 0, C44 > 0 and C11C22 −C122 > 0, confirming MnN monolayer is

2

mechanically stable. All above analyses of the dynamical, thermal, and mechanical

3

properties of MnN monolayer consistently demonstrate its stability under ambient

4

environment.

5 6

Figure 1. Schematic diagrams of the top and side views of 2D MnN 2×2×1 supercell structure, the purple and blue

7

balls represent Mn and N atom, respectively,

8 9

Figure 2. (a) Phonon spectrum, total and partial density of phonon states; (b) total potential energy fluctuations of

10

MnN monolayer during 30 ps AIMD simulation at 300 K, and the final puckered structures after AIMD simulation

11

are also shown.

12 5



1

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Electronic structure and magnetic properties at equilibrium lattice

2 3

Electronic structure and magnetic properties of the material at equilibrium lattice are

4

important to investigate its potential application for spintronic devices. We firstly

5

found out that the total energy of spin-polarized MnN monolayer is lower than that of

6

the spin-unpolarized MnN monolayer by more than 0.40 eV/atom. Then, we

7

calculated the magnetocrystalline anisotropy energies (MAEs) of MnN unit cell by

8

considering the effect of spin-orbital coupling. Herein, two magnetization directions

9

in plane, namely [100] and [110] direction, and two directions out of plane, namely

10

[001] and [111] directions, are considered. The calculated MAEs by the hybrid

11

functional HSE06 for [100], [110], and [111] directions are 135.59, 134.27, and

12

160.00 μeV/Mn atom relative to the [001] direction, respectively, as shown in Table

13

S3, which indicates the magnetic moment along the [001] direction (out-of-plane) is

14

much more stable than other directions. Thus, the easy axis (EA) of MnN monolayer

15

is along the [001] direction (out-of-plane), which is consistent with 2D Fe2Si62 and

16

FeC235 sheet.

17 18

The 4×4 supercells of MnN monolayer with one ferromagnetic (FM) and six

19

antiferromagnetic (AFM) spin orderings along the [001] direction were constructed

20

based on the previous work of 2D hexagonal ferromagnetic materials42,

21

schematically shown in Figure S1. The exchange energy (Eex) between FM and AFM

22

spin ordering structures is thus calculated by the formulas of Eex = EAFM – EFM based

23

on the GGA+U method, which has been already successfully applied for 2D metal

24

halides42. If the exchange energy is positive, the ground state of 2D MnN monolayer

25

system is ferromagnetic. To evaluate the sensitiveness of the magnetic state to the

26

Hubbard U parameter, Eex of the MnN 4×4 supercell with different U values have

27

been calculated, as shown in Figure S2. It confirms that FM state is more preferable

28

than the AFM state for all considered U values and Eex converges to 0.410 eV/Mn

29

atom around U = 6.0 eV, which validates our choice for Hubbard U parameter for

30

Manganese of 5.5 eV based on the previous study on manganese (III) compound52.

31

According to these calculated positive exchange energies of other antiferromagnetic

32

(AFM) spin orderings (Figure S1), MnN monolayer prefers the FM ground state with

33

magnetic moment along the [001] direction. Therefore, we only focus on the FM 6


63

, as

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1

ground state with magnetic moment along the [001] direction to study the electronic

2

structure and magnetic properties in the following.

3 4

The spin-polarized band structures and total density of electron states (TDOS) were

5

calculated at HSE06 level for better understanding of the electronic structures and

6

magnetic properties of MnN monolayer. Viewed from Figure 3, MnN monolayer

7

exhibits completely different electron conductivities of the spin-up and spin-down

8

channels. The spin-down channel shows a very large direct band gap of 5.249 eV with

9

an insulator feature, while the spin-up channel shows metallic characteristic due to the

10

considerable occupied electron states cross the Fermi energy level. Therefore, MnN

11

monolayer is intrinsically half-metallic, and hence has 100% spin polarization near

12

the Fermi level, which is quite different from its rocksalt-structured phase without any

13

spin polarization (Figure S3). Moerover, the partial density of electron states (PDOS)

14

and partial charge distributions were also calculated to understand the bonding

15

mechanism of Mn-N (see details in Supporting Information, Figure S4).

16 17

We note from Figure S4 that Mn 3 orbital is non-degenerate and does not bond to

18

other orbitals. The double-degenerate Mn 3dxz and 3dyz spin-up and -down states

19

overlap with N pz states and form π-type bonding orbitals parallel to the plane of MnN

20

monolayer. The Mn 3dxy and Mn 3 states are doubly degenerate, hybridizing

21

with a Mn 4s state and forming three Mn sd2 hybrid orbitals. These sd2 hybrid orbitals

22

overlap with three N sp2 hybrid states and form a MnN hexagonal sheet. This Mn

23

3d-orbital split is a typical picture for the trigonal-type complexes, which is quite

24

different from the common 3d orbital splitting of the octahedral symmetry crystal

25

with lower energy orbitals t2g (3dxy, 3dxz and 3dyz) and higher energy orbitals eg

26

(3 and 3 )64-65. This is because that the symmetry and potential field of Mn

27

atom in this 2D MnN monolayer is different from that of 3D octahedral crystal, which

28

is consistent with the previous relevant report of the CrN monolayer36.

29 30

Mn 4s, 3dxy and 3 orbitals strongly overlap with N 2s, 2px and 2py orbitals,

31

respectively, and two electrons from 3dxy and 3 orbital of Mn atom exactly

32

pair with two electrons from 2px and 2py orbital of N atom, respectively, leaving three

33

unpaired 3d electrons of Mn atom and one unpaired 2p electron of N atom. Due to 7



1

100% spin polarization of these four unpaired valence electrons near the Fermi level,

2

MnN monolayer has a net magnetic moment of 4 per unit cell. Here, Mn atom

3

contributes to three quarters of the magnetism with major spin-densities, as the spin

4

charge density plots shown in Figure 3c. MnN monolayer with a wide half metallic

5

gap and large spin polarization can effectively serve in room temperature spintronic

6

devices.

7 8

Figure 3. Electronic structure of MnN monolayer at HSE06 level. (a) Spin-polarized energy band structure of MnN

9

monolayer; (b) Spin-polarized total density of electron state (TDOS) of MnN monolayer; Spin-up and spin-down

10

is depicted in black and red, respectively. The dashed lines in (a) and (b) indicate the Fermi level. (c) Top and side

11

views of the spatial spin density distribution isosurfaces (0.01 e Å−3) of MnN monolayer. The yellow and

12

light-blue isosurfaces correspond to spin-up and spin-down states, respectively.

13

8


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1

Curie temperature

2 3

Curie temperature of the ferromagnetism–paramagnetism transition for ferromagnetic

4

materials near or above 300 K is another critical determining factor for the practical

5

room temperature spintronic devices. Because of the magnetic moment of MnN

6

monolayer perferring the out-of-plane [001] direction (see details in Supporting

7

Information, Table S3), and the calculated MAEs by the HSE06 method being

8

comparable to the reported 2D Ising-like ferromagnetic CrXTe3 and Fe2Si sheets62, 66,

9

the Kosterlitz-Thouless transition is unlikely to occur in MnN monolayer67. Thus,

10

Curie temperature of MnN monolayer can be estimated by using statistical Monte

11

Carlo (MC) simulations based on the Ising model. This calculation method has been

12

widely used to estimate the Curie temperature of 2D materials35, 68. In the 2D Ising

13

model, the nearest neighboring spin interactions can be approximatively equivalent to

14

an exchange constant J, and the spin system energy is described by the classical

15

Hamiltonian of Ising model: H = − ,

16

where J represents the magnetic exchange coupling constant between two

17

neighboring i and j spins, and S and S are spin parallels or anti-parallels to the

18

vacuum direction of 2D model, respectively for i and j site. The exchange coupling

19

constant J can be evaluated from the exchange energy between FM and AFM spin

20

arrangements in Figure S1 in Supporting Information. Here, we adapted the highest

21

energy AFM spin arrangement for exchange coupling constant J calculation based on

22

the previous work about 2D hexagonal crystal structure42, 63, 69: J =

2

23

where Eex is 0.408 eV per Mn atom (unit cell), z is the number of the nearest

24

neighbors around one Mn atom (z = 6 for 2D hexagonal crystal structure), and S is the

25

net magnetic moments of 4 per unit cell of MnN monolayer. Therefore, the

26

corresponding estimated exchange coupling constants J is determined here to be 8.499

27

meV.

28

9



Page 10 of 24

1

Then, MC simulations for 105 steps by using the Metropolis algorithm and a 2D

2

hexagonal 8080 grid points with periodic boundary conditions were performed to

3

study the ferromagnetic systems. The calculated magnetizations per unit cell (Mn

4

atom) of the unstrained MnN monolayer as a function of different temperatures are

5

depicted in Figure 5a. Below the ice point of 273.15 K, all spins in MnN monolayer

6

are aligned in parallel, providing a FM state. However, when temperature exceeding

7

400 K, spins tend to be randomly aligned due to the stronger temperature perturbation,

8

resulting in zero net magnetization (PM state). Our calculated Curie temperature of

9

the FM-PM phase transition for MnN monolayer is ~368 K, which is higher than the

10

room temperature. This indicates MnN monolayer meets the basic condition of

11

applying ferromagnetic materials for the practical room temperature spintronic

12

devices. In addition, our calculated Curie temperature of MnN monolayer is

13

comparable with some other 2D ferromagnetic materials, such as metal halides MX2

14

(X = Cl, Br and I) (23–138 K)42, CrSnTe3 (170 K)66, and FeC2 (245 K)35.

15

16 17

Figure 5. (a) Variations of the calculated magnetizations (in per unit cell) of MnN monolayer with respect to

18

different temperatures and equi-biaxial strains. (b) Total magnetic moment (in per unit cell) at 0 K and Curie

19

temperature of MnN monolayer with respect to different equi-biaxial strains

20 21 22

Strain effect

23 24

Strain effect on the electronic structure and magnetism of 2D materials is another

25

important concern for their applications in spintronic devices37,

26

studied the effect of strain on the electronic structure and magnetic properties of MnN 10


40, 70-72

. Here, we

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1

monolayer, and applied a series of equi-biaxial strains from −10% to 30% to MnN

2

monolayer whose atomic positions were fully relaxed. The strain is defined as ε = (a –

3

a0)/a0 × 100% = (b – b0)/b0× 100%, where a, b and a0, b0 are the lattice constants of

4

the unit cell under strain and at equilibrium, respectively. Here, the positive and

5

negative ε represents the tensile and compressive strain, respectively. The lattice

6

constant a, Mn-Mn and Mn-N bond length of the strained MnN monolayer systems

7

are summarized in Table S4 in Supporting Information. The energy-strain and stress–

8

strain curves of MnN monolayer were calculated, as shown in Figure S5 in

9

Supporting Information. Applying strain on the equilibrium monolayer can increase

10

its total energy and stress, as expected. When applying equi-biaxial strains from 20%

11

to 30%, the stress of MnN monolayer doesn’t further change. We note that an

12

equi-biaxial strain of 30% doesn’t exceed the elastic limit of MnN monolayer,

13

because no rapid attenuation of its stress response upon strain is observed in Figure

14

S5. Considering it is difficult to reach those strains more than 10% in the

15

experimental operations and practical applications, so we only focus our discussions

16

on the electronic and magnetic property changes upon equi-biaxial strains ranging

17

from −10% to 10%. The total magnetic moments ( per unit cell) at HSE06 level of

18

MnN monolayer with respect to the realistic equi-biaxial strains ranging from −10%

19

to 10% were calculated, as shown in Figure 5b and summarized in Table S3 in

20

Supporting Information. It can be seen that both these compressive and tensile strains

21

don't change the total magnetic moment of MnN monolayer at all.

22 23

For better understanding the rigidity of the total magnetic moment under different

24

equi-biaxial strains, the spin-polarized total density of electron states (TDOS) at

25

HSE06 level of MnN monolayer under different equi-biaxial strains ranging from −10%

26

to 10% were calculated, as depicted in Figure 6. The robust band gaps of the

27

spin-down channels and the metal-like spin-up channels of those strained MnN

28

monolayer are preserved, displaying 100% spin-polarization near the Fermi level,

29

which are similar to the unstrained case. Band gaps and band edges of the spin-down

30

electron state at HSE06 level for MnN monolayer under different strains are depicted

31

in Figure 7. A closer look shows the band gaps of the spin-down electron states

32

decrease upon compressive or tensile strains (Figure 7a), especially for the

33

− 8 % and 10 % strained systems, which are similar to those cases of the band gaps 11



1

of 2D MoS273-74 and phosphorene (in the zigzag direction)75 semiconductors

2

decreasing upon the applications of tensile or compressive strains. It can be seen from

3

Figure 7b that the valence band maximum (VBM) of the spin-down electron states

4

with respect to the Fermi level goes up from -3.340 eV (unstrained system) to -2.891

5

eV (-6% compressive strain), then goes down to -3.937 eV (-10% compressive strain)

6

when the compressive strains increasing from 0% to -10%. Meanwhile, the

7

conduction band minimum (CBM) significantly shifts down from 1.909 to 0.625 eV

8

when the compressive strains increasing from 0% to -10%, whereas the shifts of band

9

edge don't display a linear function upon strain. The nonlinear shifts of

10

energy-band-edge upon strain can be explained by the Heitler-London's exchange

11

energy model75, that the energy-band-edge shifts are closely related to the

12

bonding/antibonding nature of the near-band-edge orbitals upon strain76. Even MnN

13

monolayer under moderate strains (-2% and 2%), its VBM and CBM still shift

14

significantly. During the stretching period with increased tensile strains from 0% to

15

10%, VBM markedly goes up from -3.340 to -2.415 eV, and CBM also shifts up from

16

1.909 to 2.194 eV (8% tensile strain), then goes down to 2.177 eV (10% tensile strain).

17

The increasing magnitude of VBM is larger than that of CBM, thus the corresponding

18

band gaps of spin-down states of those MnN monolayers under compressive strains

19

significantly reduce. Moreover, we also calculated the DOS of these strained MnN

20

monolayer by GGA+U method for validating those calculated results by HSE06

21

method, as shown in Figure 7 and Figure S6 in Supporting Information. The

22

calculated CBM edges of spin-down states by HSE06 method are in good accordance

23

with those by GGA+U method, while the VBM edges and band gaps calculated by

24

HSE06 method are larger than those by GGA+U method, which is common for DFT

25

calculation. Although there are absolute deviations between the band gaps calculated

26

by these two methods, the variation trend of band gaps calculated by HSE06 method

27

is basically consistent with that by GGA+U method. In this section, we only focus on

28

the variation of band gap upon different strains rather than the absolute value, so both

29

the HSE06 and GGA+U method are competent for producing the variation of band

30

gap.

31 32

In general, strains from -10% to 10% don't significantly change the electronic

33

structure of MnN monolayer (Figure 6), and 100 % spin-polarizations near the Fermi 12


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1

level of these strained system are fully preserved by the robust band gaps of

2

spin-down channels, so their magnetic properties are completely same as the

3

unstrained system (Figure 5b). MnN monolayer shows excellent FM half metallic and

4

magnetic stability upon external strains from -10% to 10%, so the lattice mismatches

5

between MnN monolayer and substrate materials in the experimental synthetic

6

process don't affect its magnetic property at all. This is different from most reported

7

two-dimensional materials with variational magnetic moments upon strain32,

8

such as half-metallic 2D Fe2Si crystal with variable magnetic moments of 3.02-3.11

9

μ! under moderate strains (-3% to 3%)62. Our predicted MnN monolayer is promising

10

to be used for the spin electronic devices where the stable spin magnetic moment

11

against strain under room environment is needed.

37, 77

,

12 13

In addition, the dependence of Curie temperature of MnN monolayer with respect to

14

strain has been also studied. The energy difference between AFM and FM spin

15

ordering structures under compressive strain sharply goes down from 0.325 to 0.057

16

eV per unit cell, and the tensile strained systems slightly go down to 0.275 eV per unit

17

cell, as summarized in Table S4 in Supporting Information. It can be seen from Figure

18

5b that the response curve of Curie temperature v.s. strain is not monotonous, and it

19

reduces more rapidly under enhanced compressive strain than those under enhanced

20

tensile strain. In other words, Curie temperatures of those strained MnN monolayers

21

decrease with the biaxial tensile or compressive strain, indicating that there is no

22

room to ramp up Curie temperature of MnN monolayer by applying strain. Wu et. al.,

23

hold that the tensile strain reduces Curie temperature of 2D Fe2Si crystal, and the

24

compressive strain enhances Curie temperature, due to the monotonous variation of

25

Fe-Fe bond length resulting in the monotonous variation of the interaction between

26

neighbor Fe atoms62, which is different from our MnN crystal with non-monotonous

27

response. For 2D FeCl2, NbS2 and NbSe2 crystals, their Curie temperatures can be

28

dramatically enhanced by the tensile strain based on DFT calculations42, 69, in contrast

29

to 2D Fe2Si crystal and our MnN monolayer. Experimentally, the enhancement of

30

Curie temperature by tensile stress has been carried out in Fe64Ni36 Invar alloy

31

because of the increase of Fe-Fe interatomic distance78. While for the single layer

32

CrSnTe3, it is found that both compressive and tensile strains can reduce its Curie

33

temperature66, which is consistent with our MnN monolayer. Therefore, the energy 13



1

differences between the strained AFM and FM spin ordering structures (effective

2

couple interactions between neighboring magnetic atoms) are not the exclusive

3

responses to structural deformation (bond length of neighbor magnetic atoms), and

4

the variation of electronic structure upon strain may be another important factor.

5

Interestingly, except for the cases of the strained MnN monolayer under larger

6

compressive strain, the variation tendency of Curie temperature for the other strained

7

MnN monolayers is generally in accordance with the variation curve of band gap and

8

VBM edge of spin-down electron state (Figure 7). Since the protective effect of 100%

9

spin polarization near the Fermi level gradually diminished by the reduced band gap

10

under enhanced compressive or tensile strain, the energy differences between FM and

11

AFM structure gets smaller, and FM spin ordering structures are more likely to switch

12

to AFM or PM spin disordered structures. It is worth to point out that some other

13

important factors may also affect Curie temperature of our strained MnN monolayer.

14

More future efforts should be made to thoroughly figure out the general influence

15

mechanism of structural deformation, electronic structure and some other factors on

16

Curie temperature of 2D materials.

14


Page 14 of 24

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1 2

Figure 6. Spin-polarized total density of electron state (TDOS) near the Fermi level at HSE06 level of MnN

3

monolayer with respect to different equi-biaxial strains. The dashed line means the Fermi level is set to zero eV.

15



1 2

Figure 7. (a) Band gap (in eV) and (b) band edge (in eV) of spin-down electron state of MnN monolayer under

3

different equal-biaxial strains. All energies are referenced to vacuum level.

4 5

Summary

6 7

A graphene-like two-dimensional hexagonal MnN monolayer with unique electronic

8

structure and stable magnetic properties was studied by first-principles calculations.

9

According to AIMD simulations, phonon spectrum and elastic constants analyses,

10

MnN monolayer is thermally, dynamically and mechanically stable. Electronic

11

structure calculations indicate that MnN monolayer is intrinsically half-metallic with

12

a net magnetic moment of 4 per unit cell, due to the 100% spin polarization and

13

large band gap near the Fermi level. The Curie temperature of ~368 K of MnN

14

monolayer is estimated by MC simulations, which is higher than the room

15

temperature and

16

two-dimensional materials with variational magnetic moments upon strain, MnN

17

monolayer can maintain the FM half metallicity and a constant magnetic moment

not enhanced

by strain.

Different from most reported

16


Page 16 of 24

Page 17 of 24 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1

even under ± 10 % strains, due to the 100% spin polarization electron states near the

2

Fermi level being fully preserved by the robust band gap of spin-down electron states.

3

Our calculations indicate that the MnN monolayer could be a promising material for

4

the room temperature spintronic devices.

5 6 7

Author Information

8 9

Corresponding Authors

10

*

11

The authors declared that they have no conflicts of interest to this work.

E-mail: [email protected]

12 13 14

Supporting Information

15 16

Energy cut-off and k-point convergence. Elastic constants. Magnetic anisotropy

17

energies. Lattice constant, magnetic moment, average energy difference between

18

AFM and FM states, exchange coupling constant, energy band edge and band gap of

19

spin-down electron state respect to different equi-biaxial strains. AFM spin

20

arrangements. Energy difference between AFM and FM spin arrangements with

21

different

22

rocksalt-structured phase calculated by GGA. Energies and stresses response under

23

different equi-biaxial strains. Spin-polarized TDOS at GGA+U level respect to

24

different equi-biaxial strains.

Hubbard

correction

U

values.

Electronic

structures

of

MnN

25 26 27

Acknowledgements

28 29

This work is supported by the National Natural Science Foundation of China

30

(51602196) and the Shanghai Sailing Program (16YF1406000). All simulations were

31

performed at the Shanghai Jiao Tong University High Performance Computing Center.

32

The authors also thank Prof. Weidong Luo for the discussions.

33 17



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