Regulating electronic and magnetic properties in chromium trihalide monolayer

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Regulating electronic and magnetic properties in chromium trihalide monolayer Yuxiao Hou , Xiangfeng Liu , Laigui Wang PII: DOI: Reference:

S0039-6028(19)30789-7 https://doi.org/10.1016/j.susc.2019.121560 SUSC 121560

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Surface Science

Received date: Revised date: Accepted date:

23 October 2019 30 December 2019 30 December 2019

Please cite this article as: Yuxiao Hou , Xiangfeng Liu , Laigui Wang , Regulating electronic and magnetic properties in chromium trihalide monolayer, Surface Science (2020), doi: https://doi.org/10.1016/j.susc.2019.121560

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HIGHLIGHTS



The magnetic interaction is rationalized via a near 90º superexchange along CrI3-xBrx series.



The introduction of both V and Mn in cation site would give rise to half metallic nature, and magnetic ordering temperature(Tc) of the former is greatly enhanced.



The improvement of Tc is rationalized by the extra Cr dxy - I px - V dxy interaction, which is ferromagnetic.

Regulating electronic and magnetic properties in chromium trihalide monolayer

Yuxiao Hou1, Xiangfeng Liu1, Laigui Wang2,* 1

Department of Basic Teaching, Liaoning Technical University, Huludao, 125105, P. R. China 2

School of Mechanics and Engineering, Liaoning Technical University, Huludao, 125105, P. R. China

E-mail: [email protected]

Abstract: The accessible exfoliation of layered CrI3 [Nature 546 (2017) 270, Ref. 1] has inspired the upsurge of two-dimensional intrinsic magnetism, which is desirable for next generation of information technology. The underlying magnetic coupling mechanism is still in debate and their magnetic ordering temperature is far less than room temperature, which prohibits their real application. Herein, anion ion(iodine being replaced by bromine) and cation ions(Cr substituted by V/Mn) substitution are conducted using density functional theory, including both electron correlation(U) and spin-orbit coupling(SOC) effect, to provide an intuitive physical picture to understand their electronic and magnetic behavior. Our results indicate that the in-plane parameters, band gap, magnetic moment and magnetic ordering temperature can be tuned linearly via the concentration of bromine. Intriguingly, Both V and Mn substitution would give rise to half metallic character, a promising spintronic candidate. Moreover, V3+(3d2) would give rise to a V dxy - I px - Cr dxy exchange path, which is ferromagnetic, and thus hold great promise to enhance the magnetic ordering temperature (397K) being above room temperature.

Key words: CrI3; DFT; substitution; half metal; 2D intrinsic magnetism

1、Introduction In the limitation of long range magnetic ordering, graphene and its modified counterparts,[2-4] yet displaying a broad range of electronic properties, are beyond the utilization of spintronics. The successful exfoliation of two-dimensional(2D) CrI3 layers[1] has triggered tremendous interest[5-7] in which the ferromagnetic(FM) coupling between transition metal Chromium survives even down to monolayer, creating ample opportunity for both fundamental science and industrial applications. Further studies[8, 9] indicate that the low dimensional magnetic interaction can be ascribed to the spin-orbit coupling(SOC) effects of iodine, which breaks the SU(2) symmetry and thus Mermin-Wagner theorem[10] does not apply. The key to sustain FM in 2D material is the magnetic anisotropy-a tendency of spins to align in a certain crystallographic direction known as easy-axis, which is measured by the anisotropy energy. The experimental results[4] indicate that the CrI3 monolayer is an Ising FM with out-of-plane spin direction and a Curie temperature(Tc) of ~45K. It is of great interest to find that the spin orientation can be tuned by the in-plane lateral strain and/or charge doping,[11] that is, a tensile strain gives rise to a flip from off-plane to in-plane for the magnetic orientation. In addition, electron doping would further enhance this transition, making the in-plane FM phase stable under slight strain. Abramchuk et al have recently reported an experimental study on controlling the magnetic anisotropy via mixed halide in series CrCl3−xBrx[Ref. 5]. As a matter of fact, both CrCl3 and CrBr3 layers have been fabricated,[12, 13] following the pioneering work of CrI3. CrBr3 monolayer is confirmed to be Ising anisotropy with out-of-plane spin orientation, alike its sister-compound CrI3, whereas CrCl3 monolayer is found to

be with in-plane FM ordering, i.e., XY anisotropy. Abramchuk et al synthesized CrCl3-xBrx and demonstrated that a continuous change of easy-axis from in-plane to out-of-plane as a function of Br concentration(x). It is also revealed that the magnetic ordering temperature, optical gap, and the interlayer spacing are regulated linearly with x, providing a powerful technique to produce functional materials for spintronic devices. Nevertheless, the low dimensional intrinsic magnetism is far beyond the room temperature application in view of the low magnetic transition temperature. In this regard, much endeavor has been dedicated to enhance the FM interaction.[14-17] For instance, Li adsorption has been reported to be an effective measurement to improve Tc of CrI3 monolayer, and a semiconductor to half metal(HM)[18] transition can be turned.[14] Furthermore, cation deficiency(i.e., Cr defect) can also increase Tc and the defected case is HM,[15,16] similar as the Li-adsorption counterpart. Wang et al[17] interpreted the FM as the result of near-90º superexchange interaction and in their study, electron doping and hole doping are both positive to raise Tc. Yet it is regretful that none of the aforementioned measurements has effectively enhanced Tc to room temperature. Herein, CrI3 monolayer is studied with both anion and cation ions substitution using density functional theory(DFT) and both electron correlation(U) and spin-orbital coupling(SOC) are involved to guarantee an accurate description for both transition metal and heavy elements. It is revealed that physical properties of the titled monolayer would be tuned linearly by the concentration of Br, providing a promising platform for deep understanding of the low dimension magneto-electronics. Attractively, with V substituting Cr, the Tc can be improved greatly, making the resultant compound a great promise for room temperature application for 2D spintronics.

2、Computational method

The calculations were executed by VASP,[19-22] based on the projector augmented-wave(PAW) method.[23, 24] The exchange-correlation energy was treated by the GGA-PBE.[25] The plane wave cut-off energy was set to be 500eV. A mesh of 5×5×1 is used for optimization and a finer one with 9×9×1 was chosen for electronic calculations. A vacuum space of 15Å is adopted to avoid interactions between adjacent layers and Van der Waals(vdW) interaction correlation is considered by using the semiempirical dispersion-corrected DFT(DFT-D2) force-field approach.[26-27] The convergence criterion is 1.0×10-5eV for energy and 1.0×10-2eV/Å for force, respectively. Electron-electron Coulomb repulsion interactions(U) are involved in the rotationally invariant form (GGA+U)[28] with Ueff being tested for Cr (from 3.0 to 6.0eV (from 3.0 to 5.0 eV) and Mn (from 3.0 to 5.0 eV). SOC is included by a second variational procedure on a fully self-consistent basis.[29]

3、Results and discussion 3.1 anion substitution Bulk CrX3(X=Cl, Br and I) crystallize in the rhombohedral BiI3 structure(space group R3) at low temperature and can be transformed into the monoclinic AlCl3 structure(space group C2/m) with temperature increasing. The only difference for these two symmetries comes from the stacking pattern along c direction. In other words, only one framework of monolayer can be obtained after cleavage where the Cr3+ ions are arranged in a honeycomb network and coordinated by edge-sharing octahedra I/Br ions. We start with CrI3 monolayer and Br is introduced steadily from x=0.5 to 3 with per step of 0.5. Fig. 1 shows the most stable geometry structures for each concentration for simplicity (consistent conclusions can be drawn for other geometries, which is given in Table SI and Fig. S1) and Table 1 lists the in-plane parameters(a/b), the thickness of the monolayer(c), Cr-I/Br bond distance and the bond angles of I(Br)-Cr-I(Br). To be more intuitive, the evolution of lattice

parameters and volume are depicted in Fig. 2, which are decreased steadily with Br component increasing. This is understandable in view of the fact that the radii of Br is smaller than that of I and the slight fluctuation might come from the electronic effect. This also applies for the longer Cr-I bond distances and shorter Cr-Br bond distances. As far as the bond angles are concerned, the ∠ Cr-I-Cr is smaller than that of ∠ Cr-Br-Cr for specified x in all CrI3-xBrx monolayer. In order to confirm the magnetic coupling behavior for the mixed cases, the energy difference(∆E=EAFM - EFM) is examined and the results are given in Table 2. It is found that the FM ordering is more stable, independent on either the Br concentration or the value of U. Overall, the energy difference drops with Br increasing, consistent with the experimental findings that the Tc(scales with ∆E according to the mean fielsd theory as will be discussed later) of CrI3 monolayer is higher than that of CrBr3 counterpart. Besides, the values are larger when U is included and the larger the magnitude of U, the larger the energy difference. The individual spin magnetic moment of Cr, I/Br and total magnetic moment are shown in Table 3. For the parent compound, the spin moment of Cr is 3.01µB in GGA method and it is -0.08 µB for I, resulting in total moment of 2.79µB. This is well consistent with the reports in literature.[6, 7] The different sign from Cr to I indicates the spin moment are in opposite directions. When U is concerned, the electron of Cr 3d states becomes more localized and the magnitude is thus enhanced. For instance, it is 2.98µB and 3.09µB for U=4.0eV and U=6.0eV, respectively. Interestingly, the moment for I increases as well which can be understandable in view of the fact that the covalent effect is weaken with Cr 3d localization. On the other hand, with Br substituting I, the total magnetic moment drops slightly because of the small reduction of Cr moment, which can also be ascribed to the declined covalent effect. Semiconducting character is inherited form its bulk counterpart for CrI3 monolayer[4] and this is confirmed by Zhang's theoretical studies.[6] Our calculations for the pristine CrI3 monolayer is semiconducting with a band gap of ~0.9eV in the

spin up channel and a larger one of 2.0eV in the spin down channel in GGA method (Fig. 3). With U involved, the gap in the spin up channel remains while that in the spin down channel enlarged with U enhancement. That is, the unoccupied state is pushed upwards to higher energy region, making the gap in the spin down channel widen. On the other hand, the introduce of Br would also enlarge the band gap, especially that in the spin down channel. As shown in Fig. 3, with the content of Br growing, the valence band move downwards steadily from CrI3 to BrI3 monolayer. In regards of the individual substituted case, the inclusion of U would further push the conduction band to upper energy region, strengthening the band gap. In other words, the CrI3-xBrx (x=0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0) monolayers are semiconducting, regardless of U values. The magnetic ordering temperature is a critical parameter for industrial application, therefore, the Curie temperature(Tc) is evaluated from mean field approximation(MFA), according to which Tc=∆E/3kB. The calculated results are given in Table 4. Overall, the Tc is depressed with Br content growing. This is in good agreement of the experimental findings that the Tc of CrI3 monolayer is higher than that of CrBr3 counterpart. However, the value calculated is much higher than experimental value, for example, it is 301K for CrI3 monolayer in GGA calculation and even higher for GGA+U methods from our calculation, which is at least seven times as large as that from experiment(45K). When SOC is also involved, the estimated value drops to 224K (GGA+SOC), still five times as large as the real value. This is because the MFA neglects the effect of fluctuation of spins from their average values, which will overestimate the the true values. In the literature, the upper limitation can be twice to eight times as large as the true value.[30] However, the trend is useful for a series of compound. A retrospect of the electron structure reveals that the widen gap should be responsible for reduction of magnetic ordering temperature. This is because, with the Br increasing, the conduction band is narrowed,

which would be in favor of AFM coupling, instead of FM interaction along Cr-I/Br-Cr path, and hence the Tc is reduced. As far as the overall trend is concerned, the descent of Tc is almost linearly dependent on the concentration of Br from GGA and GGA+U methods. Whereas the involvement of SOC leads to a deviation of the linearity. This is consistent with the experimental findings[5] which rationalizes this trend from the stronger SOC and hybridization effect when moving from lighter to heavier halogen (Br to I in this case). This is also well agreed with our electronic structure analysis as mentioned above, i.e., the more Br, the more narrowed conduction band. Different spin orientation is considered to find the easy-axis, i.e., [001] (out-of-plane) and [110] (in-plane) direction. The energy difference (∆E = E001 - E110), i.e., magnetic anisotropy energy (MAE) is depicted in Table 5(with UCr=4.0eV, a typical value in literature) which is all negative, indicating the [001] direction is the easy-axis. This is consistent with experimental findings for CrI3 and CrBr3 monolayer. On the other hand, it is seen that the energy difference becomes smaller with Br content increasing, and this is understandable in view of weaken SOC effect for 4d (Br) compared with 5d electron(I).

3.2 cation substitution A magnetic material with practical application should have a large magnetic moment, a considerable spin polarization ratio, and a high TC in one. Bearing this in mind, cation substitution of Cr by V and Mn is studied to introduce additional freedom thus modify its electronic and magnetic properties. According to Wang's study, the FM interaction is attributed to the superexchange channels via the near-90º Cr-I-Cr bonds, i.e., one from the stronger pdσ hybridization via the orthogonal (px, py) osuperexchange interactionrbitals, and the other involves the relatively weak pdπ hybridization via the same px orbital.(Fig. 4a and 4b) With V/Mn introduced, the

picture would be changed in view of the fact that V3+(3d2) and Mn3+(3d4) would give rise to additional potential exchange interaction. We start with V substituted case and the DOS are shown in Fig. 5. In GGA method, it is HM with spin up electrons crossing the Fermi level, and the conduction electrons are contributed by V 3d states. With U concerned, the V 3d electron would be pushed down to lower energy region, leaving it semiconducting(i.e., UV=3.0 eV and 4.0eV). Attractively, with U enlarged to be 5.0eV, the HM is recovered. To understand the peculiar electronic behavior, possible magnetic exchange interaction is discussed in Fig. 4c. In contrast to Cr3+(3d3) which is half filled in t2g state, V3+ has two electrons in the triple-degenerated orbitals. This would trigger a charge transfer from the Cr dxy to V dxy via I px, which is kinetically favored by FM. In view of the strong covalent ability of I, it would be stronger than the aforementioned Cr dx2-y2 - I px - Cr dxy interaction. Also, the additional freedom in t2g state and the charge transfer would give rise to metallic character as in CoGa2X4(X=S, Se, or Te).[31] Furthermore, since the extra magnetic coupling is FM, Tc would be enhanced. The hypothesis is verified by the value calculated in Table 6. It is seen that Tc is raised from 301.7K to 463.3K in GGA method and the enhancement would be more remarkable with U included. For instance, with UCr=5.0eV and UV=3.0eV, Tc would be 2783.5K. Even though the calculated value for CrI3 monolayer is seven times as large as the true value, after correcting such overestimation by a scaling factor of 1/7, the value for V substituted case(2783.5K/7=397K) still holds great promise to be higher than room temperature. On the other hand, the Mn replaced resultant monolayer is HM as well(Fig. 7), regardless U(and its value) included or not. However, magnetic ordering temperature would be reduced greatly(Table 6). This is because, as shown in Fig. 4d, the extra electron in dx2y2 orbital would result in a charge transfer along dx2y2-px-dx2y2 path, which is double exchange, yet it would be depressed in view of the near-90º rather than 180º Mn-I-Cr bond angle. Meanwhile, the strong pdσ superexchange is prohibited. As a result, the FM interaction is weaken.

4、Conclusion In conclusion, the electronic and magnetic behavior is investigated for two-dimensional CrI3 monolayer via both anion and cation ion substitution, within the framework of density function theory, including both electron correlation and spin-orbital coupling. The evolution of lattice parameters, band gap, magnetic moment for transition metals, magnetic temperature and magnetic anisotropy energy is predicted via mixed halide chemistry. With V and Mn substitution, it is half metallic and the former hold great promise to enhance the magnetic ordering temperature with the introduction of V dxy - I px - Cr dxy magnetic interaction.

Author statement The authors´ contribution to the paper entitled “Regulating electronic and magnetic properties in chromium trihalide monolayer” is as following: Dr Hou and Prof. Wang conceived the research plan. Dr Hou and Dr Liu did the computational work and data analysis. Dr. Hou drafted the manuscript and with final approval by all authors.

Conflict of interest This statement is to certify that authors of the paper entitled “Regulating electronic and magnetic properties in chromium trihalide monolayer” declared that they have no conflicts of interest to this work.

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Table 1 Structure parameters for CrI3-xBrx (x=0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0). x

0

0.5

1.0

1.5

2.0

2.5

3.0

Space group

P-31M

CM

CM

P31M

CM

CM

P-31M

a/b(Å)

6.868

6.766

6.763

6.670

6.535

6.470

6.340

c(Å)

3.143

3.208

3.206

3.008

3.077

3.089

2.887

α/(°)

90.0

90.0

90.0

90.0

90.0

90.0

90.0

β(°)

90.0

90.0

90.0

90.0

90.0

90.0

90.0

γ(°)

120.0

119.1

121.1

120.0

119.5

120.8

120.0

V(Å3)

128.37

128.25

125.60

115.90

114.34

111.04

100.50

2.724

2.718

2.733×2

2.728×2

2.720×3

2.714×2

2.711

2.736×2

2.736 2.527×2

2.520×2

2.534

2.522

2.540

2.530×2

89.5

89.0

94.1

93.6

94.2

93.7

97.8

97.3

Cr-I(Å)

2.737×6

Cr-Br(Å)

∠ Cr-I-Cr(°)

∠ Cr-Br-Cr(°)

2.544

92.8

2.543×2

89.1

89.5

93.1

93.4

93.2

93.8

97.4

97.8

2.542×3

90.2

98.5

2.517×6

93.3

Table 2 Energy difference(∆E=EAFM-EFM in eV) for CrI3-xBrx (x=0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0) from GGA and GGA+U methods. x

0

0.5

1.0

1.5

2.0

2.5

3.0

GGA

0.039

0.043

0.036

0.036

0.033

0.031

0.028

UCr=3.0eV

0.052

0.057

0.047

0.047

0.044

0.042

0.040

UCr=4.0eV

0.053

0.060

0.051

0.049

0.047

0.045

0.042

UCr=5.0eV

0.060

0.063

0.054

0.052

0.049

0.047

0.045

UCr=6.0eV

0.064

0.068

0.057

0.054

0.052

0.049

0.047

---

0.029

0.030

0.025

0.023

0.023

0.021

0.020

UCr=3.0eV

0.047

0.049

0.039

0.040

0.035

0.031

0.029

UCr=4.0eV

0.048

0.046

0.040

0.039

0.036

0.033

0.030

UCr=5.0eV

0.050

0.050

0.044

0.036

0.032

0.031

0.030

UCr=6.0eV

0.052

0.054

0.045

0.040

0.038

0.035

0.032

GGA+U

GGA+SOC +U

Table 3 Individual and total spin moment(µB) for CrI3-xBrx (x=0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0) from GGA and GGA+U methods. x

0

0.5

1.0

1.5

2.0

2.5

3.0

Cr

3.01

3.01

3.00

2.99

2.97

2.95

2.93

I

-0.08

-0.08

-0.08

-0.09

-0.09

-0.08

--

Br

--

-0.04

-0.04

-0.04

-0.05

-0.05

-0.05

total

2.89

2.89

2.89

2.89

2.89

2.89

2.89

Cr

3.32

3.30

3.27

3.25

3.22

3.19

3.15

I

-0.13

-0.13

-0.13

-0.14

-0.14

-0.13

--

Br

--

-0.08

-0.08

-0.08

-0.09

-0.09

-0.09

total

2.94

2.93

2.93

2.92

2.91

2.90

2.90

Cr

3.42

3.39

3.36

3.34

3.30

3.26

3.22

I

-0.14

-0.15

-0.15

-0.15

-0.15

-0.15

--

Br

--

-0.10

-0.10

-0.10

-0.10

-0.10

-0.10

total

2.99

2.98

2.97

2.96

2.95

2.94

2.94

Cr

3.51

3.48

3.45

3.42

3.38

3.33

3.29

I

-0.16

-0.16

-0.17

-0.17

-0.17

-0.16

--

Br

--

-0.11

-0.11

-0.11

-0.11

-0.11

-0.11

total

3.03

3.02

3.01

3.00

2.99

2.97

2.96

Cr

3.61

3.57

3.54

3.50

3.46

3.41

3.36

I

-0.18

-0.18

-0.18

-0.18

-0.18

-0.18

--

Br

--

-0.12

-0.12

-0.12

-0.12

-0.12

-0.12

total

3.08

3.07

3.05

3.04

3.03

3.01

3.00

GGA

3.0eV

4.0eV

5.0eV

6.0eV

Table 4 Curie temperature(Tc, in K) calculated for CrI3-xBrx (x=0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0) from GGA and GGA+U methods. x

0

0.5

1.0

1.5

2.0

2.5

3.0

GGA

301.7

332.6

278.5

278.5

255.3

239.8

216.6

UCr=3.0eV

402.3

440.9

363.6

363.6

340.4

324.9

309.4

UCr=4.0eV

410.0

464.2

394.5

379.0

363.6

348.1

324.9

UCr=5.0eV

464.3

487.4

417.7

402.3

379.0

363.6

348.1

UCr=6.0eV

495.1

526.0

440.9

417.7

402.3

379.0

363.6

--

224.2

231.9

193.3

177.8

177.7

162.3

154.6

UCr=3.0eV

363.3

378.8

300.3

309.2

270.1

239.6

224.2

UCr=4.0eV

369.2

355.6

309.2

301.4

278.2

255.1

255.0

UCr=5.0eV

386.5

386.5

340.1

278.2

247.4

239.6

231.9

UCr=6.0eV

401.9

417.4

347.8

309.2

293.7

270.6

247.4

GGA+U

GGA+SOC+ U

Table 5 Magnetic anisotropy energy(eV) calculated for CrI3-xBrx (x=0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0) from [001] to [011] orientation. x

0

0.5

1.0

1.5

2.0

2.5

3.0

GGA+U(UCr=4.0eV)

-0.036

-0.030

-0.028

-0.022

-0.026

-0.024

-0.020

Table 6 Curie temperature(Tc, in K) calculated for V and Mn substituted cases from GGA and GGA+U methods. V substitution

Mn substitution

463.3

14.9

UCr=3.0eV

703.6

139.4

UCr=4.0eV

2757.0

167.2

UCr=5.0eV

2783.5

195.0

UCr=6.0eV

495.1

221.5

GGA

GGA+U

Top view

Side view x Cr atom

0.0

0.5 I atom

1.0

1.5

2.0

2.5

Br atom

Fig. 1. Side view and top view for the CrI3-xBrx (x = 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0) schematically.

Fig. 2. Variation of volume and in-plane lattice as a function of Br conten

3.0

x

0.0

0.5

1.0

GGA

U=3.0eV

U=4.0eV

U=5.0eV

U=6.0eV

1.5

2.0

2.5

3.0

Fig. 3. Density of States for the CrI3-xBrx (x = 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0) from GGA and GGA+U methods.

Fig. 4. Schematic plot of FM superexchange interactions in CrI3 monolayer and V/Mn substituted cases. (a) and (b) dx2-y2- (px, py)-dx2-y2 path and dx2-y2- px-dxy path in CrI3 monolayer, (c) dxy- px-dxy path in V substitution, (d) dx2-y2- (px, py)-dx2-y2 path in Mn substitution.

Fig. 5. Density of States for the VCrI6 from (a) GGA and (b-d) GGA+U methods. UCr=5.0 eV and UV= 3.0-5.0eV from (b)-(d).

Fig. 6. Density of States for the MnCrI6 from (a) GGA and (b-d) GGA+U methods. UCr=5.0 eV and UMn= 3.0-5.0eV from (b)-(d).

GRAPHICAL ABSTRACT