- Email: [email protected]
Band engineering in intrinsically magnetic CrBr3 monolayer
Journal of Magnetism and Magnetic Materials 502 (2020) 166608
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Research articles
Band engineering in intrinsically magnetic CrBr3 monolayer ⁎
Jinjin Yang, Jing Wang , Qian Liu, Rui Xu, Yuling Sun, Zhiping Li, Faming Gao, Meirong Xia
⁎
T
Key Laboratory of Applied Chemistry, Hebei Key Laboratory of Heavy Metal Deep-Remediation in Water and Resource Reuse, School of Environmental and Chemistry Engineering, Yanshan University, No. 438, Hebei St(W), Qinhuangdao 066004, PR China
A R T I C LE I N FO
A B S T R A C T
Keywords: CrI3 Vacancy Carrier doping Strain Half metal
The discovery of the intrinsic magnetism of CrI3 monolayers (Nature 2017, 546, 270) serves as a new platform to regulate electrons. In this study, the electronic structure of the CrBr3 monolayer, a sister compound of CrI3, has been studied based on the first principle calculations and band engineering strategies involving carrier doping, vacancies (Cr vacancy, Br vacancy and the co-presence of Cr and Br vacancies) and in-plane strain. An insulator to half metal character transition could be actualized via charge doping (both hole and electron doping) and Cr vacancy. With co-existing Cr and Br vacancies, the half metallic character is sensitive to the distance between the defects. In contrast, the insulating nature would survive under conditions of Br vacancy defect as well as in-plane strain; however, the cooperation of strain and carrier doping would lead to half metal behavior. With regard to stabilization of ferromagnetic coupling, hole doping, electron doping and tensile strain would be effective; hole doping is more efficient than electron doping, and the co-existence of hole doping and tensile strain would further enable this enhancement.
1. Introduction The accessible exfoliation of layered Cr2Ge2Te6 and CrI3 from their bulk counterparts has closed the gap for two-dimensional (2D) intrinsic magnets [1,2]. Spintronics [3], which utilizes spin instead of charge in electronic devices, has long been desired by material scientists, and these 2D intrinsic magnets enable a significant step forward to achieve full spin polarization [4]. Attractively, exotic electronic and magnetic characteristics have been reported among these 2D intrinsic magnets [5–9]. For instance, the CrI3 monolayer is ferromagnetic (FM), as is its bulk counterpart; however, the bilayer is antiferromagnetic (AFM) between layers. With increasing layers, the FM nature is recovered in the tri-layered system [1]. More interestingly, the CrI3 bilayer displays an AFM-FM transition with increasing magnetic field [5], and this transition can also be tuned via voltage control [6]. To understand the unique physical behavior, electronic structure and magnetic coupling manner of chromium trihalides CrX3 (X = Cl, Br, I), as well as their monolayers have been investigated in the literature [10–12]. The exceptional FM magnetic coupling of the CrI3 monolayer is well rationalized by Wu et al. based on a model Hamiltonian. Moreover, to make the most of the 2D intrinsic magnet, Wu et al. reported an insulator to half metal (HM) transition via charge doping in a CrI3 monolayer [12]. Similarly, HM is also designed through Li atom adsorption [13]. In both cases, not only is 100% spin
⁎
polarization manipulated via the unique HM quantum state, but also the FM interaction is enhanced as a result of the appearance of itinerant electrons. Vacancy, which is omnipresent in samples, have now been widely adopted as a powerful tool for band modification. It has been found that either Cr vacancy [14] or I vacancy [15] would strengthen the magnetic moment and thus improve the Curie temperature (Tc). Moreover, Zheng et al. found that the magnetic ground state of the CrI3 monolayer is sensitive to lateral strain, and a FM to AFM flip can be triggered easily by compression strain [6]. As one of the chromium trihalides, the study of the CrBr3 monolayer is less common, not to mention its band engineering. In fact, CrBr3 and CrI3 have several similarities, i.e., FM and insulating properties [16,17]. Another common trait is that both of them exhibit 3D-Ising character [18,19]. This is different from the CrCl3 monolayer, which performs 2DHeisenberg behavior. In our previous studies [14,20], an insulator to HM transition could be fabricated in both CrCl3 and CrI3 monolayers; however, certain details are different. For instance, although the nominal valence states of Cr are 3+ in both cases, the magnetic moment is larger in the CrI3 monolayer: this can be ascribed to the strong covalent ability of I which, in return, is accounted for the higher magnetic ordering temperature of CrI3. Since CrBr3 is intermediate within this family and is seldom disclosed, understanding the electronic and magnetic behavior is of great importance. Inspired by these considerations, band engineering, including atomic vacancy, charge doping
Corresponding authors. E-mail addresses: [email protected] (J. Wang), [email protected] (M. Xia).
https://doi.org/10.1016/j.jmmm.2020.166608 Received 19 July 2019; Received in revised form 11 December 2019; Accepted 10 February 2020 Available online 11 February 2020 0304-8853/ © 2020 Elsevier B.V. All rights reserved.
Journal of Magnetism and Magnetic Materials 502 (2020) 166608
J. Yang, et al.
Fig. 1. (a) Top and side views of the CrBr3 monolayer. (b) Density of states for CrBr3 monolayer from GGA + U (UCr = 5.0 eV) method. Table 1 Structure parameters for bulk and monolayer CrBr3. Our calculations
Ref. 19
Ref. 7
Ref. 8
Ref. 32
Space group
Bulk C2/m
Bulk R-3
Single layer P-31M
Bulk R-3
Bulk R-3
Bulk R-3
Single layer
Bulk R-3
a(Å) b(Å) c(Å) β/γ(°) Cr-Br(Å)
6.337 10.972 6.474 108.6 2.513 × 2 2.515 × 2 2.519 × 2
6.335 6.335 18.356 120.0 2.516 × 6
6.340 6.340 2.889 120.0 2.517 × 6
– – – – 2.496 × 6
6.496 6.496 – – 2.545 × 6
6.435 6.435 20.836 – –
6.433 6.433 – – –
6.260 6.260 18.20 – –
Fig. 2. Density of states for CrBr3 monolayer with (a) 0.2 h and (b) 0.2 e doping from GGA + U (UCr = 5.0 eV) method.
6.0 eV. To maintain consistency with our previous studies [14,20], only the result from U = 5.0 eV is discussed. The phonon dispersion is calculated using the Phonopy package [31] with the finite displacement method. The other calculation parameters are consistent with our previous works [14,20].
and lateral strain, has been conducted on the CrBr3 monolayer. The results are compared with those from CrCl3 and CrI3 to complete the study of this family. 2. Computational details
3. Results
Structural relaxations and electronic properties were calculated by VASP [21–24], based on the projector augmented-wave (PAW) method [25,26]. The van der Waals interaction (vdW) correlation is considered by using the semiempirical dispersion-corrected density functional theory (DFT-D2) force-field approach [27,28] and a vacuum space of 15 Å is employed to avoid the influence of interlayer interaction. The exchange–correlation energy was treated by the GGA-PBE [29]. Electron-electron Coulomb repulsion interactions (U) for Cr are tested in the rotationally invariant form (GGA + U) [30] with Ueff from 3.0 to
We start our research with a pristine CrBr3 monolayer (Fig. 1(a)). We do not discuss this part in details, but it agrees well with those in the literature [7–8,19,32] and serves as a basis for the next step of calculations. The results of cleavage energy (0.20 J/m2 for C2/m and 0.13 J/ m2 for R-3 phase, Fig. S1) and phonon dispersion (Fig. S2) provide evidence that the isolation from bulk is feasible and that the monolayer is thermodynamically stable. The 2D Young's modulus is then estimated 2
Journal of Magnetism and Magnetic Materials 502 (2020) 166608
J. Yang, et al.
the spin down channel would remain under a critical doping concentration. To verify this speculation, carrier (including both hole and electron) doping is simulated. With regard to hole doping, as expected, an insulator to HM transition would take place even with a small amount of dopant, such as 0.1 h. Interestingly, the HM state could survive until 1.0 h (Fig. 2(a) for 0.2 h and Fig. S3 for 0.1 h and 1.0 h). On the other hand, electron doping will also lead to HM character, but the difference lies in the fact that the EF moves upwards to the conduction band. As shown in Fig. 2(b) for 0.2e doping, the Cr eg state resides across the EF, thus playing the role of conduction electrons. It is essential to verify whether the FM coupling still survives after carrier doping. To do this, the relative energy from AFM to FM is examined (Fig. 3). It is obvious that the FM coupling is guaranteed regardless of the dopant types (black line in Fig. 3). However, the promotion of FM stability is stronger via hole doping, which is similar to the case of the CrI3 monolayer [12]. Since magnetic ordering temperature scales with the energy difference (T = ΔE/3kB) from the mean field theory (MFT), the Curie temperature (Tc) would be enhanced as well, especially for hole doping. According to our calculations, the FM state is lower by ~ 44.8 meV in the pristine case, which gives rise to an estimation of Tc as 173 K, much larger than the real value (37 K). Although the MFT always overestimates the true value(it neglects the effect of fluctuation of spins from their average values), the trend is convincing. It is observed that the energy difference is 75.3 meV and the value increases to 136.9 meV for 0.5 h concentration with 0.2 h doping. Ultimately, it would be ~ 223.8 meV for the 1.0 h-doped case, double that of pristine case. Thus, the Tc would also be strengthened eightfold from the real value to ~ 296 K, close to room temperature. However, in the CrI3 monolayer, a doping concentration of 0.5 h would lead Tc to room temperature. In reality, carrier doping can be manipulated via a voltage gate or adsorption [33,34]. However, we notice that the modification of electron structure to include a cation (anion) vacancy would work in the same manner as hole (electron) doping. Taking the titled compound as an example, if one Cr (Br) is removed, either the valence values of the remaining Cr atoms increase (decrease), and thus they lose electrons, or those of Br decrease (increase) by receiving electrons. This is exactly the same as in hole (electron) doping. In this scenario, both Cr and Br vacancies are designed in the CrBr3 monolayer. Three sizes of slabs are built, i.e., 2 × 2, 3 × 3 and 4 × 4, to investigate the influence of vacancy concentration, and the Cr (Br) vacancy concentrations are 12.5% (4.16%), 5.56% (1.85%) and 3.12% (1.04%), respectively. Similarly to CrCl3 and CrI3 monolayers [7–8,19,32], Cr vacancy would tune an insulator to the HM transition (Fig. 4(a) for 5.56% case and Fig.
Fig. 3. Energy difference from AFM to FM under carrier doping for CrBr3 monolayer with/without biaxial strain (+2%, −2%, +4%, −4%) from GGA + U (UCr = 5.0 eV) method. The positive and negative values are for electron and hole doping, respectively.
to be 24.3 N/m, comparable with that of CrI3, yet about one order of magnitude smaller than those for graphene (340 N/m) and MoS2 (180 N/m). This implies that CrBr3 can be easily compressed or stretched, inspiring our study on lateral strain. The lattice parameters, as well as those for the bulk counterpart, are listed in Table 1. It is observed that the in-plane lattice a/b does not change much compared with that in the bulk phase. Neither does the Cr-Br distance (Table 1) of 2.517 Å, which is between those of the Cr-Cl (2.355 Å) and Cr-I (2.737 Å) distances. The thickness of the monolayer is 2.889 Å, also in the middle of those for CrCl3 (2.439 Å) [20] and CrI3 (3.143 Å) monolayers [14]. These are reasonable in view of the fact that the radius of Br is between those of Cl and I ions. The calculated density of states (DOS, Fig. 1(b)) indicates that the insulating nature survives within the monolayer, similar to CrCl3 and CrI3 [6–7,14,20]. A close inspection of the electronic structure reveals that the hybrid Cr 3d-Br 4p state is just below the Fermi level (EF) and that a small amount of hole doping will lead the EF downward to the valence band. However, in view of the enormous distinction between the band gaps from the two spin channels, the insulating character in
Fig. 4. Density of states for CrBr3 monolayer with (a) 5.56% Cr vacancy concentration and (b) 1.85% Br vacancy concentration from GGA + U (UCr = 5.0 eV) method. 3
Journal of Magnetism and Magnetic Materials 502 (2020) 166608
J. Yang, et al.
Fig. 5. Band structure for a 2 × 2 slab CrBr3 monolayer in the presence of Cr and Br vacancies with three configurations (a) DVI, (b) DVII and (c) DVIII from GGA + U (UCr = 5.0 eV) method.
Fig. 6. Density of states for CrBr3 monolayer under −2%, −4%, +2% and +4% biaxial strain (a) without carrier doping, (b) with 0.2 e and (c) with 0.2 h doping from GGA + U (UCr = 5.0 eV) method.
4
Journal of Magnetism and Magnetic Materials 502 (2020) 166608
J. Yang, et al.
magnetic moment and would simultaneously provoke double exchange coupling, is suggested to enhance the magnetic coupling. However, this would pose a great challenge for current synthesis technology.
S4 for 12.5% and 3.12% cases). However, in Br defect cases, the insulating nature remains (Fig. 4(b) for 1.85% and Fig. S5 for 4.16% and 1.04%). In fact, once cation vacancies have been introduced, the anion vacancies are unavoidable. Therefore, to acquire deeper insight, CrBr3 monolayers with both Cr and Br vacancies are studied. In addition to different sizes of slabs, the distances between the Cr and Br vacancies are also considered. We will take the 2 × 2 case as an example. As denoted in Fig. 1(a), three types of Br vacancies (Br1, Br2 and Br3 in Fig. 1(a)) are considered to be co-present with Cr vacancy (Cr1 in Fig. 1(a)); hence, three configurations are simulated, which are indicated as DVI (in which the bonded Cr1-Br1 is removed), DVII (Br2 and Cr1 are removed) and DVIII (Br3 and Cr1 are removed). As seen from the band structure (Fig. 5), the gap in the spin up channel is deduced to be neglectable, and thus it can be classified as a spin gapless semiconductor (SPS) [35]. In contrast, DVII and DVIII give rise to HM character. This also applies for 3 × 3 (Fig. S6) and 4 × 4 slabs (Fig. S7), in which the Cr and Br defects with the longest distance are HM, while those with the shortest distance remain insulating. In other words, with the co-presence of Cr and Br vacancies, HM is sensitive to the defect distance. In-plane strain is also a common tool for 2D material design, and the magnetic state can be tuned by in-plane strain for the CrI3 monolayer; therefore, we also studied the effect of strain for the CrBr3 monolayer. As shown in Fig. 3, the FM state would be enhanced by tensile strain, i.e., the energy difference is enlarged to 49.91 meV for 2% and 50.59 meV for 4% elongation of the in-plane lattice. In contrast, compression strain decreases the energy difference, i.e., FM is lower by 36.56 meV for −2% and by 23.90 meV for −4% compression. This is consistent with that of the CrI3 monolayer, in which a compression strain tends to trigger a FM-AFM transition. In the CrBr3 monolayer, with the help of electron doping, the FM-AFM transition takes place with 0.5e doping for −2% and 0.3e doping for −4% cases. Moreover, from the calculation of DOS (Fig. 6(a)), it is observed that the insulating character is retained for both tensile and compression strains. With the aim of introducing polarized conduction electrons, carrier doping is also loaded and, as expected, HM is formed in all doping cases, regardless of the strain type and magnitude (Fig. 6(b) and Fig. 6(c)). It is also found that the stabilization of FM coupling by hole doping would be increased (attenuated) by tensile (compressive) strain. For instance, the FM is favored by 81.44 meV (~62.20 meV) with 0.2 h for + 2% tensile (−2% compressive) strain, which is larger (smaller) than the ~75.30 meV with only 0.2 h doping (Fig. 3).
Acknowledgements The authors thank the National Natural Science Foundation of China (No. 21403185), the Foundation from Yanshan University (No. 14LGB020) and the Science and Technology Research Foundation for Colleges and Universities in Hebei Province (No. Z2015008) for financial support. Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.jmmm.2020.166608. References [1] B. Huang, G. Clark, E. Navarro-Moratalla, D.R. Klein, R. Cheng, K.L. Seyler, D. Zhong, E. Schmidgall, M.A. McGuire, D.H. Cobden, Nature 546 (2017) 270–273. [2] C. Gong, L. Li, Z.L. Li, H.W. Ji, A. Stern, Y. Xia, T. Cao, W. Bao, C.Z. Wang, Y. Wang, Z.Q. Qiu, R.J. Cava, S.G. Louie, J. Xia, X. Zhang, Nature 546 (2017) 265–269. [3] S.A. Wolf, D.D. Awschalom, R.A. Buhrman, J.M. Daughton, S. von Molnár, M.L. Roukes, A.Y. Chtchelkanova, D.M. Treger, Science 294 (2001) 1488–1495. [4] J. Wang, N.N. Zu, Y. Wang, J. Magn. Magn. Mater 339 (2013) 163–167. [5] B. Huang, G. Clark, D.R. Klein, D. MacNeill, E. Navarro-Moratalla, K.L. Seyler, N. Wilson, M.A. McGuire, D.H. Cobden, D. Xiao, Nature Nanotechnol. 13 (2018) 544. [6] F.W. Zheng, J. Zhao, Z. Liu, M.L. Li, M. Zhou, S.B. Zhang, P. Zhang, Nanoscale 10 (2018) 14298–14303. [7] J. Liu, Q. Sun, Y. Kawazoe, P. Jena, Phys. Chem. Chem. Phys. 18 (2016) 8777–8784. [8] W.B. Zhang, Q. Qua, P. Zhua, C.H. Lam, J. Mater. Chem. C 3 (2015) 12457–12468. [9] M.A. McGuire, H. Dixit, H.V.R. Cooper, B.C. Sales, Chem. Mater. 27 (2015) 612–620. [10] G.T. Lin, X. Luo, F.C. Chen, J. Yan, J.J. Gao, Y. Sun, W. Tong, P. Tong, W.J. Lu, Z.G. Sheng, Appl. Phys. Lett. 112 (2018) 072405. [11] Z. Wang, I. Gutiéerrezlezama, N. Ubrig, M. Kroner, M. Gibertini, T. Taniguchi, K. Watanabe, A. Imamoģglu, E. Giannini, A.F. Morpurgo, Nat. Commun. 9 (2018) 2516. [12] H.B. Wang, F.R. Fan, S.S. Zhu, H. Wu, Europhys. Lett. 114 (2016) 47001. [13] Y.L. Guo, S.J. Yuan, B. Wang, L. Shi, J.L. Wang, J. Mater. Chem. C 6 (2018) 5716–5720. [14] Y. Gao, J. Wang, Z.P. Li, J.J. Yang, M.R. Xia, X.F. Hao, Y.H. Xu, F.M. Gao, Phys. Status Solidi RRL 13 (2018) 1800410. [15] Y. Zhao, L. Lin, Q. Zhou, Y. Li, S. Yuan, Q. Chen, S. Dong, J. Wang, Nano Lett. 18 (2018) 2943–2949. [16] Lado J.L., Fernández-Rossier J., 2D Mater. 4 (2017) 035002. [17] M.A. McGuire, G. Clark, S. KC, W. Michael Chance, G.E. Jellison Jr, V.R. Cooper, X. Xu, B.C. Sales, Phys. Rev. Mater. 1 (2017) 014001. [18] L.F. Pan, L. Huang, M.Z. Zhong, X.W. Jiang, H.X. Deng, J.B. Li, J.B. Xia, Z.M. Wei, Nanoscale 10 (2018) 22196–22202. [19] H. Wang, V. Eyert, U. Schwingenschlögl, J. Phys.: Condens. Matter. 23 (2011) 116003. [20] Y. Gao, J. Wang, Y. Li, M.R. Xia, Z.P. Li, F.M. Gao, Phys. Status Solidi RRL 12 (2018) 1800105. [21] G. Kresse, J. Hafner, Phys. Rev. B 47 (1993) 558. [22] G. Kresse, J. Hafner, Phys. Rev. B 49 (1994) 14251. [23] G. Kresse, J. Furthmüller, Comput. Mater. Sci. 6 (1996) 15–50. [24] G. Kresse, J. Furthmüller, Phys. Rev. B 54 (1996) 11169. [25] P.E. Blöchl, Phys. Rev. B 50 (1994) 17953. [26] G. Kresse, D. Joubert, Phys. Rev. B 59 (1999) 1758. [27] S. Grimme, J. Comput. Chem. 27 (2006) 1787–1799. [28] S. Grimme, J. Antony, S. Ehrlich, H. Krieg, J. Chem. Phys. 132 (2010) 154104. [29] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [30] A.I. Liechtenstein, V.I. Anisimov, J. Zaanen, Phys. Rev. B 52 (1995) 5467. [31] A. Togo, I. Tanaka, Scr. Mater. 108 (2015) 1–5. [32] L.L. Handy, N.W. Gregory, J, Am. Chem Soc. 74 (1952) 891–893. [33] Y. Yang, J. Li, H. Wu, Nano Letters 12 (2012) 5890–5896. [34] J. Lee, Y. Jung, J.H.D. Kim, Appl. Phys. Lett. 100 (2012) 51. [35] X.L. Wang, Phys. Rev. Lett. 2008 (100) (2008) 156404.
4. Conclusion In conclusion, band engineering within the framework of density functional theory is fabricated for the CrBr3 monolayer via carrier doping, vacancies and lateral strain. Full spin polarization is accessible via charge doping and Cr vacancy, i.e., an insulator to half metal character transition is induced. Both charge doping and tensile strain would stabilize the ferromagnetic coupling, and the cooperation of these two effects further contributes to the stabilization. Along with the sister compounds, i.e., CrI3 and CrCl3, it is found that the results are not satisfying, even though the magnetic ordering temperature can be improved by band engineering for this family; in other words, the temperatures are not as high as room temperature. From our study of this series, this could be ascribed to the relatively weak ferromagnetic interaction between Cr3+ and Cr3+. Hence, the introduction of extra magnetic ions, such as Mn3+(t2g3eg1, S = 2), which possesses a larger
5
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Research articles
Band engineering in intrinsically magnetic CrBr3 monolayer ⁎
Jinjin Yang, Jing Wang , Qian Liu, Rui Xu, Yuling Sun, Zhiping Li, Faming Gao, Meirong Xia
⁎
T
Key Laboratory of Applied Chemistry, Hebei Key Laboratory of Heavy Metal Deep-Remediation in Water and Resource Reuse, School of Environmental and Chemistry Engineering, Yanshan University, No. 438, Hebei St(W), Qinhuangdao 066004, PR China
A R T I C LE I N FO
A B S T R A C T
Keywords: CrI3 Vacancy Carrier doping Strain Half metal
The discovery of the intrinsic magnetism of CrI3 monolayers (Nature 2017, 546, 270) serves as a new platform to regulate electrons. In this study, the electronic structure of the CrBr3 monolayer, a sister compound of CrI3, has been studied based on the first principle calculations and band engineering strategies involving carrier doping, vacancies (Cr vacancy, Br vacancy and the co-presence of Cr and Br vacancies) and in-plane strain. An insulator to half metal character transition could be actualized via charge doping (both hole and electron doping) and Cr vacancy. With co-existing Cr and Br vacancies, the half metallic character is sensitive to the distance between the defects. In contrast, the insulating nature would survive under conditions of Br vacancy defect as well as in-plane strain; however, the cooperation of strain and carrier doping would lead to half metal behavior. With regard to stabilization of ferromagnetic coupling, hole doping, electron doping and tensile strain would be effective; hole doping is more efficient than electron doping, and the co-existence of hole doping and tensile strain would further enable this enhancement.
1. Introduction The accessible exfoliation of layered Cr2Ge2Te6 and CrI3 from their bulk counterparts has closed the gap for two-dimensional (2D) intrinsic magnets [1,2]. Spintronics [3], which utilizes spin instead of charge in electronic devices, has long been desired by material scientists, and these 2D intrinsic magnets enable a significant step forward to achieve full spin polarization [4]. Attractively, exotic electronic and magnetic characteristics have been reported among these 2D intrinsic magnets [5–9]. For instance, the CrI3 monolayer is ferromagnetic (FM), as is its bulk counterpart; however, the bilayer is antiferromagnetic (AFM) between layers. With increasing layers, the FM nature is recovered in the tri-layered system [1]. More interestingly, the CrI3 bilayer displays an AFM-FM transition with increasing magnetic field [5], and this transition can also be tuned via voltage control [6]. To understand the unique physical behavior, electronic structure and magnetic coupling manner of chromium trihalides CrX3 (X = Cl, Br, I), as well as their monolayers have been investigated in the literature [10–12]. The exceptional FM magnetic coupling of the CrI3 monolayer is well rationalized by Wu et al. based on a model Hamiltonian. Moreover, to make the most of the 2D intrinsic magnet, Wu et al. reported an insulator to half metal (HM) transition via charge doping in a CrI3 monolayer [12]. Similarly, HM is also designed through Li atom adsorption [13]. In both cases, not only is 100% spin
⁎
polarization manipulated via the unique HM quantum state, but also the FM interaction is enhanced as a result of the appearance of itinerant electrons. Vacancy, which is omnipresent in samples, have now been widely adopted as a powerful tool for band modification. It has been found that either Cr vacancy [14] or I vacancy [15] would strengthen the magnetic moment and thus improve the Curie temperature (Tc). Moreover, Zheng et al. found that the magnetic ground state of the CrI3 monolayer is sensitive to lateral strain, and a FM to AFM flip can be triggered easily by compression strain [6]. As one of the chromium trihalides, the study of the CrBr3 monolayer is less common, not to mention its band engineering. In fact, CrBr3 and CrI3 have several similarities, i.e., FM and insulating properties [16,17]. Another common trait is that both of them exhibit 3D-Ising character [18,19]. This is different from the CrCl3 monolayer, which performs 2DHeisenberg behavior. In our previous studies [14,20], an insulator to HM transition could be fabricated in both CrCl3 and CrI3 monolayers; however, certain details are different. For instance, although the nominal valence states of Cr are 3+ in both cases, the magnetic moment is larger in the CrI3 monolayer: this can be ascribed to the strong covalent ability of I which, in return, is accounted for the higher magnetic ordering temperature of CrI3. Since CrBr3 is intermediate within this family and is seldom disclosed, understanding the electronic and magnetic behavior is of great importance. Inspired by these considerations, band engineering, including atomic vacancy, charge doping
Corresponding authors. E-mail addresses: [email protected] (J. Wang), [email protected] (M. Xia).
https://doi.org/10.1016/j.jmmm.2020.166608 Received 19 July 2019; Received in revised form 11 December 2019; Accepted 10 February 2020 Available online 11 February 2020 0304-8853/ © 2020 Elsevier B.V. All rights reserved.
Journal of Magnetism and Magnetic Materials 502 (2020) 166608
J. Yang, et al.
Fig. 1. (a) Top and side views of the CrBr3 monolayer. (b) Density of states for CrBr3 monolayer from GGA + U (UCr = 5.0 eV) method. Table 1 Structure parameters for bulk and monolayer CrBr3. Our calculations
Ref. 19
Ref. 7
Ref. 8
Ref. 32
Space group
Bulk C2/m
Bulk R-3
Single layer P-31M
Bulk R-3
Bulk R-3
Bulk R-3
Single layer
Bulk R-3
a(Å) b(Å) c(Å) β/γ(°) Cr-Br(Å)
6.337 10.972 6.474 108.6 2.513 × 2 2.515 × 2 2.519 × 2
6.335 6.335 18.356 120.0 2.516 × 6
6.340 6.340 2.889 120.0 2.517 × 6
– – – – 2.496 × 6
6.496 6.496 – – 2.545 × 6
6.435 6.435 20.836 – –
6.433 6.433 – – –
6.260 6.260 18.20 – –
Fig. 2. Density of states for CrBr3 monolayer with (a) 0.2 h and (b) 0.2 e doping from GGA + U (UCr = 5.0 eV) method.
6.0 eV. To maintain consistency with our previous studies [14,20], only the result from U = 5.0 eV is discussed. The phonon dispersion is calculated using the Phonopy package [31] with the finite displacement method. The other calculation parameters are consistent with our previous works [14,20].
and lateral strain, has been conducted on the CrBr3 monolayer. The results are compared with those from CrCl3 and CrI3 to complete the study of this family. 2. Computational details
3. Results
Structural relaxations and electronic properties were calculated by VASP [21–24], based on the projector augmented-wave (PAW) method [25,26]. The van der Waals interaction (vdW) correlation is considered by using the semiempirical dispersion-corrected density functional theory (DFT-D2) force-field approach [27,28] and a vacuum space of 15 Å is employed to avoid the influence of interlayer interaction. The exchange–correlation energy was treated by the GGA-PBE [29]. Electron-electron Coulomb repulsion interactions (U) for Cr are tested in the rotationally invariant form (GGA + U) [30] with Ueff from 3.0 to
We start our research with a pristine CrBr3 monolayer (Fig. 1(a)). We do not discuss this part in details, but it agrees well with those in the literature [7–8,19,32] and serves as a basis for the next step of calculations. The results of cleavage energy (0.20 J/m2 for C2/m and 0.13 J/ m2 for R-3 phase, Fig. S1) and phonon dispersion (Fig. S2) provide evidence that the isolation from bulk is feasible and that the monolayer is thermodynamically stable. The 2D Young's modulus is then estimated 2
Journal of Magnetism and Magnetic Materials 502 (2020) 166608
J. Yang, et al.
the spin down channel would remain under a critical doping concentration. To verify this speculation, carrier (including both hole and electron) doping is simulated. With regard to hole doping, as expected, an insulator to HM transition would take place even with a small amount of dopant, such as 0.1 h. Interestingly, the HM state could survive until 1.0 h (Fig. 2(a) for 0.2 h and Fig. S3 for 0.1 h and 1.0 h). On the other hand, electron doping will also lead to HM character, but the difference lies in the fact that the EF moves upwards to the conduction band. As shown in Fig. 2(b) for 0.2e doping, the Cr eg state resides across the EF, thus playing the role of conduction electrons. It is essential to verify whether the FM coupling still survives after carrier doping. To do this, the relative energy from AFM to FM is examined (Fig. 3). It is obvious that the FM coupling is guaranteed regardless of the dopant types (black line in Fig. 3). However, the promotion of FM stability is stronger via hole doping, which is similar to the case of the CrI3 monolayer [12]. Since magnetic ordering temperature scales with the energy difference (T = ΔE/3kB) from the mean field theory (MFT), the Curie temperature (Tc) would be enhanced as well, especially for hole doping. According to our calculations, the FM state is lower by ~ 44.8 meV in the pristine case, which gives rise to an estimation of Tc as 173 K, much larger than the real value (37 K). Although the MFT always overestimates the true value(it neglects the effect of fluctuation of spins from their average values), the trend is convincing. It is observed that the energy difference is 75.3 meV and the value increases to 136.9 meV for 0.5 h concentration with 0.2 h doping. Ultimately, it would be ~ 223.8 meV for the 1.0 h-doped case, double that of pristine case. Thus, the Tc would also be strengthened eightfold from the real value to ~ 296 K, close to room temperature. However, in the CrI3 monolayer, a doping concentration of 0.5 h would lead Tc to room temperature. In reality, carrier doping can be manipulated via a voltage gate or adsorption [33,34]. However, we notice that the modification of electron structure to include a cation (anion) vacancy would work in the same manner as hole (electron) doping. Taking the titled compound as an example, if one Cr (Br) is removed, either the valence values of the remaining Cr atoms increase (decrease), and thus they lose electrons, or those of Br decrease (increase) by receiving electrons. This is exactly the same as in hole (electron) doping. In this scenario, both Cr and Br vacancies are designed in the CrBr3 monolayer. Three sizes of slabs are built, i.e., 2 × 2, 3 × 3 and 4 × 4, to investigate the influence of vacancy concentration, and the Cr (Br) vacancy concentrations are 12.5% (4.16%), 5.56% (1.85%) and 3.12% (1.04%), respectively. Similarly to CrCl3 and CrI3 monolayers [7–8,19,32], Cr vacancy would tune an insulator to the HM transition (Fig. 4(a) for 5.56% case and Fig.
Fig. 3. Energy difference from AFM to FM under carrier doping for CrBr3 monolayer with/without biaxial strain (+2%, −2%, +4%, −4%) from GGA + U (UCr = 5.0 eV) method. The positive and negative values are for electron and hole doping, respectively.
to be 24.3 N/m, comparable with that of CrI3, yet about one order of magnitude smaller than those for graphene (340 N/m) and MoS2 (180 N/m). This implies that CrBr3 can be easily compressed or stretched, inspiring our study on lateral strain. The lattice parameters, as well as those for the bulk counterpart, are listed in Table 1. It is observed that the in-plane lattice a/b does not change much compared with that in the bulk phase. Neither does the Cr-Br distance (Table 1) of 2.517 Å, which is between those of the Cr-Cl (2.355 Å) and Cr-I (2.737 Å) distances. The thickness of the monolayer is 2.889 Å, also in the middle of those for CrCl3 (2.439 Å) [20] and CrI3 (3.143 Å) monolayers [14]. These are reasonable in view of the fact that the radius of Br is between those of Cl and I ions. The calculated density of states (DOS, Fig. 1(b)) indicates that the insulating nature survives within the monolayer, similar to CrCl3 and CrI3 [6–7,14,20]. A close inspection of the electronic structure reveals that the hybrid Cr 3d-Br 4p state is just below the Fermi level (EF) and that a small amount of hole doping will lead the EF downward to the valence band. However, in view of the enormous distinction between the band gaps from the two spin channels, the insulating character in
Fig. 4. Density of states for CrBr3 monolayer with (a) 5.56% Cr vacancy concentration and (b) 1.85% Br vacancy concentration from GGA + U (UCr = 5.0 eV) method. 3
Journal of Magnetism and Magnetic Materials 502 (2020) 166608
J. Yang, et al.
Fig. 5. Band structure for a 2 × 2 slab CrBr3 monolayer in the presence of Cr and Br vacancies with three configurations (a) DVI, (b) DVII and (c) DVIII from GGA + U (UCr = 5.0 eV) method.
Fig. 6. Density of states for CrBr3 monolayer under −2%, −4%, +2% and +4% biaxial strain (a) without carrier doping, (b) with 0.2 e and (c) with 0.2 h doping from GGA + U (UCr = 5.0 eV) method.
4
Journal of Magnetism and Magnetic Materials 502 (2020) 166608
J. Yang, et al.
magnetic moment and would simultaneously provoke double exchange coupling, is suggested to enhance the magnetic coupling. However, this would pose a great challenge for current synthesis technology.
S4 for 12.5% and 3.12% cases). However, in Br defect cases, the insulating nature remains (Fig. 4(b) for 1.85% and Fig. S5 for 4.16% and 1.04%). In fact, once cation vacancies have been introduced, the anion vacancies are unavoidable. Therefore, to acquire deeper insight, CrBr3 monolayers with both Cr and Br vacancies are studied. In addition to different sizes of slabs, the distances between the Cr and Br vacancies are also considered. We will take the 2 × 2 case as an example. As denoted in Fig. 1(a), three types of Br vacancies (Br1, Br2 and Br3 in Fig. 1(a)) are considered to be co-present with Cr vacancy (Cr1 in Fig. 1(a)); hence, three configurations are simulated, which are indicated as DVI (in which the bonded Cr1-Br1 is removed), DVII (Br2 and Cr1 are removed) and DVIII (Br3 and Cr1 are removed). As seen from the band structure (Fig. 5), the gap in the spin up channel is deduced to be neglectable, and thus it can be classified as a spin gapless semiconductor (SPS) [35]. In contrast, DVII and DVIII give rise to HM character. This also applies for 3 × 3 (Fig. S6) and 4 × 4 slabs (Fig. S7), in which the Cr and Br defects with the longest distance are HM, while those with the shortest distance remain insulating. In other words, with the co-presence of Cr and Br vacancies, HM is sensitive to the defect distance. In-plane strain is also a common tool for 2D material design, and the magnetic state can be tuned by in-plane strain for the CrI3 monolayer; therefore, we also studied the effect of strain for the CrBr3 monolayer. As shown in Fig. 3, the FM state would be enhanced by tensile strain, i.e., the energy difference is enlarged to 49.91 meV for 2% and 50.59 meV for 4% elongation of the in-plane lattice. In contrast, compression strain decreases the energy difference, i.e., FM is lower by 36.56 meV for −2% and by 23.90 meV for −4% compression. This is consistent with that of the CrI3 monolayer, in which a compression strain tends to trigger a FM-AFM transition. In the CrBr3 monolayer, with the help of electron doping, the FM-AFM transition takes place with 0.5e doping for −2% and 0.3e doping for −4% cases. Moreover, from the calculation of DOS (Fig. 6(a)), it is observed that the insulating character is retained for both tensile and compression strains. With the aim of introducing polarized conduction electrons, carrier doping is also loaded and, as expected, HM is formed in all doping cases, regardless of the strain type and magnitude (Fig. 6(b) and Fig. 6(c)). It is also found that the stabilization of FM coupling by hole doping would be increased (attenuated) by tensile (compressive) strain. For instance, the FM is favored by 81.44 meV (~62.20 meV) with 0.2 h for + 2% tensile (−2% compressive) strain, which is larger (smaller) than the ~75.30 meV with only 0.2 h doping (Fig. 3).
Acknowledgements The authors thank the National Natural Science Foundation of China (No. 21403185), the Foundation from Yanshan University (No. 14LGB020) and the Science and Technology Research Foundation for Colleges and Universities in Hebei Province (No. Z2015008) for financial support. Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.jmmm.2020.166608. References [1] B. Huang, G. Clark, E. Navarro-Moratalla, D.R. Klein, R. Cheng, K.L. Seyler, D. Zhong, E. Schmidgall, M.A. McGuire, D.H. Cobden, Nature 546 (2017) 270–273. [2] C. Gong, L. Li, Z.L. Li, H.W. Ji, A. Stern, Y. Xia, T. Cao, W. Bao, C.Z. Wang, Y. Wang, Z.Q. Qiu, R.J. Cava, S.G. Louie, J. Xia, X. Zhang, Nature 546 (2017) 265–269. [3] S.A. Wolf, D.D. Awschalom, R.A. Buhrman, J.M. Daughton, S. von Molnár, M.L. Roukes, A.Y. Chtchelkanova, D.M. Treger, Science 294 (2001) 1488–1495. [4] J. Wang, N.N. Zu, Y. Wang, J. Magn. Magn. Mater 339 (2013) 163–167. [5] B. Huang, G. Clark, D.R. Klein, D. MacNeill, E. Navarro-Moratalla, K.L. Seyler, N. Wilson, M.A. McGuire, D.H. Cobden, D. Xiao, Nature Nanotechnol. 13 (2018) 544. [6] F.W. Zheng, J. Zhao, Z. Liu, M.L. Li, M. Zhou, S.B. Zhang, P. Zhang, Nanoscale 10 (2018) 14298–14303. [7] J. Liu, Q. Sun, Y. Kawazoe, P. Jena, Phys. Chem. Chem. Phys. 18 (2016) 8777–8784. [8] W.B. Zhang, Q. Qua, P. Zhua, C.H. Lam, J. Mater. Chem. C 3 (2015) 12457–12468. [9] M.A. McGuire, H. Dixit, H.V.R. Cooper, B.C. Sales, Chem. Mater. 27 (2015) 612–620. [10] G.T. Lin, X. Luo, F.C. Chen, J. Yan, J.J. Gao, Y. Sun, W. Tong, P. Tong, W.J. Lu, Z.G. Sheng, Appl. Phys. Lett. 112 (2018) 072405. [11] Z. Wang, I. Gutiéerrezlezama, N. Ubrig, M. Kroner, M. Gibertini, T. Taniguchi, K. Watanabe, A. Imamoģglu, E. Giannini, A.F. Morpurgo, Nat. Commun. 9 (2018) 2516. [12] H.B. Wang, F.R. Fan, S.S. Zhu, H. Wu, Europhys. Lett. 114 (2016) 47001. [13] Y.L. Guo, S.J. Yuan, B. Wang, L. Shi, J.L. Wang, J. Mater. Chem. C 6 (2018) 5716–5720. [14] Y. Gao, J. Wang, Z.P. Li, J.J. Yang, M.R. Xia, X.F. Hao, Y.H. Xu, F.M. Gao, Phys. Status Solidi RRL 13 (2018) 1800410. [15] Y. Zhao, L. Lin, Q. Zhou, Y. Li, S. Yuan, Q. Chen, S. Dong, J. Wang, Nano Lett. 18 (2018) 2943–2949. [16] Lado J.L., Fernández-Rossier J., 2D Mater. 4 (2017) 035002. [17] M.A. McGuire, G. Clark, S. KC, W. Michael Chance, G.E. Jellison Jr, V.R. Cooper, X. Xu, B.C. Sales, Phys. Rev. Mater. 1 (2017) 014001. [18] L.F. Pan, L. Huang, M.Z. Zhong, X.W. Jiang, H.X. Deng, J.B. Li, J.B. Xia, Z.M. Wei, Nanoscale 10 (2018) 22196–22202. [19] H. Wang, V. Eyert, U. Schwingenschlögl, J. Phys.: Condens. Matter. 23 (2011) 116003. [20] Y. Gao, J. Wang, Y. Li, M.R. Xia, Z.P. Li, F.M. Gao, Phys. Status Solidi RRL 12 (2018) 1800105. [21] G. Kresse, J. Hafner, Phys. Rev. B 47 (1993) 558. [22] G. Kresse, J. Hafner, Phys. Rev. B 49 (1994) 14251. [23] G. Kresse, J. Furthmüller, Comput. Mater. Sci. 6 (1996) 15–50. [24] G. Kresse, J. Furthmüller, Phys. Rev. B 54 (1996) 11169. [25] P.E. Blöchl, Phys. Rev. B 50 (1994) 17953. [26] G. Kresse, D. Joubert, Phys. Rev. B 59 (1999) 1758. [27] S. Grimme, J. Comput. Chem. 27 (2006) 1787–1799. [28] S. Grimme, J. Antony, S. Ehrlich, H. Krieg, J. Chem. Phys. 132 (2010) 154104. [29] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [30] A.I. Liechtenstein, V.I. Anisimov, J. Zaanen, Phys. Rev. B 52 (1995) 5467. [31] A. Togo, I. Tanaka, Scr. Mater. 108 (2015) 1–5. [32] L.L. Handy, N.W. Gregory, J, Am. Chem Soc. 74 (1952) 891–893. [33] Y. Yang, J. Li, H. Wu, Nano Letters 12 (2012) 5890–5896. [34] J. Lee, Y. Jung, J.H.D. Kim, Appl. Phys. Lett. 100 (2012) 51. [35] X.L. Wang, Phys. Rev. Lett. 2008 (100) (2008) 156404.
4. Conclusion In conclusion, band engineering within the framework of density functional theory is fabricated for the CrBr3 monolayer via carrier doping, vacancies and lateral strain. Full spin polarization is accessible via charge doping and Cr vacancy, i.e., an insulator to half metal character transition is induced. Both charge doping and tensile strain would stabilize the ferromagnetic coupling, and the cooperation of these two effects further contributes to the stabilization. Along with the sister compounds, i.e., CrI3 and CrCl3, it is found that the results are not satisfying, even though the magnetic ordering temperature can be improved by band engineering for this family; in other words, the temperatures are not as high as room temperature. From our study of this series, this could be ascribed to the relatively weak ferromagnetic interaction between Cr3+ and Cr3+. Hence, the introduction of extra magnetic ions, such as Mn3+(t2g3eg1, S = 2), which possesses a larger
5