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The magnetism of two-dimensional material is an important research topic. In particular, the long-range magnetic order of two-dimensional material is of great significance in theoretical research and practical application. According to the Mermin-Wagner theory, the isotropic Heisenberg model in a two-dimensional system cannot produce long-range magnetic orders at non-vanishing temperatures. Considering the existence of strong magnetic anisotropy, possible two-dimensional long-range magnetic orders may exist in 5d atom doped two-dimensional aluminum nitride (AlN) monolayer. This research is performed by first-principles calculations based on the density functional theory. Geometries, electronic structures, magnetic properties, and magnetic anisotropy energies from spin-orbital coupling effects in AlN monolayers doped by 5d transition metal atoms (Hf, Ta, W, Re, Os, Ir, Pt, Au, and Hg) are calculated. Four kinds of supercells are used in the calculation, i.e, 22, 33, 44, and 55, with one aluminum atom substituted by one 5d atom. Projection augmented wave method is used to describe the interaction between the valence electrons and the ions. The plane wave is used to expand the wave function of the valence electron. For an optimized geometry, the bond length between the 5d metal atom and the nearest N atom is the largest in Hg-doped supercells, which is 2.093 , followed by the Au, Hf, Pt, Ta, and Ir according to the order of bond length magnitude. For the densities of states (DOSs), obvious impurity energy levels appear in the forbidden bands. For all the supercells, spin-up and spin-down DOSs of Ta and Ir doped systems are symmetric, indicating non-magnetic states. DOSs of Hf, W, Re, and Os doped systems are asymmetric, indicating magnetic states. For Pt, Au, and Hg, DOSs are symmetric in 22 supercells, but asymmetric in the 33, 44, and 55 supercells. Total magnetic moments and the spin densities are also given. In 55 supercells, they are 1.00, 0.00, 0.39, 1.99, 1.17, 0.00, 1.00, 2.00, and 1.00 for Hf, Ta, W, Re, Os, Ir, Pt, Au, and Hg, respectively. The magnetic moment is mainly concentrated in the vicinity of the 5d atoms. The energy differences between ferromagnetic and antiferromagnetic states are calculated. For Hf, Re, Pt and Au systems, the differences in 48 supercells reach the maximum values of -187.2563 meV, 286.2320 meV, -48.0637 meV and -61.7889 meV, respectively. The results indicate that there is a strong interaction between the magnetic centers. Magnetic anisotropy energy originating from spin-orbital effect is calculated in the 44 supercells. For the Re system, it is the highest, reaching 11.622 meV. For W, Os, and Au, the values are larger than 1 meV, showing strong magnetic anisotropies. The magnetic anisotropy can produce a spin wave energy gap, resulting in long-range magnetic orders. Based on the results above, it is predicted that with appropriate 5d atoms and suitable doping concentration, two-dimensional long-range magnetic orders may exist in 5d transition metal atom doped AlN monolayers.
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Keywords:
- aluminum nitride monolayer /
- first-principles /
- density functional theory /
- spin-orbital coupling
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[29] Gonze X, Beuken J M, Caracas R, Detraux F, Fuchs M, Rignanese G M, Sindic L, Verstraete M, Zerah G, Jollet F, Torrent M, Roy A, Mikami M, Ghosez P, Raty J Y, Allan D C 2002 Comput. Mater. Sci. 25 478
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[1] Novoselov K S, Geim A K, Morozov S V, Jiang D, Katsnelson M I, Grigorieva I V, Dubonos S V, Firsov A A 2005 Nature 438 197
[2] Cahangirov S, Topsakal M, Aktrk E, Sahin H, Ciraci S 2009 Phys. Rev. Lett. 102 236804
[3] Wang Q H, Kalantar-Zadeh K, Kis A, Coleman J N, Strano M S 2012 Nat. Nanotechnol. 7 699
[4] Fleischer J W, Segev M, Efremidis N K, Demetrios N 2003 Nature 422 147
[5] Lu W, Lieber C M 2007 Nat. Mater. 6 841
[6] Zhirnov V V, Cavin R K 2008 Nat. Nanotechnol. 3 77
[7] Xu X D, Yao W, Xiao D, Heinz T F 2014 Nat. Phys. 10 343
[8] Awschalom D D, Flatt M E 2007 Nat. Phys. 3 153
[9] Prinz G A 1998 Science 282 1660
[10] Huang B, Xiang H J, Yu J, Wei S H 2012 Phys. Rev. Lett. 108 206802
[11] Cocchi C, Prezzi D, Calzolari A, Molinari E 2010 J. Chem. Phys. 133 124703
[12] Chan K T, Lee H, Cohen M L 2011 Phys. Rev. B 83 035405
[13] Mermin N D, Wagner H 1966 Phys. Rev. Lett. 17 1133
[14] Luo H M, Wang D H, He J B, Lu Y F 2005 J. Phys. Chem. B 109 1919
[15] Xu C, Gao J, Gao C Y 2006 Acta Phys. Sin. 55 4221 (in Chinese) [徐灿, 曹娟, 高晨阳 2006 物理学报 55 4221]
[16] Kaplan B, Kaplan R 2014 J. Magn. Magn. Mater. 356 95
[17] Ou X, Wu H 2014 Sci. Rep. 4 4609
[18] Liu C C, Feng W X, Yao Y G 2011 Phys. Rev. Lett. 107 076802
[19] Laguna-Marco M A, Haskel D, Souza-Neto N, Lang J C, Krishnamurthy V V, Chikara S, Cao G, van Veenendaal M 2010 Phys. Rev. Lett. 105 216407
[20] Zhang Z F, Zhou T G, Zhao H Y, Wei X L 2014 Chin. Phys. B 23 016801
[21] Shitade A, Katsura H, Kune J, Qi X L, Zhang S C, Nagaosa N 2009 Phys. Rev. Lett. 102 256403
[22] Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 226801
[23] He W Y, He L 2013 Phys. Rev. B 88 085411
[24] Zhang H B, Lazo C, Blgel S, Heinze S, Mokrousov Y 2012 Phys. Rev. Lett. 108 056802
[25] Hu J, Alicea J, Wu R Q, Franz M 2012 Phys. Rev. Lett. 109 266801
[26] Xiao Z L, Shi L B 2011 Acta Phys. Sin. 60 027502 (in Chinese) [肖振林, 史力斌 2011 物理学报 60 027502]
[27] Sebastian K C, Chawda M, Jonny L, Bodas D 2010 Mater. Lett. 64 2269
[28] Chen S, Wu Q Y, Chen Z G, Xu G G, Huang Z G 2009 Acta Phys. Sin. 58 2011 (in Chinese) [陈珊, 吴青云, 陈志高, 许桂贵, 黄志高 2009 物理学报 58 2011]
[29] Gonze X, Beuken J M, Caracas R, Detraux F, Fuchs M, Rignanese G M, Sindic L, Verstraete M, Zerah G, Jollet F, Torrent M, Roy A, Mikami M, Ghosez P, Raty J Y, Allan D C 2002 Comput. Mater. Sci. 25 478
[30] Gonze X, Amadon B, Anglade P M, Beuken J M, Bottin F, Boulanger P, Bruneval F, Caliste D, Caracas R, Ct M, Deutsch T, Genovese L, Ghosez P, Giantomassi M, Goedecker S, Hamann D R, Hermet P, Jollet F, Jomard G, Leroux S, Mancini M, Mazevet S, Oliveira M J T, Onida G, Pouillon Y, Rangel T, Rignanese G M, Sangalli D, Shaltaf R, Torrent M, Verstraete M J, Zerah G, Zwanziger J W 2009 Comput. Mater. Commun. 180 2582
[31] Torrent M, Jollet F, Bottin F, Zrah G, Gonze X 2008 Comput. Mater. Sci. 42 337
[32] Perdew J P, Yue W 1986 Phys. Rev. B 33 8800
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