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Based on density functional theory, the extraordinary magnetic properties of finite graphene fragments (graphene nanoflake, GNF) with different shapes are studied by first-principles electronic structure calculations with all electron numerical-orbital basis set scheme as implemented in DMol3 code of Materials Studio 8.0 software package. According to the graph theory, the spin characteristics of several typical hydrogen-terminated GNF shaped into 3-fold and 6-fold highly rotational symmetries as well as two specific geometrical structures related to graphene nanoribbon are analyzed and verified by first-principles calculations. In some characteristic GNFs shaped into a singular graph, the electron energy matrix becomes singular and multiple states of zero eigenvalue appear which is called nonbonding state (NBS). In these singular graph structures, all the -bonds cannot be satisfied simultaneously and spin-aligned singly occupied molecular orbitals are generated from degeneracy at Fermi-level, which means that the topological frustration occurs. It is proved that the electronic spin magnetic order of GNF originates from topological frustration of conjugate -bonds determined by its shape. The net spin of triangular GNF with zigzag edges is not zero, like an artificial ferromagnetic atom, increasing proportionally with its linear dimension. According to the principle of topological frustration, the large net spins and specific spin distributions can be reasonably introduced into graphene nanocrystals, such as by triangulation. The NBSs of zigzag-edged triangular GNFs with nanoscale dimension create 0.4-0.7 eV energy gaps at Fermi-level to achieve stable spin-alignment at ambient temperature. Even though the linear size of zigzag-edged triangular GNF increases beyond nanoscale, the maximum energy gap is still ~0.68 eV and thus the magnetic moment measurement is feasible at room ambient temperature. The total spin of the complex fractal structure constructed by zigzag-edged triangular GNF unit increases exponentially with the fractal level, due to the increased possibility of topological frustration from aggrandizing boundary. In addition, a large net spin can also be acquired by hollowed-out zigzag triangle in graphene with a net spin value of at least 1.00 and a spin-polarization split band gap of ~0.40 eV. The basic design principle for obtaining large spin and controlling spin state distribution by etching GNF of various patterns in graphene atomic layer is presented. In contrast to traditional chemical synthesis of obtaining large spin limited by complicated reaction pathways, the GNF with large spin easily exceeding the reported highest spin in conjugated polymers can be practically produced by carving lithography. It is suggested that the GNF with designed topological structures fabricated by pattern carving technique can be efficiently used to realize the controllable spintronic nanomaterials and devices.
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Keywords:
- graphene nanoflake /
- electronic spin /
- graph theory /
- first-principles calculation
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[25] Jiang D E, Sumpter B G, Dai S 2007 J. Chem. Phys. 126 124701
[26] Li F, Li T, Chen F, Zhang F P 2015 Sci. Rep. 5 9355
[27] Ezawa M 2008 Physica E 40 1421
[28] Fernndez-Rossier J, Palacios J J 2007 Phys. Rev. Lett. 99 177204
[29] Hod O, Barone V, Scuseria G E 2008 Phys. Rev. B 77 035411
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[1] Jabar A, Masrour R 2017 Superlattice. Microst. 112 541
[2] Masrour R, Jabar A 2018 Physica A 497 211
[3] Son Y W, Cohen M L, Louie S G 2006 Nature 444 347
[4] Meyer J C, Geim A K, Katsnelson M I, Novoselov K S, Booth T J, Roth S 2007 Nature 446 60
[5] Berger C, Song Z, Li X B, Wu X S, Brown N, Naud C, Mayou D, Li T B, Hass J, Marchenkov A N, Conrad E H, First P N, de Heer W A 2006 Science 312 1191
[6] Novoselov K S, Jiang Z, Zhang Y, Morozov S V, Stormer H L, Zeitler U, Maan J C, Boebinger G S, Kim P, Geim A K 2007 Science 315 1379
[7] Jellal A 2016 Phys. Lett. A 380 1514
[8] Lai W C, Wang Z M, Li Y L, Wang X, Liu Y, Liu X Y 2018 J. Phys. Chem. C 122 8473
[9] Ding Y, Wang Y 2017 J. Mater. Chem. C 5 10728
[10] Son Y W, Cohen M L, Louie S G 2006 Phys. Rev. Lett. 97 216803
[11] Chuang C, Roy P, Ravindranath R, Periasamy A P, Chang H T, Liang C T 2016 Mater. Lett. 170 110
[12] Xie H, Lu W C, Zhang W, Qin P H, Wang C Z, Ho K M 2013 Chem. Phys. Lett. 572 48
[13] Fajtlowicz S, John P E, Sachs H 2005 Croat. Chem. Acta 78 195
[14] Hod O, Barone V, Peralta J E, Scuseria G E 2007 Nano Lett. 7 2295
[15] Wang W L, Meng S, Kaxiras E 2008 Nano Lett. 8 241
[16] Khler C, Seifert G, Frauenheim T 2005 Chem. Phys. 309 23
[17] Andzelm J, King-Smith R D, Fitzgerald G 2001 Chem. Phys. Lett. 335 321
[18] Perdew J P, Ruzsinszky A, Csonka G I, Vydrov O A, Scuseria G E, Constantin L A, Zhou X L, Burke K 2008 Phys. Rev. Lett. 100 136406
[19] Chantis A N, Christensen N E, Svane A, Cardona M 2010 Phys. Rev. B 81 205205
[20] Baker J, Kessi A, Delley B 1996 J. Chem. Phys. 105 192
[21] Edwards D M, Katsnelson M I 2006 J. Phys. B 18 7209
[22] Zha X H, Ren J C, Feng L, Bai X J, Luo K, Zhang Y Q, He J, Huang Q, Franciscod J S, Du S Y 2018 Nanoscale 10 8763
[23] Trauzettel B, Bulaev D V, Loss D, Burkard G 2007 Nat. Phys. 3 192
[24] Fairbrother A, Ramon J, Valencia S, Lauber B, Shorubalko I, Ruffieux P, Hintermann T, Fasel R 2017 Nanoscale 9 2785
[25] Jiang D E, Sumpter B G, Dai S 2007 J. Chem. Phys. 126 124701
[26] Li F, Li T, Chen F, Zhang F P 2015 Sci. Rep. 5 9355
[27] Ezawa M 2008 Physica E 40 1421
[28] Fernndez-Rossier J, Palacios J J 2007 Phys. Rev. Lett. 99 177204
[29] Hod O, Barone V, Scuseria G E 2008 Phys. Rev. B 77 035411
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