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Based on density functional theory calculations, we elucidate the atomic and electronic structures of Co atom of hexgonal BN (Co/h-BN). The interaction between magnetic moments of Co atoms is realized through Co-N_-B_ grid, which is indicated by the analysis of spin charge contour plot and partial density of states of each atom, where and denote the site of B or N atom close to and away from Co atom, respectively. Then the dispersion relations E(q) and E(-q) (q denotes the direction vector of spin spiral) between energy and wave vector of spin spiral in the opposite directions are calculated with generalized Bloch equations. In the incommensurate spin spiral calculations, all the magnetic moments of Co atom are arranged in the same plane that is perpendicular to the Co/h-BN film. The difference between E(q) and E(-q) is caused by the interface of Co/h-BN, where the symmetry of space perpendicular to the film is broken. Moreover, the effective Heisenberg exchange interaction (HBI) and Dzyaloshinsky-Moriya interaction (DMI) parameters between different neighbors (Ji and di) are derived by well fitting the ab initio magnon dispersion E(q) to HBI with DMI model and E(q)-E(-q) to DMI model, respectively. The J1 has a negative value and plays a major role, J3 is one order of magnitude smaller than J1, and other parameters are close to zero. Hence, Co/h-BN is triangular antiferromagnetic material with the q at k point in the first Brillouin zone. However, the spin spiral with the q at M point is only 2 meV larger than the basic state with the only negative J1 and smaller positive J2. The DMI is not shown in this interface with d1 and d2 close to zero. Based on the non DMI character and its stability in air, h-BN can be capped on other DMI interfaces. The reason that the DMI in Co/h-BN is much smaller than in Co/Gra is much larger height between Co and h-BN. It is 0.192 nm for h-BN but it is 0.156 nm for Co/Gra. We may reduce the height to enhance the DMI by other ways, such as adding electrical and magnetic fields in the future.
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Keywords:
- first principles /
- Co/h-BN /
- Dzyaloshinsky-Moriya interaction /
- Skyrmion
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[38] Seki S, Onose Y, Tokura Y 2008 Phys. Rev. Lett. 101 067204
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[1] Skyrme T H R 1962 Nucl. Phys. 31 556
[2] Belavin A A, Polyakov A M 1975 JETP Lett. 22 245
[3] Rler U K, Bogdanov A N, Pfleiderer C 2006 Nature 442 797
[4] Mhlbauer S, Binz B, Jonietz F, Pfleiderer C, Rosch A, Neubauer A, Georgii R, Bni P 2009 Science 323 915
[5] Yu X Z, Onose Y, Kanazawa N, Park J H, Han J H, Matsui Y, Nagaosa N, Tokura Y 2010 Nature 456 901
[6] Dzyaloshinsky I 1958 J. Phys. Chem. Solids 4 241
[7] Moriya T 1960 Phys. Rev. 120 91
[8] Shu L, Chen Y G, Chen H 2002 Acta Phys. Sin. 51 902(in Chinese) [殳蕾, 陈宇光, 陈鸿 2002 物理学报 51 902]
[9] Cai Z, Lu W B, Liu Y J 2008 Acta Phys. Sin. 57 7267(in Chinese) [蔡卓, 陆文彬, 刘拥军 2008 物理学报 57 7267]
[10] Zhang Y L, Zhou B 2011 Acta Phys. Sin. 60 120301(in Chinese) [张英丽, 周斌 2011 物理学报 60 120301]
[11] Bode M, Heide M, von Bergmann K, Ferriani P, Heinze S, Bihlmayer G, Kubetzka A, Pietzsch O, Blgel S, Wiesendanger R 2007 Nature 447 190
[12] Romming N, Hanneken C, Menzel M, Bickel J, Wolter B, Bergmann K, Kubetzka A, Wiesendanger R 2013 Science 341 636
[13] Neto A H C, Guinea F, Peres N M R, Novoselov K S, Geim A K 2009 Rev. Mod. Phys. 81 109
[14] Han W, Kawakami R K, Gmitra M, Fabian J 2014 Nat. Nanotech. 9 794
[15] Roche S, Xu L, Dai Z H, Wang S, Liu B, Sun Y M, Wang W T 2014 Acta Phys. Sin. 63 107102(in Chinese) [徐雷, 戴振宏, 王森, 刘兵, 孙玉明, 王伟田 2014 物理学报 63 107102]
[16] Xu L, Dai Z H, Wang S, Liu B, Sun Y M, Wang W T 2014 Acta Phys. Sin. 63 107102 (in Chinese) [徐雷, 戴振宏, 王森, 刘兵, 孙玉明, 王伟田 2014 物理学报 63 107102]
[17] Xu L, Dai Z H, Sui P F, Wang W T, Sun Y M 2014 Acta Phys. Sin. 63 186101(in Chinese) [徐雷, 戴振宏, 隋鹏飞, 王伟田, 孙玉明 2014 物理学报 63 186101]
[18] Yang H X, Chen G, Cotta A A C, N'Diaye A T, Nikolaev S A, Soares E A, Macedo W A A, Schmid A K, Fert A, Chshiev M 2017 ArXiv 1704 09023
[19] Pacil D, Meyer J C, Girit , Zettl A 2008 Appl. Phys. Lett. 92 133107
[20] Xu M S, Liang T, Shi M M, Chen H Z 2013 Chem. Rev. 113 3766
[21] Guo S J, Dong S J 2011 Chem. Soc. Rev. 40 2644
[22] Chen Q L, Dai Z H, Liu Z Q, An Y F, Liu Y L 2016 Acta Phys. Sin. 65 136101(in Chinese) [陈庆玲, 戴振宏, 刘兆庆, 安玉凤, 刘悦林 2016 物理学报 65 136101]
[23] Auwrter W, Muntwiler M, Greber T, Osterwalder J 2002 Surf. Sci. 511 379
[24] Zhou Y G, Xiao-Dong J, Wang G, Xiao Y, Gao F, Zu X T 2010 Phys. Chem. Phys. 12 7588
[25] Ma D W, Lu Z S, Ju W W, Tang Y N 2012 J. Phys. Condens. Matter 24 145501
[26] Kresse G, Joubert D 1999 Phys. Rev. B 59 1758
[27] Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[28] Yang H X, Boulle O, Cros V, Fert A, Chshiev M 2016 ArXiv 1603 01847
[29] Zhu Y, Ma C L, Shi D N, Zhang K C 2014 Phys. Lett. A 378 2234
[30] Yang H, Thiaville A, Rohart S, Fert A, Chshiev M 2015 Phys. Rev. Lett. 115 267210
[31] Pan Y, Zhu Y, Shi D N, Wei X Y, Ma C L, Zhang K C 2015 J. Alloys Compd. 644 341
[32] Marsman M, Hafner J 2002 Phys. Rev. B 66 224409
[33] Hobbs D, Kresse G, Hafner J 2000 Phys. Rev. B 62 11556
[34] Mryasov O N, Lichtenstein A I, Sandratskii L M, Gubanov V A 1991 J. Phys. Condens. Matter 3 8565
[35] Knpfle K, Sandratskii L M, Kbler J 2000 Phys. Rev. B 62 5564
[36] Paszkowicz W, Pelka J B, Knapp M, Szyszko T, Podsiadlo S 2002 Appl. Phys. A 75 431
[37] Liu X F, Han J R, Jiang X F 2010 Acta Phys. Sin. 59 6487(in Chinese) [刘先锋, 韩玖荣, 江学范 2010 物理学报 59 6487]
[38] Seki S, Onose Y, Tokura Y 2008 Phys. Rev. Lett. 101 067204
[39] Albaalbaky A, Kvashnin Y, Ledue D, Patte R, Frsard R 2017 Phys. Rev. B 96 064431
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