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We use the group theory and molecular orbital theory to systematically study the origin of magnetic moment of cation-vacancy in un-doped magnetic semiconductors, and illustrate the mechanism of exchange-coupling between magnetic moments by Heisenberg model. It is found that the magnetic moment is related to the number of unpaired electrons, and the distribution of defects energy level is correlated closely with the symmetry of vacancy crystal field. The exchange-coupling coefficients J0 is estimated by the energy difference between antiferromagnetic and ferromagnetic states. And J0 can be used to predict the magnetic coupling. Positive J0 means the ferromagnetic coupling between magnetic moments, otherwise the coupling is antiferromagnetic. Moreover, we indicate that reduction of degeneracy of defect energy-level bears a direct relationship to the electron number occupied in the defect energy-level orbital, and therefore results in the structure distortion (John-Teller effect) of a cation-vacancy.
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Keywords:
- cation-vacancy /
- magnetic moment /
- electronic structure /
- symmetry
[1] Dietl T, Ohno H, Matsukura F, Cibert J, Ferrand D 2000 Science 287 1019
[2] Ohno H 1998 Science 281 951
[3] Ohno H, Munekata H, von Molnár S, Chang L 1991 J. Appl. Phys. 69 6103
[4] Ohno H, Shen A, Matsukura F, Oiwa A, Endo A, Katsumoto S, Iye Y 1996 Appl. Phys. Lett. 69 363
[5] Park Y D, Hanbicki A T, Erwin S C, Hellberg C S, Sullivan J M, Mattson J E, Ambrose T F, Wilson A, Spanos G, Jonker B T 2002 Science 295 651
[6] Li A P, Wendelken J F, Shen J, Feldman L C, Thompson J R, Weitering H H 2005 Phys. Rev. B 72 195205
[7] Gareev R, Bugoslavsky Yu V, Schreiber R, Paul A, Sperl M, Döppe M 2006 Appl. Phys. Lett. 88 222508
[8] Tsui F, He L, Ma L, Tkachuk A, Chu Y S, Nakajima K, Chikyow T 2003 Phys. Rev. Lett. 91 177203
[9] Shuto Y, Tanaka M, Sugahara S 2006 J. Appl. Phys. 99 08D516
[10] Chen Y X, Yan S S, Fang Y, Tian Y F, Xiao S Q, Liu G L, Liu Y H, Mei L M 2007 Appl. Phys. Lett. 90 052508
[11] Dietl T, Ohno H, Matsukura F, Cibert J, Ferrand D 2000 Nature 287 1019
[12] Shen L, Wu R Q, Pan H, Peng G W, Yang M, Sha Z D, Feng Y P 2008 Phys. Rev. B 78 073306
[13] Sato K, Katayama-Yoshida H 2000 Jpn. J. Appl. Phys. 39 L555
[14] Yamamoto T, Katayama-Yoshida H 1999 Jpn. J. Appl. Phys. 38 L166
[15] Sharma P, Gupta A, Rao K V, Owens F J, Sharma R, Ahuja R, Osorio Guillen J M, Johansson B, Gethring G A 2003 Nature Mat. 2 673
[16] Park J H, Kim M G, Jang H M, Ryu S, Kim Y M 2004 Appl. Phys. Lett. 84 1338
[17] Shim J H, Hwang T, Lee S, Park J H, Han S J, Jeong Y H 2015 Appl. Phys. Lett. 86 082503
[18] Liu G L, Cao Q, Deng J X, Xing P F, Tian Y F, Chen Y X, Yan S S, Mei L M 2007 Appl. Phys. Lett. 90 052504
[19] Xie L L, Chen S Y, Liu F J, Zhang J M, Lin Y B, Huang Z G 2014 Acta Phys. Sin. 63 077102 (in Chinese) [谢玲玲, 陈水源, 刘凤金, 张建敏, 林应斌, 黄志高 2014 物理学报 63 077102]
[20] Wang F, Wang Y Y, Huang W W, Zhang X T, Li S Y 2012 Acta Phys. Sin. 61 157503 (in Chinese) [王锋, 王月燕, 黄伟伟, 张小婷, 李珊瑜 2012 物理学报 61 157503]
[21] Venkatesan M, Fitzgerald C B, Coey J M D 2004 Nature 430 630
[22] Liu Y, Wang G, Wang S, Yang J, Chen L, Qin X, Song B, Wang B, Chen X 2011 Phys. Rev. Lett. 106 087205
[23] Song B, Bao H, Li H, Lei M, Peng T, Jian J, Liu J, Wang W, Wang W, Chen X 2009 J. Am. Chem. Soc. 131 1376
[24] Wang G X 1986 Atomic Orbital and Molecular Orbital (Higher Education Press) p168 (in Chinese) [王国雄 1986 原子轨道与分子轨道 (高等教育出版社) 第168页]
[25] Lin X L, Yan S S, Zhao M W, Hu S J, Han C, Chen Y X, Liu G L, Dai Y Y, Mei L M 2011 Phys. Lett. A 375 678
[26] Lin X L, Pan F C 2014 Journal of Shandong University (Natural Science) 49 3 (in Chinese) [林雪玲, 潘凤春 2014 山东大学学报(理学版) 49 3]
[27] Wang X P, Zhao M W, He T, Wang Z H, Liu X 2013 Appl. Phys. Lett. 102 062411
[28] Lin X L, Pan F C 2013 Acta Phys. Sin. 62 166102 (in Chinese) [林雪玲, 潘凤春 2013 物理学报 62 166102]
[29] Pan F C, Zhao M W, Mei L M 2010 J. Appl. Phys 108 043917
[30] Wang F G, Pang Z Y, Lin L, Fang S J, Dai Y, Han S H 2009 Phys. Rev. B 80 144424
[31] Rahman G, García-Suárez V M, Hong S C 2008 Phys. Rev. B 78 184404
[32] Fernandes V, Mossanek R J O, Schio P, Klein J J, de Oliveira A J A, Ortiz W A, Mattoso N, Varalda J, Schreiner W H, Abbate M, Mosca D H 2009 Phys. Rev. B 80 035202
[33] Dev P, Xue Y, Zhang P H 2008 Phys. Rev. Lett. 100 117204
[34] Kim D, Yang J, Hong J 2009 J. Appl. Phys 106 013908
[35] Lin X L, Pan F C, Chen H M, Wang X M 2014 J. Supercond. Nov. Magn. 27 2397
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[1] Dietl T, Ohno H, Matsukura F, Cibert J, Ferrand D 2000 Science 287 1019
[2] Ohno H 1998 Science 281 951
[3] Ohno H, Munekata H, von Molnár S, Chang L 1991 J. Appl. Phys. 69 6103
[4] Ohno H, Shen A, Matsukura F, Oiwa A, Endo A, Katsumoto S, Iye Y 1996 Appl. Phys. Lett. 69 363
[5] Park Y D, Hanbicki A T, Erwin S C, Hellberg C S, Sullivan J M, Mattson J E, Ambrose T F, Wilson A, Spanos G, Jonker B T 2002 Science 295 651
[6] Li A P, Wendelken J F, Shen J, Feldman L C, Thompson J R, Weitering H H 2005 Phys. Rev. B 72 195205
[7] Gareev R, Bugoslavsky Yu V, Schreiber R, Paul A, Sperl M, Döppe M 2006 Appl. Phys. Lett. 88 222508
[8] Tsui F, He L, Ma L, Tkachuk A, Chu Y S, Nakajima K, Chikyow T 2003 Phys. Rev. Lett. 91 177203
[9] Shuto Y, Tanaka M, Sugahara S 2006 J. Appl. Phys. 99 08D516
[10] Chen Y X, Yan S S, Fang Y, Tian Y F, Xiao S Q, Liu G L, Liu Y H, Mei L M 2007 Appl. Phys. Lett. 90 052508
[11] Dietl T, Ohno H, Matsukura F, Cibert J, Ferrand D 2000 Nature 287 1019
[12] Shen L, Wu R Q, Pan H, Peng G W, Yang M, Sha Z D, Feng Y P 2008 Phys. Rev. B 78 073306
[13] Sato K, Katayama-Yoshida H 2000 Jpn. J. Appl. Phys. 39 L555
[14] Yamamoto T, Katayama-Yoshida H 1999 Jpn. J. Appl. Phys. 38 L166
[15] Sharma P, Gupta A, Rao K V, Owens F J, Sharma R, Ahuja R, Osorio Guillen J M, Johansson B, Gethring G A 2003 Nature Mat. 2 673
[16] Park J H, Kim M G, Jang H M, Ryu S, Kim Y M 2004 Appl. Phys. Lett. 84 1338
[17] Shim J H, Hwang T, Lee S, Park J H, Han S J, Jeong Y H 2015 Appl. Phys. Lett. 86 082503
[18] Liu G L, Cao Q, Deng J X, Xing P F, Tian Y F, Chen Y X, Yan S S, Mei L M 2007 Appl. Phys. Lett. 90 052504
[19] Xie L L, Chen S Y, Liu F J, Zhang J M, Lin Y B, Huang Z G 2014 Acta Phys. Sin. 63 077102 (in Chinese) [谢玲玲, 陈水源, 刘凤金, 张建敏, 林应斌, 黄志高 2014 物理学报 63 077102]
[20] Wang F, Wang Y Y, Huang W W, Zhang X T, Li S Y 2012 Acta Phys. Sin. 61 157503 (in Chinese) [王锋, 王月燕, 黄伟伟, 张小婷, 李珊瑜 2012 物理学报 61 157503]
[21] Venkatesan M, Fitzgerald C B, Coey J M D 2004 Nature 430 630
[22] Liu Y, Wang G, Wang S, Yang J, Chen L, Qin X, Song B, Wang B, Chen X 2011 Phys. Rev. Lett. 106 087205
[23] Song B, Bao H, Li H, Lei M, Peng T, Jian J, Liu J, Wang W, Wang W, Chen X 2009 J. Am. Chem. Soc. 131 1376
[24] Wang G X 1986 Atomic Orbital and Molecular Orbital (Higher Education Press) p168 (in Chinese) [王国雄 1986 原子轨道与分子轨道 (高等教育出版社) 第168页]
[25] Lin X L, Yan S S, Zhao M W, Hu S J, Han C, Chen Y X, Liu G L, Dai Y Y, Mei L M 2011 Phys. Lett. A 375 678
[26] Lin X L, Pan F C 2014 Journal of Shandong University (Natural Science) 49 3 (in Chinese) [林雪玲, 潘凤春 2014 山东大学学报(理学版) 49 3]
[27] Wang X P, Zhao M W, He T, Wang Z H, Liu X 2013 Appl. Phys. Lett. 102 062411
[28] Lin X L, Pan F C 2013 Acta Phys. Sin. 62 166102 (in Chinese) [林雪玲, 潘凤春 2013 物理学报 62 166102]
[29] Pan F C, Zhao M W, Mei L M 2010 J. Appl. Phys 108 043917
[30] Wang F G, Pang Z Y, Lin L, Fang S J, Dai Y, Han S H 2009 Phys. Rev. B 80 144424
[31] Rahman G, García-Suárez V M, Hong S C 2008 Phys. Rev. B 78 184404
[32] Fernandes V, Mossanek R J O, Schio P, Klein J J, de Oliveira A J A, Ortiz W A, Mattoso N, Varalda J, Schreiner W H, Abbate M, Mosca D H 2009 Phys. Rev. B 80 035202
[33] Dev P, Xue Y, Zhang P H 2008 Phys. Rev. Lett. 100 117204
[34] Kim D, Yang J, Hong J 2009 J. Appl. Phys 106 013908
[35] Lin X L, Pan F C, Chen H M, Wang X M 2014 J. Supercond. Nov. Magn. 27 2397
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