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Exchange coupling is one of the most important fundamental interactions in ferromagnetic systems. Understanding of the parameters in this interaction may help describe numerous properties of metal magnetic materials. However, in the localized electron theory or itinerant electron theory there are also certain difficulties when utilizing this approximation method to study magnetic ordering problems for multi-atom systems. In realistic magnets exchange coupling is also related to the coexistence of localized and itinerant degrees of freedom. In this case Heisenberg exchange relationship has some limitations. If the exchange relationship only depends on the structure of the magnet, and is not related to energy differences between the phases, we can better avoid the Heisenberg exchange limits. Based on this, we use the general principle of the exchange coupling theory to analyse the usual approximation, and discuss the opportunity to calculate the parameters of such coupling rigorously without specific assumptions about the range of magnetic order or any approximation about the form of magnetization density. We propose a method for calculating the exchange coupling parameter to any approximation. The range of applicability of the above relation is discussed quantitatively for real magnetic systems (magnetic metal materials Gd, Fe, Ni) and spin waves, and the relevance for the exchange coupling is also analysed. This analysis for metal magnetic system (Fe, Ni and Gd) shows that the most significant improvement is obtained for exchange coupling between nearest magnetic atoms and for spin wave spectrum at finite wave vectors. It can be described by the relationship between the exchange coupling approximation and spin wave spectrum, and also interaction between the nearest neighbor magnetic atoms in ferromagnetic systems; these will give reasonable description to the large wave vectors part of spin wave spectra in any magnet with not fully localized magnetism. This point of view from the magnetism theory is consistent with the experimental results.
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Keywords:
- metal magnetic material /
- exchange coupling interactions /
- spin waves function /
- Fe /
- Ni
[1] Xing D Y 2005 Physics 34 348 (in Chinese) [邢定钰 2005 物理 34 348]
[2] Yang H, Yun G H, Cao Y J 2014 Chin. Phys. B 23 097501
[3] Zheng Y L, Wang X X, Ge Z L, Gou H L, Yang G F, Dai S H, Zhu X L, Tian X B 2013 Acta Phys. Sin. 62 227701 (in Chinese) [郑勇林, 王晓茜, 葛泽玲, 郭红力, 严刚峰, 戴松晖, 朱晓玲, 田晓滨 2013 62 227701]
[4] Tokura Y, Tomioka Y 1999 J. Magn. Magn. Mater. 200 1
[5] Jiang S T 1993 Theory of Ferromagnetic. (Beijing: Science Press) p202, 34, 117 (in Chinese) [姜寿亭 1993 铁磁性理论 (北京: 科学出版社) 第202, 34, 117页]
[6] Moriya T 1985 Spin Fluctuations in Itinerant Electron Magnetism, Springer, Berlin, Heidelberg
[7] Oguchi T, Terakura K, Hamada N 1983 J. Phys. F 13 145
[8] Korenman V, Murray L J, Prange E R 1977 Phys. Rev. B 16 4032
[9] Wang S C, Prange E R, Korenman V 1982 Phys. Rev. B 25 5766
[10] Antropov P V 2001 D. P. Landau(Ed. ), Computer Simulation Studies in Condensed Matter Physics XIII 86 Springer, Berlin, Heidenberg p7
[11] Antropov P V 2003 D. P. Landau(Ed. ), Computer Simulation Studies in Condensed Matter Physics, in press
[12] Cyrot M 1982 (Ed. ) Magnetism of Metals and Alloys North Holland, Amsterdam
[13] Antropov P V, Katsnelson I M, Van Schilfgaarde M, Harmon N B, Kusnezov N 1996 Phys. Rev. B 54 1019
[14] Liechtenstein I A, Katsnelson I M, Gubanov A V 1984 J. Phys. F 14 l125
[15] Van Schilfgaarde M, Antropov P V 1999 J. Appl. Phys. 85 4827
[16] Antropov P V, Katsnelson I M, Liechtenstein I A 1997 Phys. B 237-238 336
[17] Wang S C, Prange E R, Korenman V 1982 Phy. Rev. B 25 5766
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[1] Xing D Y 2005 Physics 34 348 (in Chinese) [邢定钰 2005 物理 34 348]
[2] Yang H, Yun G H, Cao Y J 2014 Chin. Phys. B 23 097501
[3] Zheng Y L, Wang X X, Ge Z L, Gou H L, Yang G F, Dai S H, Zhu X L, Tian X B 2013 Acta Phys. Sin. 62 227701 (in Chinese) [郑勇林, 王晓茜, 葛泽玲, 郭红力, 严刚峰, 戴松晖, 朱晓玲, 田晓滨 2013 62 227701]
[4] Tokura Y, Tomioka Y 1999 J. Magn. Magn. Mater. 200 1
[5] Jiang S T 1993 Theory of Ferromagnetic. (Beijing: Science Press) p202, 34, 117 (in Chinese) [姜寿亭 1993 铁磁性理论 (北京: 科学出版社) 第202, 34, 117页]
[6] Moriya T 1985 Spin Fluctuations in Itinerant Electron Magnetism, Springer, Berlin, Heidelberg
[7] Oguchi T, Terakura K, Hamada N 1983 J. Phys. F 13 145
[8] Korenman V, Murray L J, Prange E R 1977 Phys. Rev. B 16 4032
[9] Wang S C, Prange E R, Korenman V 1982 Phys. Rev. B 25 5766
[10] Antropov P V 2001 D. P. Landau(Ed. ), Computer Simulation Studies in Condensed Matter Physics XIII 86 Springer, Berlin, Heidenberg p7
[11] Antropov P V 2003 D. P. Landau(Ed. ), Computer Simulation Studies in Condensed Matter Physics, in press
[12] Cyrot M 1982 (Ed. ) Magnetism of Metals and Alloys North Holland, Amsterdam
[13] Antropov P V, Katsnelson I M, Van Schilfgaarde M, Harmon N B, Kusnezov N 1996 Phys. Rev. B 54 1019
[14] Liechtenstein I A, Katsnelson I M, Gubanov A V 1984 J. Phys. F 14 l125
[15] Van Schilfgaarde M, Antropov P V 1999 J. Appl. Phys. 85 4827
[16] Antropov P V, Katsnelson I M, Liechtenstein I A 1997 Phys. B 237-238 336
[17] Wang S C, Prange E R, Korenman V 1982 Phy. Rev. B 25 5766
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