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We establish a general model of a finite periodic system by n pairs of alternating ferromagnetic and nonmagnetic (FNF) layers. Using Bloch spin wave quantum theory, the basic properties of alternating FNF layers and the dependence of property of electron wave scattering in alternating layers on the number of layers are investigated. It is found that an electron wavefunction in the system can be expressed as the superposition of eigenvectors of a transfer matrix or Bloch-like functions in an infinite periodic system. Form this function we can obtain an exact solution for monochromatic wave scattering of a system with an arbitrary number of layers. On this basis, the dependences of reflection and transmission coefficients on energy for the electron wavefunction in a periodic system are determined. The calculation of spectral window shows that its energy position and width are the same as those of almost full reflection region. The system can be used as spin filter due to high-energy dispersion and dependence of exchange energy on electron spin direction.
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Keywords:
- multilayer film of magnetic /
- ferromagnetic and nonmagnetic structure /
- electron wave scattering /
- spin filter of electron
[1] Liang S D, Huang G Y 2012 Physics B 407 3382
[2] Sulston K W, Burrows B L 2000 Solid State Commun. 114 567
[3] Lu M W, Yan X H 2006 Solid State Commun. 138 147
[4] Zhou W P, Yun G H, Liang X X 2009 Chin. Phys. B 18 5496
[5] Zhou G H, Pan X, Zhu Y F 2013 Acta Phys. Sin. 62 097501 (in Chinese) [周广宏, 潘旋, 朱雨富 2013 62 097501]
[6] Liu Y, Peng X P 2012 Chin. Phys. Lett. 29 057701
[7] Bloch F Z 1930 Physica 61 206
[8] Jiang S T 1993 Theory of Ferromagnetic (Beijing: Science Press) p88 (in Chinese) [姜寿亭 1993 铁磁性理论 (北京: 科学出版社)第88页]
[9] Pedesen F B, Hemmer P C 1994 Phys. Rev. B 50 7724
[10] Ren S Y 2001 Phys. Rev. B 64 035322
[11] Pereyra P, Castillo E 2002 Phys. Rev. B 65 205120
[12] Einevoll G T, Hammer P C, Thomsen J 1990 Physics B 42 3485
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[1] Liang S D, Huang G Y 2012 Physics B 407 3382
[2] Sulston K W, Burrows B L 2000 Solid State Commun. 114 567
[3] Lu M W, Yan X H 2006 Solid State Commun. 138 147
[4] Zhou W P, Yun G H, Liang X X 2009 Chin. Phys. B 18 5496
[5] Zhou G H, Pan X, Zhu Y F 2013 Acta Phys. Sin. 62 097501 (in Chinese) [周广宏, 潘旋, 朱雨富 2013 62 097501]
[6] Liu Y, Peng X P 2012 Chin. Phys. Lett. 29 057701
[7] Bloch F Z 1930 Physica 61 206
[8] Jiang S T 1993 Theory of Ferromagnetic (Beijing: Science Press) p88 (in Chinese) [姜寿亭 1993 铁磁性理论 (北京: 科学出版社)第88页]
[9] Pedesen F B, Hemmer P C 1994 Phys. Rev. B 50 7724
[10] Ren S Y 2001 Phys. Rev. B 64 035322
[11] Pereyra P, Castillo E 2002 Phys. Rev. B 65 205120
[12] Einevoll G T, Hammer P C, Thomsen J 1990 Physics B 42 3485
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