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By using the Hartree approximation and the simplified method of quasidiscreteness multiple scales, we have studied quantum solitary wave solutions for a one-dimensional ferromagnetic chain with exchange interaction and classical magnetic moment interaction. In this chain there are both traveling and stationary quantum solilary waves. With the help of the obtained quantum solitary wave solution, the energy levels and magnetic moments of the quantum solitary wave have been investigated further. It is shown that the energy and magnetic moments of the quantum solitary wave are quantized. These novel results provide a possible way for understanding macroscopic quantum effects such as quantum steps of the hysteresis loop in magnetic materials.
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Keywords:
- one-dimensional ferromagnetic chain /
- quantum solitary wave /
- energy level /
- magnetic moment
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[2] Klitzing K V, Dorda G, Pepper M 1980 Phys. Rev. Lett. 45 494
[3] Tsui D C, Stomer H L,Gossard A C 1982 Phys. Rev. Lett. 48 1559
[4] Friedman J R, Sarachik M P, Tejada J 1996 Phys. Rev. Lett. 76 3830
[5] Friedman J R, Sarachik M P, Tejada J 1996 J. Appl. Phys. 79 6031
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[7] Ying H P, Ji D R 1993 Acta Phys. Sin. 42 1845 (in Chinese)[应和平、季达人 1993 42 1845]
[8] Lin N, Yu Z R 1993 Acta Phys. Sin. 42 1990 (in Chinese)[林 念、于祖荣 1993 42 1990]
[9] Cheng T M, Xian Y Z 2006 Acta Phys. Sin. 55 4828 (in Chinese)[成泰民、鲜于泽 2006 55 4828]
[10] Cheng T M 2007 Acta Phys. Sin. 56 1066 (in Chinese)[成泰民 2007 56 1066]
[11] Wang H Y, Xia Q 2007 Acta Phys. Sin. 56 5466 (in Chinese)[王怀玉、夏 青 2007 56 5466]
[12] Zhang S J, Jiang J J, Liu Y J 2008 Acta Phys. Sin. 57 531 (in Chinese)[张松俊、蒋建军、刘拥军 2008 57 531]
[13] He B, Ying H P, Ji D R 1996 Acta Phys. Sin. 45 522 (in Chinese)[何 兵、应和平、季达人1996 45 522]
[14] Bao S Q, Zhao H, Shen J L, Yang G Z 1996 Phys. Rev. B 53 735
[15] Gao Y, Zhang Y M, Chen H 2000 Acta Phys. Sin. 49 1586 (in Chinese)[高 阳、章豫梅、陈 鸿2000 49 1586]
[16] Xi X Q, Chen W X, Liu Q, Yue R H 2006 Acta Phys. Sin. 55 3026 (in Chinese)[惠小强、陈文学、刘 起、岳瑞宏 2006 55 3026]
[17] Zheng Q, Zhang X P, Zhi Q J, Ren Z Z 2009 Chin. Phys. B 18 3210
[18] Huang L Y, Fang M F 2008 Chin. Phys. B 17 2339
[19] Zhang T, Xi X Q, Yue R H 2004 Acta Phys. Sin. 53 2755 (in Chinese)[张 涛、惠小强、岳瑞宏 2004 53 2755]
[20] 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 57 7267]
[21] Qin M, Tian D P, Tao Y J 2008 Acta Phys. Sin. 57 5395 (in Chinese)[秦 猛、田东平、陶应娟 2008 57 5395]
[22] Qin M, Xu S L, Tao Y J, Tian D P 2008 Chin. Phys. B 17 2800
[23] Zhu Y, Zhu S Q, Hao X 2007 Chin. Phys. 16 2229
[24] Wallis R F, Mills D L, Boardman A D 1995 Phys. Rev. B 52 3828
[25] Takeno S, Kawasaki K 1992 Phys. Rev. B 45 5083
[26] Lai R, Kiselev S A, Sievers A J 1996 Phys. Rev. B 54 12655
[27] Lai R, Sievers A J 1997 J. Appl. Phys. 81 3972
[28] Lai R, Kiselev S A, Sievers A J 1997 Phys. Rev. B 56 5345
[29] English L Q, Sato M, Sievers A J 2001 J. Appl. Phys. 89 6707
[30] Sato M, English L Q, Hubbard B E, Sievers A J 2002 J. Appl. Phys. 91 8676
[31] Li D J, Mi X W, Deng K, Tang Y 2006 Chin. Phys. 15 39
[32] Li D J, Wang X Y, Mi X W,Xue J 2008 Commun. Theor. Phys. 50 1177
[33] Holstein T, Primakoff H 1940 Phys. Rev. 58 1098
[34] Wright E, Eilbeck J C, Hays M H 1993 Physica D 69 18
[35] Schwarz U T, English L Q, Sievers A J 1999 Phys. Rev. Lett. 83 223
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[1] Baibich M N,Broto J M 1988 Phys. Rev. Lett. 67 2472
[2] Klitzing K V, Dorda G, Pepper M 1980 Phys. Rev. Lett. 45 494
[3] Tsui D C, Stomer H L,Gossard A C 1982 Phys. Rev. Lett. 48 1559
[4] Friedman J R, Sarachik M P, Tejada J 1996 Phys. Rev. Lett. 76 3830
[5] Friedman J R, Sarachik M P, Tejada J 1996 J. Appl. Phys. 79 6031
[6] Zhong J 1990 Acta Phys. Sin. 39 486 (in Chinese)[钟 健 1990 39 486]
[7] Ying H P, Ji D R 1993 Acta Phys. Sin. 42 1845 (in Chinese)[应和平、季达人 1993 42 1845]
[8] Lin N, Yu Z R 1993 Acta Phys. Sin. 42 1990 (in Chinese)[林 念、于祖荣 1993 42 1990]
[9] Cheng T M, Xian Y Z 2006 Acta Phys. Sin. 55 4828 (in Chinese)[成泰民、鲜于泽 2006 55 4828]
[10] Cheng T M 2007 Acta Phys. Sin. 56 1066 (in Chinese)[成泰民 2007 56 1066]
[11] Wang H Y, Xia Q 2007 Acta Phys. Sin. 56 5466 (in Chinese)[王怀玉、夏 青 2007 56 5466]
[12] Zhang S J, Jiang J J, Liu Y J 2008 Acta Phys. Sin. 57 531 (in Chinese)[张松俊、蒋建军、刘拥军 2008 57 531]
[13] He B, Ying H P, Ji D R 1996 Acta Phys. Sin. 45 522 (in Chinese)[何 兵、应和平、季达人1996 45 522]
[14] Bao S Q, Zhao H, Shen J L, Yang G Z 1996 Phys. Rev. B 53 735
[15] Gao Y, Zhang Y M, Chen H 2000 Acta Phys. Sin. 49 1586 (in Chinese)[高 阳、章豫梅、陈 鸿2000 49 1586]
[16] Xi X Q, Chen W X, Liu Q, Yue R H 2006 Acta Phys. Sin. 55 3026 (in Chinese)[惠小强、陈文学、刘 起、岳瑞宏 2006 55 3026]
[17] Zheng Q, Zhang X P, Zhi Q J, Ren Z Z 2009 Chin. Phys. B 18 3210
[18] Huang L Y, Fang M F 2008 Chin. Phys. B 17 2339
[19] Zhang T, Xi X Q, Yue R H 2004 Acta Phys. Sin. 53 2755 (in Chinese)[张 涛、惠小强、岳瑞宏 2004 53 2755]
[20] 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 57 7267]
[21] Qin M, Tian D P, Tao Y J 2008 Acta Phys. Sin. 57 5395 (in Chinese)[秦 猛、田东平、陶应娟 2008 57 5395]
[22] Qin M, Xu S L, Tao Y J, Tian D P 2008 Chin. Phys. B 17 2800
[23] Zhu Y, Zhu S Q, Hao X 2007 Chin. Phys. 16 2229
[24] Wallis R F, Mills D L, Boardman A D 1995 Phys. Rev. B 52 3828
[25] Takeno S, Kawasaki K 1992 Phys. Rev. B 45 5083
[26] Lai R, Kiselev S A, Sievers A J 1996 Phys. Rev. B 54 12655
[27] Lai R, Sievers A J 1997 J. Appl. Phys. 81 3972
[28] Lai R, Kiselev S A, Sievers A J 1997 Phys. Rev. B 56 5345
[29] English L Q, Sato M, Sievers A J 2001 J. Appl. Phys. 89 6707
[30] Sato M, English L Q, Hubbard B E, Sievers A J 2002 J. Appl. Phys. 91 8676
[31] Li D J, Mi X W, Deng K, Tang Y 2006 Chin. Phys. 15 39
[32] Li D J, Wang X Y, Mi X W,Xue J 2008 Commun. Theor. Phys. 50 1177
[33] Holstein T, Primakoff H 1940 Phys. Rev. 58 1098
[34] Wright E, Eilbeck J C, Hays M H 1993 Physica D 69 18
[35] Schwarz U T, English L Q, Sievers A J 1999 Phys. Rev. Lett. 83 223
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