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热扰动导致的磁反转是越过能量势垒的不可逆反转, 称为热助隧穿. 本文研究Pr-Fe-B磁体热扰动导致的磁反转弛豫现象, 反转磁矩与时间自然对数关系可表示为与能垒之间的关系, 因此反磁化弛豫现象可用磁振子按能量的玻色统计分布率来解释, 是磁振子宏观效应的体现. 反磁化不可逆过程的临界尺寸为纳米级, 与理论磁畴壁尺寸接近, 证实热扰动反磁化经过磁畴壁形核去钉扎过程. 在实空间反磁化耦合体积增大能减小磁振子隧穿的反磁化概率, 热扰动场减小; 热扰动后效场测量值与热扰动场计算值基本是一致的. 温度升高, 热扰动能量增大, 由于耦合作用热扰动后效场有所减小, 但热扰动后效场相对于矫顽力的作用增大.The magnetization reversal resulting from the thermal fluctuation is irreversible for overcoming the energy barrier, ant it is called the thermally assisted tunneling. In this paper the relaxation in magnetizaition reversal resulting from the thermal fluctuation is observed in Pr-Fe-B permanent magnet. The dependence of magnetic moment on the time natural logarithm is the same as that on the energy barrier in the thermally assisted tunneling. So the relaxation in magnetization reversal originates from the macroeffect of magnons which follow Bose distribution law. The critical size in the irreversible magnetization reversal obtained by the fluctuation field is on a nanometer scale and close to the theoretical domain wall size, indicating that the thermally assisted magnetization reversal undergoes the nucleation and de-pinning of domain wall. The increase of coupling volume will reduce the possibility of magnons tunneling in magnetization reversal due to the weakening effect of thermal fluctuation. The variation of fluctuation field with the field verifies the effect of exchange coupling in Pr-Fe-B magnets, and the calculated value of fluctuation field is consistent with the aftereffect of thermal activation. With the increase of temperature the thermal fluctuation energy increases, and though the aftereffect of thermal fluctuation weakens due to the exchange coupling, the ratio of thermal fluctuation aftereffect to coercivity increases in Pr-Fe-B magnet.
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Keywords:
- thermal fluctuation /
- magnons /
- domain wall /
- magnetization reversal
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图 1 (a) Pr-Fe-B磁体薄带在300 K的磁滞回线(1 emu/g = 1 A·m2/kg); (b) 分别施加反向场15, 18, 20 kOe并保持1200 s条件下磁矩的变化
Fig. 1. (a) Hysteresis loop of Pr-Fe-B magnet at temperature of 300 K; (b) the variations of magnetic moments with the time under the field of –15, –18 and –20 kOe, respectively.
图 2 (a) 反转磁矩与时间自然对数关系; (b) 热扰动反磁化后效场Haf的测量和拟合
Fig. 2. (a) Dependence of magnetic moments on the natural logarithm of time; (b) the fitting and measurement of the aftereffect of thermal fluctuation.
图 3 Pr-Fe-B磁体的(a)磁黏滞系数S、不可逆磁化率xirr和(b)由公式Hf = S/xirr得到Hf
Fig. 3. (a) Magnetic viscosity coefficient S and irreversible magnetic susceptibility xirr, (b) the fluctuation field obtained by the formula of Hf = S/xirr of Pr-Fe-B magnet.
图 4 Pr-Fe-B磁体从120 K到380 K的热扰动后效场Haf和Haf/Hc比值
Fig. 4. Aftereffect field Haf of thermal fluctuation and the ration of Haf and Hc in Pr-Fe-B magnet between 120 K and 380 K.
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[1] Toga Y, Miyashita S, Sakuma A, Miyake T 2020 NPJ Comput. Mater. 6 67
Google Scholar
[2] Zhang H W, Zhang S Y, Shen B G, Goll D, Kronmüller H 2001 Chin. Phys. 10 1169
Google Scholar
[3] 钟文定 1996 物理 25 37
Zhong W D 1996 Physics 25 37
[4] Naser H, Rado C, Lapertot G, Raymond S 2020 Phys. Rev. B 102 014443
Google Scholar
[5] Zhao G P, Wang X L, Yang C, Xie L H, Zhou G 2007 J. Appl. Phys. 101 09K102
Google Scholar
[6] Zhu M G, Liu X M, Fang Y K, Li Z B, Li W 2006 Rare. Metals. 25 630
Google Scholar
[7] Zhao G P, Zhao M G, Lim H S, Feng Y P, Ong C K 2005 Appl. Phys. Lett. 87 162513
Google Scholar
[8] Li Z B, Shen B G, Niu E, Sun J R 2013 Appl. Phys. Lett. 103 062405
Google Scholar
[9] Givord D, Rossignol M, Barthem V M T S 2003 J. Magn. Magn. Mater. 258-259 1
Google Scholar
[10] Zhang H W, Rong C B, Du X B, Zhang S Y, Shen B G 2004 J. Magn. Magn. Mater. 278 127
Google Scholar
[11] Liu D, Zhao, T Y, Shen, B G, Peng F, Zhang M, Hu F X, Sun J R 2021 J. Magn. Magn. Mater. 527 167773
Google Scholar
[12] Tang X, Li J, Miyazaki Y, Sepehri-Amin H, Ohkubo T, Schreflc T, Hono K 2020 Acta Mater. 183 408
Google Scholar
[13] 李柱柏, 李赟, 秦渊, 张雪峰, 沈保根 2019 68 177501
Google Scholar
Li Z B, Li Y, Qin Y, Zhang X F, Shen B G 2019 Acta Phys. Sin. 68 177501
Google Scholar
[14] Fischbacher J, Kovacs A, Oezelt H, Gusenbauer M, Schrefl T, Exl L, Givord D, Dempsey N M, Zimanyi G, Winklhofer M, Hrkac G, Chantrell R, Sakuma N, Yano M, Kato A, Shoji T, Manabe A 2017 Appl. Phys. Lett. 111 072404
Google Scholar
[15] Wohlfarth E P 1984 J. Phys. F: Met. Phys. 14 L155
Google Scholar
[16] 姜寿亭, 李卫 2003 凝聚态磁性物理 (北京: 科学出版社) 第242页
Jiang S T, Li W 2003 Condensed Matter Physics of Magnetism (Bejing: Science Press) p242 (in Chinese)
[17] Zhang H W, Rong C B, Zhang J, Zhang S Y, Shen B G 2002 Phys. Rev. B 66 184436
Google Scholar
[18] Gong Q H, Yi M, Xu B X 2019 Phys. Rev. Mater. 3 084406
Google Scholar
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