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Magnetization reversal and coercivity in rare-earth permanent magnets and composite magnets

Li Zhu-Bai Li Yun Qin Yuan Zhang Xue-Feng Shen Bao-Gen

Magnetization reversal and coercivity in rare-earth permanent magnets and composite magnets

Li Zhu-Bai, Li Yun, Qin Yuan, Zhang Xue-Feng, Shen Bao-Gen
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  • The coercivities in rare earth permanent magnets even with the same intrinsic properties may differ largely. In this paper, what determines the coercivity is discussed via the investigation of thermal activation in Pr-Fe-B ribbons prepared by melt-spinning method. The thermal activation, resulting from thermal fluctuation overcoming the energy barrier under the applied field, is the critical behavior of magnetization reversal. The activation size is comparable to the theoretical domain wall size, implying that the magnetization reversal undergoes the nucleation of revered domain wall at grain outer-layer in Pr-Fe-B ribbons, and the defects near the grain boundary are critical for the magnetization reversal and coercivity. The exchange coupling between the defect region at grain outer-layer and the perfect region in the inside of grain promotes the nucleation of reversed domain and the depinning of domain wall motion. The reduced anisotropy of the defect region also contributes to the overcoming of energy barrier of magneto crystallie anisotropy in the inside of Pr-Fe-B grains by the coupling effect, so the nucleation field of reversed domain and coercivity decrease largely, and the domain wall size is a little larger than the theoretical value due to the coupling between the defect region at grain outer-layer and the perfect region in the inside of grain in the critical magnetization reversal. In Pr2Fe14B/α-Fe composite magnets, the exchange coupling between the soft and hard magnetic phase leads the domain wall size to increase in the critical magnetization reversal of thermal activation, and so the exchange energy plays a role in overcoming the energy barrier, resulting in the further decrease of coercivity. Via the addition of Ti and Nb element, the coercivity increases significantly. Based on the investigation of thermal activation, the size of defect region involved in the domain wall decreases, and the contribution of the anisotropy in the defect region and interface to the overcoming of energy barrier is weakened, so the applied magnetic field should be increased in the magnetization reversal. The coercivity can be enhanced by reducing the size of defect region at grain outer-layer and by making the anisotropy change abruptly at the interface between the hard and soft magnetic phase.
      Corresponding author: Li Zhu-Bai, lzbgj@163.com
    [1]

    Herbst J F 1991 Rev. Mod. Phys. 63 819

    [2]

    Kou X C, Kronmüller H, Givord D, Rossignol M F 1994 Phys. Rev. B 50 3849

    [3]

    Zhao G P, Zhao M G, Lim H S, Feng Y P, Ong C K 2005 Appl. Phys. Lett. 87 162513

    [4]

    Zhang H W, Rong C B, Zhang J, Zhang S Y, Shen B G 2002 Phys. Rev. B 66 184436

    [5]

    Kronmüller H 1987 Phys. Stat. Sol. B 144 385

    [6]

    Sepehri-Amin H, Ohkubo T, Shima T, Hono K 2012 Acta Mater. 60 819

    [7]

    Chen S L, Liu W, Zhang Z D 2005 Phys. Rev. B 72 224419

    [8]

    Yue M, Liu W Q, Zhang D T, Jian Z G, Cao A L, Zhang J X 2009 Appl. Phys. Lett. 94 092501

    [9]

    Givord D, Tenaud P, Viadieu T 1988 IEEE Trans. Magn. 24 1921

    [10]

    Gao R W, Zhang D H, Li H, Jiang S T, Zhou S Z, Li F B, Zhang L D 1995 J. Appl. Phys. 78 1156

    [11]

    Zhao G P, Wang X L, Yang C, Xie L H, Zhou G 2007 J. Appl. Phys. 101 09K102

    [12]

    Givord D, Rossignol M, Barthem V M T S 2003 J. Magn. Magn. Mater. 258-259 1

    [13]

    Li Z B, Shen B G, Niu E, Sun J R 2013 Appl. Phys. Lett. 103 062405

    [14]

    Kronmüller H, Durst K D, Sagawa M 1988 J. Magn. Magn. Mater. 74 291

    [15]

    Wohlfarth E P 1984 J. Phys. F: Met. Phys. 14 L155

    [16]

    张宏伟, 荣传兵, 张健, 张绍英, 沈保根 2003 物理学报 52 722

    Zhang H W, Rong C B, Zhang J, Zhang S Y, Shen B G 2003 Acta Phys. Sin. 52 722

    [17]

    Li Z B, Shen B G, Niu E, Liu R M, Zhang M, Sun J R 2013 Chin. Phys. B 22 117503

    [18]

    Li Z B, Zhang Y, Shen B G, Zhang M, Hu F X, Sun J R 2017 J. Magn. Magn. Mater. 422 249

    [19]

    Bauer J, Seeger M, Zern A, Kronmüller H 1996 J. Appl. Phys. 80 1667

    [20]

    Zhang H W, Rong C B, Du X B, Zhang S Y, Shen B G 2004 J. Magn. Magn. Mater. 278 127

    [21]

    Kronmüller H, Fahnle M 2003 Micromagnetism and the Microstructure of Ferromagnetic Solids (Cambridge: Cambridge University Press) p420

    [22]

    Zhang H W, Zhang S Y, Shen B G, Goll D, Kronmüller H 2001 Chin. Phys. 10 1169

    [23]

    Li Z B, Shen B G, Zhang M, Zhang Y, Hu F X, Sun J R 2015 Appl. Phys. Lett. 106 042403

    [24]

    张宏伟, 张文勇, 阎阿儒, 沈保根 1999 物理学报 48 211

    Zhang H W, Zhang W Y, Yan A R, Shen B G 1999 Acta Phys. Sin. 48 211

    [25]

    Li H L, Lou L, Hou F C, Guo D F, Li W, Li X H, Gunderov D V, Sato K, Zhang X Y 2013 Appl. Phys. Lett. 103 142406

    [26]

    Seeger M, Köhler D, Kronmüller H 1994 J. Magn. Magn. Mater. 130 165

    [27]

    Liu W, Liu X H, Cui W B, Gong W J, Zhang Z D 2013 Chin. Phys. B 22 027104

    [28]

    Zhang J, Takahashi Y K, Gopalan R, Hono K 2005 Appl. Phys. Lett. 86 122509

    [29]

    Si W J, Zhao G P, Ran N, Peng Y, Morvan F J, Wan X L 2015 Sci. Rep. 5 16212

    [30]

    Cui W B, Takahashi Y K, Hono K 2012 Adv. Mater. 24 6530

    [31]

    Kelly P E, O’Grady K, Mayo P I, Chantrell R W 1989 IEEE Trans. Magn. 25 3881

    [32]

    Choi Y, Jiang J S, Ding Y, Rosenberg R A, Pearson J E, Bader S D, Zambano A, Murakami M, Takeuchi I, Wang Z L, Liu J P 2007 Phys. Rev. B 75 104432

  • 图 1  样品粉末的X射线衍射谱

    Figure 1.  The X-ray diffraction patterns of powders for the samples.

    图 2  样品在温度300 K的磁滞回线

    Figure 2.  The hysterisis loops of the samples at temperature of 300 K.

    图 3  样品的${\mu _0}{H_{\rm{c}}}/{J_{\rm{s}}}$${\mu _0}H_{\rm{N}}^{{\rm{min}}}/{J_{\rm{s}}}$之间的关系

    Figure 3.  The dependences of ${\mu _0}{H_{\rm{c}}}/{J_{\rm{s}}}$ on ${\mu _0}H_{\rm{N}}^{{\rm{min}}}/{J_{\rm{s}}}$ for all samples.

    图 4  温度300 K磁场保持1200 s样品的热激活后的磁行为, 插图为热激活不可逆过程的激活尺寸和理论磁畴壁尺寸

    Figure 4.  The magnetization behaviors of thermal activation for 1200 s of waiting time at temperature of 300 K, and the inset shows the activation size of thermal activation and the ideal domain wall size.

    图 5  样品在温度300 K的${\text{δ}} m$曲线(Henkel点)

    Figure 5.  ${\text{δ}} m$ curves (Henkel plots) for the samples at temperature of 300 K.

  • [1]

    Herbst J F 1991 Rev. Mod. Phys. 63 819

    [2]

    Kou X C, Kronmüller H, Givord D, Rossignol M F 1994 Phys. Rev. B 50 3849

    [3]

    Zhao G P, Zhao M G, Lim H S, Feng Y P, Ong C K 2005 Appl. Phys. Lett. 87 162513

    [4]

    Zhang H W, Rong C B, Zhang J, Zhang S Y, Shen B G 2002 Phys. Rev. B 66 184436

    [5]

    Kronmüller H 1987 Phys. Stat. Sol. B 144 385

    [6]

    Sepehri-Amin H, Ohkubo T, Shima T, Hono K 2012 Acta Mater. 60 819

    [7]

    Chen S L, Liu W, Zhang Z D 2005 Phys. Rev. B 72 224419

    [8]

    Yue M, Liu W Q, Zhang D T, Jian Z G, Cao A L, Zhang J X 2009 Appl. Phys. Lett. 94 092501

    [9]

    Givord D, Tenaud P, Viadieu T 1988 IEEE Trans. Magn. 24 1921

    [10]

    Gao R W, Zhang D H, Li H, Jiang S T, Zhou S Z, Li F B, Zhang L D 1995 J. Appl. Phys. 78 1156

    [11]

    Zhao G P, Wang X L, Yang C, Xie L H, Zhou G 2007 J. Appl. Phys. 101 09K102

    [12]

    Givord D, Rossignol M, Barthem V M T S 2003 J. Magn. Magn. Mater. 258-259 1

    [13]

    Li Z B, Shen B G, Niu E, Sun J R 2013 Appl. Phys. Lett. 103 062405

    [14]

    Kronmüller H, Durst K D, Sagawa M 1988 J. Magn. Magn. Mater. 74 291

    [15]

    Wohlfarth E P 1984 J. Phys. F: Met. Phys. 14 L155

    [16]

    张宏伟, 荣传兵, 张健, 张绍英, 沈保根 2003 物理学报 52 722

    Zhang H W, Rong C B, Zhang J, Zhang S Y, Shen B G 2003 Acta Phys. Sin. 52 722

    [17]

    Li Z B, Shen B G, Niu E, Liu R M, Zhang M, Sun J R 2013 Chin. Phys. B 22 117503

    [18]

    Li Z B, Zhang Y, Shen B G, Zhang M, Hu F X, Sun J R 2017 J. Magn. Magn. Mater. 422 249

    [19]

    Bauer J, Seeger M, Zern A, Kronmüller H 1996 J. Appl. Phys. 80 1667

    [20]

    Zhang H W, Rong C B, Du X B, Zhang S Y, Shen B G 2004 J. Magn. Magn. Mater. 278 127

    [21]

    Kronmüller H, Fahnle M 2003 Micromagnetism and the Microstructure of Ferromagnetic Solids (Cambridge: Cambridge University Press) p420

    [22]

    Zhang H W, Zhang S Y, Shen B G, Goll D, Kronmüller H 2001 Chin. Phys. 10 1169

    [23]

    Li Z B, Shen B G, Zhang M, Zhang Y, Hu F X, Sun J R 2015 Appl. Phys. Lett. 106 042403

    [24]

    张宏伟, 张文勇, 阎阿儒, 沈保根 1999 物理学报 48 211

    Zhang H W, Zhang W Y, Yan A R, Shen B G 1999 Acta Phys. Sin. 48 211

    [25]

    Li H L, Lou L, Hou F C, Guo D F, Li W, Li X H, Gunderov D V, Sato K, Zhang X Y 2013 Appl. Phys. Lett. 103 142406

    [26]

    Seeger M, Köhler D, Kronmüller H 1994 J. Magn. Magn. Mater. 130 165

    [27]

    Liu W, Liu X H, Cui W B, Gong W J, Zhang Z D 2013 Chin. Phys. B 22 027104

    [28]

    Zhang J, Takahashi Y K, Gopalan R, Hono K 2005 Appl. Phys. Lett. 86 122509

    [29]

    Si W J, Zhao G P, Ran N, Peng Y, Morvan F J, Wan X L 2015 Sci. Rep. 5 16212

    [30]

    Cui W B, Takahashi Y K, Hono K 2012 Adv. Mater. 24 6530

    [31]

    Kelly P E, O’Grady K, Mayo P I, Chantrell R W 1989 IEEE Trans. Magn. 25 3881

    [32]

    Choi Y, Jiang J S, Ding Y, Rosenberg R A, Pearson J E, Bader S D, Zambano A, Murakami M, Takeuchi I, Wang Z L, Liu J P 2007 Phys. Rev. B 75 104432

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  • Received Date:  14 March 2019
  • Accepted Date:  07 June 2019
  • Available Online:  26 November 2019
  • Published Online:  01 September 2019

Magnetization reversal and coercivity in rare-earth permanent magnets and composite magnets

    Corresponding author: Li Zhu-Bai, lzbgj@163.com
  • 1. Key Laboratory of Integrated Exploitation of Bayan Obo Multi-Metal Resources, Inner Mongolia University of Science and Technology, Baotou 014010, China
  • 2. School of Science, Inner Mongolia University of Science and Technology, Baotou 014010, China
  • 3. State Key Laboratory of Magnetism, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China

Abstract: The coercivities in rare earth permanent magnets even with the same intrinsic properties may differ largely. In this paper, what determines the coercivity is discussed via the investigation of thermal activation in Pr-Fe-B ribbons prepared by melt-spinning method. The thermal activation, resulting from thermal fluctuation overcoming the energy barrier under the applied field, is the critical behavior of magnetization reversal. The activation size is comparable to the theoretical domain wall size, implying that the magnetization reversal undergoes the nucleation of revered domain wall at grain outer-layer in Pr-Fe-B ribbons, and the defects near the grain boundary are critical for the magnetization reversal and coercivity. The exchange coupling between the defect region at grain outer-layer and the perfect region in the inside of grain promotes the nucleation of reversed domain and the depinning of domain wall motion. The reduced anisotropy of the defect region also contributes to the overcoming of energy barrier of magneto crystallie anisotropy in the inside of Pr-Fe-B grains by the coupling effect, so the nucleation field of reversed domain and coercivity decrease largely, and the domain wall size is a little larger than the theoretical value due to the coupling between the defect region at grain outer-layer and the perfect region in the inside of grain in the critical magnetization reversal. In Pr2Fe14B/α-Fe composite magnets, the exchange coupling between the soft and hard magnetic phase leads the domain wall size to increase in the critical magnetization reversal of thermal activation, and so the exchange energy plays a role in overcoming the energy barrier, resulting in the further decrease of coercivity. Via the addition of Ti and Nb element, the coercivity increases significantly. Based on the investigation of thermal activation, the size of defect region involved in the domain wall decreases, and the contribution of the anisotropy in the defect region and interface to the overcoming of energy barrier is weakened, so the applied magnetic field should be increased in the magnetization reversal. The coercivity can be enhanced by reducing the size of defect region at grain outer-layer and by making the anisotropy change abruptly at the interface between the hard and soft magnetic phase.

    • 稀土永磁体矫顽力源于磁体高磁晶各向异性场[1], 磁晶各向异性场与晶体周期性点阵结构和结构对称性破缺密切相关. 但是即使磁体内秉性质磁晶各向异性场相同, 矫顽力可能相差很大[2,3]. 一般认为这是磁体微结构差异造成的, 因此矫顽力被认为是结构敏感量[4]. 但是如何理解微结构对矫顽力的影响, 以及控制磁体微结构提高磁性能, 一直处于探索过程中. 实际晶体点阵结构不可能是完美的, 磁体的缺陷如空位、间隙原子、弛豫、替代原子, 会严重影响磁晶各向异性场. 在晶粒边界点阵结构的周期性失去, 空位等缺陷密集, 因此晶粒边界磁晶各向异性场显著降低[4,5]. 反磁化从弱各向异性的缺陷处或软磁相开始[68], 但是需要越过晶粒内部磁晶各向异性势垒[9,10], 这是反磁化畴形核理论, 实际上这也是磁畴壁去钉扎过程[1113]. 一旦磁畴壁在内部形核, 就可以在晶粒内甚至跨过多个晶粒自由移动, 直至移动到另一晶粒边界处被反转场更高的晶粒钉扎, 这时需要增大外磁场促进新的磁畴壁形核去钉扎[13]. 所以从这个层面上来说, 磁畴形核和钉扎是一致的[11], 这两个概念并不一定矛盾[11,13]. 但是形核过程是如何决定磁体矫顽力[14], 这依然是需要清晰阐述的问题. 热激活是不可逆过程, 是反磁化的临界过程[15,16], 这为研究反磁化和矫顽力提供了途径. 本文制备三种Pr-Fe-B磁体, 对热激活形核的磁畴壁尺寸进行对比分析, 期望能对反磁化过程和矫顽力进行更清晰深入的阐述.

    2.   实验方法
    • 在氩气保护下通过电弧熔炼制备名义成分为Pr12Fe82B6, Pr9Fe85.5B5.5, Pr9Fe82.5Ti2Nb1B5.5母合金. 然后将母合金破为小块, 将约2.5 g的合金小块放入石英管中, 采用熔体快淬甩带方法用氩气将石英管中合金熔体吹到旋转的铜轮上, 制成快淬条带. 对于Pr12Fe82B6, Pr9Fe85.5B5.5合金, 铜轮表面线速度在20—25 m/s的范围内调整, 使磁性能最佳. 对于Pr9Fe82.5Ti2Nb1B5.5合金, 铜轮表面线速度为10 m/s磁性能最佳. 采用X射线衍射方法检验薄带相组成, 采用超导量子干涉仪振动磁强计(SQUID VSM)测量样品的磁性能、热激活反磁化曲线, 薄带平面与磁场方向平行, 从宏观上样品退磁因子忽略不计.

    3.   结果与讨论
    • 图1为样品粉末的X射线衍射谱. Pr12Fe82B6组成相主要为Pr2Fe14B晶体相, 平均晶粒尺寸约为20—30 nm[17]. Pr9Fe85.5B5.5, Pr9Fe82.5Ti2Nb1B5.5薄带在2θ为44.3°的衍射峰更强, 这应为α-Fe的衍射峰与Pr2Fe14B的衍射峰叠加增强所致, 因此薄带为Pr2Fe14B和α-Fe相复合结构. 2θ为44.3°的X射线衍射峰强度几乎相同, 可以认为这两种薄带软磁相α-Fe含量基本相同[18]. 透射电镜显示晶粒尺寸大多在20—30 nm之间, 但Pr9Fe85.5B5.5薄带大尺寸晶粒较多, Pr9Fe82.5Ti2Nb1B5.5薄带晶粒稍显细小、尺寸更为一致[18]. 图2为快淬薄带的磁滞回线, Pr12Fe82B6薄带矫顽力为13.30 kOe (1 Oe = 79.5775 A/m), 而具有Pr2Fe14B/α-Fe复合结构的Pr9Fe85.5B5.5薄带矫顽力下降到6.07 kOe, 但添加高熔点元素Ti, Nd的薄带Pr9Fe82.5Ti2Nb1B5.5矫顽力升至10.99 kOe.

      Figure 1.  The X-ray diffraction patterns of powders for the samples.

      Figure 2.  The hysterisis loops of the samples at temperature of 300 K.

      为探索这些磁体矫顽力差异的原因, 对不同温度下磁体矫顽力进行测试, 可以获得矫顽力和磁晶各向异性场之间的关系[19,20]. 从图3可以看出, 矫顽力和硬磁相磁晶各向异性场成线性关系, 符合Kronmüller公式 ${\mu _0}{H_{\rm{c}}}(T)/{J_{\rm{s}}}(T) ={a_{\rm{K}}}{a_{{\rm{ex}}}}{\mu _0}H_{\rm{N}}^{\min }(T)/ $${J_{\rm{s}}}(T) - {N_{{\rm{eff}}}} $[19], $H_{\rm{N}}^{{\rm{min}}}$为各向同性磁体反磁化的理论形核场, 即磁晶各向异性场的1/2, 数值上为$H_{\rm{N}}^{\min } = {K_1}/{J_{\rm{s}}}$, ${K_1}$为磁晶各向异性常数, ${J_{\rm{s}}}$为饱和磁化强度, 取值于文献[20]. 图3说明硬磁相晶粒磁晶各向异性场是获得高矫顽力的基础, 反磁化畴形核和位移需要越过硬磁相晶粒内部磁晶各向异性场势垒[12]. 微结构因子${a_{\rm{K}}}$表示硬磁相晶粒表层由于缺陷造成的各向异性降低对矫顽力的影响;${a_{{\rm{ex}}}}$表示晶粒之间交换耦合作用对矫顽力的影响;${N_{{\rm{eff}}}}$为退磁因子, 反映磁体内部偶极作用对矫顽力降低的程度. 由图3可知, 磁体矫顽力差异主要体现在因子${a_{\rm{K}}}{a_{{\rm{ex}}}}$上. Pr12Fe82B6薄带基本为单相, 可认为${a_{{\rm{ex}}}}=1$[19]. Pr9Fe85.5B5.5和Pr9Fe82.5Ti2Nb1B5.5复合磁体中因为软磁相α-Fe含量基本相同, ${a_{{\rm{ex}}}}$可认为是一样的[19]. 所以Pr9Fe82.5Ti2Nb1B5.5复合磁体${a_{\rm{K}}}$比Pr9Fe85.5B5.5大得多, 说明Pr9Fe82.5Ti2Nb1B5.5硬磁相晶粒边界得到优化[19], 这也是矫顽力增加的原因. 因此, 尽管反磁化需要越过硬磁相晶粒内部磁晶各向异性场势垒, 由于晶粒边界和内部耦合以及软、硬磁相晶粒之间交换耦合作用对磁反转越过势垒具有推动作用, 晶粒表层缺陷区的特性及软磁相对反磁化形核过程和矫顽力的影响很关键[14].

      Figure 3.  The dependences of ${\mu _0}{H_{\rm{c}}}/{J_{\rm{s}}}$ on ${\mu _0}H_{\rm{N}}^{{\rm{min}}}/{J_{\rm{s}}}$ for all samples.

      虽然反磁化过程基本清晰, 但对晶粒边界和内部耦合是如何决定磁反转场和矫顽力问题还需进一步研究. 在外场小于磁反转场的情况下磁反转是可逆的, 当越过晶粒内部磁晶各向异性场势垒才能实现不可逆的反磁化[10,12]. 反磁化的热激活源于热扰动通过激活体积越过势垒的不可逆反磁化[15,16], 研究热激活可以探索反磁化临界过程的磁反转场和矫顽力. 图4为薄带在温度300 K磁场保持1200 s测量的热激活反磁化曲线. 首先, 将样品在正方向饱和磁化, 然后负方向加一约为矫顽力大小的磁场并保持1200 s. 由于热扰动, 即使外磁场并没有增加, 一些反转场稍高的磁矩会发生反转. 保持磁场1200 s之后, 以较慢速度10 Oe/s增加磁场, 这时磁体磁矩较稳定, 只有磁场升到一定值时才出现显著的磁反转, 这段磁场增加值就是热扰动的后效场, 也就是热扰动场. 如图4所示, 可通过对反磁化曲线做切线来获得热扰动场${H_{\rm{f}}}$[17].

      Figure 4.  The magnetization behaviors of thermal activation for 1200 s of waiting time at temperature of 300 K, and the inset shows the activation size of thermal activation and the ideal domain wall size.

      热稳定性不但与温度相关, 也与物质体积相关. 物质体积越小, 热稳定性越差, 热扰动场越大[21]. 可通过公式${d_{{\rm{active}}}} = \sqrt[3]{v}$, $v = {k_{\rm{B}}}T/({H_{\rm{f}}}{M_{\rm{s}}})$[kB = 1.38 × 10–23 J/K, T = 300 K, Ms = 1.55 T]计算出热激活尺寸${d_{{\rm{active}}}}$[15,16,20]. Pr12Fe82B6, Pr9Fe85.5B5.5, Pr9Fe82.5Ti2Nb1B5.5薄带热激活尺寸分别为5.47, 6.25, 4.80 nm (见图4插图), 与Pr2Fe14B磁体理论磁畴壁尺寸3.70 nm在同一数量级(根据${\delta _{\rm{m}}} = $${\text{π}}\sqrt {A/K}$, A为交换耦合常数, 为7.8 × 10–12 J/m, K为磁晶各向异性常数, 在温度为300 K时等于5.6 MJ/m3)[20], 这符合在硬磁相晶粒磁畴壁形核反磁化理论. 由于晶粒表层缺陷区和内部耦合推动反磁化畴从边界到内部形核, 热激活尺寸${d_{{\rm{active}}}}$稍微大于理论磁畴壁尺寸${\delta _{\rm{m}}}$, 小于晶粒尺寸[22,23], 实际上为反磁化临界过程磁畴壁尺寸[23]. 反磁化过程是外磁场以及磁体偶极作用克服硬磁相晶粒内部磁晶各向异性势垒的过程. 但是晶粒表层也具有较小的各向异性场, 由于表层和内部的耦合作用, 晶粒表层各向异性对克服晶粒内部势垒也有贡献, 所以反磁化所需外磁场就减小, 磁体矫顽力降低. 相对于Pr12Fe82B6薄带, Pr9Fe85.5B5.5热激活尺寸增加, 这说明在反磁化临界过程中更多的硬磁相表层缺陷区和软磁相包含在这个磁畴壁内, 其他研究也说明软磁相的存在使得热激活体积增大[24]. 软磁相的交换耦合能和硬磁相晶粒表层缺陷区的各向异性能对克服晶粒内部势垒的贡献增大, 所以磁反转所需外磁场减小, 矫顽力进一步降低. 添加Ti, Nb后, 热激活尺寸减小, 这应归结为硬磁相晶粒表层缺陷区的特性发生变化[25], 很可能硬磁相晶粒表层缺陷区尺寸减小, 从硬磁相到软磁相各向异性的过渡更急剧[11,23], 反磁化过程晶粒表面各向异性的能量就下降, 为克服晶粒内部势垒所需外磁场就升高, 磁体矫顽力增强. 如图3所示, Pr9Fe82.5Ti2Nb1B5.5薄带微结构因子${a_{\rm{K}}}$比Pr9Fe85.5B5.5大得多也证明Pr9Fe82.5Ti2Nb1B5.5硬磁相晶粒边界得到优化, 缺陷较少[26], 这样缺陷区的尺寸就会减小. 一些研究也发现, 软、硬磁相界面原子扩散会降低复合磁体矫顽力[2729], 而在界面加Ta等元素, 阻止Fe原子扩散破坏硬磁相的晶体结构, 软硬磁界面更加清晰[30], 磁体矫顽力显著升高, 这应归结于硬磁相晶粒表层缺陷区尺寸减小, 反磁化过程中表层缺陷区各向异性对克服硬磁相晶粒内部势垒的贡献减弱.

      软、硬磁相晶间交换耦合作用对克服硬磁相晶粒内部势垒也有贡献. Henkel点可检验纳米晶各向同性磁体晶间交换耦合作用的强弱, 可由公式${\text{δ}} m = \left[ {2{M_{\rm{r}}}(H) + {M_{\rm{d}}}(H)} \right]/{M_{\rm{r}}} - 1$获得[31] (如图5所示). ${M_{\rm{r}}}(H)$为热退磁磁体正方向加磁场H后将磁场降到零的剩磁, ${M_{\rm{r}}}$ 是饱和磁化后的剩磁, ${M_{\rm{d}}}(H)$为磁体饱和磁化、加反方向磁场H后将磁场降到零的剩磁. 正${\text{δ}} m$值说明晶粒之间存在很强的交换耦合作用. Pr12Fe82B6薄带${\text{δ}} m$值最大, 但Pr9Fe85B6薄带的${\text{δ}} m$最大值下降. 对于各向同性磁体, ${\text{δ}} m$值主要反映硬磁相晶粒反磁化的一致性[13]. 而在复合磁体中, 由于软磁相的存在, 硬磁相晶粒之间反磁化过程就变得不一致, 所以${\text{δ}} m$最大值下降[13]. 但反磁化曲线并没有出现台阶, 说明软、硬磁相交换耦合作用良好, 交换耦合能会促进克服硬磁相晶粒内部各向异性势垒, 因此磁体矫顽力降低. ${\text{δ}} m$负值增大, 这可能是由于晶粒尺寸分布不均匀造成的, 磁体内部不规则区域磁偶极作用更容易增大. 在外磁场的作用下这些不规则区域更容易首先反磁化, 所以Pr9Fe85B6薄带退磁因子${N_{{\rm{eff}}}}$增大. 依据前面推测, 如果硬磁相晶粒表层缺陷区尺寸较大、各向异性过渡较为平缓, 虽然矫顽力降低, 但交换耦合长度增加[32], 所以即使软磁相晶粒较大也能良好耦合. Ti, Nb弱磁性元素添加并没有使${\text{δ}} m$降低, 反而有所升高, 这应归结为晶粒较为细小、尺寸分布趋于一致. 前面推测软、硬磁相界面各向异性的过渡更急剧, 磁体矫顽力升高, 但这样软、硬磁交换耦合长度会减小[32]. 为使两相反磁化一致, 磁体内不能出现大尺寸的软磁相.

      Figure 5.  ${\text{δ}} m$ curves (Henkel plots) for the samples at temperature of 300 K.

    4.   结 论
    • 主要从反磁化热激活的角度分析Pr12Fe82B6磁体和Pr9Fe85.5B5.5, Pr9Fe82.5Ti2Nb1B5.5软、硬磁相复合磁体的反磁化过程和矫顽力. 热激活为克服能量势垒的不可逆反磁化过程. 硬磁相晶粒表面缺陷区、软磁相都可以通过耦合作用推动硬磁相晶粒内部反磁化畴形核克服磁晶各向异性势垒, 因而硬磁相表层缺陷区各向异性能、交换耦合能对克服晶粒内部的势垒都有贡献, 导致磁体矫顽力降低. 同时由于耦合, 反磁化临界过程磁畴壁尺寸都稍大于理论尺寸. 通过热激活尺寸和矫顽力分析, 降低硬磁相晶粒表层缺陷区尺寸, 或使软、硬磁界面各向异性急剧过渡, 反磁化磁畴壁尺寸会减小, 硬磁相表层缺陷和界面对克服势垒的贡献减小, 磁体矫顽力得到增强. 期望本文的研究能对进一步理解磁体反磁化过程、优化磁体微结构提高矫顽力提供理论基础和实践依据.

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