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界面原子扩散对SmCo/Fe交换弹簧双层膜磁性能影响的微磁学研究

何鑫鑫 赵倩

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界面原子扩散对SmCo/Fe交换弹簧双层膜磁性能影响的微磁学研究

何鑫鑫, 赵倩

Micromagnetic studies of influence of interface atomic diffusion on magnetic properties of SmCo/Fe exchange-spring bilayers

He Xin-Xin, Zhao Qian
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  • 本文通过三维微磁学数值模拟, 研究了界面处原子扩散形成的界面层对易轴平行和垂直膜面取向SmCo/Fe双层膜磁性能的影响. 当易轴取向平行膜面时, 体系成核在第二象限. 随着界面层厚度的增加, 尽管剩磁逐渐减小, 而成核场和钉扎场逐渐增加, 以致最大磁能积先增加后减小, 直至体系由交换弹簧磁体过渡到刚性磁体. 当易轴取向垂直膜面时, 随着界面层厚度的增加, 体系成核由第一象限逐渐过渡到第二象限, 虽然钉扎场从减小、不变到略有增加, 但成核场和剩磁逐渐增加, 导致最大磁能积逐渐增加. 在退磁过程中, 膜面内自旋偏转: 易轴平行膜面取向系统显示了flower 态和C态的产生与消失的过程; 而易轴垂直膜面取向系统显示了vortex态的产生与消失的过程. 随着易轴平行膜面SmCo/Fe双层膜界面层中SmCo原子扩散比例的增加, 成核场和钉扎场增加但剩磁减小, 最大磁能积先增加后降低. 当易轴两种取向时, 对任一界面层厚度, 成核场随界面交换耦合常数的增大而增大, 这表明界面层的存在增强了硬磁/软磁层之间的交换耦合作用. 本文建立的模型很好地模拟了相关的实验结果[ 2007 Appl. Phys. Lett. 91 072509].
    In this paper, based on three-dimensional micromagnetic numerical simulation, the influences of the interface layer formed by the atomic diffusion at the interface on magnetic properties in parallel SmCo/Fe bilayer and perpendicular SmCo/Fe bilayer are investigated. For the parallel system, whose nucleation occurs in the second quadrant, as the interface layer thickness increases, the nucleation field and the pinning field increase gradually though the remanence decreases gradually, hence the maximum energy product first goes up and then comes down. As a result, in the system there occurs the transition from the exchange-spring to the rigid magnet. For the perpendicular system, with the increase of the interface layer thickness, a gradual transition from the first quadrant to the second quadrant happens to its nucleation. Although the pinning field experiences the changes from decreasing to unchanging and to increasing, the nucleation field and remanence both rise gradually. Therefore, the energy product is enhanced gradually. During the demagnetization, there appears a spin deviation within the film plane: the parallel system shows a progress of generation and disappearance of the flower and C states; however, the perpendicular system shows a progress of generation and disappearance of the vortex state. With the increase of the ratio of the SmCo atomic diffusion in the interface layer of parallel SmCo/Fe bilayers, the nucleation and pinning field go up, but the remanence decreases, and hence the maximum energy product first rises and then drops. For the two easy axis orientations and any interface layer thickness, the nucleation field rises with the increase of interface exchange energy constant, indicating that the existence of an interface layer between the soft layer and hard layer enhances the exchange coupling interaction between them. The model in this paper well simulates the relevant experimental results [ 2007 Appl. Phys. Lett. 91 072509].
      通信作者: 赵倩, zhaoqianqm@163.com
    • 基金项目: 国家自然科学基金(批准号: 51861030)和内蒙古自治区自然科学基金(批准号: 2019MS01002)资助的课题
      Corresponding author: Zhao Qian, zhaoqianqm@163.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51861030) and the Natural Science Foundation of Inner Mongolia Autonomous Region, China (Grant No. 2019MS01002)
    [1]

    Kneller E F, Hawing R 1991 IEEE Trans. Magn. 27 3588Google Scholar

    [2]

    Neu V, Häfner K, Patra A K, Chultz L 2006 J. Phys. D: Appl. Phys. 39 5116Google Scholar

    [3]

    Brown W F 1945 Rev. Mod. Phys. 17 15Google Scholar

    [4]

    Pellicelli R, Solzi M, Neu V, Pernechele C 2014 J. Phys. D: Appl. Phys. 47 115002Google Scholar

    [5]

    Zhao Q, He X X, Morvan F J, Zhang X F, Zhao G P, Li Z B, Ma Q 2019 J. Magn. Magn. Mater. 476 40Google Scholar

    [6]

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

    [7]

    Xia J, Zhao G P, Zhang H W, Cheng Z H, Feng Y P, Ding J, Yang H T 2012 J. Appl. Phys. 112 013918Google Scholar

    [8]

    Skomski R, Coey J M D 1993 Phys. Rev. B 48 15812Google Scholar

    [9]

    邓娅, 赵国平, 薄鸟 2011 物理学报 60 037502Google Scholar

    Deng Y, Zhao G P, Bo N 2011 Acta Phys. Sin. 60 037502Google Scholar

    [10]

    Liu Y L, Zhou J J, Wang X, Ma Q, Liu F, Liu J, Zhao T Y, Hu F X, Sun J R, Shen B G 2020 J. Magn. Magn. Mater. 513 167162Google Scholar

    [11]

    Li Y Q, Yue M, Wu Q, Wang T, Cheng C X, Chen H X 2015 J. Magn. Magn. Mater. 394 117Google Scholar

    [12]

    Liu D, Ma T Y, Wang L C, Liu Y L, Zhao T Y, Hu F X, Sun J R, Shen B G 2019 J. Phys. D: Appl. Phys. 52 135002Google Scholar

    [13]

    Fan J P, Zhang X Y, Dong W J, Bai Y H, Xu X H 2019 Appl. Phys. A 125 111Google Scholar

    [14]

    Wang J P, Shen W K, Bai J M, Victora R H, Judy J H, Song W L 2005 Appl. Phys. Lett. 86 142504Google Scholar

    [15]

    陈传文, 项阳 2016 物理学报 65 127502Google Scholar

    Chen C W, Xiang Y 2016 Acta Phys. Sin. 65 127502Google Scholar

    [16]

    Zhao Q, Chen J, Wang J Q, Zhang X F, Zhao G P, Ma Q 2018 Sci. Rep. 7 4286

    [17]

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

    [18]

    Zhang J, Wang F, Zhang Y, Song J Z, Zhang Y, Shen B G, Sun J R 2012 J. Nanosci. Nanotechnol. 12 1109Google Scholar

    [19]

    Zhang J, Li Y X, Wang F, Shen B G, Sun J R 2010 J. Appl. Phys. 107 043911Google Scholar

    [20]

    Neu V, Sawatzki S, Kopte M, Mickel C, Schultz L 2012 IEEE Trans. Magn. 48 3599Google Scholar

    [21]

    Sawatzki S, Heller R, Mickel C, Seifert M, Schultz L, Neu V 2011 J. Appl. Phys. 109 123922Google Scholar

    [22]

    Weng X J, Shen L C, Tang H, Zhao G P, Xia J, Morvan F J, Zou J 2019 J. Magn. Magn. Mater. 475 352Google Scholar

    [23]

    Zhang X C, Zhao G P, Xia J, Yue M, Yuan X H, Xie L H 2014 Chin. Phys. B 23 097504Google Scholar

    [24]

    Asti G, Solzi M, Ghidini M, Neri F M 2004 Phys. Rev. B 69 174401Google Scholar

    [25]

    Sang C X, Zhao G P, Xia W X, Wan X L, Morvan F J, Zhang X C, Xie L H, Zhang J, Du J, Yan A R, Liu P 2016 Chin. Phys. B 25 037501Google Scholar

    [26]

    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 104432Google Scholar

    [27]

    Jiang J S, Pearson J E, Liu Z Y, Kabius B, Trasobares S, Miller D J, Bader S D, Lee D R, Haskel D, Srajer G, Liu J P 2004 Appl. Phys. Lett. 85 5293Google Scholar

    [28]

    Jiang J S, Pearson J E, Liu Z Y, Kabius B, Trasobares S, Miller D J, Bader S D 2005 J. Appl. Phys. 97 10K311Google Scholar

    [29]

    Liu Y Z, Wu Y Q, Kramer M J, Choi Y, Jiang J S, Wang Z L, Liu J P 2008 Appl. Phys. Lett. 93 92502Google Scholar

    [30]

    Choi Y, Jiang J S, Pearson J E, Bader S D, Kavich J J, Freeland J W, Liu J P 2007 Appl. Phys. Lett. 91 072509Google Scholar

    [31]

    Zhao Q, He X X, Morvan F J, Zhang X F, Zhao G P, Li Z B, Li L F, Liu Y L 2020 J. Magn. Magn. Mater. 495 165858Google Scholar

    [32]

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

    [33]

    Donahue M J, Porter D G 1999 OOMMF Users Guide, Version 1.0 (Gaithersburg: National Institute of Standards and Technology)

    [34]

    Gilbert T L 2004 IEEE Trans. Magn. 40 3443Google Scholar

    [35]

    Gilbert T L 1955 Phys. Rev. 100 1243

    [36]

    Landau L, Lifshitz E 1935 Physik. Z. Sowjetunion 8 153

    [37]

    Thiaville A, Rohart S, Jué É, Cros V, Fert A 2012 Europhys. Lett. 100 57002Google Scholar

    [38]

    Huang Z Y 2003 J. Comput. Math. 21 33

    [39]

    Zhang W, Zhao G P, Yuan X H, Ye L N 2012 J. Magn. Magn. Mater. 324 4231Google Scholar

    [40]

    彭懿, 赵国平, 吴绍全, 斯文静, 万秀琳 2014 物理学报 63 167505Google Scholar

    Peng Y, Zhao G P, Wu S Q, Si W J, Wan X L 2014 Acta Phys. Sin. 63 167505Google Scholar

    [41]

    Zhao Q, He X X, Morvan F J, Zhao G P, Li Z B 2020 Chin. Phys. B 29 037501Google Scholar

    [42]

    Zhao G P, Deng Y, Zhang H W, Chen L, Feng Y P, Bo N 2010 J. Appl. Phys. 108 093928Google Scholar

  • 图 1  本文基本方案为t s + t i + t h = 15 nm, 计算范围从–t st h. 计算模型 (a) 易轴平行膜面; (b) 易轴垂直膜面

    Fig. 1.  The basic scheme in our work, with regions calculated from –t s to t h when t s + t i + t h = 15 nm. Fig. 1(a) and (b) show the model for the calculation of the easy axis parallel and perpendicular to the film plane, respectively.

    图 2  界面层厚度ti不同时SmCo(5 nm)/Fe(10–ti nm)双层膜的退磁曲线 (a) 易轴平行膜面; (b) 易轴垂直膜面. 插图是HN, HPHCti的变化曲线

    Fig. 2.  Demagnetization curves of SmCo(5 nm)/Fe(10–ti nm) bilayers for various interface layer thicknesses ti. Fig. 2(a) and 2(b) show the demagnetization curves of the easy axis parallel and perpendicular to the film plane, respectively. The inset shows the change curves of the HN, HP and HC as functions of ti.

    图 3  $ t^{\rm i} $ = 4 nm时SmCo(5 nm)/Fe(10–$ t^{\rm i} $ nm)双层膜在不同外磁场下膜厚方向上的自旋分布 (a) 易轴平行膜面; (b) 易轴垂直膜面. 插图是四个关键角$ {\theta }^{\text{s}}$, $ {\theta }^{{\text{i}}_{\text{1}}} $, $ {\theta ^{{{\text{i}}_{\text{2}}}}} $$ {\theta ^{\text{h}}} $随外磁场的变化曲线

    Fig. 3.  Spin distributions in the thickness direction for the SmCo(5 nm)/Fe(10–$ t^{\rm i} $ nm) bilayer with $ t^{\rm i} $ = 4 nm under various applied magnetic fields. Fig. 3(a) and (b) show the spin distributions of the easy axis parallel and perpendicular to the film plane, respectively. The inset shows the evolution of four key angles, i.e., $ {\theta ^{\text{s}}} $, $ {\theta ^{{{\text{i}}_{\text{1}}}}} $, $ {\theta ^{{{\text{i}}_{\text{2}}}}} $ and $ {\theta ^{\text{h}}} $ as functions of the applied magnetic field.

    图 4  $ t^{\rm i} $ = 4 nm时易轴平行膜面SmCo(5 nm)/Fe(10–$ t^{\rm i} $nm)双层膜在不同外磁场下一些膜面内的自旋分布 (a) H = –5.3 kOe时的软磁层表面; (b) H = –8.7 kOe时的软磁层表面; (c) H = –10.7 kOe时的硬磁层与界面层第二界面; (d) H = –11.3 kOe时的硬磁层表面. 显示比例为1∶12, 即图中的每一个磁矩代表12 × 12个计算的磁矩

    Fig. 4.  The spin distributions within some film planes for the parallel SmCo(5 nm)/Fe(10–$ t^{\rm i} $ nm) bilayer with $ t^{\rm i} $ = 4 nm under various applied magnetic fields: (a) H = –5.3 kOe, the soft layer surface; (b) H = –8.7 kOe, the soft layer surface; (c) H = –10.7 kOe, the second interface between the hard and interface layers; (d) H = –11.3 kOe, the hard layer surface. The adopted ratio 1∶12 for presentation. This means that one displayed magnetic moment at the figure stands for 12 × 12 calculated moments.

    图 5  $ t^{\rm i} $ = 4 nm时易轴垂直膜面取向SmCo(5 nm)/Fe(10–$ t^{\rm i} $ nm)双层膜不同外磁场下四个关键角对应膜面内的自旋分布 (a) H = 10.7 kOe时的软磁层表面; (b) H = 10.7 kOe时的软磁层与界面层第一界面; (c) H = 2.7 kOe时的硬磁层与界面层第二界面; (d) H = –14.0 kOe时的硬磁层表面. 显示比例为1∶12, 即图中的每一个磁矩代表12 × 12个计算的磁矩

    Fig. 5.  The spin distributions corresponding to four key angles within the film plane for the perpendicular SmCo(5 nm)/Fe(10–$ t^{\rm i} $ nm) bilayer with $ t^{\rm i} $ = 4 nm under various applied magnetic fields: (a) H = 10.7 kOe, the soft layer surface; (b) H = 10.7 kOe, the first interface between the soft and interface layers; (c) H = 2.7 kOe, the second interface between the hard and interface layers; (d) H = –14.0 kOe, the hard layer surface. The adopted ratio 1∶12 for presentation. This means that one displayed magnetic moment at the figure stands for 12 × 12 calculated moments.

    图 6  界面层厚度$ t^{\rm i} $不同时SmCo(5 nm)/Fe(10–$ t^{\rm i} $ nm)双层膜的磁能积(BH) (a) 易轴平行膜面; (b) 易轴垂直膜面

    Fig. 6.  Energy products (BH) of SmCo(5 nm)/Fe(10–$ t^{\rm i} $ nm) bilayers for various interface layer thicknesses $ t^{\rm i} $: (a) and (b) show the energy products of the easy axis parallel and perpendicular to the film plane, respectively.

    图 7  界面层厚度$ t^{\rm i} $不同时易轴平行膜面SmCo(20 nm)/Fe(20–$ t^{\rm i} $ nm)双层膜的磁能积(BH) (a)实验测量[30]; (b)理论计算

    Fig. 7.  Energy products (BH) in parallel SmCo(20 nm)/Fe(20–$ t^{\rm i} $ nm) bilayers for various interface layer thicknesses $ t^{\rm i} $: (a) The experimental measurement[30]; (b) the theoretical calculation.

    图 8  易轴平行膜面SmCo(5 nm)/Fe(10–$ t^{\rm i} $ nm)双层膜, 当$ t^{\rm i} $ = 4 nm时SmCo原子的扩散比例为10%, 30%, 50%, 70%和90%的 (a) 成核场HN、钉扎场HP和矫顽力HC; (b)剩磁Mr和最大磁能积 (BH)max.

    Fig. 8.  (a) Calculated nucleation field HN, pinning field HP, and coercivity HC; (b) remanence Mr and maximum energy product (BH)max as functions of t i for parallel SmCo (5 nm)/Fe(10–$ t^{\rm i} $ nm) with $ t^{\rm i} $ = 4 nm when the ratio of SmCo atomic diffusion are 10%, 30%, 50%, 70% and 90%, respectively.

    图 9  界面层厚度$ t^{\rm i} $不同时SmCo(5 nm)/Fe(10–$ t^{\rm i} $ nm)双层膜的成核场HN随界面交换耦合常数Aint的变化曲线 (a) 易轴平行膜面; (b) 易轴垂直膜面

    Fig. 9.  Nucleation field HN as a function of the interface exchange energy constant Aint for various interface layer thicknesses $ t^{\rm i} $ in SmCo(5 nm)/Fe(10–$ t^{\rm i} $ nm) bilayers. (a) and (b) show the curves of the easy axis parallel and perpendicular to the film plane, respectively.

  • [1]

    Kneller E F, Hawing R 1991 IEEE Trans. Magn. 27 3588Google Scholar

    [2]

    Neu V, Häfner K, Patra A K, Chultz L 2006 J. Phys. D: Appl. Phys. 39 5116Google Scholar

    [3]

    Brown W F 1945 Rev. Mod. Phys. 17 15Google Scholar

    [4]

    Pellicelli R, Solzi M, Neu V, Pernechele C 2014 J. Phys. D: Appl. Phys. 47 115002Google Scholar

    [5]

    Zhao Q, He X X, Morvan F J, Zhang X F, Zhao G P, Li Z B, Ma Q 2019 J. Magn. Magn. Mater. 476 40Google Scholar

    [6]

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

    [7]

    Xia J, Zhao G P, Zhang H W, Cheng Z H, Feng Y P, Ding J, Yang H T 2012 J. Appl. Phys. 112 013918Google Scholar

    [8]

    Skomski R, Coey J M D 1993 Phys. Rev. B 48 15812Google Scholar

    [9]

    邓娅, 赵国平, 薄鸟 2011 物理学报 60 037502Google Scholar

    Deng Y, Zhao G P, Bo N 2011 Acta Phys. Sin. 60 037502Google Scholar

    [10]

    Liu Y L, Zhou J J, Wang X, Ma Q, Liu F, Liu J, Zhao T Y, Hu F X, Sun J R, Shen B G 2020 J. Magn. Magn. Mater. 513 167162Google Scholar

    [11]

    Li Y Q, Yue M, Wu Q, Wang T, Cheng C X, Chen H X 2015 J. Magn. Magn. Mater. 394 117Google Scholar

    [12]

    Liu D, Ma T Y, Wang L C, Liu Y L, Zhao T Y, Hu F X, Sun J R, Shen B G 2019 J. Phys. D: Appl. Phys. 52 135002Google Scholar

    [13]

    Fan J P, Zhang X Y, Dong W J, Bai Y H, Xu X H 2019 Appl. Phys. A 125 111Google Scholar

    [14]

    Wang J P, Shen W K, Bai J M, Victora R H, Judy J H, Song W L 2005 Appl. Phys. Lett. 86 142504Google Scholar

    [15]

    陈传文, 项阳 2016 物理学报 65 127502Google Scholar

    Chen C W, Xiang Y 2016 Acta Phys. Sin. 65 127502Google Scholar

    [16]

    Zhao Q, Chen J, Wang J Q, Zhang X F, Zhao G P, Ma Q 2018 Sci. Rep. 7 4286

    [17]

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

    [18]

    Zhang J, Wang F, Zhang Y, Song J Z, Zhang Y, Shen B G, Sun J R 2012 J. Nanosci. Nanotechnol. 12 1109Google Scholar

    [19]

    Zhang J, Li Y X, Wang F, Shen B G, Sun J R 2010 J. Appl. Phys. 107 043911Google Scholar

    [20]

    Neu V, Sawatzki S, Kopte M, Mickel C, Schultz L 2012 IEEE Trans. Magn. 48 3599Google Scholar

    [21]

    Sawatzki S, Heller R, Mickel C, Seifert M, Schultz L, Neu V 2011 J. Appl. Phys. 109 123922Google Scholar

    [22]

    Weng X J, Shen L C, Tang H, Zhao G P, Xia J, Morvan F J, Zou J 2019 J. Magn. Magn. Mater. 475 352Google Scholar

    [23]

    Zhang X C, Zhao G P, Xia J, Yue M, Yuan X H, Xie L H 2014 Chin. Phys. B 23 097504Google Scholar

    [24]

    Asti G, Solzi M, Ghidini M, Neri F M 2004 Phys. Rev. B 69 174401Google Scholar

    [25]

    Sang C X, Zhao G P, Xia W X, Wan X L, Morvan F J, Zhang X C, Xie L H, Zhang J, Du J, Yan A R, Liu P 2016 Chin. Phys. B 25 037501Google Scholar

    [26]

    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 104432Google Scholar

    [27]

    Jiang J S, Pearson J E, Liu Z Y, Kabius B, Trasobares S, Miller D J, Bader S D, Lee D R, Haskel D, Srajer G, Liu J P 2004 Appl. Phys. Lett. 85 5293Google Scholar

    [28]

    Jiang J S, Pearson J E, Liu Z Y, Kabius B, Trasobares S, Miller D J, Bader S D 2005 J. Appl. Phys. 97 10K311Google Scholar

    [29]

    Liu Y Z, Wu Y Q, Kramer M J, Choi Y, Jiang J S, Wang Z L, Liu J P 2008 Appl. Phys. Lett. 93 92502Google Scholar

    [30]

    Choi Y, Jiang J S, Pearson J E, Bader S D, Kavich J J, Freeland J W, Liu J P 2007 Appl. Phys. Lett. 91 072509Google Scholar

    [31]

    Zhao Q, He X X, Morvan F J, Zhang X F, Zhao G P, Li Z B, Li L F, Liu Y L 2020 J. Magn. Magn. Mater. 495 165858Google Scholar

    [32]

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

    [33]

    Donahue M J, Porter D G 1999 OOMMF Users Guide, Version 1.0 (Gaithersburg: National Institute of Standards and Technology)

    [34]

    Gilbert T L 2004 IEEE Trans. Magn. 40 3443Google Scholar

    [35]

    Gilbert T L 1955 Phys. Rev. 100 1243

    [36]

    Landau L, Lifshitz E 1935 Physik. Z. Sowjetunion 8 153

    [37]

    Thiaville A, Rohart S, Jué É, Cros V, Fert A 2012 Europhys. Lett. 100 57002Google Scholar

    [38]

    Huang Z Y 2003 J. Comput. Math. 21 33

    [39]

    Zhang W, Zhao G P, Yuan X H, Ye L N 2012 J. Magn. Magn. Mater. 324 4231Google Scholar

    [40]

    彭懿, 赵国平, 吴绍全, 斯文静, 万秀琳 2014 物理学报 63 167505Google Scholar

    Peng Y, Zhao G P, Wu S Q, Si W J, Wan X L 2014 Acta Phys. Sin. 63 167505Google Scholar

    [41]

    Zhao Q, He X X, Morvan F J, Zhao G P, Li Z B 2020 Chin. Phys. B 29 037501Google Scholar

    [42]

    Zhao G P, Deng Y, Zhang H W, Chen L, Feng Y P, Bo N 2010 J. Appl. Phys. 108 093928Google Scholar

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出版历程
  • 收稿日期:  2021-04-02
  • 修回日期:  2021-05-23
  • 上网日期:  2021-06-07
  • 刊出日期:  2021-10-05

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