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

He Xin-Xin; Zhao Qian

doi:10.7498/aps.70.20210623

Abstract

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].

Keywords:

Authors and contacts

College of Science, Inner Mongolia University of Science and Technology, Baotou 014010, China

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)

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References

[1]	Kneller E F, Hawing R 1991 IEEE Trans. Magn. 27 3588 Google Scholar
[2]	Neu V, Häfner K, Patra A K, Chultz L 2006 J. Phys. D: Appl. Phys. 39 5116 Google Scholar
[3]	Brown W F 1945 Rev. Mod. Phys. 17 15 Google Scholar
[4]	Pellicelli R, Solzi M, Neu V, Pernechele C 2014 J. Phys. D: Appl. Phys. 47 115002 Google 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 40 Google Scholar
[6]	Cui W B, Takahashi Y K, Hono Y 2012 Adv. Mater. 24 6530 Google 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 013918 Google Scholar
[8]	Skomski R, Coey J M D 1993 Phys. Rev. B 48 15812 Google Scholar
[9]	邓娅, 赵国平, 薄鸟 2011 物理学报 60 037502 Google Scholar Deng Y, Zhao G P, Bo N 2011 Acta Phys. Sin. 60 037502 Google 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 167162 Google Scholar
[11]	Li Y Q, Yue M, Wu Q, Wang T, Cheng C X, Chen H X 2015 J. Magn. Magn. Mater. 394 117 Google 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 135002 Google Scholar
[13]	Fan J P, Zhang X Y, Dong W J, Bai Y H, Xu X H 2019 Appl. Phys. A 125 111 Google 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 142504 Google Scholar
[15]	陈传文, 项阳 2016 物理学报 65 127502 Google Scholar Chen C W, Xiang Y 2016 Acta Phys. Sin. 65 127502 Google 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 122509 Google Scholar
[18]	Zhang J, Wang F, Zhang Y, Song J Z, Zhang Y, Shen B G, Sun J R 2012 J. Nanosci. Nanotechnol. 12 1109 Google Scholar
[19]	Zhang J, Li Y X, Wang F, Shen B G, Sun J R 2010 J. Appl. Phys. 107 043911 Google Scholar
[20]	Neu V, Sawatzki S, Kopte M, Mickel C, Schultz L 2012 IEEE Trans. Magn. 48 3599 Google Scholar
[21]	Sawatzki S, Heller R, Mickel C, Seifert M, Schultz L, Neu V 2011 J. Appl. Phys. 109 123922 Google 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. 475 352 Google Scholar
[23]	Zhang X C, Zhao G P, Xia J, Yue M, Yuan X H, Xie L H 2014 Chin. Phys. B 23 097504 Google Scholar
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[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 037501 Google 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 104432 Google Scholar
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[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 10K311 Google 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 92502 Google 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 072509 Google 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 165858 Google Scholar
[32]	Si W J, Zhao G P, Ran N, Peng Y, Morvan F J, Wan X L 2015 Sci. Rep. 5 16212 Google Scholar
[33]	Donahue M J, Porter D G 1999 OOMMF User’s Guide, Version 1.0 (Gaithersburg: National Institute of Standards and Technology)
[34]	Gilbert T L 2004 IEEE Trans. Magn. 40 3443 Google 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 57002 Google 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 4231 Google Scholar
[40]	彭懿, 赵国平, 吴绍全, 斯文静, 万秀琳 2014 物理学报 63 167505 Google Scholar Peng Y, Zhao G P, Wu S Q, Si W J, Wan X L 2014 Acta Phys. Sin. 63 167505 Google Scholar
[41]	Zhao Q, He X X, Morvan F J, Zhao G P, Li Z B 2020 Chin. Phys. B 29 037501 Google Scholar
[42]	Zhao G P, Deng Y, Zhang H W, Chen L, Feng Y P, Bo N 2010 J. Appl. Phys. 108 093928 Google Scholar

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

Figure 1. The basic scheme in our work, with regions calculated from –t^s to t^h when t^s + tⁱ + 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.

DownLoad: Full-Size Img PowerPoint

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H_N, H_P 和H_C随tⁱ的变化曲线

Figure 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 H_N, H_P and H_C as functions of tⁱ.

DownLoad: Full-Size Img PowerPoint

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}}}}} $和$ {\theta ^{\text{h}}} $随外磁场的变化曲线

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

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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

Figure 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.

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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H_N、钉扎场H_P和矫顽力H_C; (b)剩磁M_r和最大磁能积 (BH)_max.

Figure 8. (a) Calculated nucleation field H_N, pinning field H_P, and coercivity H_C; (b) remanence Mr and maximum energy product (BH)_max as functions of tⁱ 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.

DownLoad: Full-Size Img PowerPoint

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H_N随界面交换耦合常数A^int的变化曲线　(a) 易轴平行膜面; (b) 易轴垂直膜面

Figure 9. Nucleation field H_N as a function of the interface exchange energy constant A^int 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.

DownLoad: Full-Size Img PowerPoint

[1]	Kneller E F, Hawing R 1991 IEEE Trans. Magn. 27 3588 Google Scholar
[2]	Neu V, Häfner K, Patra A K, Chultz L 2006 J. Phys. D: Appl. Phys. 39 5116 Google Scholar
[3]	Brown W F 1945 Rev. Mod. Phys. 17 15 Google Scholar
[4]	Pellicelli R, Solzi M, Neu V, Pernechele C 2014 J. Phys. D: Appl. Phys. 47 115002 Google 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 40 Google Scholar
[6]	Cui W B, Takahashi Y K, Hono Y 2012 Adv. Mater. 24 6530 Google 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 013918 Google Scholar
[8]	Skomski R, Coey J M D 1993 Phys. Rev. B 48 15812 Google Scholar
[9]	邓娅, 赵国平, 薄鸟 2011 物理学报 60 037502 Google Scholar Deng Y, Zhao G P, Bo N 2011 Acta Phys. Sin. 60 037502 Google 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 167162 Google Scholar
[11]	Li Y Q, Yue M, Wu Q, Wang T, Cheng C X, Chen H X 2015 J. Magn. Magn. Mater. 394 117 Google 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 135002 Google Scholar
[13]	Fan J P, Zhang X Y, Dong W J, Bai Y H, Xu X H 2019 Appl. Phys. A 125 111 Google 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 142504 Google Scholar
[15]	陈传文, 项阳 2016 物理学报 65 127502 Google Scholar Chen C W, Xiang Y 2016 Acta Phys. Sin. 65 127502 Google 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 122509 Google Scholar
[18]	Zhang J, Wang F, Zhang Y, Song J Z, Zhang Y, Shen B G, Sun J R 2012 J. Nanosci. Nanotechnol. 12 1109 Google Scholar
[19]	Zhang J, Li Y X, Wang F, Shen B G, Sun J R 2010 J. Appl. Phys. 107 043911 Google Scholar
[20]	Neu V, Sawatzki S, Kopte M, Mickel C, Schultz L 2012 IEEE Trans. Magn. 48 3599 Google Scholar
[21]	Sawatzki S, Heller R, Mickel C, Seifert M, Schultz L, Neu V 2011 J. Appl. Phys. 109 123922 Google 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. 475 352 Google Scholar
[23]	Zhang X C, Zhao G P, Xia J, Yue M, Yuan X H, Xie L H 2014 Chin. Phys. B 23 097504 Google Scholar
[24]	Asti G, Solzi M, Ghidini M, Neri F M 2004 Phys. Rev. B 69 174401 Google 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 037501 Google 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 104432 Google 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 5293 Google 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 10K311 Google 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 92502 Google 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 072509 Google 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 165858 Google Scholar
[32]	Si W J, Zhao G P, Ran N, Peng Y, Morvan F J, Wan X L 2015 Sci. Rep. 5 16212 Google Scholar
[33]	Donahue M J, Porter D G 1999 OOMMF User’s Guide, Version 1.0 (Gaithersburg: National Institute of Standards and Technology)
[34]	Gilbert T L 2004 IEEE Trans. Magn. 40 3443 Google 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 57002 Google 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 4231 Google Scholar
[40]	彭懿, 赵国平, 吴绍全, 斯文静, 万秀琳 2014 物理学报 63 167505 Google Scholar Peng Y, Zhao G P, Wu S Q, Si W J, Wan X L 2014 Acta Phys. Sin. 63 167505 Google Scholar
[41]	Zhao Q, He X X, Morvan F J, Zhao G P, Li Z B 2020 Chin. Phys. B 29 037501 Google Scholar
[42]	Zhao G P, Deng Y, Zhang H W, Chen L, Feng Y P, Bo N 2010 J. Appl. Phys. 108 093928 Google Scholar

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