Effect of defects on magnetostriction and magnetic moment evolution of iron thin films

Zhang Shuo; Long Lian-Chun; Liu Jing-Yi; Yang Yang

doi:10.7498/aps.71.20211177

Abstract

Magnetostrictive materials have broad application prospects in sensing, control, energy conversion, and information conversion. The improving of the performances and applications of such materials has become a research hotspot, but defects will inevitably appear in the preparation and use of materials. In this study, the magnetostrictive structure model of iron elemental material with no defect or hole defect or crack defect is established by the molecular dynamics method. The influences of different defects on the magnetostrictive behavior of iron thin films are analyzed, and the mechanism of the influence of defects on the magnetostrictive behavior is depicted from the perspective of atomic magnetic moment. The results show that the films with 60 × 2 × 1 defects in the center are the easiest to reach saturation magnetostriction, and the magnetostriction is the least after reaching saturation, with respect to the films without defects. The films with 10 × 10 × 1 and 2 × 60 × 1 defects in the center require a larger magnetic field to approach to saturation, and the magnetostriction of the film with 2 × 60 × 1 defects in the center reaches a maximum value after saturation. This is because the defects will affect the magnetic moment of the surrounding atoms and make them deflect to the direction parallel to the defects, thus affecting the magnetostriction of the iron thin film. Among them, the hole defects have less influence on the magnetostriction, while the crack defects have stronger influence on the magnetostriction. The direction of the crack also has an effect on the magnetostriction of Fe thin film. When the crack is parallel to the direction of magnetization, the maximum magnetostriction of the film in the direction of magnetization from the initial state to the saturation of magnetization will decrease. When the crack is perpendicular to the direction of magnetization, the maximum magnetostriction of the film in the direction of magnetization from the initial state to the saturation of magnetization will increase. These results suggest that the defects affect the magnetostriction of the model as a whole during magnetization by affecting the initial magnetic moment orientation of the surrounding atoms.

Keywords:

PACS:

75.80.+q	(Magnetomechanical effects, magnetostriction)
02.70.Ns	(Molecular dynamics and particle methods)
13.40.Em	(Electric and magnetic moments)

Authors and contacts

1.
Faculty of Materials and Manufacturing, Beijing University of Technology, Beijing 100124, China
2.
Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China

Corresponding author: Long Lian-Chun, longlc@bjut.edu.cn ; Yang Yang, yang.yang@iphy.ac.cn

Funds: Project supported by the National Key R&D Program of China (Grant No. 2018YFB0703500)

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1. 引　言

性能优良且成本低廉的铁磁性材料广泛应用于各类工程中, 其中磁致伸缩性能较好的材料在传感器、机械控制、线性马达、能量收集、能量转换、位移器件和水下声呐扫描等领域呈现出重要的应用价值及广阔的应用前景^[1-3]. 磁致伸缩材料也常被用于制造多重铁性的磁电复合材料^[4,5], 而磁致伸缩效应的逆效应-压磁效应, 也被应用于铁磁性材料的无损检测领域^[6]. 目前多数磁致伸缩材料是以铁为基础进行合金或掺杂制成, 如Terfenol-D(铽镝铁合金)、Fe-Ga合金等, 因此从微观结构层面研究铁单质的磁致伸缩对改善传统磁致伸缩材料性能和研制新型磁致伸缩材料均有一定帮助.

温度、应力、形变和缺陷等都会对材料的磁致伸缩性能产生影响, 为了研究这些因素对磁致伸缩的影响规律, 学者们已取得了诸多研究成果. Ren等^[7]建立了描述多晶铁非线性、各向异性的磁致伸缩的有限元模型, 预测了多晶铁在300—900 K温度范围内的磁致伸缩曲线. M'Zali等^[8]提出了一种识别电工钢在机械载荷下的磁致伸缩行为的方法, 并与直接测量电工钢在不同应力下的磁致伸缩结果对比, 结果吻合良好.

缺陷对磁致伸缩材料影响的研究多集中在金属磁记忆检测技术^[9]上. 金属磁记忆检测技术是以压磁效应为基础的新型无损检测技术, 它通过测量铁磁性材料的磁记忆信号来探测材料中的应力集中区域和微型损伤, 可用来评估铁磁性材料的早期损伤^[10]. 这项技术首先由Dubov^[11]于1997年提出, 此后研究者们开展了一系列有关无损检测的理论和试验研究^[12,13], 快速发展形成了一套全新的无损检测技术. 其技术原理基于磁致伸缩效应中的Villari效应(压磁效应), 当铁磁性材料在受力工作时, 在工作荷载的作用下, 应力会使材料内部微观磁畴发生变化, 使得应力集中的位置处磁畴产生不可逆的重新取向, 并且这种不可逆的变化与所受应力大小和方式有关, 因此使用金属磁记忆检测技术可以检测出材料的应力集中部位.

Dubov^[11]指出铁磁性材料应力集中区域的切向磁信号会达到局部最大, 而法向磁信号会有归零的现象. Zhang等^[14]研究了带肋钢筋疲劳损伤与压磁信号之间的关系, 通过对HRB400加肋钢筋进行单轴静态加载和循环拉伸加载试验, 证明了这种无损检测技术对分析带肋钢筋疲劳过程的有效性. 宋凯等^[15]将断裂机制与位错理论相结合, 建立了铁磁性材料在荷载作用下应力集中区和微观损伤区域磁信号变化的相关模型. 张卫民等^[16]通过研究中低碳钢静拉伸时的磁信号变化, 得到了试件拉伸至塑性变形之后表面磁场强度的变化规律, 为在弹性区域内检测低碳钢的应力变化提供了依据.

尽管学者们已经对磁致伸缩材料的制备^[17]、改良^[18]、测试^[19]和应用^[20]等领域进行了诸多研究, 但缺陷对铁磁性材料, 尤其是铁单质的磁致伸缩的影响仍缺乏系统的微观机理研究和仿真模拟机理解释. 本文采用分子动力学方法分别构建无缺陷、孔洞缺陷与裂纹缺陷的体心立方结构(bcc)铁薄膜磁致伸缩模型, 研究缺陷对其磁致伸缩性能的影响, 并从原子磁矩层面分析缺陷对其内部微观结构变化的影响机理.

2. 计算方法

采用分子动力学方法分析bcc铁薄膜内缺陷对磁致伸缩和磁化构型演化的影响. 所使用的原子间势包括EAM势、spin/exchange势^[21-23]和spin/neel势^[21]. 模型原始尺寸为N_x × N_y × N_z, 其中N_x, N_y, N_z分别表示沿着 x, y, z 这3个方向的晶格数, 其中晶格常数为2.86 Å, 模拟盒子的尺寸为160 × 160 × 1个晶格大小. 分别建立了无缺陷、孔洞缺陷及裂纹缺陷模型, 通过在模型中心删除掉10 × 10 × 1个晶格的原子构建孔洞缺陷, 通过在模型中心删除掉60 × 2 × 1和2 × 60 × 1个晶格的原子分别构建两个方向的裂纹缺陷.

边界条件为在x和y方向上设定非周期性边界条件, z方向设定为周期性边界条件, 铁原子的原子磁矩为2.2 μ_B, 原子的初始磁矩方向设置为随机分布. 在300 K温度条件下进行模拟, 采用nve/spin系综, 并使用langevin/spin控温器控温, 积分步长为5 fs, 数据输出间隔为50 fs, 基于LAMMPS分子动力学模拟软件进行模拟.

3. 结果与讨论

采用上述方法模拟驰豫300 ps并进行结构优化, 将驰豫平衡之后的模型输出作为初始模型, 初始模型内各原子磁矩投影到xy面上的磁化构型, 如图1所示. 图中颜色越深的区域表示其原子磁矩越接近x方向或y方向, 浅色区域表示原子磁矩与x方向或y方向间有较大夹角的偏转, 图中箭头表示该区域内原子的磁矩方向.

$图 1 模型初始磁化构型　(a)无缺陷; (b)中心10 × 10 × 1缺陷; (c)中心60 × 2 × 1缺陷; (d)中心2 × 60 × 1缺陷\r\nFig. 1. Initial magnetized configuration diagram of the model: (a) No defect; (b) 10 × 10 × 1 defect in the center; (c) 60 × 2 × 1 defect in the center; (d) 2 × 60 × 1 defect in the center.$

图 1 模型初始磁化构型　(a)无缺陷; (b)中心10 × 10 × 1缺陷; (c)中心60 × 2 × 1缺陷; (d)中心2 × 60 × 1缺陷

Fig. 1. Initial magnetized configuration diagram of the model: (a) No defect; (b) 10 × 10 × 1 defect in the center; (c) 60 × 2 × 1 defect in the center; (d) 2 × 60 × 1 defect in the center.

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无缺陷薄膜内原子磁矩出现了顺时针旋转的磁化漩涡, 其中磁化漩涡的中心位于模型中心处, 漩涡中心到模型的四边分成了4个三角形区域, 上下边界处的三角形区域内原子磁化方向分别沿x轴正方向和负方向, 左右边界处的三角形区域内原子磁化方向分别沿y轴正方向和负方向, 中心空白处原子磁矩沿z轴正方向, 在x, y方向上无偏转, 因此在xy面上的投影为空白. 如图1(a) 所示.

与无缺陷薄膜的初始磁化构型对比, 中心有缺陷的薄膜不再产生磁化漩涡, 而是形成了, 3种不同的磁化构型, 其中中心10 × 10 × 1缺陷模型驰豫完成后, 模型的整体磁化强度不再为0, 而是沿x轴与y轴正方向, 其中模型上下边界处原子磁矩沿x轴正方向, 左右边界处原子磁矩沿y轴正方向, 缺陷周围大量原子磁矩沿x轴与y轴之间的过渡方向偏转. 如图1(b) 所示.

中心60 × 2 × 1缺陷模型驰豫完成后, 模型的整体磁化强度仍大约为0, 由于缺陷的存在, 模型在缺陷与模型上下边界之间形成了两个梯形区域, 梯形区域内原子磁矩分别沿x轴负、正方向, 缺陷与模型左右边界之间形成了两个三角形区域, 三角形区域内原子磁矩分别沿y轴负、正方向, 4个区域之间的原子磁矩则处于过渡方向. 如图1(c) 所示.

中心2 × 60 × 1缺陷模型驰豫完成后, 模型的整体磁化强度沿y轴正方向, x, z方向的磁化强度依然为0, 模型内形成了由左至右将整个缺陷包含在内的区域, 该区域内原子磁矩沿y轴正方向, 只有上下边界处少部分原子磁矩分别沿x轴正、负方向, 各区域之间有部分原子磁矩处于过渡方向. 如图1(d) 所示.

分别将驰豫完成后的模型作为模拟的初始模型, 对初始模型沿x轴正方向进行磁化, 改变磁场大小并得出磁致伸缩应变数据, 取不同磁场下磁致伸缩平衡后的应变数据, 做出不同磁场下磁致伸缩拟合曲线图, 如图2和图3所示. 图中横坐标为归一化磁场强度, H为外加磁场大小, H_m为使模型磁致伸缩饱和的最大外加磁场.

$图 2 不同缺陷模型在x方向上磁致伸缩应变\r\nFig. 2. Magnetostrictive strain in the x direction for different defect models.$

图 2 不同缺陷模型在x方向上磁致伸缩应变

Fig. 2. Magnetostrictive strain in the x direction for different defect models.

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$图 3 不同缺陷模型在y方向上磁致伸缩应变\r\nFig. 3. Magnetostrictive strain in the y direction for different defect models.$

图 3 不同缺陷模型在y方向上磁致伸缩应变

Fig. 3. Magnetostrictive strain in the y direction for different defect models.

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由图2可以看出, 对比x方向上的磁致伸缩应变, 与无缺陷薄膜相比, 中心60 × 2 × 1缺陷薄膜最易达到饱和磁致伸缩, 其达到饱和后的磁致伸缩应变也最小; 中心10 × 10 × 1与2 × 60 × 1缺陷薄膜则需要较大磁场才能接近饱和, 其中中心2 × 60 × 1缺陷薄膜达到饱和后的磁致伸缩应变最大.

图3为模型沿x轴正方向磁化过程中, y方向上的磁致伸缩应变曲线图.

由图3可知, 对比y方向上的磁致伸缩应变, 与无缺陷薄膜相比, 中心10 × 10 × 1缺陷薄膜的收缩量有所下降. 中心60 × 2 × 1与2 × 60 × 1缺陷薄膜的收缩量有所增大, 达到饱和后, 中心2 × 60 × 1缺陷薄膜的收缩应变最大.

为进一步探索磁化时缺陷对铁单质磁化构型演化的影响, 分别做出了铁单质薄膜在不同磁场强度磁化作用下达到平衡后的磁化构型图. 图4为无缺陷铁单质磁化构型演化图.

$图 4 无缺陷铁单质磁化构型演化图　(a) 0.025Hm; (b) 0.0625Hm; (c) 0.375Hm; (d) 1Hm\r\nFig. 4. Evolution of magnetization structure in iron film without defect: (a) 0.025Hm; (b) 0.0625Hm; (c) 0.375Hm; (d) 1Hm.$

图 4 无缺陷铁单质磁化构型演化图　(a) 0.025H_m; (b) 0.0625H_m; (c) 0.375H_m; (d) 1H_m

Fig. 4. Evolution of magnetization structure in iron film without defect: (a) 0.025H_m; (b) 0.0625H_m; (c) 0.375H_m; (d) 1H_m.

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由图4可看出, 在外加0.025H_m磁场磁化作用下, 无缺陷模型中心的磁化漩涡消失, 原子磁矩转向磁化方向, 磁矩沿y方向的原子迅速减少. 在外加0.0625H_m磁场磁化作用下, 模型原子磁矩沿x轴正方向的区域面积增大, 但大多数是由磁矩沿过渡方向的原子转变而来, 原子磁矩沿y方向的区域面积变化不大. 在外加0.375H_m磁场磁化作用下, 多数原子磁矩转向x轴正方向, 此时铁单质磁化已接近饱和, 磁致伸缩曲线也变得平缓. 在外加1H_m磁场磁化作用下, 此时在强磁场磁化作用下, 铁单质薄膜内已经没有了原子磁矩沿y轴方向的区域, 除了左右边界处有少量原子磁矩尚未完全转向x轴方向外, 其余原子磁矩均已转向x轴正方向.

图5为中心10 × 10 × 1缺陷铁单质在不同强度磁场作用下的磁化构型演化图. 与无缺陷模型相比, 在外加0.025H_m磁场磁化作用下, 模型内部并未出现较大的原子磁矩相同的区域. 在外加0.0625H_m磁场磁化作用下, 模型内上下边界处两个原子磁矩沿x轴正方向的区域有融合的趋势, 但在缺陷的影响下, 连接处的原子磁矩仍是处于过渡方向. 外加磁场增大到0.375H_m, 模型内多数原子磁矩转向x轴正方向, 在缺陷影响下, 缺陷周围仍有部分原子磁矩处于过渡方向. 当外加磁场增大到1H_m, 此时在强磁场磁化作用下, 缺陷周围的原子磁矩也转向x轴正方向, 只有左右边界处有少量原子磁矩尚未完全转向x轴方向.

$图 5 中心10×10×1缺陷铁单质磁化构型演化　(a) 0.025Hm; (b) 0.0625Hm; (c) 0.375Hm; (d) 1Hm\r\nFig. 5. Evolution of magnetization structure in iron film with 10 × 10 × 1 defect: (a) 0.025Hm; (b) 0.0625Hm; (c) 0.375Hm; (d) 1Hm.$

图 5 中心10×10×1缺陷铁单质磁化构型演化　(a) 0.025H_m; (b) 0.0625H_m; (c) 0.375H_m; (d) 1H_m

Fig. 5. Evolution of magnetization structure in iron film with 10 × 10 × 1 defect: (a) 0.025H_m; (b) 0.0625H_m; (c) 0.375H_m; (d) 1H_m.

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图6为中心60 × 2 × 1缺陷铁单质在不同强度磁场作用下的磁化构型演化图. 在外加0.025H_m磁场磁化作用下, 模型在磁化作用下, 4个磁矩方向不同的区域以缺陷为中心沿顺时针方向发生了一定的位移和形变, 但各区域所占面积变化不大. 外加磁场增大到0.0625H_m, 模型在磁化作用下, 原本原子磁矩沿x轴负方向的区域消失, 原子磁矩沿x轴正方向区域迅速增大. 外加磁场增大到0.375H_m, 模型磁化已接近饱和, 原子磁矩沿x轴正方向的区域已将整个裂纹完全包含在内. 当外加磁场增大到1H_m, 此时模型磁化构型图与无缺陷模型磁化构型图相似, 除了左右边界处有少量原子磁矩尚未完全转向x轴方向, 其余原子磁矩均已转向x轴正方向.

$图 6 60 × 2 × 1缺陷铁单质磁化构型演化图　(a) 0.025Hm; (b) 0.0625Hm; (c) 0.375Hm; (d) 1Hm\r\nFig. 6. Evolution of magnetization structure in iron film with 60 × 2 × 1 defect: (a) 0.025Hm; (b) 0.0625Hm; (c) 0.375Hm; (d) 1Hm.$

图 6 60 × 2 × 1缺陷铁单质磁化构型演化图　(a) 0.025H_m; (b) 0.0625H_m; (c) 0.375H_m; (d) 1H_m

Fig. 6. Evolution of magnetization structure in iron film with 60 × 2 × 1 defect: (a) 0.025H_m; (b) 0.0625H_m; (c) 0.375H_m; (d) 1H_m.

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图7为中心2 × 60 × 1缺陷铁单质在不同强度磁场作用下的磁化构型演化图. 在外加0.025H_m磁场磁化作用下, 模型在磁化作用下, 原子磁矩沿y方向的区域面积缩小, 但由于缺陷的存在, 模型内附近的原子磁矩仍沿y轴方向. 外加磁场增大到0.0625H_m, 模型内原子磁矩沿y方向的区域继续缩小, 但由于缺陷的存在, 该区域仍占有较大面积. 外加磁场增大到0.375H_m, 此时其余模型磁化已接近饱和, 缺陷对模型的磁化构型有较大影响, 缺陷附近的原子磁矩处于过渡方向, 其在x方向的磁化效率是4个模型中最差的. 当外加磁场增大到1H_m, 此时模型内缺陷周围有部分原子磁矩尚未完全转向x轴正方向.

$图 7 2 × 60 × 1缺陷铁单质磁化构型演化图　(a) 0.025Hm; (b) 0.0625Hm; (c) 0.375Hm; (d) 1Hm\r\nFig. 7. Evolution of magnetization structure in iron film with 2 × 60 × 1 defect: (a) 0.025Hm; (b) 0.0625Hm; (c) 0.375Hm; (d) 1Hm.$

图 7 2 × 60 × 1缺陷铁单质磁化构型演化图　(a) 0.025H_m; (b) 0.0625H_m; (c) 0.375H_m; (d) 1H_m

Fig. 7. Evolution of magnetization structure in iron film with 2 × 60 × 1 defect: (a) 0.025H_m; (b) 0.0625H_m; (c) 0.375H_m; (d) 1H_m.

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4. 结　论

采用分子动力学方法, 建立了含缺陷磁致伸缩bcc铁薄膜模型, 研究了无缺陷、孔洞缺陷与裂纹缺陷对铁单质薄膜磁致伸缩行为的影响, 并分析了沿x轴正方向磁化作用时, 铁单质磁致伸缩过程中内部微观结构的变化, 得到以下结论:

1)缺陷的形状和方向均影响铁单质薄膜的磁致伸缩性能, 其中孔洞形缺陷对磁致伸缩的影响较小, 裂纹形缺陷对磁致伸缩的影响较大.

2) 裂纹的方向影响铁单质薄膜的磁致伸缩性能, 若构件中的裂纹方向与磁化方向平行, 则裂纹周围的原子更容易被磁化, 从而降低构件在磁化方向上由初始状态至磁化达到饱和的最大磁致伸缩量; 若构件中的裂纹方向与磁化方向垂直, 则裂纹周围的原子更难被磁化, 会提高构件在磁化方向上由初始状态至磁化达到饱和的最大磁致伸缩量.

3)若构件中为孔洞缺陷, 则当外加磁场较小时, 孔洞对周围的原子磁矩的影响较为明显, 若外加磁场较大时, 孔洞对周围原子磁矩的影响会越来越小.

References

[1]	Makarova L A, Alekhina Y A, Isaev D A, Khairullin M F, Perov N S 2021 J. Phys. D-Appl. Phys. 54 15003 Google Scholar
[2]	Garcia M H, Barrera D, Amat R, Kurlyandskaya G V, Sales S 2016 Measurement 80 201 Google Scholar
[3]	Pei H F, Jing J H, Zhang S Q 2020 Measurement 151 107172 Google Scholar
[4]	Yu G L, Li Y X, Zeng Y Q, Li J, Zuo L, Li Q, Zhang H W 2013 Chin. Phys. B 22 077504 Google Scholar
[5]	周勇, 李纯健, 潘昱融 2018 物理学报 67 077702 Google Scholar Zhou Y, Li C J, Pan Y R 2018 Acta Phys. Sin. 67 077702 Google Scholar
[6]	苏三庆, 刘馨为, 王威, 左付亮, 邓瑞泽, 秦彦龙 2020 工程科学学报 42 1557 Google Scholar Su S Q, Liu X W, Wang W, Zuo F L, Deng R Z, Qin Y L 2020 Chin. J. Eng. 42 1557 Google Scholar
[7]	Ren W P, Xu K, Dixon S, Zhang C 2019 NDT E Int. 101 34 Google Scholar
[8]	M'Zali N, Martin F, Aydin U, Belahcen A, Benabou A, Henneron T 2020 J. Magn. Magn. Mater. 500 166299 Google Scholar
[9]	时朋朋, 郝帅 2021 物理学报 70 034101 Google Scholar Shi P P, Hao S 2021 Acta Phys. Sin. 70 034101 Google Scholar
[10]	Zhao B X, Yao K, Wu L B, Li X L, Wang Y S 2020 Appl. Sci. -Basel 10 7083 Google Scholar
[11]	Dubov A A 1997 Met. Sci. Heat Treat. 39 401 Google Scholar
[12]	Wang P, Zhang Y, Yao E T, Mi Y, Zheng Y, Tang C L 2021 Measurement 168 108187 Google Scholar
[13]	Bao S, Gu Y B, Fu M L, Zhang D, Hu S N 2017 J. Magn. Magn. Mater. 423 191 Google Scholar
[14]	Zhang J, Jin W L, Mao J H, Xia J, Fan W J 2020 Constr. Build. Mater. 239 117885 Google Scholar
[15]	宋凯, 任吉林, 任尚坤, 唐继红 2007 无损检测 29 312 Google Scholar Song K, Ren J L, Ren S K, Tang J H 2007 Nondestruct. Test. 29 312 Google Scholar
[16]	张卫民, 刘红光, 孙海涛 2004 北京理工大学学报 24 571 Google Scholar Zhang W M, Liu H G, Sun H T 2004 Trans. Beijing Inst. Technol. 24 571 Google Scholar
[17]	李川, 刘敬华, 陈立彪, 蒋成保, 徐惠彬 2011 物理学报 60 097505 Google Scholar Li C, Liu J H, Chen L B, Jiang C B, Xu H B 2011 Acta Phys. Sin. 60 097505 Google Scholar
[18]	Kharel P, Talebi S, Ramachandran B, Dixit A, Naik V M, Sahana M B, Sudakar C, Naik R, Rao M S R, Lawes G 2009 J. Phys. -Condes. Matter. 21 36001 Google Scholar
[19]	张辉, 曾德长 2010 物理学报 59 2808 Google Scholar Zhang H, Zeng D C 2010 Acta Phys. Sin. 59 2808 Google Scholar
[20]	Suzuki S, Kawamata T, Simura R, Asano S, Fujieda S, Umetsu R Y, Fujita M, Imafuku M, Kumagai T, Fukuda T 2019 Mater. Trans. 60 2235 Google Scholar
[21]	Tranchida J, Plimpton S J, Thibaudeau P, Thompson, A P 2018 J. Comput. Phys. 372 406 Google Scholar
[22]	Jeong J, Goremychkin E A, Guidi T, Nakajima K, Jeon G S, Kim S A, Furukawa S, Kim Y B, Lee S, Kiryukhin V, Cheong S W, Park J G 2012 Phys. Rev. Lett. 108 077202 Google Scholar
[23]	Kvashnin Y O, Cardias R, Szilva A, Di Marco I, Katsnelson M I, Lichtenstein A I, Nordstrom L, Klautau A B, Eriksson O 2016 Phys. Rev. Lett. 116 217202 Google Scholar

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图 1 模型初始磁化构型　(a)无缺陷; (b)中心10 × 10 × 1缺陷; (c)中心60 × 2 × 1缺陷; (d)中心2 × 60 × 1缺陷

Figure 1. Initial magnetized configuration diagram of the model: (a) No defect; (b) 10 × 10 × 1 defect in the center; (c) 60 × 2 × 1 defect in the center; (d) 2 × 60 × 1 defect in the center.

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图 2 不同缺陷模型在x方向上磁致伸缩应变

Figure 2. Magnetostrictive strain in the x direction for different defect models.

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图 3 不同缺陷模型在y方向上磁致伸缩应变

Figure 3. Magnetostrictive strain in the y direction for different defect models.

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图 4 无缺陷铁单质磁化构型演化图　(a) 0.025H_m; (b) 0.0625H_m; (c) 0.375H_m; (d) 1H_m

Figure 4. Evolution of magnetization structure in iron film without defect: (a) 0.025H_m; (b) 0.0625H_m; (c) 0.375H_m; (d) 1H_m.

DownLoad: Full-Size Img PowerPoint

图 5 中心10×10×1缺陷铁单质磁化构型演化　(a) 0.025H_m; (b) 0.0625H_m; (c) 0.375H_m; (d) 1H_m

Figure 5. Evolution of magnetization structure in iron film with 10 × 10 × 1 defect: (a) 0.025H_m; (b) 0.0625H_m; (c) 0.375H_m; (d) 1H_m.

DownLoad: Full-Size Img PowerPoint

图 6 60 × 2 × 1缺陷铁单质磁化构型演化图　(a) 0.025H_m; (b) 0.0625H_m; (c) 0.375H_m; (d) 1H_m

Figure 6. Evolution of magnetization structure in iron film with 60 × 2 × 1 defect: (a) 0.025H_m; (b) 0.0625H_m; (c) 0.375H_m; (d) 1H_m.

DownLoad: Full-Size Img PowerPoint

图 7 2 × 60 × 1缺陷铁单质磁化构型演化图　(a) 0.025H_m; (b) 0.0625H_m; (c) 0.375H_m; (d) 1H_m

Figure 7. Evolution of magnetization structure in iron film with 2 × 60 × 1 defect: (a) 0.025H_m; (b) 0.0625H_m; (c) 0.375H_m; (d) 1H_m.

DownLoad: Full-Size Img PowerPoint

[1]	Makarova L A, Alekhina Y A, Isaev D A, Khairullin M F, Perov N S 2021 J. Phys. D-Appl. Phys. 54 15003 Google Scholar
[2]	Garcia M H, Barrera D, Amat R, Kurlyandskaya G V, Sales S 2016 Measurement 80 201 Google Scholar
[3]	Pei H F, Jing J H, Zhang S Q 2020 Measurement 151 107172 Google Scholar
[4]	Yu G L, Li Y X, Zeng Y Q, Li J, Zuo L, Li Q, Zhang H W 2013 Chin. Phys. B 22 077504 Google Scholar
[5]	周勇, 李纯健, 潘昱融 2018 物理学报 67 077702 Google Scholar Zhou Y, Li C J, Pan Y R 2018 Acta Phys. Sin. 67 077702 Google Scholar
[6]	苏三庆, 刘馨为, 王威, 左付亮, 邓瑞泽, 秦彦龙 2020 工程科学学报 42 1557 Google Scholar Su S Q, Liu X W, Wang W, Zuo F L, Deng R Z, Qin Y L 2020 Chin. J. Eng. 42 1557 Google Scholar
[7]	Ren W P, Xu K, Dixon S, Zhang C 2019 NDT E Int. 101 34 Google Scholar
[8]	M'Zali N, Martin F, Aydin U, Belahcen A, Benabou A, Henneron T 2020 J. Magn. Magn. Mater. 500 166299 Google Scholar
[9]	时朋朋, 郝帅 2021 物理学报 70 034101 Google Scholar Shi P P, Hao S 2021 Acta Phys. Sin. 70 034101 Google Scholar
[10]	Zhao B X, Yao K, Wu L B, Li X L, Wang Y S 2020 Appl. Sci. -Basel 10 7083 Google Scholar
[11]	Dubov A A 1997 Met. Sci. Heat Treat. 39 401 Google Scholar
[12]	Wang P, Zhang Y, Yao E T, Mi Y, Zheng Y, Tang C L 2021 Measurement 168 108187 Google Scholar
[13]	Bao S, Gu Y B, Fu M L, Zhang D, Hu S N 2017 J. Magn. Magn. Mater. 423 191 Google Scholar
[14]	Zhang J, Jin W L, Mao J H, Xia J, Fan W J 2020 Constr. Build. Mater. 239 117885 Google Scholar
[15]	宋凯, 任吉林, 任尚坤, 唐继红 2007 无损检测 29 312 Google Scholar Song K, Ren J L, Ren S K, Tang J H 2007 Nondestruct. Test. 29 312 Google Scholar
[16]	张卫民, 刘红光, 孙海涛 2004 北京理工大学学报 24 571 Google Scholar Zhang W M, Liu H G, Sun H T 2004 Trans. Beijing Inst. Technol. 24 571 Google Scholar
[17]	李川, 刘敬华, 陈立彪, 蒋成保, 徐惠彬 2011 物理学报 60 097505 Google Scholar Li C, Liu J H, Chen L B, Jiang C B, Xu H B 2011 Acta Phys. Sin. 60 097505 Google Scholar
[18]	Kharel P, Talebi S, Ramachandran B, Dixit A, Naik V M, Sahana M B, Sudakar C, Naik R, Rao M S R, Lawes G 2009 J. Phys. -Condes. Matter. 21 36001 Google Scholar
[19]	张辉, 曾德长 2010 物理学报 59 2808 Google Scholar Zhang H, Zeng D C 2010 Acta Phys. Sin. 59 2808 Google Scholar
[20]	Suzuki S, Kawamata T, Simura R, Asano S, Fujieda S, Umetsu R Y, Fujita M, Imafuku M, Kumagai T, Fukuda T 2019 Mater. Trans. 60 2235 Google Scholar
[21]	Tranchida J, Plimpton S J, Thibaudeau P, Thompson, A P 2018 J. Comput. Phys. 372 406 Google Scholar
[22]	Jeong J, Goremychkin E A, Guidi T, Nakajima K, Jeon G S, Kim S A, Furukawa S, Kim Y B, Lee S, Kiryukhin V, Cheong S W, Park J G 2012 Phys. Rev. Lett. 108 077202 Google Scholar
[23]	Kvashnin Y O, Cardias R, Szilva A, Di Marco I, Katsnelson M I, Lichtenstein A I, Nordstrom L, Klautau A B, Eriksson O 2016 Phys. Rev. Lett. 116 217202 Google Scholar

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