铁磁薄膜图形化单元磁特性的微磁学研究
|
摘要
微磁学模拟为人们在纳米／微米尺度范围内研究铁磁材料的磁化、反磁化及相关磁特性提供了重要的方法和手段，在铁磁薄膜研究特别是在图形化铁磁薄膜及其微磁器件(磁记录、磁传感)和现在正兴起的磁电子学及应用研究方面得到了广泛的应用。近十年来，随着薄膜材料制备与加工技术的进步，制备精度达到纳米级的图形化铁磁薄膜单元与器件已成为可能。在这种尺寸范围内，图形化铁磁薄膜单元的几何尺寸和在加工与制备过程中产生的应力将对其磁性能产生重要的影响，也是相应微磁器件设计和研制的关键参数之一。因此，开展图形化铁磁薄膜单元的微磁学模拟研究，对于弄清单元中磁化与反磁化的微观过程具有重要理论意义和应用价值。
本论文正是针对上述背景，选择NiFe、FeCoSiB等典型铁磁薄膜材料为研究对象，以图形化铁磁薄膜单元磁化、反磁化过程中磁矩分布与转变规律为研究目标，根据微磁学基本原理分析了数值微磁学计算方法与计算过程；应用OOMMF微磁学软件，在建立铁磁薄膜单元物理模型的基础上，研究了磁性随机存储器(MRAM)图形化存储单元的微磁学设计、应力与磁矩的相互作用及图形化单元的动态响应特性等。本论文主要包含以下内容：
1．扼要介绍了微磁学基本原理，建立了有限差分形式下磁各向异性能、铁磁交换能、静磁能、磁势能和磁弹性能和有效场的表达式，分析了共轭梯度法求解多元函数最小值的基本思想以及用欧拉法求解Landau—Lifshitz-Gilbert(LLG)方程的基本过程，为正确建立铁磁单元物理模型，分析和讨论计算结果奠定了基础。
2．通过与矩形NiFe薄膜单元的对比，发现菱形NiFe薄膜单元形状有独特的磁化反转特性，具有成为优良磁记录单元的巨大潜力；同时，基于优化的菱形NiFe薄膜单元，模拟并分析了字／位线宽度、厚度以及字／位线与磁存储单元之间的距离对菱形单元反磁化状态的影响规律。研究表明：菱形NiFe单元临界短轴长度为100nm，且其易轴方向沿其长轴方向；当菱形单元的长宽比小于2．4时，其反转场随长宽比的增大而增大，反之单元的反转场几乎不随长宽比变化而变化；钉扎层反转场最小时对应的字线厚度为70nm，最大时对应的字线厚度为50nm，且字／位线到存储单元的距离对单元反转过程和单元磁阻效应的影响最大。研究结果可为MRAM的设计和研制提供新思路。
3．提出将应力和磁晶各向异性等效为一个单轴磁各向异性等效场，来研究应力对磁矩作用的方法，建立了应力作用下的等效模型，求解出等效各向异性大小和方向的表达式。利用这一模型，研究了应力对亚微米尺寸FeCoSiB图形化单元磁化与反磁化特征的影响规律。研究表明：大的单元尺寸有利于提高应力对剩磁影响的敏感度，最高可达0．9％／MPa，但随应力的增加趋于饱和；对于长度较小的单元，矫顽力对应力敏感性为40 mT／GPa，而在宽度较窄的单元达到80 mT／GPa，且线性增加；选择合适的单元尺寸，在无外磁场的情况下，通过应力的作用可以显著地改变磁性单元的磁化状态。研究结果为图形化单元的剩磁、矫顽力和磁化状态的人工调控，设计和研制新型微磁器件提供了新途径。
4．论文研究了在x和z方向的短脉冲磁场作用下，不同尺寸的NiFe椭圆及菱形单元的动态响应特征，从理论上确认和解释了z方向的脉冲磁场不能产生涡旋中心移动的磁矩响应模式，发现了非旋转对称单元中低频下的激发模式，即绕涡旋中心产生节点，为调控磁矩弛豫，实现存储器的纳秒级精确写入(通过减少脉冲宽度)提供了理论指导。
Micromagnetic simulation has long been used in investigation of magnetic properties of ferromagnetic materials on a mesoscope scale. Particularly this method is every predictive and accurate in patterned thin film magnetic devices, such as magnetic sensors, magnetic recording media, and magnetoelectronic devices, etc.. In the past ten years with the rapid development of the experimental techniques, mesoscopic fabrication can be precisely controlled. Magnetic properties are quite sensitive to dimensionality of the elements and stress developed during fabrications on this micrometer/nanometer scale. They are also keys to design and investigation of the micro magnetic devices. It is, therefore, of great importance to know the mesoscopic magnetic processes in these patterned thin films by micromagnetic simulations.
In this thesis magnetization, demagnetization and dynamic processes in these patterned magnetic thin film elements are investigated by micromagnetic simulations. Materials specified in these simulations are NiFe, FeCoSiB which are typical materials in magnetic recording and stress sensors. Numerical methods in the open source micromagnetic codes OOMMF are presented in great details. A phenomenological model is established in order to cope the stress effect into the present code. The contents are organized as foliowings:
1. Energy terms including exchange, magnetoanisotropic, magnetoelastic, magnetostatic and Zeeman effects are explicitly written out, and Brown equations for static problems and Landau-Lifschitz-Gilbert equations for dynamic problems are deduced. Finite difference methods are used to solve the equations. The static problems are solved by the conjugated gradient method while the dynamic one is solved by the Euler's method. These serve as the basis for further calculations and discussions.
2. NiFe elements with diamond shape show potential applications in magnetic recording with unique magnetic reversal characters compared with rectangle shape. Influence of the width and thickness of the bit/word lines, and their distance to the magnetic properties of the elements are investigated. Our results show that the critical length of the short axis is 100 ran, and the easy axis should be in the direction of the long axis. The reversal field increases with the increase of the aspect ratio when the aspect ratio is beyond 2.4. Otherwise, it does not vary noticeably. A minimum switching field is achieved to the thickness of the word lines of 70 nm, while a maximum of 50 nm. The magnetoresistance is mostly sensitive to the distances between the word/bit lines and the elements. The simulation provides a new solution to MRAM.
3. An equivalent field model is proposed to include the effect of uniaxial stress. The strength and direction of the equivalent field is worked out. Stress effects in the magnetization and demagnetization characters of the patterned FeCoSiB elements are studied based on the model above. Remanence in larger elements is more sensitive to the stress and this effect also saturates when the stress is increased. The sensitivity can reach as high as 0.9%/Mpa. Coercivity also increases with the stress. This ratio in a wider element is about 40 mT/GPa and 80 mT/GPa in a narrower element when the elements are short. Stress can effectively change the magnetic state when the size of it is properly chosen. The results can be used to envisage new stress/strain sensors.
4. Dynamic properties of the patterned NiFe elements in diamond and ellipse are investigated under pulse magnetic field in the x and z directions. We confirm that the vortex center does not move under the pulse in z directions. The excitation modes at low frequency have nodes around the vortex center in elements without rotational symmetry. This is a first step pointing to short writing field design in MRAM within nanosecond.
本论文正是针对上述背景，选择NiFe、FeCoSiB等典型铁磁薄膜材料为研究对象，以图形化铁磁薄膜单元磁化、反磁化过程中磁矩分布与转变规律为研究目标，根据微磁学基本原理分析了数值微磁学计算方法与计算过程；应用OOMMF微磁学软件，在建立铁磁薄膜单元物理模型的基础上，研究了磁性随机存储器(MRAM)图形化存储单元的微磁学设计、应力与磁矩的相互作用及图形化单元的动态响应特性等。本论文主要包含以下内容：
1．扼要介绍了微磁学基本原理，建立了有限差分形式下磁各向异性能、铁磁交换能、静磁能、磁势能和磁弹性能和有效场的表达式，分析了共轭梯度法求解多元函数最小值的基本思想以及用欧拉法求解Landau—Lifshitz-Gilbert(LLG)方程的基本过程，为正确建立铁磁单元物理模型，分析和讨论计算结果奠定了基础。
2．通过与矩形NiFe薄膜单元的对比，发现菱形NiFe薄膜单元形状有独特的磁化反转特性，具有成为优良磁记录单元的巨大潜力；同时，基于优化的菱形NiFe薄膜单元，模拟并分析了字／位线宽度、厚度以及字／位线与磁存储单元之间的距离对菱形单元反磁化状态的影响规律。研究表明：菱形NiFe单元临界短轴长度为100nm，且其易轴方向沿其长轴方向；当菱形单元的长宽比小于2．4时，其反转场随长宽比的增大而增大，反之单元的反转场几乎不随长宽比变化而变化；钉扎层反转场最小时对应的字线厚度为70nm，最大时对应的字线厚度为50nm，且字／位线到存储单元的距离对单元反转过程和单元磁阻效应的影响最大。研究结果可为MRAM的设计和研制提供新思路。
3．提出将应力和磁晶各向异性等效为一个单轴磁各向异性等效场，来研究应力对磁矩作用的方法，建立了应力作用下的等效模型，求解出等效各向异性大小和方向的表达式。利用这一模型，研究了应力对亚微米尺寸FeCoSiB图形化单元磁化与反磁化特征的影响规律。研究表明：大的单元尺寸有利于提高应力对剩磁影响的敏感度，最高可达0．9％／MPa，但随应力的增加趋于饱和；对于长度较小的单元，矫顽力对应力敏感性为40 mT／GPa，而在宽度较窄的单元达到80 mT／GPa，且线性增加；选择合适的单元尺寸，在无外磁场的情况下，通过应力的作用可以显著地改变磁性单元的磁化状态。研究结果为图形化单元的剩磁、矫顽力和磁化状态的人工调控，设计和研制新型微磁器件提供了新途径。
4．论文研究了在x和z方向的短脉冲磁场作用下，不同尺寸的NiFe椭圆及菱形单元的动态响应特征，从理论上确认和解释了z方向的脉冲磁场不能产生涡旋中心移动的磁矩响应模式，发现了非旋转对称单元中低频下的激发模式，即绕涡旋中心产生节点，为调控磁矩弛豫，实现存储器的纳秒级精确写入(通过减少脉冲宽度)提供了理论指导。
Micromagnetic simulation has long been used in investigation of magnetic properties of ferromagnetic materials on a mesoscope scale. Particularly this method is every predictive and accurate in patterned thin film magnetic devices, such as magnetic sensors, magnetic recording media, and magnetoelectronic devices, etc.. In the past ten years with the rapid development of the experimental techniques, mesoscopic fabrication can be precisely controlled. Magnetic properties are quite sensitive to dimensionality of the elements and stress developed during fabrications on this micrometer/nanometer scale. They are also keys to design and investigation of the micro magnetic devices. It is, therefore, of great importance to know the mesoscopic magnetic processes in these patterned thin films by micromagnetic simulations.
In this thesis magnetization, demagnetization and dynamic processes in these patterned magnetic thin film elements are investigated by micromagnetic simulations. Materials specified in these simulations are NiFe, FeCoSiB which are typical materials in magnetic recording and stress sensors. Numerical methods in the open source micromagnetic codes OOMMF are presented in great details. A phenomenological model is established in order to cope the stress effect into the present code. The contents are organized as foliowings:
1. Energy terms including exchange, magnetoanisotropic, magnetoelastic, magnetostatic and Zeeman effects are explicitly written out, and Brown equations for static problems and Landau-Lifschitz-Gilbert equations for dynamic problems are deduced. Finite difference methods are used to solve the equations. The static problems are solved by the conjugated gradient method while the dynamic one is solved by the Euler's method. These serve as the basis for further calculations and discussions.
2. NiFe elements with diamond shape show potential applications in magnetic recording with unique magnetic reversal characters compared with rectangle shape. Influence of the width and thickness of the bit/word lines, and their distance to the magnetic properties of the elements are investigated. Our results show that the critical length of the short axis is 100 ran, and the easy axis should be in the direction of the long axis. The reversal field increases with the increase of the aspect ratio when the aspect ratio is beyond 2.4. Otherwise, it does not vary noticeably. A minimum switching field is achieved to the thickness of the word lines of 70 nm, while a maximum of 50 nm. The magnetoresistance is mostly sensitive to the distances between the word/bit lines and the elements. The simulation provides a new solution to MRAM.
3. An equivalent field model is proposed to include the effect of uniaxial stress. The strength and direction of the equivalent field is worked out. Stress effects in the magnetization and demagnetization characters of the patterned FeCoSiB elements are studied based on the model above. Remanence in larger elements is more sensitive to the stress and this effect also saturates when the stress is increased. The sensitivity can reach as high as 0.9%/Mpa. Coercivity also increases with the stress. This ratio in a wider element is about 40 mT/GPa and 80 mT/GPa in a narrower element when the elements are short. Stress can effectively change the magnetic state when the size of it is properly chosen. The results can be used to envisage new stress/strain sensors.
4. Dynamic properties of the patterned NiFe elements in diamond and ellipse are investigated under pulse magnetic field in the x and z directions. We confirm that the vortex center does not move under the pulse in z directions. The excitation modes at low frequency have nodes around the vortex center in elements without rotational symmetry. This is a first step pointing to short writing field design in MRAM within nanosecond.
引文
[1]李言荣，恽正中．电子材料导论．北京：清华大学出版社，2001，1-4
[2]沈能珏，孙同年，余声明，等．现代电子材料技术．北京：国防工业出版社，2002，1-11
[3]Rainer Waster.Nanoelectronics and information Technology.WILEY-VCH,2003,593-600
[4]张立德，牟季美．纳米材料与纳米结构．北京：科学出版社，2001，491-493
[5]朱静．纳米材料和器件．北京：清华大学出版社，2003，15-17
[6]李言荣，谢孟贤，恽正中，等．纳米电子材料与器件．北京：国防工业出社，2005，135-150
[7]姜寿亭，李卫．凝聚态磁性物理．北京：科学出版社，2002，366-374
[8]A．Aharoni著，杨正译．铁磁性理论导论．兰州：兰州大学出版社，2002，94-95
[9]钟文定．铁磁学(中)．北京：科学出版社，1998，149-150
[10]E.D.Torre,F.Vajda.Physical basis for parameter identification in magnetic materials.IEEE Trans.Magn.,1996,32(5):4186-4191
[11]J.J.Miles,B.K Middleton.The role of microstructure in micromagnetic models of longitudinalthin film magnetic media.IEEE Trans.Magn.,1990,26(6):2137-2140
[12]G.Porter,E.Glavinas,P.Dhagat,et al.Irregular grain structure in micromagnetic simulation.J.Appl.Phys.,1996,79(8):4695-4697
[13]G.J.Parker,C.Cerjan,D.W.Hewett Embedded curve boundary method simulations.J.Magn.Magn.Mater.,2000,214:130-138
[14]D.R Fredkin,T.R.Koehler.Numerical micromagnetics by the finite element method.IEEE Trans.Magn.,1987,23(5):3385-3387
[15]D.R.Fredkin,T.R.Koehler.Abinitio micromagnetic calculations for particles.J.Appl.Phys.,1990,67(9):5544-5548
[16]T.Schrefl,J.Fidler,H.Kronmuller.Nucleation fields of hard magnetic particles in 2D and 3D micromagnetic calculations.J.Magn.Magn.Mater.,1994,138(1-2):15-30
[17]H.Kronmueller,R.Fischer,R.Hertel,et al.Micromagnetism and the microstructure in nanocrystalline materials.J.Magn.Magn.Mater.,1997,175(1-2):177-192
[18]K.M.Tako,T.Schrefl,M.A.Wongsam,et al.Finite element micromagnetic simulations with adaptive mesh refinement.J.Appl.Phys.,1997,81(8):4082-4084
[19]T.R.Koehler.Hybrid FEM-BEM method for fast micromagnetic calculations.Phys.B,1997,233(4):302-307
[20] M. Mansuripur, R. Giles. Demagnetizing field computation for dynamic simulation of the magnetization reversal process. IEEE Trans.Magn., 1988,24(6):2326-2328
[21] D. M. Apalkov, P. B. Visscher. Fast Multipole Method for Micromagnetic Simulation of Periodic Systems. IEEE Trans.Magn., 2003, 39(6):3478-3480
[22] W. Scholz W., J. Fidler, T. Schrefl, et al. Scalable Parallel Micromagnetic Solvers for Magnetic Nanostructures. Comp.Mat.Sci., 2003,28:366-383
[23] http://magnet.atp.tuwien.ac.at/scholz/magpar/
[24] J. H. Xue. Micromagnetic simulation of hysteresis characteristics for thin magnetic films. [D]:Doctor Dissertation, University of Minnesota, 2004
[25] E. Martinez, L. Lopez-Diaz, L. Torres, et al. Minimizing cell size dependence in micromagnetics simulations with thermal noise. IEEE Trans.Magn., 1987, 23(5): 3385-3387
[26] C. C. Shir Computations of the micromagnetic dynamics in domain walls. J.Appl.Phys., 1978, 49 (6):3413-3416
[27] E. D. Torre. Magnetization calculation of fine particles. IEEE Trans.Magn., 1986, 22(2):484-487
[28] Y. D. Yan, M. Jursich. Micromagnetic predictions of closure domain patterns in magnetic thin films. IEEE Trans.Magn., 1989, 25:742
[29] J. G. Zhu, H. N. Bertram. Micromagnetic studies of thin-film metallic films. J.Appl.Phys., 1988, 63(8):3248-3253
[30] S. W. Yuan, H. N. Bertram. Micromagnetics of small unshielded MR elements. J.Appl.Phys., 1993, 73(10):6235-6237
[31] H. Kano, T. Mizuquchi. Sensor Design of Vertical type GMR head. IEEE Trans.Magn., 2000, 36:2596-2598
[32] J. O. Oti, R. W. Cross, S. E. Russek, et al. Magnetoresistive Behavior of Geometrically Assymmetric Spin Valves. IEEE Trans.Magn., 1996, 32(5):4606-4608
[33] J. J. Miles, M. R. Parker. Micromagnetic modelling of spin valve and GMR read heads. IEEE Trans.Magn., 1996, 32(5):4597-4602
[34] J. G. Zhu, X. G.. Micromagnetics of Dual Spin Valve GMR Heads. J.Appl.Phys., 1996, 79(8):5886-5888
[35] T. Schrefl, J. Fidler, J. N. Chapman. Micromagnetic modelling of multilayer media. J.Phys.D, 1996,29:2352-2361
[36] J. O. Oti, S. E. Russek, S. C. Sanders, et al. Models of granular giant magnetoresistance multilayer thin films. IEEE Trans.Magn., 1996,32(2):590-598
[37] T. Schrefl, J. Fidler, K. J. Kirk. Micromagnetic simulation of domain structures in patterned magnetic tunnel junctions. J.Appl.Phys., 2001, 89(11):758
[38] T. Schrefl, J. Fidler, H. Kronmuller. Remanence and coercivity in isotropic nanocrystalline permanent magnets. Phys.Rev.B, 1994,49(9):6100-6110
[39] H. F. Schmidts, H. Kronmuller. An algorithm for two-dimensional micromagnetic calculations for ferromagnetic materials. J.Magn. Magn. Mater., 1994, 130:329-341
[40] H. Kronmuller, R. Fischer, M. Seeger, et al. Micromagnetism and microstructure of hard magnetic materials. J.Phys.D, 1996, 29:2274-2283
[41] J. G Zhu, H. N. Bertram. Micromagnetic studies of thin-film metallic films. J.Appl.Phys., 1988, 63(8):3248-3253
[42] R. Giles, P. S. Alexopoulos, M. Mansuripur. Micromagnetics of thin film cobalt-based media for magnetic recording .Computers in Physics., 1992,6(1):53-70
[43] Y. F. Zheng, J. G. Zhu Micromagnetics of spin valve memory cells. IEEE Trans.Magn., 1996, 32(5):4237-4239
[44] J. G. Zhu, Y. F. Zheng. The micromagnetics of magnetoresistive random access memory: Spin Dynamics in Confined Magnetic Structures. Heidelberg: Springer-Verlag Berlin, 2002,83:289-326
[45] J. Gadbois, A. Hurst. The effect of end and edge shape on the performance of pseudo-spin valve memories. IEEE Trans.Magn., 1998, 34(4):1066-1068
[46] D. K. Koltsov, R. P. Cowburn, M. E. Welland. Micromagnetics of ferromagnetic equilateral triangular prisms. J.Appl.Phys., 2000, 88: 5315-53.16
[47] J. O. Oti, S. E. Russek. Micromagnetic simulations of magnetoresistive behavior of sub-micrometer spin-valve MRAM devices. IEEE Trans.Magn., 1997, 33(5): 3298-3300
[48] T. Schrefl, J. Fidler, J. Chapman, et al. Micromagnetic simulation of domain structures in patterned magnetic tunnel junctions. J.Appl.Phys., 2001, 89:7000
[49] J. Miltat, G. Albuquerque, A. Thiaville. An introduction to micromagnetics in the dynamic regime: Spin Dynamics in Confined Magnetic Structures. Heidelberg:Springer-Verlag Berlin, 2002, 83:1-34
[50] T. Schrefl, J. Fidler. Reversal modes and reversal times in submicron sized elements for MRAM applications. Comp.Mat.Sci., 2000, 17(2-4):490-495
[51] T. Schrefl, W. Scholz, D. S(?)ss, et al. Computational micromagnetics:prediction of time dependent and thermal properties. J.Magn.Magn.Mater., 2001, 226-230:1213-1219
[52] D. Liu, C. Garcia-Cervera. Magnetic switching of ferromagnetic thin films under thermal perturbation. J.Appl.Phys., 2005, 98:023903.1-023903.10
[53] H. T. Wang, S. T. Chui, A. Oriade, et al. Temperature dependence of the fluctuation of the switching field in small magnetic structures. Phys.Rev.B, 2004, 69:064417.1-064417.5
[54]B.Zhu,C.C.H.Lo.Micromagnetic modeling of the effects of stress on magnetic properties.J.Appl.Phys.,2003,189:7009-7011
[55]Daniel,Z.Bai,Jian-Gang Zhu.Micromagnetic simulation of effect of stress-induced anisotropy in soft magnetic thin films.J.Appl.Phys.,2004,95:6864-6866
[56]R.L.Hu,A.K.Soh.Micromagnetic simulation of size effects on the properties of ferromagnetic materials.J.Phys.D,2006,39:1987-1992
[57]朱冰．应力作用下铁磁薄膜单元的微磁学研究．[D]：硕士学位论文，电子科技大学，中国：2008
[58]B.Peng,Q.Y.Xie,W.L.Zhang,Z.Y.Zhong.Stress dependence of magnetic domains in FeCoSiB amorphous films.J.Appl.Phys.,2007,101:09c511.1-09c511.3
[59]杨国宁．FeCoSiB非晶磁弹性薄膜材料及应用研究．[D]：硕士学位论文，电子科技大学，中国：2005
[60]谢巧英．应力对FeCoSiB非晶磁弹性薄膜磁特性影响的研究．[D]：硕士学位论文，电子科技大学，2007，中国：2008
[61]苏鼎．柔性FeCoSiB非晶磁弹性薄膜应力阻抗效应研究．[D]：硕士学位论文，电子科技大学，中国：2008
[62]W.Scholz,J.Fidler,et al.Micromagnetic Simulation of Domain Wall Pinning in Sm(Co,Fe,Cu,Zr)z Magnets.1~(st)Joint European Magnetic Symposia,Grenoble,2001
[63]W.Scholz,J.Fidler,et al Micromagnetic three-dimensional simulation of the pinning field in high temperature Sm(Co,Fe,Cu,Zr)z magnets.J.Appl.Phys.,2002,91(10):456-459
[64]刘正方，伍清萍．硬/软磁双层膜体系反磁化机制的微磁学研究．华东交通大学学报，2006，23(5)：149-152
[65]荣传兵，张宏伟，陈仁杰，等．纳米晶永磁材料晶间交换耦合作用的模拟计算研究．物理学报，2004，53(12)：4353-4357
[66]Brown,WF.Domains,micromagnetics and beyond,reminiscences and assessments.J.Appl.Phys.,1978,49:1937-1942
[67]Manfred Fahnle.Micromagnetism and the microstucture of ferromagnetic solids.Cambridge University:2003,320-400
[68]David,J.Sellmyer,Yi Liu,et al.Handbook of advanced magnetic materials.Beijing:Tsinghua University Press,2005,421-430
[69]T.L.Gilbert.A lagrangian formulation of gyromagnetic equation of the magnetization field.Phys.Rev.,1955,100:1243
[70]W.Scholz.Micromagnetic Simulation of Thermally Activated Switching in Fine Particles.[D]:PM Dissertation,Vienna University of Technology,1999
[71]J.C.Mallinson.On damped gyromagnetic precession.IEEE Trans.Magn.,1987, 23：2003-2004。
[72]塞尔米厄，刘义，沙因多．先进磁性材料的模拟和检测．北京：清华大学出版社，2005，78-140
[73]解可新，韩健，林友联．最优化方法．天津：天津大学出版社，1997，94-124
[74]M.Donahue,D.Porter.Objiect oriented micromagneticframework(oommf)home page.Avilable from http://math.nist.gov/oommf/,2002
[75]M.R.Scheinfein.LLG(Landau-Lifshitz-Filbert)micromagnetics simulator home page.Available from http://llgmicro.home.mindspring.com/,2003
[76]A.Aharoni.Introduction to the Theory of Ferromagnetism.Monographs on Physics.Oxford University Press,1996,15-20
[77]F.Xie.A micromagnetic model of Barium ferrites for microwave circulator design:[Doctor dissertation].Moscow:University of Idaho,2006
[78]J.G..Zhu,H.N.Bertram.Micromagnetic studies of thin films.J.Appl.Phys.,1988,63(4):3248-3249
[79]H.N.Bertram.Monte Carlo calculation of magnetic anhysteresis.J.Phys.,1971,32:648-649
[80]J.J.Miles,B.K.Middleton.A hierarchical micromagnetic model of longitudinal thin film recording media.J.Magn.Magn.Mater.,1991,95:99
[81]A.J.Newell,W.Williams,D.J.Dunlop.A generalization of the demagnetizing tensor for nonuniform magnetization.J.Geo.Res.,1998,9551-9552
[82]http://www.fftw.org
[83]W.H.Press,B.P.Flannery,S.A.Teukolsky,et al.Numercial Recipes.Cambridge U K:Cambridge University Press,1986,410-412
[84]钟尔杰，黄廷祝．数值分析．北京：高等教育出版社，2004，79-98
[85]M.J.Donahue.OOMMF user's guide 1.2a3,2005
[86]方光旦．巨磁电阻效应在信息存储等领域中的应用．物理，1998，27(5)：301-306
[87]卢正启．自旋阀巨磁电阻效应及其应用．物理，1998．27(6)：373-376
[88]詹文山．磁电子学——一门新型交叉学科．物理，1998，27(7)：435-440
[89]麦振洪，徐明金．属磁性多层膜的结构及其对巨磁电阻效应的影响．物理，1999，28(5)：302-307
[90]J.H.Paterson,S.J.Cooke,A.D.R.Phelps.Finite-difference calculation of demagnetizing factors for shapes with cylindrical symmetry.J.Magn.Magn.Mater.,1998,177:1472-1473
[91]A.Thiele.Steady-State Motion of Magnetic Domains.Phys.Rev.Lett.,1973,30:230-233
[92]T.Duenas,A.Sehrbrock,M.Lohndorf,et al.Micro-sensor coupling magnetostriction and magnetoresistive phenomena.J.Magn.Magn.Mater.,2002,242-245:1132-1135
[93] S. Dokupil, M. T. Bootsmann, S. Stein, et al. Positive/negative magnetostrictive GMR trilayer systems as strain gauges. J.Magn.Magn.Mater., 2005, 290-291:795-799
[94] M. Lohndorf, T. Duenas, M. Tewes, et al. Highly sensitive strain sensors based on magnetic tunneling junctions. Appl.Phys.Lett., 2002, 81(2):313-315
[95] M. Lohndorf, S. Dokupil, J. Wecker, et al. Characterization of magnetic tunnel junctions (MTJ) with magnetostrictive free layer materials. J.Magn.Magn.Mater., 2004, 272-276:2023-2024
[96] V. Novosad, Y. Otani,A. Ohsawa, et al. Novel magnetostrictive memory device. J.Appl.Phys., 2000, 87(9):6400-6402
[97] S. K. Kim, J, W. Lee, S. C. Shin, et al. Voltage control of a magnetization easy axis in piezoelectric/ ferromagnetic hybrid films. J.Magn.Magn.Mater., 2003, 167:127-132
[98] S. K. Kim, S. C. Shin. Voltage Control of magnetization easy-axes:a potential candidate for spin switching in future ultrahigh-density nonvolatile magnetic random access memory. IEEE Trans.Magn., 2004,40(4):2637-2639
[99] B. Choi, J. Ho, Y. Hong. Magnetization switching dynamics depending on as-patterned magnetization state in magnetic thin-film elements. IEEE Trans.Magn., 200, 41:2709-2711
[100] J. Fidler, T. Schrefl. Micromagnetic modeling - the current state of the art. J.Phys.D, 2 000, 33:135-R156
[101] S. Goolaup, A. O. Adeyeye, N. Singh. Magnetization reversal mechanisms in diamond shaped Co nanomagnets. Phys.Rev.B, 2006, 73:104444
[102] K. Y. Guslienko K, W. Scholz, R. W. Chantrell, et al. Vortex-state oscillations in soft magnetic cylindrical dots. Phys.Rev.B, 2005, 71:144407
[103] I. Neudecker, K. Perzlmaier, F. Hoffmann, et al. Modal spectrum of permalloy disks excited by in-plane magnetic fields. Phys.Rev.B, 2006, 73: 134426
[104] P. Vavassori, N. Zaluzec, V. Metlushko, et al. Magnetization reversal via single and double vortex states in submicron Permalloy ellipses. Phys.Rev.B, 2004,69:214404
[105] H. Wang, C. E. Campbell. Spin dynamics of a magnetic antivortex: Micromagnetic simulations. Phys.Rev.B, 2007, 76:220407
[106] Y. Acremann, C. H. Back, M. Buess, et al. Imaging Precessional Motion of the Magnetization Vector. Science, 2000, 290:492-495
[107] K. Y. Guslienko, B. A. Ivanov, V. Novosad, et al. Eigenfrequencies of vortex state excitations in magnetic submicron-size disks. AIP, 2002,91:8037-8039
[108] M. Buess, T. Haug, M. R. Scheinfein, et al. Micromagnetic Dissipation Dispersion and Mode Conversion in Thin Permalloy Platelets. Phys.Rev.Lett., 2005, 94:127205
[109] Hillebrands, K. Ounadjela .Spin Dynamics in Confined Magnetic Structures Ⅰ . Verlag Berlin Heidelberg, 2002, 1-34
[110] S. Choe, Y. Acremann, A. Scholl, et al. Vortex Core-Driven Magnetization Dynamics. Science, 2004, 304: 420-422
[111] F. Hoffmann, G. Woltersdorf, et al. Mode degeneracy due to vortex core removal in magnetic disks. Phys.Rev.B, 2007, 76:014416
[112] M. Yan, G. Leaf, H. Kaper, et al. Spin-wave modes in a cobalt square vortex: Micromagnetic simulations. Phys.Rev.B, 2006,73:014425
[2]沈能珏，孙同年，余声明，等．现代电子材料技术．北京：国防工业出版社，2002，1-11
[3]Rainer Waster.Nanoelectronics and information Technology.WILEY-VCH,2003,593-600
[4]张立德，牟季美．纳米材料与纳米结构．北京：科学出版社，2001，491-493
[5]朱静．纳米材料和器件．北京：清华大学出版社，2003，15-17
[6]李言荣，谢孟贤，恽正中，等．纳米电子材料与器件．北京：国防工业出社，2005，135-150
[7]姜寿亭，李卫．凝聚态磁性物理．北京：科学出版社，2002，366-374
[8]A．Aharoni著，杨正译．铁磁性理论导论．兰州：兰州大学出版社，2002，94-95
[9]钟文定．铁磁学(中)．北京：科学出版社，1998，149-150
[10]E.D.Torre,F.Vajda.Physical basis for parameter identification in magnetic materials.IEEE Trans.Magn.,1996,32(5):4186-4191
[11]J.J.Miles,B.K Middleton.The role of microstructure in micromagnetic models of longitudinalthin film magnetic media.IEEE Trans.Magn.,1990,26(6):2137-2140
[12]G.Porter,E.Glavinas,P.Dhagat,et al.Irregular grain structure in micromagnetic simulation.J.Appl.Phys.,1996,79(8):4695-4697
[13]G.J.Parker,C.Cerjan,D.W.Hewett Embedded curve boundary method simulations.J.Magn.Magn.Mater.,2000,214:130-138
[14]D.R Fredkin,T.R.Koehler.Numerical micromagnetics by the finite element method.IEEE Trans.Magn.,1987,23(5):3385-3387
[15]D.R.Fredkin,T.R.Koehler.Abinitio micromagnetic calculations for particles.J.Appl.Phys.,1990,67(9):5544-5548
[16]T.Schrefl,J.Fidler,H.Kronmuller.Nucleation fields of hard magnetic particles in 2D and 3D micromagnetic calculations.J.Magn.Magn.Mater.,1994,138(1-2):15-30
[17]H.Kronmueller,R.Fischer,R.Hertel,et al.Micromagnetism and the microstructure in nanocrystalline materials.J.Magn.Magn.Mater.,1997,175(1-2):177-192
[18]K.M.Tako,T.Schrefl,M.A.Wongsam,et al.Finite element micromagnetic simulations with adaptive mesh refinement.J.Appl.Phys.,1997,81(8):4082-4084
[19]T.R.Koehler.Hybrid FEM-BEM method for fast micromagnetic calculations.Phys.B,1997,233(4):302-307
[20] M. Mansuripur, R. Giles. Demagnetizing field computation for dynamic simulation of the magnetization reversal process. IEEE Trans.Magn., 1988,24(6):2326-2328
[21] D. M. Apalkov, P. B. Visscher. Fast Multipole Method for Micromagnetic Simulation of Periodic Systems. IEEE Trans.Magn., 2003, 39(6):3478-3480
[22] W. Scholz W., J. Fidler, T. Schrefl, et al. Scalable Parallel Micromagnetic Solvers for Magnetic Nanostructures. Comp.Mat.Sci., 2003,28:366-383
[23] http://magnet.atp.tuwien.ac.at/scholz/magpar/
[24] J. H. Xue. Micromagnetic simulation of hysteresis characteristics for thin magnetic films. [D]:Doctor Dissertation, University of Minnesota, 2004
[25] E. Martinez, L. Lopez-Diaz, L. Torres, et al. Minimizing cell size dependence in micromagnetics simulations with thermal noise. IEEE Trans.Magn., 1987, 23(5): 3385-3387
[26] C. C. Shir Computations of the micromagnetic dynamics in domain walls. J.Appl.Phys., 1978, 49 (6):3413-3416
[27] E. D. Torre. Magnetization calculation of fine particles. IEEE Trans.Magn., 1986, 22(2):484-487
[28] Y. D. Yan, M. Jursich. Micromagnetic predictions of closure domain patterns in magnetic thin films. IEEE Trans.Magn., 1989, 25:742
[29] J. G. Zhu, H. N. Bertram. Micromagnetic studies of thin-film metallic films. J.Appl.Phys., 1988, 63(8):3248-3253
[30] S. W. Yuan, H. N. Bertram. Micromagnetics of small unshielded MR elements. J.Appl.Phys., 1993, 73(10):6235-6237
[31] H. Kano, T. Mizuquchi. Sensor Design of Vertical type GMR head. IEEE Trans.Magn., 2000, 36:2596-2598
[32] J. O. Oti, R. W. Cross, S. E. Russek, et al. Magnetoresistive Behavior of Geometrically Assymmetric Spin Valves. IEEE Trans.Magn., 1996, 32(5):4606-4608
[33] J. J. Miles, M. R. Parker. Micromagnetic modelling of spin valve and GMR read heads. IEEE Trans.Magn., 1996, 32(5):4597-4602
[34] J. G. Zhu, X. G.. Micromagnetics of Dual Spin Valve GMR Heads. J.Appl.Phys., 1996, 79(8):5886-5888
[35] T. Schrefl, J. Fidler, J. N. Chapman. Micromagnetic modelling of multilayer media. J.Phys.D, 1996,29:2352-2361
[36] J. O. Oti, S. E. Russek, S. C. Sanders, et al. Models of granular giant magnetoresistance multilayer thin films. IEEE Trans.Magn., 1996,32(2):590-598
[37] T. Schrefl, J. Fidler, K. J. Kirk. Micromagnetic simulation of domain structures in patterned magnetic tunnel junctions. J.Appl.Phys., 2001, 89(11):758
[38] T. Schrefl, J. Fidler, H. Kronmuller. Remanence and coercivity in isotropic nanocrystalline permanent magnets. Phys.Rev.B, 1994,49(9):6100-6110
[39] H. F. Schmidts, H. Kronmuller. An algorithm for two-dimensional micromagnetic calculations for ferromagnetic materials. J.Magn. Magn. Mater., 1994, 130:329-341
[40] H. Kronmuller, R. Fischer, M. Seeger, et al. Micromagnetism and microstructure of hard magnetic materials. J.Phys.D, 1996, 29:2274-2283
[41] J. G Zhu, H. N. Bertram. Micromagnetic studies of thin-film metallic films. J.Appl.Phys., 1988, 63(8):3248-3253
[42] R. Giles, P. S. Alexopoulos, M. Mansuripur. Micromagnetics of thin film cobalt-based media for magnetic recording .Computers in Physics., 1992,6(1):53-70
[43] Y. F. Zheng, J. G. Zhu Micromagnetics of spin valve memory cells. IEEE Trans.Magn., 1996, 32(5):4237-4239
[44] J. G. Zhu, Y. F. Zheng. The micromagnetics of magnetoresistive random access memory: Spin Dynamics in Confined Magnetic Structures. Heidelberg: Springer-Verlag Berlin, 2002,83:289-326
[45] J. Gadbois, A. Hurst. The effect of end and edge shape on the performance of pseudo-spin valve memories. IEEE Trans.Magn., 1998, 34(4):1066-1068
[46] D. K. Koltsov, R. P. Cowburn, M. E. Welland. Micromagnetics of ferromagnetic equilateral triangular prisms. J.Appl.Phys., 2000, 88: 5315-53.16
[47] J. O. Oti, S. E. Russek. Micromagnetic simulations of magnetoresistive behavior of sub-micrometer spin-valve MRAM devices. IEEE Trans.Magn., 1997, 33(5): 3298-3300
[48] T. Schrefl, J. Fidler, J. Chapman, et al. Micromagnetic simulation of domain structures in patterned magnetic tunnel junctions. J.Appl.Phys., 2001, 89:7000
[49] J. Miltat, G. Albuquerque, A. Thiaville. An introduction to micromagnetics in the dynamic regime: Spin Dynamics in Confined Magnetic Structures. Heidelberg:Springer-Verlag Berlin, 2002, 83:1-34
[50] T. Schrefl, J. Fidler. Reversal modes and reversal times in submicron sized elements for MRAM applications. Comp.Mat.Sci., 2000, 17(2-4):490-495
[51] T. Schrefl, W. Scholz, D. S(?)ss, et al. Computational micromagnetics:prediction of time dependent and thermal properties. J.Magn.Magn.Mater., 2001, 226-230:1213-1219
[52] D. Liu, C. Garcia-Cervera. Magnetic switching of ferromagnetic thin films under thermal perturbation. J.Appl.Phys., 2005, 98:023903.1-023903.10
[53] H. T. Wang, S. T. Chui, A. Oriade, et al. Temperature dependence of the fluctuation of the switching field in small magnetic structures. Phys.Rev.B, 2004, 69:064417.1-064417.5
[54]B.Zhu,C.C.H.Lo.Micromagnetic modeling of the effects of stress on magnetic properties.J.Appl.Phys.,2003,189:7009-7011
[55]Daniel,Z.Bai,Jian-Gang Zhu.Micromagnetic simulation of effect of stress-induced anisotropy in soft magnetic thin films.J.Appl.Phys.,2004,95:6864-6866
[56]R.L.Hu,A.K.Soh.Micromagnetic simulation of size effects on the properties of ferromagnetic materials.J.Phys.D,2006,39:1987-1992
[57]朱冰．应力作用下铁磁薄膜单元的微磁学研究．[D]：硕士学位论文，电子科技大学，中国：2008
[58]B.Peng,Q.Y.Xie,W.L.Zhang,Z.Y.Zhong.Stress dependence of magnetic domains in FeCoSiB amorphous films.J.Appl.Phys.,2007,101:09c511.1-09c511.3
[59]杨国宁．FeCoSiB非晶磁弹性薄膜材料及应用研究．[D]：硕士学位论文，电子科技大学，中国：2005
[60]谢巧英．应力对FeCoSiB非晶磁弹性薄膜磁特性影响的研究．[D]：硕士学位论文，电子科技大学，2007，中国：2008
[61]苏鼎．柔性FeCoSiB非晶磁弹性薄膜应力阻抗效应研究．[D]：硕士学位论文，电子科技大学，中国：2008
[62]W.Scholz,J.Fidler,et al.Micromagnetic Simulation of Domain Wall Pinning in Sm(Co,Fe,Cu,Zr)z Magnets.1~(st)Joint European Magnetic Symposia,Grenoble,2001
[63]W.Scholz,J.Fidler,et al Micromagnetic three-dimensional simulation of the pinning field in high temperature Sm(Co,Fe,Cu,Zr)z magnets.J.Appl.Phys.,2002,91(10):456-459
[64]刘正方，伍清萍．硬/软磁双层膜体系反磁化机制的微磁学研究．华东交通大学学报，2006，23(5)：149-152
[65]荣传兵，张宏伟，陈仁杰，等．纳米晶永磁材料晶间交换耦合作用的模拟计算研究．物理学报，2004，53(12)：4353-4357
[66]Brown,WF.Domains,micromagnetics and beyond,reminiscences and assessments.J.Appl.Phys.,1978,49:1937-1942
[67]Manfred Fahnle.Micromagnetism and the microstucture of ferromagnetic solids.Cambridge University:2003,320-400
[68]David,J.Sellmyer,Yi Liu,et al.Handbook of advanced magnetic materials.Beijing:Tsinghua University Press,2005,421-430
[69]T.L.Gilbert.A lagrangian formulation of gyromagnetic equation of the magnetization field.Phys.Rev.,1955,100:1243
[70]W.Scholz.Micromagnetic Simulation of Thermally Activated Switching in Fine Particles.[D]:PM Dissertation,Vienna University of Technology,1999
[71]J.C.Mallinson.On damped gyromagnetic precession.IEEE Trans.Magn.,1987, 23：2003-2004。
[72]塞尔米厄，刘义，沙因多．先进磁性材料的模拟和检测．北京：清华大学出版社，2005，78-140
[73]解可新，韩健，林友联．最优化方法．天津：天津大学出版社，1997，94-124
[74]M.Donahue,D.Porter.Objiect oriented micromagneticframework(oommf)home page.Avilable from http://math.nist.gov/oommf/,2002
[75]M.R.Scheinfein.LLG(Landau-Lifshitz-Filbert)micromagnetics simulator home page.Available from http://llgmicro.home.mindspring.com/,2003
[76]A.Aharoni.Introduction to the Theory of Ferromagnetism.Monographs on Physics.Oxford University Press,1996,15-20
[77]F.Xie.A micromagnetic model of Barium ferrites for microwave circulator design:[Doctor dissertation].Moscow:University of Idaho,2006
[78]J.G..Zhu,H.N.Bertram.Micromagnetic studies of thin films.J.Appl.Phys.,1988,63(4):3248-3249
[79]H.N.Bertram.Monte Carlo calculation of magnetic anhysteresis.J.Phys.,1971,32:648-649
[80]J.J.Miles,B.K.Middleton.A hierarchical micromagnetic model of longitudinal thin film recording media.J.Magn.Magn.Mater.,1991,95:99
[81]A.J.Newell,W.Williams,D.J.Dunlop.A generalization of the demagnetizing tensor for nonuniform magnetization.J.Geo.Res.,1998,9551-9552
[82]http://www.fftw.org
[83]W.H.Press,B.P.Flannery,S.A.Teukolsky,et al.Numercial Recipes.Cambridge U K:Cambridge University Press,1986,410-412
[84]钟尔杰，黄廷祝．数值分析．北京：高等教育出版社，2004，79-98
[85]M.J.Donahue.OOMMF user's guide 1.2a3,2005
[86]方光旦．巨磁电阻效应在信息存储等领域中的应用．物理，1998，27(5)：301-306
[87]卢正启．自旋阀巨磁电阻效应及其应用．物理，1998．27(6)：373-376
[88]詹文山．磁电子学——一门新型交叉学科．物理，1998，27(7)：435-440
[89]麦振洪，徐明金．属磁性多层膜的结构及其对巨磁电阻效应的影响．物理，1999，28(5)：302-307
[90]J.H.Paterson,S.J.Cooke,A.D.R.Phelps.Finite-difference calculation of demagnetizing factors for shapes with cylindrical symmetry.J.Magn.Magn.Mater.,1998,177:1472-1473
[91]A.Thiele.Steady-State Motion of Magnetic Domains.Phys.Rev.Lett.,1973,30:230-233
[92]T.Duenas,A.Sehrbrock,M.Lohndorf,et al.Micro-sensor coupling magnetostriction and magnetoresistive phenomena.J.Magn.Magn.Mater.,2002,242-245:1132-1135
[93] S. Dokupil, M. T. Bootsmann, S. Stein, et al. Positive/negative magnetostrictive GMR trilayer systems as strain gauges. J.Magn.Magn.Mater., 2005, 290-291:795-799
[94] M. Lohndorf, T. Duenas, M. Tewes, et al. Highly sensitive strain sensors based on magnetic tunneling junctions. Appl.Phys.Lett., 2002, 81(2):313-315
[95] M. Lohndorf, S. Dokupil, J. Wecker, et al. Characterization of magnetic tunnel junctions (MTJ) with magnetostrictive free layer materials. J.Magn.Magn.Mater., 2004, 272-276:2023-2024
[96] V. Novosad, Y. Otani,A. Ohsawa, et al. Novel magnetostrictive memory device. J.Appl.Phys., 2000, 87(9):6400-6402
[97] S. K. Kim, J, W. Lee, S. C. Shin, et al. Voltage control of a magnetization easy axis in piezoelectric/ ferromagnetic hybrid films. J.Magn.Magn.Mater., 2003, 167:127-132
[98] S. K. Kim, S. C. Shin. Voltage Control of magnetization easy-axes:a potential candidate for spin switching in future ultrahigh-density nonvolatile magnetic random access memory. IEEE Trans.Magn., 2004,40(4):2637-2639
[99] B. Choi, J. Ho, Y. Hong. Magnetization switching dynamics depending on as-patterned magnetization state in magnetic thin-film elements. IEEE Trans.Magn., 200, 41:2709-2711
[100] J. Fidler, T. Schrefl. Micromagnetic modeling - the current state of the art. J.Phys.D, 2 000, 33:135-R156
[101] S. Goolaup, A. O. Adeyeye, N. Singh. Magnetization reversal mechanisms in diamond shaped Co nanomagnets. Phys.Rev.B, 2006, 73:104444
[102] K. Y. Guslienko K, W. Scholz, R. W. Chantrell, et al. Vortex-state oscillations in soft magnetic cylindrical dots. Phys.Rev.B, 2005, 71:144407
[103] I. Neudecker, K. Perzlmaier, F. Hoffmann, et al. Modal spectrum of permalloy disks excited by in-plane magnetic fields. Phys.Rev.B, 2006, 73: 134426
[104] P. Vavassori, N. Zaluzec, V. Metlushko, et al. Magnetization reversal via single and double vortex states in submicron Permalloy ellipses. Phys.Rev.B, 2004,69:214404
[105] H. Wang, C. E. Campbell. Spin dynamics of a magnetic antivortex: Micromagnetic simulations. Phys.Rev.B, 2007, 76:220407
[106] Y. Acremann, C. H. Back, M. Buess, et al. Imaging Precessional Motion of the Magnetization Vector. Science, 2000, 290:492-495
[107] K. Y. Guslienko, B. A. Ivanov, V. Novosad, et al. Eigenfrequencies of vortex state excitations in magnetic submicron-size disks. AIP, 2002,91:8037-8039
[108] M. Buess, T. Haug, M. R. Scheinfein, et al. Micromagnetic Dissipation Dispersion and Mode Conversion in Thin Permalloy Platelets. Phys.Rev.Lett., 2005, 94:127205
[109] Hillebrands, K. Ounadjela .Spin Dynamics in Confined Magnetic Structures Ⅰ . Verlag Berlin Heidelberg, 2002, 1-34
[110] S. Choe, Y. Acremann, A. Scholl, et al. Vortex Core-Driven Magnetization Dynamics. Science, 2004, 304: 420-422
[111] F. Hoffmann, G. Woltersdorf, et al. Mode degeneracy due to vortex core removal in magnetic disks. Phys.Rev.B, 2007, 76:014416
[112] M. Yan, G. Leaf, H. Kaper, et al. Spin-wave modes in a cobalt square vortex: Micromagnetic simulations. Phys.Rev.B, 2006,73:014425