超高密度图案化磁记录介质中偶极作用与热辅助磁化研究
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摘要
由于记录介质的超顺磁效应,传统的水平磁记录方式已经达到理论极限。为了实现特比(Tb 1Terabit=2~(40)bit)级的超高密度存储,各种记录方案正在探索之中,其中图案化介质和热辅助磁记录技术被认为是最有发展潜力的方向,如果将两者结合则记录密度会更高。本论文结合已有的实验数据与前人的理论工作,通过有限差分法求解动力学方程和Monte Carlo随机方法重点研究了以下几个与图案化介质及热辅助磁化技术有关的问题:
(1)针对数值微磁学中矩形网格处理复杂边界时计算精度较低的问题,利用磁体本身的几何对称性和退磁张量的性质,通过在实空间求积分的方法解析地推导了等边三棱柱的退磁张量。根据这一张量表达式,可以得到任意精度的退磁因子,把这一结果应用在微磁学的网格划分当中,可以提高对复杂边界的处理能力。
(2)为了能够在数值计算中高效地求出系统中的偶极作用能,解决由于偶极作用长程性带来求和速度收敛缓慢的问题,我们通过重新定义网格求和方程,并采取分段处理的方法,解决了Lekner求和法中由于对称性降低而导致的奇异性问题,成功地把Lekner求和法从三维周期性边界条件下的库仑作用系统推广到了二维周期性结构的磁偶极作用系统。应用Lekner求和法可以高效地处理图案化介质这类规则排列的磁偶极子系统中偶极作用能的计算问题。
(3)为了深入理解偶极作用能对信息位稳定性与信息写入过程的具体影响,为实际设计图案化记录系统时选择合适的图案化介质提供理论指导,我们通过求解二维系统的动力学方程,研究了有限阵列和周期性边界条件阵列磁性颗粒间偶极作用能对系统静态与动态性质的影响。发现有限阵列的静态磁学性质诸如剩磁状态、矫顽力等与系统的大小密切相关,而磁化动力学过程则不受系统大小的影响。发现偶极作用能对系统的磁化强度翻转模式有决定性的作用。对于有限阵列来说,在平面各向异性的水平磁化翻转过程中,由偶极作用强度决定了三种翻转模式,即一致转动、成核模式及这两种模式的过渡区域;在垂直各向异性的垂直磁化翻转过程中,由偶极作用强度决定了四种翻转模式,即成核模式、非线性激发、旋卷模式以及成核与旋卷的过渡区域。对于周期性边界条件下的阵列,由磁场脉冲持续时间和偶极作用强度共同决定了中心磁矩翻转类型相图,相图中可以分为五种翻转类型,即关联翻转、过冲翻转、下冲翻转、弹道翻转以及未发生翻转区。
(4)为了理解偶极作用能对系统热稳定性的影响以及温度不均匀性对热辅助写入过程的具体影响,我们运用Monte Carlo方法研究了这两个问题。发现偶极作用能的增加会导致系统闭锁温度的升高,从而提高系统的热稳定性。在高斯分布型的稳定温度场中,发现根据温度场的半高宽可以把翻转过程分为三类不同的成核模式,即边缘成核而后中心扩展模式、边缘成核而后边缘扩展模式以及两种模式的混合模式,并且翻转弛豫时间的对数与半高宽导数之间成分段的线性关系,其分段点受外场和中心温度的影响。而对于给定半高宽的温度场来说,弛豫时间与温度的关系与经典成核理论描述均匀温度场中弛豫时间与温度的关系相似,只是此时的能量势垒和比例系数都与温度场的半高宽有关。
Because of the superparamagnetism in recording media, the traditional longitude recording technology is close to the theoretical limit. At the same time, patterned media (PM) and heat assisted magnetic recording (HAMR) are regarded as the potential ways to achieve Terabit level ultrahigh area density. In this dissertation, we studied the following problems about PM and HAMR by computer simulations based on the experiment data and previous theoretical work:
(1) In order to improve the accuracy in micromagnetic simulation of complex boundary, we derived the point function demagnetization tensor of equilateral triangular prisms in terms of the symmetry of the magnetic body and a theorem about demagnetization tensor. One can obtain the demagnetization factors with any accuracy of equilateral triangular prisms by numerically integrate this expression. This result can be used in micromagnetic discretization and improve the accuracy of calculation.
(2) In order to deal with the long range effect of dipolar interaction efficiently, the Lekner summation method is extended from three dimensional Coulomb systems to two dimensional magnetic dipolar systems successfully. The Lekner method can be used to sum the dipolar interaction energy in PM and other regular arrays efficiently and can be used in other randomly distributed systems combined with other summation techniques.
(3) On solving the dynamics equations of two dimensional systems, we studied the dipolar interaction in finite arrays and periodic arrays to understand the effects of dipolar interaction energy on the writing process and stability of the reconding bits. It is found that the quasistatic properties, such as remanence and coercivity are influenced by the size of finite arrays. On the contrary, the reversal modes are only determined by the dipolar interaction strength. For the easy plane anisotropy, the dipolar interaction strength determines three reversal modes, which are coherent rotation, nucleation and the transition between them, and four reversal modes in perpendicular easy axis anisotropy case, which are nucleation, nonlinear excitation, curling and the transition between nucleation and curling. For periodic arrays, the dipolar interaction strength and the duration of magnetic field determine a phase diagram of reversal types of precession switching. There are five reversal types in the phase diagram, which are correlated reversal, overshoot reversal, undershoot reversal, ballistic reversal and nonreversal.
(4) With the help of Monte Carlo method, we studied the dipolar interaction effects on the thermal stability of magnetic systems and the nonuniformity of temperature effects on the thermally assisted magnetization processes. It is found that the block temperature of the system increase with increasing dipolar interaction strength, so the dipolar interaction can improve the thermal stability of systems. In the Gaussian stable temperature field, we found three nucleation modes according to the full width at half maximum (FWHM) of the temperature field. At the same time, the logarithmic of relaxation time is sectional linear to the inverse value of FWHM. The sectional point is determined by applied field and central temperature. In addition, for a given FWHM, the relationship between relaxation time and temperature can approximately described by the classical nucleation theory, but the energy barrier and the proportion coefficient are both related to the FWHM of the temperature field.
(1)针对数值微磁学中矩形网格处理复杂边界时计算精度较低的问题,利用磁体本身的几何对称性和退磁张量的性质,通过在实空间求积分的方法解析地推导了等边三棱柱的退磁张量。根据这一张量表达式,可以得到任意精度的退磁因子,把这一结果应用在微磁学的网格划分当中,可以提高对复杂边界的处理能力。
(2)为了能够在数值计算中高效地求出系统中的偶极作用能,解决由于偶极作用长程性带来求和速度收敛缓慢的问题,我们通过重新定义网格求和方程,并采取分段处理的方法,解决了Lekner求和法中由于对称性降低而导致的奇异性问题,成功地把Lekner求和法从三维周期性边界条件下的库仑作用系统推广到了二维周期性结构的磁偶极作用系统。应用Lekner求和法可以高效地处理图案化介质这类规则排列的磁偶极子系统中偶极作用能的计算问题。
(3)为了深入理解偶极作用能对信息位稳定性与信息写入过程的具体影响,为实际设计图案化记录系统时选择合适的图案化介质提供理论指导,我们通过求解二维系统的动力学方程,研究了有限阵列和周期性边界条件阵列磁性颗粒间偶极作用能对系统静态与动态性质的影响。发现有限阵列的静态磁学性质诸如剩磁状态、矫顽力等与系统的大小密切相关,而磁化动力学过程则不受系统大小的影响。发现偶极作用能对系统的磁化强度翻转模式有决定性的作用。对于有限阵列来说,在平面各向异性的水平磁化翻转过程中,由偶极作用强度决定了三种翻转模式,即一致转动、成核模式及这两种模式的过渡区域;在垂直各向异性的垂直磁化翻转过程中,由偶极作用强度决定了四种翻转模式,即成核模式、非线性激发、旋卷模式以及成核与旋卷的过渡区域。对于周期性边界条件下的阵列,由磁场脉冲持续时间和偶极作用强度共同决定了中心磁矩翻转类型相图,相图中可以分为五种翻转类型,即关联翻转、过冲翻转、下冲翻转、弹道翻转以及未发生翻转区。
(4)为了理解偶极作用能对系统热稳定性的影响以及温度不均匀性对热辅助写入过程的具体影响,我们运用Monte Carlo方法研究了这两个问题。发现偶极作用能的增加会导致系统闭锁温度的升高,从而提高系统的热稳定性。在高斯分布型的稳定温度场中,发现根据温度场的半高宽可以把翻转过程分为三类不同的成核模式,即边缘成核而后中心扩展模式、边缘成核而后边缘扩展模式以及两种模式的混合模式,并且翻转弛豫时间的对数与半高宽导数之间成分段的线性关系,其分段点受外场和中心温度的影响。而对于给定半高宽的温度场来说,弛豫时间与温度的关系与经典成核理论描述均匀温度场中弛豫时间与温度的关系相似,只是此时的能量势垒和比例系数都与温度场的半高宽有关。
Because of the superparamagnetism in recording media, the traditional longitude recording technology is close to the theoretical limit. At the same time, patterned media (PM) and heat assisted magnetic recording (HAMR) are regarded as the potential ways to achieve Terabit level ultrahigh area density. In this dissertation, we studied the following problems about PM and HAMR by computer simulations based on the experiment data and previous theoretical work:
(1) In order to improve the accuracy in micromagnetic simulation of complex boundary, we derived the point function demagnetization tensor of equilateral triangular prisms in terms of the symmetry of the magnetic body and a theorem about demagnetization tensor. One can obtain the demagnetization factors with any accuracy of equilateral triangular prisms by numerically integrate this expression. This result can be used in micromagnetic discretization and improve the accuracy of calculation.
(2) In order to deal with the long range effect of dipolar interaction efficiently, the Lekner summation method is extended from three dimensional Coulomb systems to two dimensional magnetic dipolar systems successfully. The Lekner method can be used to sum the dipolar interaction energy in PM and other regular arrays efficiently and can be used in other randomly distributed systems combined with other summation techniques.
(3) On solving the dynamics equations of two dimensional systems, we studied the dipolar interaction in finite arrays and periodic arrays to understand the effects of dipolar interaction energy on the writing process and stability of the reconding bits. It is found that the quasistatic properties, such as remanence and coercivity are influenced by the size of finite arrays. On the contrary, the reversal modes are only determined by the dipolar interaction strength. For the easy plane anisotropy, the dipolar interaction strength determines three reversal modes, which are coherent rotation, nucleation and the transition between them, and four reversal modes in perpendicular easy axis anisotropy case, which are nucleation, nonlinear excitation, curling and the transition between nucleation and curling. For periodic arrays, the dipolar interaction strength and the duration of magnetic field determine a phase diagram of reversal types of precession switching. There are five reversal types in the phase diagram, which are correlated reversal, overshoot reversal, undershoot reversal, ballistic reversal and nonreversal.
(4) With the help of Monte Carlo method, we studied the dipolar interaction effects on the thermal stability of magnetic systems and the nonuniformity of temperature effects on the thermally assisted magnetization processes. It is found that the block temperature of the system increase with increasing dipolar interaction strength, so the dipolar interaction can improve the thermal stability of systems. In the Gaussian stable temperature field, we found three nucleation modes according to the full width at half maximum (FWHM) of the temperature field. At the same time, the logarithmic of relaxation time is sectional linear to the inverse value of FWHM. The sectional point is determined by applied field and central temperature. In addition, for a given FWHM, the relationship between relaxation time and temperature can approximately described by the classical nucleation theory, but the energy barrier and the proportion coefficient are both related to the FWHM of the temperature field.
引文
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