磁性纳米颗粒及其集合体的磁学性质研究
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摘要
纳米磁学是指处理维度在亚微米或者亚微米以下量级的结构所具有的磁学性质的一门新兴学科。本论文属纳米磁学范畴,研究对象是纳米磁性颗粒及其集合体,研究目标包括理解和探索多体偶极体系的物理规律以及促进诸如作为纳米磁性颗粒集合体的磁记录材料以及磁性液体等的应用。
弛豫现象是纳米磁性颗粒集合体磁学性能的重要基础。它牵涉到诸如多体偶极体系对外界的响应,磁记录的时间稳定性等基本问题。目前关于磁晶易轴随机分布以及偶极相互作用对磁性纳米颗粒集合体在磁学方面弛豫性质的影响人们并不完全清楚。作为一个理论研究,本学位论文重点探索磁性纳米颗粒集合体中的偶极相互作用效应和磁晶易轴随机分布效应,主要考察的物理问题是弛豫以及势垒分布。
有别于通常的蒙特卡罗模拟,我们在弛豫方面借助于局域配分函数和主方程,该模型适用于计算磁性纳米颗粒的诸多弛豫性质;在相互作用方面,我们通过除了通过平均场方法计算颗粒的磁化问题之外,还基于Landau-Lifshitz-Gilbert(LLG)方程模拟了集合体磁矩的运动,对比蒙特卡罗方法,我们考虑了磁矩进动的因素。为了分析这些方法的可靠性,我们分别用配分函数计算了单个磁性颗粒的热力学平衡态性质,另一方面,把LLG方程应用于研究磁性颗粒的磁滞回线等,我们获得了与实验和理论相符的结果。
关于磁性液体中聚集结构的稳定态,我们以垂直于磁性液体膜面而形成的六角排列的聚集柱体结构为例,建立了颗粒聚集相与分散相的颗粒扩散模型,并利用平均场方式得到了聚集结构中颗粒之间的偶极作用场,我们模型预言的结果与实验较好一致,同时得到结论,当颗粒半径较小时,磁性液体中可以有相当可观的分散颗粒,这意味着在对磁性液体中磁能量进行分析的时候,假设所有的颗粒都参加了聚集是需要修正的。另外,我们模型还预言了特征场的存在。我们还进一步分析了聚集结构之间相互作用对本扩散模型的影响。(第二章)
关于单个磁性纳米颗粒热力学平衡态的磁学性质,我们通过数值解法求解配分函数获得了磁化强度以及平均塞曼能、各向异性能、比热的性质。我们发现,当外磁场与磁性颗粒易轴平行时,其比热随温度变化曲线上出现的峰位随着外磁场的增强而往高温区移动;而当外磁场与磁性颗粒易轴垂直时,比热与温度的曲线上其峰位随着外磁场的增强而相低温区移动。这是由磁性纳米颗粒的能量面特点所决定的。(第三章)
在弛豫方面,我们考虑了磁晶易轴随机分布效应以及加热速率的影响。我们成功得到了纳米磁性颗粒集合体在零场冷(ZFC)和场冷(FC)过程后测量所得的磁化强度,以及弛豫过程、记忆效应等性质。我们的结果表明,①在我们所研究的磁晶易轴随机分布的磁性纳米颗粒集合体中,其ZFC过程后随温度测量所得曲线上的峰值可由方程(4-14)表出,方程(4-14)预言了现在被普遍实验和模拟所证明的峰值温度与外磁场H2/3的关系,并与其定量上符合得相当好,这说明了方程(4-14)较H2/3关系更能体现其峰值温度的本质,从而给出更丰富的物理信息。②在弛豫过程方面,我们的模型支持用Tln(t/τ0)标度并支持通过S(t)的峰位来考察系统内的有效势垒;同时,在外磁场较大的情况下,用Tln(t/τ0)标度较好,S(t)的峰位置较好地对应着初始状态下的有效势垒(位于低势垒区);从S(t)上得到的分布不一定是系统的真实势垒分布。③我们的模型重现了该系统在降温后的记忆效应,表明,不存在体积分布和相互作用,仅仅存在磁晶易轴空间随机分布的体系,在降温后也具有记忆效应。(第四章)
在偶极相互作用方面,我们的结果表明,在纳米磁性颗粒集合体中,存在着两种性质的排列趋势,铁磁性的排列和反铁磁性的排列,两者分别对磁化强度的增加起促进和阻碍作用。在多层结构中两种趋势可以发生转变。我们进而分析了磁化过程中的势垒问题。对于非相互作用的纳米磁性颗粒体系,我们验证了文献上所报道的外磁场使势垒变宽并导致峰位向低势垒区移动的论点,并得到结论,同一强度的外磁场下,初始磁化的势垒分布最宽,退磁化时最均匀,而反向磁化时所获得的势垒分布最窄。相互作用对势垒分布曲线峰位和宽度的影响与磁化过程有关。在初始磁化过程中存在一个阈值磁场,当外磁场小于该阈值磁场,外磁场对系统势垒的影响不大;特别的,在我们所研究的二维六角排列的体系里面,退磁化和反向磁化的过程中,势垒分布的峰位以及宽度变化与内在偏置场有关,并且由于内在偏置场的作用系统势垒分布宽度可以出现随着外磁场的减小而增宽,或是势垒的峰位随着外磁场的减小而向低势垒区移动的情况。(第五章)
综上,我们强调,①即使是单一体积的磁性纳米颗粒集合体,磁晶易轴随机分布仍然可以用于解释当前实验和理论所证实的诸多弛豫现象;②可以通过外磁场和相互作用控制系统的势垒分布。在研究方法方面,我们所提出的基于局域配分函数的弛豫模型还可应用于处理一些静磁学问题;关于磁性液体中的扩散模型可以应用于电流体中的颗粒聚集现象等。
This dissertation is subject to the nanomagnetism which as a new discipline deals with the magnetic properties of the structures in size of submicrometer or below submicrometer. Here it focuses on magnetic nanoparticles and the magnetic nanoparticle assembly. The research aims at a better understanding of the physics in a multi-body dipolar system, and a promotion of the applications such as magnetic recording materials, and magnetic fluids.
The relaxation phenomena play an important and basic role on the magnetic properties of the magnetic nanoparticle assembly, because it is related to how the multi-body dipolar system responses to the external detect, and the time stability of magnetic recording. It is interesting but yet unclear about the effects of randomly distributed anisotropy and the dipolar interactions between particles on the relaxation in magnetic nanoparticle assembly. This dissertation was trying to explore the two effects, i.e. dipolar interaction effect and randomly distributed anisotropy effect. Emphases were put on the relaxation and the energy barrier distribution.
Being different from the commonly used Monte Carlo simulation, a local partition function and a master equation were employed to study the relaxation properties of the assembly. Two methods were used for the investigation of the dipolar interaction: one is the mean field approximation to calculate the magnetization; the other is the simulation of the magnetic moment on the basis of the Landau-Lifshitz-Gilbert (LLG) equation, which covers the precession of the moment in comparison to the method of Monte Carlo. To verify the simulation techniques used in the dissertation, we calculate the equilibrium magnetic properties of a single magnetic particle, and apply the LLG simulation to the study of the magnetic hysteresis loop of the magnetic particle assembly. The obtained results were in agreement with the published experiments and theories.
To analyze the stable state of the magnetic-field-induced aggregated structures in a ferrofluid, a particle diffusion model was set up to describe the aggregated phase and dispersed phase of the particles, and applied to the case of the hexagonal columnar structure formed in a magnetic field perpendicular to the ferrofluid film. By introducing a mean field method, we calculated the interaction field between the particles in the column, and ultimately obtained the agreeable ratio of the radius to the spacing between the columns. It was concluded that there would be considerable particles dispersed in the ferrofluid film under a perpendicular field, especially when the particles are small. This meant that at least the assumption of total aggregation of the particles should be modified in the minimization analysis of the system’s free energy. The interaction between the columns was also discussed. (see Chapter 2)
Based on the partition function, we calculated the magnetic properties of a single magnetic particle, the average anisotropy energy, the average Zeeman energy, and the specific heat of the particle. It was found that, in the case of the easy axis parallel to the magnetic field, the peak on the specific heat (vs temperature) shifted to higher temperature with the magnetic field; but to lower in that perpendicular to the field. This was explained by the character of the magnetic energy map of the particle. (see Chapter 3)
In regard to the relaxation, we took into account the effects of the randomly distributed anisotropy and the heating rate, and successfully reproduced the relaxation properties of the magnetic particle assembly, such as the magnetization curves (vs temperature) after zero-field-cooling (ZFC) and field-cooling (FC) processes, the relaxation and the memory effect. The followings are concluded.①In the studied system, the temperature (Tp) at the peak of the magnetization curve after a ZFC process could be fitted to Eq. (4-14), which predicts the H2/3 dependence commonly observed by experiments and simulations. Since the good agreement in quantification on H2/3 dependence, we believed Eq. (4-14) would reflect the nature of Tp, rather than the simple H2/3 dependence, and give more physics.②The model supported the Tln(t/τ0) scaling and the investigation on the active barrier distribution from the curve of S(t) vs Tln(t/τ0). Meanwhile, for a strong applied magnetic field, the Tln(t/τ0) scaling is improved, and the peak of the S(t) corresponds well to the active barrier in the studied system. The barrier distribution derived from S(t) was not necessarily the real distribution in the system.③The model reproduced the memory effect after temporary cooling, indicating that without a volume distribution and particle interaction, the particle assembly still possesses the memory effect if a randomly distributed anisotropy is set. (see Chapter 4)
Regarding the dipolar interaction, it was shown that in the studied system (2D hexagonal lattices and multilayer structures) the particle moments favor two kinds of alignment, ferromagnetic alignment and anti-ferromagnetic alignment, depending on the direction of the applied magnetic field. The ferromagnetic alignment acts on the magnetization, while the anti-ferromagnetic against the magnetization. As the layer number of the system increased, the system’s favorite alignment could be changed. Then we go further to the barrier distribution during the magnetization. In the case of the non-interacting assembly, we reproduced the reported phenomena, behind which, the applied magnetic field broadens the barrier distribution and causes the peak position of the distribution to shift to lower barrier area. It was also concluded that, under the magnetic field with the same magnitude, the barrier distribution was wide when the system was initially magnetized from a zero field value; and uniform in the process of reducing field down to zero; while narrow in that of reversing field. It means that the barrier distribution can be controlled by the magnetization. In the case of the interacting assembly, the effects of the dipolar interactions on the peak and the width of the barrier distribution are also related to the magnetization process. During the initial magnetization, there was a threshold field below which the effects were negligible. Particularly, for the studied 2-dimensional particle system with hexagonal configuration, as the field was dropped to zero and then became inversed, the behaviors of the peak and the width of the barrier distribution were related to a field offset. The peak may shift to lower energy and be broadened as the magnitude of the magnetic field increases. (see Chapter 5)
Finally, we stressed the following two points of view.①In spite of the uniform size of the particle in the assembly, the randomly distributed anisotropy could be, at least one of the, the origins of several kinds of observed relaxation phenomena.②The energy barrier distribution could be controlled by the external magnetic field together with the dipolar interaction between the particles. In addition, the relaxation model and the diffusion model could be applied to the study of the static magnetic properties, and to the aggregation in electrofluids.
弛豫现象是纳米磁性颗粒集合体磁学性能的重要基础。它牵涉到诸如多体偶极体系对外界的响应,磁记录的时间稳定性等基本问题。目前关于磁晶易轴随机分布以及偶极相互作用对磁性纳米颗粒集合体在磁学方面弛豫性质的影响人们并不完全清楚。作为一个理论研究,本学位论文重点探索磁性纳米颗粒集合体中的偶极相互作用效应和磁晶易轴随机分布效应,主要考察的物理问题是弛豫以及势垒分布。
有别于通常的蒙特卡罗模拟,我们在弛豫方面借助于局域配分函数和主方程,该模型适用于计算磁性纳米颗粒的诸多弛豫性质;在相互作用方面,我们通过除了通过平均场方法计算颗粒的磁化问题之外,还基于Landau-Lifshitz-Gilbert(LLG)方程模拟了集合体磁矩的运动,对比蒙特卡罗方法,我们考虑了磁矩进动的因素。为了分析这些方法的可靠性,我们分别用配分函数计算了单个磁性颗粒的热力学平衡态性质,另一方面,把LLG方程应用于研究磁性颗粒的磁滞回线等,我们获得了与实验和理论相符的结果。
关于磁性液体中聚集结构的稳定态,我们以垂直于磁性液体膜面而形成的六角排列的聚集柱体结构为例,建立了颗粒聚集相与分散相的颗粒扩散模型,并利用平均场方式得到了聚集结构中颗粒之间的偶极作用场,我们模型预言的结果与实验较好一致,同时得到结论,当颗粒半径较小时,磁性液体中可以有相当可观的分散颗粒,这意味着在对磁性液体中磁能量进行分析的时候,假设所有的颗粒都参加了聚集是需要修正的。另外,我们模型还预言了特征场的存在。我们还进一步分析了聚集结构之间相互作用对本扩散模型的影响。(第二章)
关于单个磁性纳米颗粒热力学平衡态的磁学性质,我们通过数值解法求解配分函数获得了磁化强度以及平均塞曼能、各向异性能、比热的性质。我们发现,当外磁场与磁性颗粒易轴平行时,其比热随温度变化曲线上出现的峰位随着外磁场的增强而往高温区移动;而当外磁场与磁性颗粒易轴垂直时,比热与温度的曲线上其峰位随着外磁场的增强而相低温区移动。这是由磁性纳米颗粒的能量面特点所决定的。(第三章)
在弛豫方面,我们考虑了磁晶易轴随机分布效应以及加热速率的影响。我们成功得到了纳米磁性颗粒集合体在零场冷(ZFC)和场冷(FC)过程后测量所得的磁化强度,以及弛豫过程、记忆效应等性质。我们的结果表明,①在我们所研究的磁晶易轴随机分布的磁性纳米颗粒集合体中,其ZFC过程后随温度测量所得曲线上的峰值可由方程(4-14)表出,方程(4-14)预言了现在被普遍实验和模拟所证明的峰值温度与外磁场H2/3的关系,并与其定量上符合得相当好,这说明了方程(4-14)较H2/3关系更能体现其峰值温度的本质,从而给出更丰富的物理信息。②在弛豫过程方面,我们的模型支持用Tln(t/τ0)标度并支持通过S(t)的峰位来考察系统内的有效势垒;同时,在外磁场较大的情况下,用Tln(t/τ0)标度较好,S(t)的峰位置较好地对应着初始状态下的有效势垒(位于低势垒区);从S(t)上得到的分布不一定是系统的真实势垒分布。③我们的模型重现了该系统在降温后的记忆效应,表明,不存在体积分布和相互作用,仅仅存在磁晶易轴空间随机分布的体系,在降温后也具有记忆效应。(第四章)
在偶极相互作用方面,我们的结果表明,在纳米磁性颗粒集合体中,存在着两种性质的排列趋势,铁磁性的排列和反铁磁性的排列,两者分别对磁化强度的增加起促进和阻碍作用。在多层结构中两种趋势可以发生转变。我们进而分析了磁化过程中的势垒问题。对于非相互作用的纳米磁性颗粒体系,我们验证了文献上所报道的外磁场使势垒变宽并导致峰位向低势垒区移动的论点,并得到结论,同一强度的外磁场下,初始磁化的势垒分布最宽,退磁化时最均匀,而反向磁化时所获得的势垒分布最窄。相互作用对势垒分布曲线峰位和宽度的影响与磁化过程有关。在初始磁化过程中存在一个阈值磁场,当外磁场小于该阈值磁场,外磁场对系统势垒的影响不大;特别的,在我们所研究的二维六角排列的体系里面,退磁化和反向磁化的过程中,势垒分布的峰位以及宽度变化与内在偏置场有关,并且由于内在偏置场的作用系统势垒分布宽度可以出现随着外磁场的减小而增宽,或是势垒的峰位随着外磁场的减小而向低势垒区移动的情况。(第五章)
综上,我们强调,①即使是单一体积的磁性纳米颗粒集合体,磁晶易轴随机分布仍然可以用于解释当前实验和理论所证实的诸多弛豫现象;②可以通过外磁场和相互作用控制系统的势垒分布。在研究方法方面,我们所提出的基于局域配分函数的弛豫模型还可应用于处理一些静磁学问题;关于磁性液体中的扩散模型可以应用于电流体中的颗粒聚集现象等。
This dissertation is subject to the nanomagnetism which as a new discipline deals with the magnetic properties of the structures in size of submicrometer or below submicrometer. Here it focuses on magnetic nanoparticles and the magnetic nanoparticle assembly. The research aims at a better understanding of the physics in a multi-body dipolar system, and a promotion of the applications such as magnetic recording materials, and magnetic fluids.
The relaxation phenomena play an important and basic role on the magnetic properties of the magnetic nanoparticle assembly, because it is related to how the multi-body dipolar system responses to the external detect, and the time stability of magnetic recording. It is interesting but yet unclear about the effects of randomly distributed anisotropy and the dipolar interactions between particles on the relaxation in magnetic nanoparticle assembly. This dissertation was trying to explore the two effects, i.e. dipolar interaction effect and randomly distributed anisotropy effect. Emphases were put on the relaxation and the energy barrier distribution.
Being different from the commonly used Monte Carlo simulation, a local partition function and a master equation were employed to study the relaxation properties of the assembly. Two methods were used for the investigation of the dipolar interaction: one is the mean field approximation to calculate the magnetization; the other is the simulation of the magnetic moment on the basis of the Landau-Lifshitz-Gilbert (LLG) equation, which covers the precession of the moment in comparison to the method of Monte Carlo. To verify the simulation techniques used in the dissertation, we calculate the equilibrium magnetic properties of a single magnetic particle, and apply the LLG simulation to the study of the magnetic hysteresis loop of the magnetic particle assembly. The obtained results were in agreement with the published experiments and theories.
To analyze the stable state of the magnetic-field-induced aggregated structures in a ferrofluid, a particle diffusion model was set up to describe the aggregated phase and dispersed phase of the particles, and applied to the case of the hexagonal columnar structure formed in a magnetic field perpendicular to the ferrofluid film. By introducing a mean field method, we calculated the interaction field between the particles in the column, and ultimately obtained the agreeable ratio of the radius to the spacing between the columns. It was concluded that there would be considerable particles dispersed in the ferrofluid film under a perpendicular field, especially when the particles are small. This meant that at least the assumption of total aggregation of the particles should be modified in the minimization analysis of the system’s free energy. The interaction between the columns was also discussed. (see Chapter 2)
Based on the partition function, we calculated the magnetic properties of a single magnetic particle, the average anisotropy energy, the average Zeeman energy, and the specific heat of the particle. It was found that, in the case of the easy axis parallel to the magnetic field, the peak on the specific heat (vs temperature) shifted to higher temperature with the magnetic field; but to lower in that perpendicular to the field. This was explained by the character of the magnetic energy map of the particle. (see Chapter 3)
In regard to the relaxation, we took into account the effects of the randomly distributed anisotropy and the heating rate, and successfully reproduced the relaxation properties of the magnetic particle assembly, such as the magnetization curves (vs temperature) after zero-field-cooling (ZFC) and field-cooling (FC) processes, the relaxation and the memory effect. The followings are concluded.①In the studied system, the temperature (Tp) at the peak of the magnetization curve after a ZFC process could be fitted to Eq. (4-14), which predicts the H2/3 dependence commonly observed by experiments and simulations. Since the good agreement in quantification on H2/3 dependence, we believed Eq. (4-14) would reflect the nature of Tp, rather than the simple H2/3 dependence, and give more physics.②The model supported the Tln(t/τ0) scaling and the investigation on the active barrier distribution from the curve of S(t) vs Tln(t/τ0). Meanwhile, for a strong applied magnetic field, the Tln(t/τ0) scaling is improved, and the peak of the S(t) corresponds well to the active barrier in the studied system. The barrier distribution derived from S(t) was not necessarily the real distribution in the system.③The model reproduced the memory effect after temporary cooling, indicating that without a volume distribution and particle interaction, the particle assembly still possesses the memory effect if a randomly distributed anisotropy is set. (see Chapter 4)
Regarding the dipolar interaction, it was shown that in the studied system (2D hexagonal lattices and multilayer structures) the particle moments favor two kinds of alignment, ferromagnetic alignment and anti-ferromagnetic alignment, depending on the direction of the applied magnetic field. The ferromagnetic alignment acts on the magnetization, while the anti-ferromagnetic against the magnetization. As the layer number of the system increased, the system’s favorite alignment could be changed. Then we go further to the barrier distribution during the magnetization. In the case of the non-interacting assembly, we reproduced the reported phenomena, behind which, the applied magnetic field broadens the barrier distribution and causes the peak position of the distribution to shift to lower barrier area. It was also concluded that, under the magnetic field with the same magnitude, the barrier distribution was wide when the system was initially magnetized from a zero field value; and uniform in the process of reducing field down to zero; while narrow in that of reversing field. It means that the barrier distribution can be controlled by the magnetization. In the case of the interacting assembly, the effects of the dipolar interactions on the peak and the width of the barrier distribution are also related to the magnetization process. During the initial magnetization, there was a threshold field below which the effects were negligible. Particularly, for the studied 2-dimensional particle system with hexagonal configuration, as the field was dropped to zero and then became inversed, the behaviors of the peak and the width of the barrier distribution were related to a field offset. The peak may shift to lower energy and be broadened as the magnitude of the magnetic field increases. (see Chapter 5)
Finally, we stressed the following two points of view.①In spite of the uniform size of the particle in the assembly, the randomly distributed anisotropy could be, at least one of the, the origins of several kinds of observed relaxation phenomena.②The energy barrier distribution could be controlled by the external magnetic field together with the dipolar interaction between the particles. In addition, the relaxation model and the diffusion model could be applied to the study of the static magnetic properties, and to the aggregation in electrofluids.
引文
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