Dependence of Brownian and Neel relaxation times on magnetic field strength
Dependence of Brownian and Neel relaxation times on magnetic field strength
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DOI：
10.1118/1.4837216
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发表时间：
2014-01-01
期刊：
影响因子：
3.8
通讯作者：
Martens, Michael A.
中科院分区：
文献类型：
--
作者：
Deissler, Robert J.;Wu, Yong;Martens, Michael A.
目的：在磁粒子成像（MPI）和磁粒子光谱（MPS）中，响应于外部施加的磁场的磁化的弛豫时间由布朗和尼尔弛豫机制确定。在这里，作者调查的弛豫时间对磁场强度的依赖性和MPI和MPS的影响。方法：Fokker-Planck方程与布朗弛豫和Fokker-Planck方程与Neel弛豫数值求解随时间变化的外部施加的磁场，包括阶梯函数，正弦变化，和线性斜坡磁场。对于作为阶跃函数施加的磁场，本征值方法用于直接计算磁场强度范围内的布朗弛豫时间和Neel弛豫时间。对于Neel弛豫，本征值的计算相比，布朗的高势垒approximationformula.Results：由于布朗或Neel机制的弛豫时间依赖于所施加的磁场的大小。特别地，Neel弛豫时间对磁场强度敏感，并且对于与MPI和MPS相关的纳米颗粒性质和磁场强度变化许多数量级。因此，众所周知的零场弛豫时间低估了实际弛豫时间，特别是可以低估尼尔弛豫时间许多数量级。当只存在尼尔弛豫时--例如，如果粒子嵌入固体中--作者发现，即使周期远小于零场弛豫时间，也可以对正弦驱动场产生强磁化响应。对于同时存在布朗弛豫和Neel弛豫的铁磁流体，取决于磁场强度、驱动频率，只有一种弛豫机制可能占主导地位。（或斜坡时间）和磁化相对于所施加磁场的相位。一个简单的处理尼尔松弛使用共同零-场弛豫时间高估了与MPI和MPS相关的情况下磁化的弛豫时间。对于正弦驱动（或斜坡）系统，特定弛豫机制是否占主导地位或甚至相关取决于磁场强度、频率（或斜坡时间）以及磁化相对于所施加磁场的相位。c 2014年美国医学物理学家协会。
Purpose: In magnetic particle imaging (MPI) and magnetic particle spectroscopy (MPS) the relaxation time of the magnetization in response to externally applied magnetic fields is determined by the Brownian and Neel relaxation mechanisms. Here the authors investigate the dependence of the relaxation times on the magnetic field strength and the implications for MPI and MPS.Methods: The Fokker-Planck equation with Brownian relaxation and the Fokker-Planck equation with Neel relaxation are solved numerically for a time-varying externally applied magnetic field, including a step-function, a sinusoidally varying, and a linearly ramped magnetic field. For magnetic fields that are applied as a step function, an eigenvalue approach is used to directly calculate both the Brownian and Neel relaxation times for a range of magnetic field strengths. For Neel relaxation, the eigenvalue calculations are compared to Brown's high-barrier approximation formula.Results: The relaxation times due to the Brownian or Neel mechanisms depend on the magnitude of the applied magnetic field. In particular, the Neel relaxation time is sensitive to the magnetic field strength, and varies by many orders of magnitude for nanoparticle properties and magnetic field strengths relevant for MPI and MPS. Therefore, the well-known zero-field relaxation times underestimate the actual relaxation times and, in particular, can underestimate the Neel relaxation time by many orders of magnitude. When only Neel relaxation is present-if the particles are embedded in a solid for instance-the authors found that there can be a strong magnetization response to a sinusoidal driving field, even if the period is much less than the zero-field relaxation time. For a ferrofluid in which both Brownian and Neel relaxation are present, only one relaxation mechanism may dominate depending on the magnetic field strength, the driving frequency (or ramp time), and the phase of the magnetization relative to the applied magnetic field.Conclusions: A simple treatment of Neel relaxation using the common zero-field relaxation time overestimates the relaxation time of the magnetization in situations relevant for MPI and MPS. For sinusoidally driven (or ramped) systems, whether or not a particular relaxation mechanism dominates or is even relevant depends on the magnetic field strength, the frequency (or ramp time), and the phase of the magnetization relative to the applied magnetic field. c 2014 American Association of Physicists in Medicine.