THERMAL FLUCTUATIONS OF A SINGLE-DOMAIN PARTICLE
THERMAL FLUCTUATIONS OF A SINGLE-DOMAIN PARTICLE
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DOI：
10.1103/physrev.130.1677
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发表时间：
1963-01-01
期刊：
影响因子：
--
通讯作者：
BROWN, WF
中科院分区：
文献类型：
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作者：
BROWN, WF
足够细的铁磁颗粒具有均匀的矢量磁化，其大小基本恒定，但其方向由于热扰动而波动。涨落在超顺磁性和磁后效中是重要的。这里用随机过程理论中熟悉的方法来处理这个问题。该问题的”朗之万方程”被假定为吉尔伯特运动方程加上一个”随机场”项。考虑这样的粒子的统计系综导致一个“福克-普朗克”偏微分方程，它描述了取向的概率密度的演变。无规场的概念虽然很方便，但可以用涨落耗散定理来避免。一般来说，福克-普朗克方程由于陀螺项的存在而变得复杂。在轴对称的情况下，这些都消失了：那么寻找非平衡解的问题就可以重新表述为一个最小化问题，可以近似处理。与KT相比，能量障碍大的情况下，处理近似最小化和适应Kramers的处理的逃逸的粒子的障碍。离散取向近似的有效性的限制进行了讨论。
A sufficiently fine ferromagnetic particle has a uniform vector magnetization whose magnitude is essentially constant, but whose direction fluctuates because of thermal agitation. The fluctuations are important in superparamagnetism and in magnetic aftereffect. The problem is approached here by methods familiar in the theory of stochastic processes. The" Langevin equation" of the problem is assumed to be Gilbert's equation of motion augmented by a" random-field" term. Consideration of a statistical ensemble of such particles leads to a" Fokker-Planck" partial differential equation, which describes the evolution of the probability density of orientations. The random-field concept, though convenient, can be avoided by use of the fluctuation-dissipation theorem. The Fokker-Planck equation, in general, is complicated by the presence of gyroscopic terms. These drop out in the case of axial symmetry: then the problem of finding nonequilibrium solutions can be restated as a minimization problem, susceptible to approximate treatments. The case of energy barriers large in comparison with kT is treated both by approximate minimization and by an adaptation of Kramers' treatment of the escape of particles over barriers. The limits of validity of the discrete-orientation approximation are discussed.