THE FUNDAMENTAL THEOREM OF THE THEORY OF FINE FERROMAGNETIC PARTICLES *
THE FUNDAMENTAL THEOREM OF THE THEORY OF FINE FERROMAGNETIC PARTICLES *
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细小铁磁粒子理论的基本定理 *
DOI：
10.1111/j.1749-6632.1969.tb41269.x
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发表时间：
1969
影响因子：
5.2
通讯作者：
W. Brown
中科院分区：
文献类型：
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作者：
W. Brown
硬磁材料的理论讨论通常大量使用以下思想：而块状铁磁材料（在零外加磁场中）具有磁畴结构，使得样品作为整体具有比饱和值小得多的磁矩，以足够细的颗粒形式的相同材料被均匀磁化，（非常接近）饱和值，或者换句话说由单个域组成。这样表达的观念几乎不能被称为定理，因为它不是一个已证明的命题，也不是一个严格真实的命题。已经证明的，而且仅仅是用近似方法证明的，是一个形状是椭球的某种极限形式的均匀粒子，（例如球体或平板），具有给定的轴比，在均匀磁化状态下或在一些任意选择的“多畴”状态下具有较低的自由能，根据最小的半轴A小于或大于某个临界值A，（约200 A）。粒子总是处于自由能最低的状态，这是一个经常没有明确说明的假设，显然与滞后的存在不相容。为了把这个命题提升到定理的地位，我们必须首先通过指定椭球的形状，并通过关于最低自由能的状态而不是关于粒子的实际状态的陈述来相当程度地限定它。然后，我们必须消除在“多域”状态检查的任意性;最后，我们必须消除在tbe证明近似。这个命题将这样表述：对于一个均匀铁磁椭球体，在零外加磁场中，最低自由能状态是均匀磁化状态或非均匀磁化状态，取决于最小半轴a小于或大于某个临界值a。这种形式的命题可能是真的;如果是真的，它将构成一个
Theoretical discussions of hard magnetic materials’ commonly make considerable use of the following idea: whereas a ferromagnetic material in bulk (in zero applied field) possesses a domain structure so, that the specimen as a whole has a magnetic moment considerably smaller than the saturation value, the same material in the form of a sufficiently fine particle is uniformly magnetized to (very nearly) the saturation value, or in other words consists of a single domain. The idea as thus expressed scarcely is to be called a theorem, for it is not a proved proposition nor a strictly true one. What has been proved, and that only by approximate methods, is that a homogeneous particle whose shape is some limiting form of the ellipsoid (e.g. a sphere or a plane plate), with given axis ratios, has lower free energy in a uniformly magnetized state or in some arbitrarily selected “multidomain” state, according as the smallest semiaxis a is less than or greater than some critical value a, (of the order of 200 A). That the particle will always be in its state of lowest free energy is an assumption often made without explicit statement, and obviously incompatible with the existence of hysteresis. To elevate this proposition to the status of a theorem, we must first qualify it considerably, by specifying the ellipsoidal shape and by making statements about the state of lowest free energy rather than about the actual state of the particle. We must then remove the arbitrariness in the “multidomain” state examined; and finally, we must remove the approximations in tbe proof. The proposition will then read: for a homogeneous ferromagnetic ellipsoid in zero applied field, the state of lowest free energy is one of uniform magnetization or of nonuniform magnetization according as the smallest semiaxis a is less than or greater than some critical value a,. The proposition in this form may be true; if so, it would constitute a