Single crystal rare-earth magnets, such as hexagonal-close-packed gadolinium, usually have a large second order anisotropy K 2 and a negative first order anisotropy K 1 at low temperatures, which are difficult to explain using microscopic theories. An atomic scale effective spin Hamiltonian ℱ [{ S i }] is proposed, which, apart from the usual isotropic nearest neighbor coupling J , consists of two new terms that are different for in-plane and out-of-plane neighbors and which are characterized by two new couplings C 1 and C 2 , respectively. The hybrid Monte–Carlo method is utilized to sample this system to the desired Boltzmann-like distribution exp(− ℱ / k B T ). It is found that K 2 and K 1 are compatible with the experimental values and arise naturally from the exchange anisotropy C 1 and ...

中文翻译：

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Spin自旋哈密顿量法在d晶体中的各向异性起源

单晶稀土磁体，例如六角密排g，通常在低温下具有较大的二阶各向异性K 2和负的一阶各向异性K 1，这很难用微观理论来解释。提出了一种原子尺度有效的自旋哈密顿量ℱ[{S i}]，除了通常的各向同性最近邻耦合J之外，它还包含两个新的项，它们对于面内和面外邻居是不同的，分别具有两个新的联轴器C 1和C 2。混合蒙特卡洛方法用于对该系统进行采样，以达到所需的玻尔兹曼样分布exp（−ℱ/ k BT）。发现K 2和K 1与实验值兼容，并且自然地由交换各向异性C 1和...引起。