Stochastic ferrimagnetic Landau-Lifshitz-Bloch equation for finite magnetic structures
Stochastic ferrimagnetic Landau-Lifshitz-Bloch equation for finite magnetic structures
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有限磁结构的随机亚铁磁 Landau-Lifshitz-Bloch 方程
DOI：
10.1103/physrevb.100.054401
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发表时间：
2019
影响因子：
3.7
通讯作者：
Bruckner
中科院分区：
文献类型：
--
作者：
Vogler;Bruckner
在快速变化的温度下，精确模拟具有有限尺寸效应的纳米粒子的磁化动力学是一项具有计算挑战性的任务。基于Landau-Lifshitz-Bloch(LLB)方程，我们导出了一个既快速又准确的无序亚铁磁体的粗晶模型。首先，我们将随机涨落引入到现有的亚铁磁性LLB方程中。此外，我们还推导了与温度相关的磁化率的热力学表达式，这是模拟有限尺寸效应所必需的。结合零场平衡磁化强度，在随机亚铁磁性LLB中模拟了一个直径为5 nm、高度为10 nm的亚铁磁性粒子在不同外加电场和热脉冲作用下的磁化率。得到的轨迹与原子模型的轨迹很好地吻合，该模型求解了每个原子的随机Landau-Lifshitz-Gilbert方程。最后，我们将一个最高温度为1193℃的50fS热脉冲应用于相同尺寸的粒子，以测试所提出的全光交换(AOS)模型。我们观察到了类铁磁态的跃迁，这被认为是GdFeCo中AOS的关键。虽然粗粒度模型总体上与原子模拟显示出非常好的一致性，但计算的切换概率低于预期。对于超短和非常高的热脉冲，磁化轨迹似乎离平衡太远了，这是AOS的典型特征。由此得出的结论是，要么模型需要高阶修正才能准确地描述AOS，要么双自旋模型根本不能描述确定性的AOS。
Precise modeling of the magnetization dynamics of nanoparticles with finite-size effects at fast varying temperatures is a computationally challenging task. Based on the Landau-Lifshitz-Bloch (LLB) equation we derive a coarse-grained model for disordered ferrimagnets, which is both fast and accurate. First, we incorporate stochastic fluctuations to the existing ferrimagnetic LLB equation. Further, we derive a thermodynamic expression for the temperature-dependent susceptibilities, which is essential to model finite-size effects. Together with the zero-field equilibrium magnetization the susceptibilities are used in the stochastic ferrimagnetic LLB to simulate a ferrimagneticparticle with a diameter of 5 nm and a height of 10 nm under various external applied fields and heat pulses. The obtained trajectories agree well with those of an atomistic model, which solves the stochastic Landau-Lifshitz-Gilbert equation for each atom. Finally, we apply a 50-fs heat pulse with a maximum temperature of 1193 K to aparticle of the same size to test the proposed model for all-optical switching (AOS). We observe switching with a ferromagneticlike state, which was identified to be the key for AOS in GdFeCo. Although the coarse-grained model in general shows remarkably good agreement with atomistic simulations, the computed switching probability is lower than expected. The magnetization trajectories seem to be too far away from equilibrium for ultrashort and very high heat pulses, which are typical for AOS. This leads to the conclusion that either the model needs higher-order corrections to accurately describe AOS, or that the two-spin model is not capable of describing deterministic AOS at all.
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