纳米磁体的扩展朗道-里夫希茨方程：表面诱导磁化章动的路径积分推导
Extended Landau--Lifshitz equation for nanomagnets: a path-integral derivation of surface-induced magnetization nutation
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中文总结 AI 辅助
研究纳米磁体表面诱导磁化章动问题，通过自旋相干态路径积分形式，从原子自旋哈密顿量推导有效动力学方程，经两步推导及绝热近似等处理，得到扩展朗道-里夫希茨方程，为该现象建立微观基础并提供修正估计框架。
中文摘要 AI 辅助
本文利用自旋相干态路径积分形式，从原子自旋哈密顿量推导出具有表面各向异性的纳米磁体磁化的有效动力学方程。推导分两步进行。首先得到多自旋纳米磁体的连续欧几里得作用量，包括韦斯-祖米诺-维滕（贝里相位）项以及交换、塞曼和核心/表面各向异性贡献。其次将局部磁化密度分解为缓慢变化的宏观自旋分量和由表面效应驱动的横向自旋失准涨落。对作用量进行系统展开至横向涨落变量的二次项。在绝热近似下，横向模式比宏观自旋弛豫快得多，利用其静态格林函数解消除这些模式。得到一个封闭的、扩展的宏观自旋朗道-里夫希茨方程，其有效场具有来自自旋失准的非平凡修正。这些修正重整化了塞曼场和各向异性场，并引入了类似章动和阻尼的附加项。这些结果为纳米磁体中表面诱导磁化章动建立了微观基础，并提供了一个框架来估计进动频率和有效阻尼的修正。铁磁共振频率和线宽的相应变化可用标准GHz光谱仪测量，潜在的绝热消除机制有望推广到任何与快速涨落模式浴耦合的慢磁变量。
英文摘要
An effective dynamical equation for the magnetization of a nanomagnet with surface anisotropy is derived from an atomistic spin Hamiltonian using the spin coherent-state path integral formalism. The derivation proceeds in two steps. First, the continuum Euclidean action for the many-spin nanomagnet is obtained, including the Wess--Zumino--Witten (Berry phase) term, as well as exchange, Zeeman, and core/surface anisotropy contributions. Second, the local magnetization density is decomposed into a slowly varying macrospin component and transverse spin-misalignment fluctuations driven by surface effects. A systematic expansion of the action is then performed up to quadratic order in the transverse-fluctuation variables. Under the adiabatic approximation, in which transverse modes relax much faster than the macrospin, these modes are eliminated by using their static Green's function solution. This results in a closed, extended Landau--Lifshitz equation for the macrospin, featuring an effective field with nontrivial corrections from spin misalignment. These corrections renormalize both the Zeeman and anisotropy fields and introduce additional terms that act as nutation- and damping-like contributions. ... Together, these results establish a microscopic foundation for surface-induced magnetization nutation in nanomagnets and provide a framework to estimate corrections to the precession frequency and effective damping. The corresponding shift in the ferromagnetic-resonance frequency and linewidth is measurable with standard GHz spectrometers, and the underlying adiabatic-elimination mechanism is expected to generalize to any slow magnetic variable coupled to a bath of fast-fluctuating modes.
