从自旋转移力矩朗道-里夫希茨-吉尔伯特方程到福克-普朗克方程：非轴对称磁随机存取存储器器件的准确写错误率建模
From sLLG to Fokker-Planck: Accurate WER Modeling for Non-Axisymmetric MRAM Devices
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中文总结 AI 辅助
研究非轴对称MRAM器件写错误率建模问题，开发二维有限体积求解器并验证，支持四种离散化方案，通过实验表明离散化方案影响预测结果，推荐混合自适应混合，强调可定制离散化对准确预测开关动力学的关键作用。
中文摘要 AI 辅助
福克-普朗克（FP）方程对于预测自旋转移力矩（STT）和自旋轨道力矩（SOT）磁随机存取存储器（MRAM）器件的写错误率（WER）至关重要，但传统的一维投影在面对面内场、类场转矩或各向异性势垒破坏对称性时失效。我们在单位球面上开发了一种二维有限体积（FVM）求解器，并通过\(10^6\)轨迹的随机朗道-里夫希茨-吉尔伯特（sLLG）模拟进行验证。该求解器支持四种离散化方案——中心差分、沙夫特-古梅尔（SG）、迎风和混合自适应混合，每种方案具有不同的与佩克莱特数相关的精度和单调性。我们证明中心差分在二维效应占主导的STT和SOT几何结构中能恢复真实的WER，并表明离散化方案的选择直接影响预测的WER。对于磁模拟，我们推荐混合自适应混合作为在不同佩克莱特数范围内精度和稳定性的最佳平衡。这些结果表明可定制的离散化对于准确、无偏地预测下一代磁存储器中的开关动力学至关重要。
英文摘要
The Fokker--Planck (FP) equation is essential for predicting write error rates (WER) in STT and SOT-MRAM devices, but traditional 1D projections fail when symmetry is broken by in-plane fields, field-like torques, or anisotropic barriers. We develop a 2D finite-volume (FVM) solver on the unit sphere and validate it against $10^6$-trajectory stochastic Landau--Lifshitz--Gilbert (sLLG) simulations. The solver supports four discretization schemes---central, Scharfetter--Gummel (SG), upwind, and hybrid adaptive blending---each with different Péclet-dependent accuracy and monotonicity properties. We demonstrate that central differencing recovers ground-truth WER for STT and SOT geometries where 2D effects dominate, and show that the choice of discretization scheme directly affects predicted WER. For magnetic simulations, we recommend hybrid adaptive blending as the optimal balance of accuracy and stability across variable Péclet regimes. These results establish that customizable discretization is critical for accurate, unbiased predictions of switching dynamics in next-generation magnetic memory.
