An observable effect of spin inertia in slow magneto-dynamics: Increase of the switching error rates in nanoscale ferromagnets
An observable effect of spin inertia in slow magneto-dynamics: Increase of the switching error rates in nanoscale ferromagnets
复制标题
慢磁动力学中自旋惯性的可观察效应：纳米级铁磁体中开关错误率的增加
DOI：
10.1088/1361-648x/ac0cb4
复制
发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Bandyopadhyay, Supriyo
中科院分区：
文献类型：
--
作者：
Rahman, Rahnuma;Bandyopadhyay, Supriyo
Landau-Lifshitz-吉尔伯特（LLG）方程用于模拟铁磁体中的磁动力学，默认地假设当引起旋进的真实的或有效的磁场被关闭时，与自旋旋进相关的角动量可以瞬时弛豫。这种忽略“自旋惯性”的做法是不符合物理规律的，而且违反了能量守恒定律。最近，对LLG方程进行了修改，以考虑惯性效应。然而，人们的共识似乎是，这种效应在慢磁动力学中并不重要，慢磁动力学发生的时间尺度比角动量的弛豫时间长得多，在铁磁体中，角动量的弛豫时间通常是几fs到大约100 ps。在这里，我们表明，至少有一个非常严重的和可观察到的自旋惯性效应，即使在缓慢的磁动力学。它涉及到开关错误概率与翻转磁化的纳米级铁磁体与外部代理，如磁场。当场强接近开关阈值时，开关可能需要10 ns才能完成，这比角动量弛豫时间长得多，但在开关错误概率中感觉到自旋惯性的影响。这是因为转换轨迹的最终命运，即它是否导致成功或失败，是由转换动作的最初几个ps发生的事情所影响的，当章动动力学由于自旋惯性占主导地位时。自旋惯性增加了错误概率，这使得切换更容易出错。这具有重要的技术意义，因为它关系到磁逻辑和存储器的可靠性。
The Landau–Lifshitz–Gilbert (LLG) equation, used to model magneto-dynamics in ferromagnets, tacitly assumes that the angular momentum associated with spin precession can relax instantaneously when the real or effective magnetic field causing the precession is turned off. This neglect of'spin inertia'is unphysical and would violate energy conservation. Recently, the LLG equation was modified to account for inertia effects. The consensus, however, seems to be that such effects would be unimportant in slow magneto-dynamics that take place over time scales much longer that the relaxation time of the angular momentum, which is typically few fs to perhaps∼ 100 ps in ferromagnets. Here, we show that there is at least one very serious and observable effect of spin inertia even in slow magneto-dynamics. It involves the switching error probability associated with flipping the magnetization of a nanoscale ferromagnet with an external agent, such as a magnetic field. The switching may take∼ ns to complete when the field strength is close to the threshold value for switching, which is much longer than the angular momentum relaxation time, and yet the effect of spin inertia is felt in the switching error probability. This is because the ultimate fate of a switching trajectory, ie whether it results in success or failure, is influenced by what happens in the first few ps of the switching action when nutational dynamics due to spin inertia hold sway. Spin inertia increases the error probability, which makes the switching more error-prone. This has vital technological significance because it relates to the reliability of magnetic logic and memory.