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Magnetization dynamics, Bennett clocking and associated energy dissipation in multiferroic logic

机译：多铁性逻辑中的磁化动力学，贝内特时钟和相关的能量耗散

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It has been recently shown that the magnetization of a multiferroic nanomagnet, consisting of a magnetostrictive layer elastically coupled to a piezoelectric layer, can be rotated by a large angle if a tiny voltage of a few tens of millivolts is applied to the piezoelectric layer. The potential generates stress in the magnetostrictive layer and rotates its magnetization by ～ 90° to implement Bennett clocking in nanomagnetic logic chains. Because of the small voltage needed, this clocking method is far more energy efficient than those that would employ spin transfer torque or magnetic fields to rotate the magnetization. In order to assess if such a clocking scheme can also be reasonably fast, we have studied the magnetization dynamics of a multiferroic logic chain with nearest-neighbor dipole coupling using the Landau-Lifshitz-Gilbert (LLG) equation. We find that clock rates of 2.5GHz are feasible while still maintaining the exceptionally high energy efficiency. For this clock rate, the energy dissipated per clock cycle per bit flip is ～ 52 000kT at room temperature in the clocking circuit for properly designed nanomagnets. Had we used spin transfer torque to clock at the same rate, the energy dissipated per clock cycle per bit flip would have been ～ 4 × 108kT, while with current transistor technology we would have expended ～ 106kT. For slower clock rates of 1GHz, stress-based clocking will dissipate only ～ 200kT of energy per clock cycle per bit flip, while spin transfer torque would dissipate about 108kT. This shows that multiferroic nanomagnetic logic, clocked with voltage-generated stress, can emerge as a very attractive technique for computing and signal processing since it can be several orders of magnitude more energy efficient than current technologies.
机译：最近已经显示出，如果将几十毫伏的微小电压施加到压电层上，则多弹性铁纳米磁体的磁化可以大角度旋转，该多铁纳米磁体由弹性地耦合至压电层的磁致伸缩层构成。电位在磁致伸缩层中产生应力，并将其磁化旋转约90°，以在纳米磁逻辑链中实现Bennett计时。由于所需的电压较小，因此该计时方法比采用自旋传递转矩或磁场旋转磁化的方法更节能。为了评估这种计时方案是否也可以相当快，我们使用Landau-Lifshitz-Gilbert（LLG）方程研究了具有最近邻居偶极耦合的多铁逻辑链的磁化动力学。我们发现2.5GHz的时钟速率是可行的，同时仍保持了极高的能效。对于这种时钟速率，在室温下，对于设计合理的纳米磁铁，在时钟电路中，每个时钟周期每位翻转所耗散的能量约为52 000kT。如果我们使用自旋传递转矩以相同的速率计时，则每个时钟周期每位翻转的能量消耗约为4×108kT，而采用电流晶体管技术，则将消耗〜106kT。对于1GHz的较慢时钟速率，基于应力的时钟在每个位翻转的每个时钟周期仅消耗约200kT的能量，而自旋传递扭矩将消耗约108kT的能量。这表明，以电压产生应力为时钟源的多铁纳米磁逻辑可以成为一种非常吸引人的计算和信号处理技术，因为它的能源效率比当前技术高几个数量级。

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