The LandauLifshitzGilbert (LLG) equation, used to model magnetodynamics 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 magnetodynamics 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 magnetodynamics. 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, i.e.more »
The Cost of EnergyEfficiency in Digital Hardware: The TradeOff between Energy Dissipation, Energy–Delay Product and Reliability in Electronic, Magnetic and Optical Binary Switches
Binary switches, which are the primitive units of all digital computing and information processing hardware, are usually benchmarked on the basis of their ‘energy–delay product’, which is the product of the energy dissipated in completing the switching action and the time it takes to complete that action. The lower the energy–delay product, the better the switch (supposedly). This approach ignores the fact that lower energy dissipation and faster switching usually come at the cost of poorer reliability (i.e., a higher switching error rate) and hence the energy–delay product alone cannot be a good metric for benchmarking switches. Here, we show the tradeoff between energy dissipation, energy–delay product and error–probability for an electronic switch (a metal oxide semiconductor field effect transistor), a magnetic switch (a magnetic tunnel junction switched with spin transfer torque) and an optical switch (bistable nonlinear mirror). As expected, reducing energy dissipation and/or energy–delay product generally results in increased switching error probability and reduced reliability.
 Award ID(s):
 2001255
 Publication Date:
 NSFPAR ID:
 10251180
 Journal Name:
 Applied Sciences
 Volume:
 11
 Issue:
 12
 Page Range or eLocationID:
 5590
 ISSN:
 20763417
 Sponsoring Org:
 National Science Foundation
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