Chaos Theory and Sensitive Dependence on Initial Conditions

Hollar, David

doi:10.1007/978-3-319-59626-6_9

Cited by 1 publication

(2 citation statements)

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“…This happens because the fate of a switching trajectory, i. e. whether it ends up being a switching success or failure, is influenced by what happens in the first few ps after the switching field is turned on (i. e. when nutation takes place), even though the entire switching process takes ~ns. This is reminiscent of "chaos theory", where small differences in initial conditions can yield very different outcomes even if the system is deterministic, meaning that it evolves according to a deterministic equation [17][18][19]. Stated differently, the system trajectory is extremely sensitive to initial condition or the initial behaviour.…”

Section: Introductionmentioning

confidence: 99%

“…when nutation takes place), even though the entire switching process takes ∼ns. This is reminiscent of 'chaos theory', where small differences in initial conditions can yield very different outcomes even if the system is deterministic, meaning that it evolves according to a deterministic equation [17][18][19]. Stated differently, the system trajectory is extremely sensitive to initial condition or the initial behaviour.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An observable effect of spin inertia in slow magneto-dynamics: Increase of the switching error rates in nanoscale ferromagnets

Rahman¹,

Bandyopadhyay²

2021

J. Phys.: Condens. Matter

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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, i.e. 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 holds 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.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%