Derivation of magnetic inertial effects from the classical mechanics of a circular current loop

Giordano, Stefano; Déjardin, Pierre-Michel

doi:10.1103/physrevb.102.214406

Cited by 32 publications

(10 citation statements)

References 62 publications

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“…The realization of such short and intense magnetic fields have been suggested recently designing magnetic-field enhancing metamaterials 32 , by the use of vector laser beams 33 or thanks to ultrafast electronic switches 34 . Finally, we anticipate that our findings will be relevant to much of the recent works in the magnetism community aimed at the understanding of inertial spin dynamics [35][36][37][38][39][40][41][42][43][44][45][46][47][48] . defined by a set of three unit vectors {e r , e θ , e φ }.…”

Section: Discussionmentioning

confidence: 99%

Magnetization switching in the inertial regime

Neeraj,

Pancaldi,

Scalera

et al. 2021

Preprint

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We have numerically solved the Landau-Lifshitz-Gilbert (LLG) equation in its standard and inertial forms to study the magnetization switching dynamics in a 3d thin film ferromagnet. The dynamics is triggered by ultrashort magnetic field pulses of varying width and amplitude in the picosecond and Tesla range. We have compared the solutions of the two equations in terms of switching characteristic, speed and energy analysis. Both equations return qualitatively similar switching dynamics, characterized by regions of slower precessional behavior and faster ballistic motion. In case of inertial dynamics, ballistic switching is found in a 25% wider region in the parameter space given by the magnetic field amplitude and width. The energy analysis of the dynamics is qualitatively different for the standard and inertial LLG equations. In the latter case, an extra energy channel, interpreted as the kinetic energy of the system, is available. Such extra channel is responsible for a resonant energy absorption at THz frequencies, consistent with the occurence of spin nutation.

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Section: Discussionmentioning

confidence: 99%

Magnetization switching in the inertial regime

Neeraj,

Pancaldi,

Scalera

et al. 2021

Preprint

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“…A modified LLG equation has now been derived to correct this error and it includes inertial effects in magneto-dynamics [8][9][10][11][12][13][14][15][16]. This new equation predicts the presence of nutation in magneto-dynamics.…”

Section: Introductionmentioning

confidence: 99%

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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“…independent on α and γ [16]. This generalized LLG equation has been derived in the framework of different and independent theoretical contexts [15,[17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]; its solutions have been studied in a series of publications [33][34][35][36]. The main consequence of inertia for the uniform magnetization (magnon with the wavevector k = 0) is the existence of nutation oscillations that are superimposed to the precession.…”

Section: Introductionmentioning

confidence: 99%

Anatomy of inertial magnons in ferromagnets

Lomonosov,

Temnov,

Wegrowe

2021

Preprint

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We analyze dispersion relations of magnons in ferromagnetic nanostructures with uniaxial anisotropy taking into account inertial terms, i.e. magnetic nutation. Inertial effects are parametrized by damping-independent parameter β, which allows for an unambiguous discrimination of inertial effects from Gilbert damping parameter α. The analysis of magnon dispersion relation shows its two branches are modified by the inertial effect, albeit in different ways. The upper nutation branch starts at ω = 1/β, the lower branch coincides with FMR in the long-wavelength limit and deviates from the zero-inertia parabolic dependence ≃ ωF M R + Dk 2 of the exchange magnon. Taking a realistic experimental geometry of magnetic thin films, nanowires and nanodiscs, magnon eigenfrequencies, eigenvectors and Q-factors are found to depend on the shape anisotropy. The possibility of phase-matched magneto-elastic excitation of nutation magnons is discussed and the condition was found to depend on β, exchange stiffness D and the acoustic velocity.

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Derivation of magnetic inertial effects from the classical mechanics of a circular current loop

Cited by 32 publications

References 62 publications

Magnetization switching in the inertial regime

Magnetization switching in the inertial regime

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

Anatomy of inertial magnons in ferromagnets

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