Micromagnetic study of statistical switching in magnetic tunnel junctions stabilized by perpendicular shape anisotropy

d’Aquino, M.; Perna, Salvatore; Serpico, C.

doi:10.1016/j.physb.2019.411744

Cited by 7 publications

(5 citation statements)

References 19 publications

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“…We now introduce the optimization approach, which is based on the Landau-Lifshitz equation [18][19][20]. We prescribe that the magnetization M(x) over the region R m will evolve according to the following equation of motion:…”

Section: B Optimization Schemementioning

confidence: 99%

Gradient-based optimization of permanent-magnet assemblies for any objective

Insinga,

Bjørk

2023

Phys. Rev. Applied

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We introduce a semianalytical optimization method that can be applied to find the optimal magnetization for any permanent-magnet system regarding the desired field or objective. Our approach is based on the Landau-Lifshitz equation, which is normally employed to simulate micromagnetic systems. Instead, we recognize that the same mathematical formalism is also applicable to the optimization of macroscopic magnetic assemblies. This point of view has the advantage of being easy to intuitively visualize and thus is also easy to implement. Our approach can also be seen as a special case of the adjoint method, which is a gradient-based constrained optimization method. However, most studies applying the adjoint method to magnet design adopt the point of topology optimization, where the magnetic permeability tensor field depends on the design variables, making the problem highly nonlinear. Instead, we restrict to the less general problem of optimizing the direction of the magnetization in any point of a given design region. Our strategy leads to a more robust and computationally efficient algorithm since the underlying problem is intrinsically simpler. Additionally, since the integration of the underlying magnetostatic equations is performed numerically, the method is still very flexible and versatile. Previously, an equivalent method has been considered only for solving the magnetic inverse problem. In the present work, we fully demonstrate its effectiveness by presenting several prototypical optimization problems and we discuss the strengths and limitations of the approach in relation to the existing optimization methods.

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Section: B Optimization Schemementioning

confidence: 99%

Gradient-based optimization of permanent-magnet assemblies for any objective

Insinga,

Bjørk

2023

Phys. Rev. Applied

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“…The current value in dimensional units, can be obtained with the following expression: J = βJ p /(2η) A/m 2 , where J p = eγM 2 s L z /(gµ B ) with γ the absolute value of the gyromagnetic ratio, e is the absolute value of the electron charge, g is the Landé factor, and µ B is the Bohr magneton. The coefficient η is the polarization factor, and is assumed to be η = 0.1 [57]. The ac current amplitude is much smaller than the dc one.…”

Section: Synchronization In Injection-locked Spin-torque Oscillatormentioning

confidence: 99%

Computational Micromagnetics based on Normal Modes: bridging the gap between macrospin and full spatial discretization

Perna,

Bruckner,

Serpico

et al. 2021

Preprint

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The Landau-Lifshitz equation governing magnetization dynamics is written in terms of the amplitudes of normal modes associated with the micromagnetic system's appropriate ground state. This results in a system of nonlinear ordinary differential equations, the right-hand side of which can be expressed as the sum of a linear term and nonlinear terms with increasing order of nonlinearity (quadratic, cubic, etc.). The application of the method to nanostructured magnetic systems demonstrates that the accurate description of magnetization dynamics requires a limited number of normal modes, which results in a considerable improvement in computational speed. The proposed method can be used to obtain a reduced-order dynamical description of magnetic nanostructures which allows to adjust the accuracy between low-dimensional models, such as macrospin, and fully spatially discretized micromagnetic models. This new paradigm for micromagnetic simulations is tested for three problems relevant to the areas of spintronics and magnonics: directional spin-wave coupling in magnonic waveguides, high power ferromagnetic resonance in a magnetic nanodot, and injection-locking in spin-torque nano-oscillators. The case studies considered the validity of the proposed approach as a new systematic method to obtain an intermediate order dynamical model based on normal modes for the analysis of magnetic nanosystems. The time-consuming calculation of the normal modes has to be done only one time for the system. These modes can be used to optimize and predict the system response for all possible time varying external magnetic fields. This is of utmost importance for various applications where a fast and accurate system response is required, such as in electronic circuit simulation software where an accurate response of the magnetic device has to be predicted.

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“…These measurements show that both t 0 and ∆t present in general skewed statistical distributions [16, 19-21, 27, 42, and 43]. The stochasticity of the STT-driven dynamics has also been analyzed theoretically in a few publications [45][46][47][48][49][50], but there has been little synergy between the experimental and theoretical approaches. At the experimental level, the choice of a specific distribution to fit the data has been seldom guided by physical considerations.…”

Section: Introductionmentioning

confidence: 99%

“…At the experimental level, the choice of a specific distribution to fit the data has been seldom guided by physical considerations. At the theoretical level, exact but rather complex and mathematically non-explicit distribution functions have been proposed [45][46][47][48][49][50], which prevent an intuitive understanding of the underlying physical processes and limit the applicability of the derived equations. In addition, most theoretical models rest on the assumption of coherent macrospin dynamics, which is rarely fulfilled.…”

Section: Introductionmentioning

confidence: 99%

Deterministic and stochastic aspects of current-induced magnetization reversal in perpendicular nanomagnets

et al. 2023

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We study the incubation and transition times that characterize the magnetization switching induced by spin-orbit torques in nanomagnets with perpendicular anisotropy. We present a phenomenological model to interpret the dependence of the incubation time on the amplitude of the voltage pulse and assisting magnetic field, and estimate the volume of the seed domain that triggers the switching. Our measurements evidence a correlation between the incubation and transition times that is mediated by the temperature variation during the electric pulse. In addition, we discuss the stochastic distributions of the two times in terms of the energy barriers opposing the nucleation and expansion of the seed domain. We propose two models based on the log-normal and gamma functions to account for the different origin of the variability of the incubation and transition times, which are associated with a single nucleation barrier and multiple pinning sites, respectively.

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Micromagnetic study of statistical switching in magnetic tunnel junctions stabilized by perpendicular shape anisotropy

Cited by 7 publications

References 19 publications

Gradient-based optimization of permanent-magnet assemblies for any objective

Gradient-based optimization of permanent-magnet assemblies for any objective

Computational Micromagnetics based on Normal Modes: bridging the gap between macrospin and full spatial discretization

Deterministic and stochastic aspects of current-induced magnetization reversal in perpendicular nanomagnets

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