Nonlinear Auto-Oscillator Theory of Microwave Generation by Spin-Polarized Current

Slavin, A. N.; Tiberkevich, Vasil

doi:10.1109/tmag.2008.2009935

Cited by 739 publications

(1,125 citation statements)

References 141 publications

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“…Anisotropy-mediated magnon interactions dominate in the long-wave lengths regime considered here [58][59][60]. Adopting the Markov approximation and to leading order in the magnon density, we arrive at a dissipative discrete nonlinear Schrödinger (DNLS) equation with stochastic sources and a local interaction,…”

Section: E Magnon-magnon Interactionsmentioning

confidence: 99%

Energy repartition in the nonequilibrium steady state

2017

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The concept of temperature in nonequilibrium thermodynamics is an outstanding theoretical issue. We propose an energy repartition principle that leads to a spectral (mode-dependent) temperature in steady-state nonequilibrium systems. The general concepts are illustrated by analytic solutions of the classical Heisenberg spin chain connected to Langevin heat reservoirs with arbitrary temperature profiles. Gradients of external magnetic fields are shown to localize spin waves in a Wannier-Zeemann fashion, while magnon interactions renormalize the spectral temperature. Our generic results are applicable to other thermodynamic systems such as Newtonian liquids, elastic solids, and Josephson junctions.

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Section: E Magnon-magnon Interactionsmentioning

confidence: 99%

Energy repartition in the nonequilibrium steady state

2017

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“…As it has been seen that spin-transfer torques can redistribute energy across fluctuation modes in a nanomagnet [34,35], competing fluctuation modes could be the origin of a distribution of switching pathways. We begin with a Gaussian distribution of switching rates i , each with their own energy barrier ξ i .…”

Section: Testing the Model: Switching Field Distributions Under Cmentioning

confidence: 99%

Switching field distributions with spin transfer torques in perpendicularly magnetized spin-valve nanopillars

et al. 2014

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We present switching field distributions of spin-transfer-assisted magnetization reversal in perpendicularly magnetized Co/Ni multilayer spin-valve nanopillars at room temperature. Switching field measurements of the Co/Ni free layer of spin-valve nanopillars with a 50 nm × 300 nm ellipse cross section were conducted as a function of current. The validity of a model that assumes a spin-current-dependent effective barrier for thermally activated reversal is tested by measuring switching field distributions under applied direct currents. We show that the switching field distributions deviate significantly from the double exponential shape predicted by the effective barrier model, beginning at applied currents as low as half of the zero field critical current. Barrier heights extracted from switching field distributions for currents below this threshold are a monotonic function of the current. However, the thermally induced switching model breaks down for currents exceeding the critical threshold.

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“…In light of these differences, our formula can be regarded as a generalization of the formulae in Ref. [25].…”

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confidence: 99%

“…The term ∆ω 0 /(2π) in Eq. (9) arises from the phase fluctuation and is called the phase noise or linear linewidth [25]. On the other hand, the term ∆ω 0 ν 2 /(2π) [25].…”

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Linewidth of power spectrum originated from thermal noise in spin torque oscillator

Taniguchi

2014

Appl. Phys. Express

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A theoretical formula of the linewidth caused by the thermal activation in a spin torque oscillator with a perpendicularly magnetized free layer and an in-plane magnetized pinned layer was developed by solving the stochastic Landau-Lifshitz-Gilbert equation in the energy-phase representation. It is shown that the linewidth can be suppressed down to 0.1 MHz by applying a large current (10 mA for typical material parameters). A quality factor larger than 10 4 is predicted in the large current limit, which is two orders of magnitude larger than the recently observed experimental value.The spin torque oscillator (STO) [1-6] is a promising candidate for a future nanocommunication device because of its small size, high emission power, and frequency tunability. Recently, it was found [7,8] that an STO with a perpendicularly magnetized free layer and an in-plane magnetized pinned layer [9-14] can achieve a large emission power of close to 1 µW. Therefore, this type of STO will be the model structure for practical STO applications.Another important quantity characterizing the STO's properties is the linewidth ∆f of the power spectrum. For example, a narrow linewidth is necessary to obtain a high quality factor (Q-factor) Q = f 0 /∆f , where f 0 is the peak frequency of the power spectrum. The physical origin of the linewidth is the nonuniform magnetization dynamics due to thermal activation. Therefore, theoretical evaluation of the linewidth due to thermal activation and of the Q-factor is desirable to clarify the theoretically possible values of these parameters.In the self-oscillation state of an STO, the energy supplied by the spin torque balances the energy dissipation due to damping; therefore, the magnetization steadily precesses almost on a constant energy curve. This situation is very similar to magnetization switching in the thermally activated region, where the magnetization precesses on a constant energy curve many times during switching. Recent studies [15][16][17][18][19][20] have shown that the energy-phase representation of the Landau-LifshitzGilbert (LLG) equation is useful for theoretical investigations of the magnetization switching properties, such as the switching probability, in the thermally activated region. Accordingly, we were motivated to develop a theory of the linewidth of an STO based on the LLG equation in the energy-phase representation.In this letter, the theoretical formula for the linewidth of an STO is derived on the basis of the LLG equation in the energy-phase representation. It is shown that the linewidth can be suppressed to 0.1 MHz by applying a large current (∼ 10 mA). The Q-factor can reach more than 10 4 in this type of STO, which is two orders of magnitude larger than the previously reported value [7]. netization directions of the free and pinned layers are denoted as m and p, respectively. The z-axis is normal to the film-plane, and the x-axis is parallel to p. The external field H appl is applied along the z-axis. The current I flows uniformly along the z-axis, where positive...

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Nonlinear Auto-Oscillator Theory of Microwave Generation by Spin-Polarized Current

Cited by 739 publications

References 141 publications

Energy repartition in the nonequilibrium steady state

Energy repartition in the nonequilibrium steady state

Switching field distributions with spin transfer torques in perpendicularly magnetized spin-valve nanopillars

Linewidth of power spectrum originated from thermal noise in spin torque oscillator

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