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We study the theoretical conditions to excite a stable self-oscillation in a spin torque oscillator with an in-plane magnetized free layer and a perpendicularly magnetized pinned layer in the presence of magnetic field pointing in an…

Mesoscale and Nanoscale Physics · Physics 2016-05-06 Tomohiro Taniguchi , Hitoshi Kubota

The Landau-Lifshitz-Gilbert-Slonczewski equation describes magnetization dynamics in the presence of an applied field and a spin polarized current. In the case of axial symmetry and with focus on one space dimension, we investigate the…

Analysis of PDEs · Mathematics 2017-03-31 Christof Melcher , Jens D. M. Rademacher

The magnetization dynamics of spin torque oscillator (STO) consisting of a perpendicularly magnetized free layer and an in-plane magnetized pinned layer was studied by solving the Landau-Lifshitz-Gilbert equation. We derived the analytical…

Mesoscale and Nanoscale Physics · Physics 2014-02-07 Tomohiro Taniguchi , Hiroko Arai , Hitoshi Kubota , Hiroshi Imamura

The ultra-fast magnetisation relaxation rates during the laser-induced magnetisation process are analyzed in terms of the Landau-Lifshitz-Bloch (LLB) equation for different values of spin $S$. The LLB equation is equivalent in the limit $S…

Materials Science · Physics 2015-05-20 U. Atxitia , O. Chubykalo-Fesenko

We simulate the stochastic Landau-Lifshitz-Gilbert (LLG) dynamics of a uniaxial nanomagnet out to sub-millisecond timescales using a graphical processing unit based micromagnetic code and determine the effect of geometrical tilts between…

Mesoscale and Nanoscale Physics · Physics 2013-02-05 D. Pinna , Aditi Mitra , D. L. Stein , A. D. Kent

It is crucially important to investigate effects of temperature on magnetic properties such as critical phenomena, nucleation, pinning, domain wall motion, coercivity, etc. The Landau-Lifshitz-Gilbert (LLG) equation has been applied…

Materials Science · Physics 2015-07-14 Masamichi Nishino , Seiji Miyashita

The magnetization reversal of Stoner particles is investigated from the point of view of nonlinear dynamics within the Landau-Lifshitz-Gilbert formulation. The following results are obtained. 1) We clarify that the so-called…

Materials Science · Physics 2009-11-11 Z. Z. Sun , X. R. Wang

The Landau-Lifshitz-Gilbert (LLG) equation is widely used to describe magnetization dynamics. We develop a unified framework of the microscopic LLG equation based on the nonequilibrium Green's function formalism. We present a unified…

Mesoscale and Nanoscale Physics · Physics 2023-10-16 Fuming Xu , Gaoyang Li , Jian Chen , Zhizhou Yu , Lei Zhang , Baigeng Wang , Jian Wang

In this paper we show that the spin transfer torque can be described by a pseudo magnetic field, proportional to the magnetic moment of the itinerant electrons that enters the Landau-Lifshitz-Gilbert equation in the same way as other…

Mesoscale and Nanoscale Physics · Physics 2008-11-24 Sayeef Salahuddin , Deepanjan Datta , Supriyo Datta

A macroscopic equation of motion for the magnetization of a ferromagnet at elevated temperatures should contain both transverse and longitudinal relaxation terms and interpolate between Landau-Lifshitz equation at low temperatures and the…

Statistical Mechanics · Physics 2009-10-31 D. A. Garanin

There is little doubt that the magnetization dynamics of ferromagnetic systems is governed by the Landau-Lifshitz-Gilbert equation or its generalization with various spin torques. In contrast, there are several sets of dynamic equations for…

Mesoscale and Nanoscale Physics · Physics 2019-08-05 H. Y. Yuan , Qian Liu , Ke Xia , Zhe Yuan , X. R. Wang

Here we consider the magnetization dynamics in ferromagnetic nanoparticles or films driven by external magnetic field pulses directed transverse to the initial equilibrium state. The excitation pulse drives large-angle ultra-fast…

Dynamical Systems · Mathematics 2024-10-23 Alessandro Fortunati , Massimiliano d'Aquino , Claudio Serpico

A keen interest towards technological implications of spin-orbit driven magnetization dynamics requests a proper theoretical description, especially in the context of a microscopic framework, to be developed. Indeed, magnetization dynamics…

Mesoscale and Nanoscale Physics · Physics 2018-11-22 Anastasiia A. Pervishko , Mikhail I. Baglai , Olle Eriksson , Dmitry Yudin

We show that spin-polarized dc current passing through a small magnetic element induces two-state, random telegraph switching of the magnetization via the spin-momentum transfer effect. The resistances of the states differ by up to 50% of…

The current-induced magnetisation dynamics in a ferromagnet at elevated temperatures can be described by the Landau--Lifshitz--Bloch (LLB) equation with spin-torque terms. In this paper, we focus on the regime above the Curie temperature.…

Numerical Analysis · Mathematics 2025-06-30 Agus L. Soenjaya

We consider the numerical approximation of the inertial Landau-Lifshitz-Gilbert equation (iLLG), which describes the dynamics of the magnetization in ferromagnetic materials at subpicosecond time scales. We propose and analyze two fully…

Numerical Analysis · Mathematics 2021-10-07 Michele Ruggeri

Spin-transfer is a typical spintronics effect that allows a ferromagnetic layer to be switched by spin-injection. Most of the experimental results about spin transfer are described on the basis of the Landau-Lifshitz-Gilbert equation of the…

Materials Science · Physics 2015-06-25 J. -E. Wegrowe , C. Ciornei , H. -J. Drouhin

A number of recent experimental works have shown that the dynamics of a single spin torque oscillator can exhibit complex behavior that stems from interactions between two or more modes of the oscillator. Examples are observed mode-hopping…

Mesoscale and Nanoscale Physics · Physics 2013-12-02 Olle Heinonen , Yan Zhou , Dong Li

Simulations of magnetization dynamics in a multiscale environment enable rapid evaluation of the Landau-Lifshitz-Gilbert equation in a mesoscopic sample with nanoscopic accuracy in areas where such accuracy is required. We have developed a…

Computational Physics · Physics 2016-11-28 Andrea De Lucia , Benjamin Krüger , Oleg A. Tretiakov , Mathias Kläui

We study the switching-process of the magnetization in a ferromagnetic-normal-metal multilayer system by a spin polarized electrical current via the spin transfer torque. We use a spin drift-diffusion equation (SDDE) and the…

Mesoscale and Nanoscale Physics · Physics 2013-01-16 M. Wenin , A. Windisch , W. Poetz