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Register a new userAsymptotic behavior for the 1-D stochastic Landau Lifshitz Bloch equation
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The stochastic Landau-Lifshitz-Bloch equation describes the phase spins in a ferromagnetic material and has significant role in simulating heat-assisted magnetic recording. In this paper, we consider the deviation of the solution to the 1-D stochastic Landau-Lifshitz-Bloch equation, that is, we give the asymptotic behavior of the trajectory $frac{u_varepsilon-u_0}{sqrt{varepsilon}lambda(varepsilon)}$ as $varepsilonrightarrow 0+$, for $lambda(varepsilon)=frac{1}{sqrt{varepsilon}}$ and $1$ respectively. In other words, the large deviation principle and the central limit theorem are established respectively.
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Precise modeling of the magnetization dynamics of nanoparticles with finite size effects at fast varying temperatures is a computationally challenging task. Based on the Landau-Lifshitz-Bloch (LLB) equation we derive a coarse grained model for disordered ferrimagnets, which is both fast and accurate. First, we incorporate stochastic fluctuations to the existing ferrimagnetic LLB equation. Further, we derive a thermodynamic expression for the temperature dependent susceptibilities, which is essential to model finite size effects. Together with the zero field equilibrium magnetization the susceptibilities are used in the stochastic ferrimagnetic LLB to simulate a $5times10$ nm$^2$ ferrimagnetic GdFeCo particle with 70 % FeCo and 30 % Gd under various external applied fields and heat pulses. The obtained trajectories agree well with those of an atomistic model, which solves the stochastic Landau-Lifshitz-Gilbert equation for each atom. Additionally, we derive an expression for the intergrain exchange field which couple the ferromagnetic sublattices of a ferrimagnet. A comparison of the magnetization dynamics obtained from this simpler model with those of the ferrimagnetic LLB equation shows a perfect agreement.
We derive the Landau-Lifshitz-Bloch (LLB) equation for a two-component magnetic system valid up to the Curie temperature. As an example, we consider disordered GdFeCo ferrimagnet where the ultrafast optically induced magnetization switching under the action of heat alone has been recently reported. The two-component LLB equation contains the longitudinal relaxation terms responding to the exchange fields from the proper and the neighboring sublattices. We show that the sign of the longitudinal relaxation rate at high temperatures can change depending on the dynamical magnetization value and a dynamical polarisation of one material by another can occur. We discuss the differences between the LLB and the Baryakhtar equation, recently used to explain the ultrafast switching in ferrimagnets. The two-component LLB equation forms basis for the largescale micromagnetic modeling of nanostructures at high temperatures and ultrashort timescales.
In this paper, we consider homogenization of the Landau-Lifshitz equation with a highly oscillatory material coefficient with period $varepsilon$ modeling a ferromagnetic composite. We derive equations for the homogenized solution to the problem and the corresponding correctors and obtain estimates for the difference between the exact and homogenized solution as well as corrected approximations to the solution. Convergence rates in $varepsilon$ over times $O(varepsilon^sigma)$ with $0leq sigmaleq 2$ are given in the Sobolev norm $H^q$, where $q$ is limited by the regularity of the solution to the detailed Landau-Lifshitz equation and the homogenized equation. The rates depend on $q$, $sigma$ and the the number of correctors.
In this work, we derive the Landau-Lifshitz-Bloch equation accounting for the multi-domain antiferromagnetic (AFM) lattice at finite temperature, in order to investigate the domain wall (DW) motion, the core issue for AFM spintronics. The continuity equation of the staggered magnetization is obtained using the continuum approximation, allowing an analytical calculation on the domain wall dynamics. The influence of temperature on the static domain wall profile is investigated, and the analytical calculations reproduce well earlier numerical results on temperature gradient driven saturation velocity of the AFM domain wall, confirming the validity of this theory. Moreover, it is worth noting that this theory could be also applied to dynamics of various wall motions in an AFM system. The present theory represents a comprehensive approach to the domain wall dynamics in AFM materials, a crucial step toward the development of AFM spintronics.
The detailed derivation of the quantum Landau-Lifshitz-Bloch (qLLB) equation for simple spin-flip scattering mechanisms based on spin-phonon and spin-electron interactions is presented and the approximations are discussed. The qLLB equation is written in the form, suitable for comparison with its classical counterpart. The temperature dependence of the macroscopic relaxation rates is discussed for both mechanisms. It is demonstrated that the magnetization dynamics is slower in the quantum case than in the classical one.
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