The Calculations of Dynamical Magnetization Distributions for Ferromagnetic Materials by GPS-RK4

• Main Authors: Yu-Ling Ku, 辜玉玲
• Other Authors: Chein-Shan Liu
• Format: Others
• Language: zh-TW
• Published: 2005
• Online Access: http://ndltd.ncl.edu.tw/handle/89987476351060492175

碩士 === 國立臺灣海洋大學 === 機械與輪機工程學系 === 93 === The continuum foundations of micromagnetic thin films are the Maxwell equations and the Landau-Lifshitz equation. Therefore, this thesis uses the Landau-Lifshitz equation to predict the magnetization evolution and hysteresis behavior of ferromagnetic thin films under applied field. An accurate magnetization requires that both the reversible and irreversible components of the magnetization be modeled. The classical Landau-Lifshitz model computes only the irreversible component of the magnetization. We first subject the Landau-Lifshitz equation to an AC external field by performing a closed-form solution and the resulting hysteresis loop is displayed to show its deficiency. Then we modify the Landau-Lifshitz model into a reversible part and an irreversible part accompanying with the switching criteria between these two states. With the new solutions we discuss the influence of the parameters on the hysteresis loops of magnetic materials. The new method which combines with the group preserving scheme and the Runge-Kutta method not only conserves the magnetization magnitude and has a four order accuracy, but also preserves the Lyapunov property of the Landau-Lifshitz equation. In the limit of zero damping, the new method also well conserves the free energy constant in time. Numerical tests are performed to confirm the effectiveness of GPS-RK4 method.