Abstract
我們由Landau-Lifshitz-Gilbert方程式推導出磁壁的運動方程式,利用此方程式可以分析磁壁在任何方向以及任意大小的橫向場(垂直於異向性軸方向的外加磁場)下的運動行為.當平行於異向性軸方向的外加磁場(驅動場),大(小)於Walker的臨界場時,磁壁為震盪(穩定)態運動.我們的方程式,無論磁壁是在震盪或穩定態運動皆可適用.近年來根據自旋波(spinwave)理論發現磁性材料的阻尼與自旋波的波向量有關,於是Bar'yakhtar基於Landau-Lifshitz方程式導出一個更廣義的方程式,其結果更能符合自旋波理論.Bar'yakhtar方程式與Landau-Lifshitz方程式不同之處除了考慮空間色散引起的阻尼外,局部的磁化量不守恆也是不可避免的效應.我們根據Bar'yakhtar的方程式導出磁壁的運動方程式,研究顯示磁化量不守恆也會造阻尼效應.進一步推導磁壁的Mobility,發現由Mobility得到的阻尼,與由鐵磁共振的實驗得到的阻尼,理論上並不相同.而且透過這兩種阻尼的關係式可看出,兩種阻尼的值差距越大,表示由於磁化量不守恆引起的阻尼效應越顯著.換句話說,若兩種阻尼的值很接近,那麼用Landau-Lifshitz-Gilbert方程式得到的結果,與Bar'yakhtar方程式得到的結果相差不大.我們還可以用此關係式推算磁性材料的磁化係數,對於那些異向性場大於飽和磁化量的iron garnets,我們得到的磁化係數與自旋波理論預測的結果非常接近.關於外加磁場作用的分析,發現驅動場對磁化量不守恆的影響有放大的作用,而橫向場卻有壓抑的作用.The generalized Slonczewski equations have been applied to studythe influenceof the field normal to the anisotropy axis on theWalker critical field, critical velocity and the maximumvelocity of the steady-state domain wall motion. It is shownthat the maximum value of the steady-state velocity of thedomain wall is the Schlomann limiting velocity which is drivefield dependent. The dependences of the Walker critical fieldand velocity as well as Schlomann limiting velocity on the fieldnormal to the anisotropy axis have been obtained. The newequations take into account the relaxational dynamics ofmagnetization modulus first introduced into the Landau-Lifshitzequation by Bar'yakhtar. In the derivation of linear mobility, anew expression of a relaxation parameter is obtained. Itreaveals a relation between ferromagnetic resonance(FMR) linewidth and the relaxation parameter obtained from mobilitymeasurement. Based on this relation, it is found that thenonconservation of magnetization modulus gives rise to a largercontribution to the domain wall drag in ferromagnets with anarrower FMR line width than in ones with a wider line width.The description of the steady state domain wall motion in thetraditional Landau-Lifshitz-Gilbert equation may giveessentially the same dependency upon the drive field andtransverse field provided if the phenomenological relaxationconstant is deduced directly from experimental data on thedomain wall mobility, instead of from a ferromagnet with a wideresonance line width. It is also found that the drag force dueto nonconservation of magnetization modulus is enhanced by drivefield but depressed by transeverse field.