磁涡旋极性翻转的局域能量∗

摘要

The polarity of magnetic vortex core can be switched by current or magnetic field through a vortex-antivortex pair creation and annihilation process, in which the significant change of the exchange energy during the switching takes an important role. To further unveil the energetic origin of magnetic vortex switching, we investigate the evolution of the maximum exchange energy density of the sample by using micromagnetic finite-element simulations based on the Landau-Lifshitz-Gilbert equation including the adiabatic and the nonadiabatic spin torque terms. Our micromagnetic calculations indicate that maximum exchange energy density for the considered sample must exceed a critical value of∼3.0 × 106 J/m3 in order to achieve the magnetic vortex switching. The threshold value corresponds to the maximum exchange energy density at the time of creation of new vortex-antivortex pair. Following the nucleation of antivortex, the maximum exchange energy density increases rapidly with the antivortex approaching the original vortex. The maximum exchange energy density can become large at the time of annihilation of two vortexes. To explain well the critical value of the local maximum exchange energy density, we use the rigid vortex model (in which the spin distribution is unchangeable while vortex is displaced) to develop an analytical model. For a magnetic vortex confined in a thin ferromagnetic nanodisk, the magnetization distribution is unchanged along the thickness and can be seen as a two-dimensional model when the thickness is less than or on the order of the exchange length. The components of vortex magnetization vector in a ferromagnetic dot can be expressed by using a complex function w(ζ,ζ¯). Corresponding to the trivortex state appearing in vortex core reversal process, the local exchange energy density Wex around the vortexes cores is obtained. Simultaneously, we obtain the maximum exchange energy density: Wex≈2.3×106 J/m3. In a realistic system, the shape of vortexes will deform during the vortex core reversal, which leads to the analytical result lower than the simulation value. Based on this reason, the analytical result matches well with our simulation value.%针对坡莫合金纳米圆盘中的单个磁涡旋结构，采用微磁学模拟研究了磁涡旋极性翻转过程中的局域能量密度。磁涡旋的极性翻转通过与初始涡旋极性相反的涡旋与反涡旋对的生成，以及随后发生的反涡旋与初始涡旋的湮没来实现。模拟结果显示当纳米圆盘样品中局域能量密度的最大值达到一临界值时，磁涡旋将会实现极性翻转，其中交换能起主导作用。基于涡旋极性翻转过程中出现的三涡旋态结构，应用刚性磁涡旋模型对局域交换能量密度进行了理论分析。通过刚性磁涡旋模型得到的磁涡旋极性翻转所需的局域交换能量密度的临界值与模拟结果符合得较好。