Department of Physics, Kansas State University, Manhattan, KS 66506-2601, USA.
J Phys Condens Matter. 2010 Sep 22;22(37):376002. doi: 10.1088/0953-8984/22/37/376002. Epub 2010 Aug 31.
Vortex states in thin circular magnetic nanodots are studied using auxiliary constraining fields as a way to map out the potential energy space of a vortex, while avoiding a rigid vortex approximation. In the model, isotropic Heisenberg exchange competes with the demagnetization field caused by both surface and volume magnetization charge densities. The system energy is minimized while applying a constraint on the vortex core position, using Lagrange's method of undetermined multipliers. The undetermined multiplier is seen to be the external field needed to hold the vortex core in place at a desired radial distance r from the dot center. This auxiliary field is applied only in the core region of the vortex. For a uniform nanodot, the potential energy is found to be very close to parabolic with r, as in the rigid vortex approximation, while the constraining field increases linearly with r. Effects of nonmagnetic impurities and holes in the medium can also be estimated. An impurity or hole in the dot can lead to bistable operation between the two minima that result under the application of a transverse applied magnetic field.
使用辅助约束场研究了薄圆形磁性纳米点中的涡旋态，作为绘制涡旋势能空间的一种方法，同时避免了刚性涡旋近似。在该模型中，各向同性海森堡交换与由表面和体积磁化电荷密度引起的退磁场竞争。通过使用拉格朗日未定乘子法对涡旋核位置施加约束，使系统能量最小化。未确定的乘数是保持涡旋核在期望的半径 r 处固定在纳米点中心的外部场。这个辅助场仅应用于涡旋的核心区域。对于均匀的纳米点，发现势能与 r 非常接近抛物线，就像在刚性涡旋近似中一样，而约束场与 r 呈线性增加。也可以估计非磁性杂质和介质中的孔的影响。纳米点中的杂质或孔会导致在施加横向外磁场下产生的两个最小值之间的双稳操作。
