Department of Physics, Oakland University, Rochester, MI 48309, USA.
J Phys Condens Matter. 2010 Apr 7;22(13):136001. doi: 10.1088/0953-8984/22/13/136001. Epub 2010 Mar 12.
It is demonstrated analytically that the spectrum of small-amplitude spatially uniform magnetization excitations in an in-plane magnetized magnetic pillar with two ferromagnetic layers coupled by dipole-dipole interaction can be approximately described by the traditional Kittel formula with reduced saturation magnetization and effective anisotropy field. The spectrum consists of a quasi-symmetric and a quasi-antisymmetric mode, and the apparent reduction of saturation magnetization for the quasi-symmetric mode (≤50%) is much larger than that for the quasi-antisymmetric mode (≤10%). The effect of dynamic dipolar coupling between the nano-pillar layers could be partly responsible for the apparent reduction of static magnetization seen in many spin-torque experiments performed on magnetic nano-pillars.
理论分析表明，在由偶极力耦合的两层铁磁材料构成的面内磁化的磁性圆柱中，小振幅空间均匀磁化激发的能谱可以用传统的 Kittel 公式近似描述，其中饱和磁化强度和有效各向异性场都有所降低。该能谱由一个准对称模式和一个准反对称模式组成，准对称模式的饱和磁化强度明显降低（≤50%），比准反对称模式的降低幅度（≤10%）大得多。纳米柱层之间的动态偶极力耦合的影响可能部分解释了在许多针对磁性纳米柱的自旋扭矩实验中观察到的静态磁化强度的明显降低。
