Haghshenasfard Zahra, Cottam Michael G
Department of Physics and Astronomy, The University of Western Ontario, London, Ontario N6A 3K7, Canada.
J Phys Condens Matter. 2016 May 11;28(18):186001. doi: 10.1088/0953-8984/28/18/186001. Epub 2016 Apr 6.
A microscopic (or Hamiltonian-based) theory is presented for the spin-wave instability thresholds in ferromagnetic nanowires under conditions of parallel pumping with a microwave field. A dipole-exchange Hamiltonian is employed in which the external magnetic field is either longitudinal or transverse to the length of the nanowire. This contrasts with most previous work on nonlinear spin waves which concentrate on situations where a macroscopic (or continuum) theory is appropriate. In nanowire stripes with lateral dimensions of order 100 nm or less, the quantization of the eigenmodes becomes modified due to strong spatial confinement and edge effects, making it appropriate to employ a microscopic dipole-exchange approach analogous to that used recently for ultrathin films. Numerical applications are presented for the dependence of the threshold microwave field amplitude for instability on the static applied field (the analog of the butterfly curves). The cases of longitudinal and transverse applied fields are found to lead to distinctly different behaviors, which are illustrated using EuS and permalloy as materials with different ratios of dipolar to exchange interactions. Structural effects due to the discrete spin-wave branches lead to structural aspects of the butterfly curves that are significantly modified compared with those for ultrathin films due to the edge modes in the nanowires.
本文提出了一种微观（或基于哈密顿量）理论，用于研究在微波场平行泵浦条件下铁磁纳米线中的自旋波不稳定性阈值。采用了偶极 - 交换哈密顿量，其中外部磁场与纳米线长度方向平行或垂直。这与之前大多数关于非线性自旋波的工作形成对比，那些工作主要集中在宏观（或连续介质）理论适用的情况。在横向尺寸为100纳米及以下的纳米线条纹中，由于强烈的空间限制和边缘效应，本征模的量子化会发生改变，这使得采用类似于最近用于超薄薄膜的微观偶极 - 交换方法变得合适。给出了关于不稳定性的阈值微波场振幅对静态外加磁场的依赖性的数值应用（类似于蝴蝶曲线）。发现纵向和横向外加磁场的情况会导致明显不同的行为，以具有不同偶极与交换相互作用比例的材料EuS和坡莫合金为例进行了说明。由于离散自旋波分支导致的结构效应，使得蝴蝶曲线的结构方面与超薄薄膜相比有显著改变，这是由纳米线中的边缘模式引起的。
