Hussain Bushra, Cottam Michael G
Department of Physics and Astronomy, University of Western Ontario, London, Ontario N6A 3K7, Canada.
J Phys Condens Matter. 2022 Sep 2;34(44). doi: 10.1088/1361-648X/ac8a82.
A spin-wave (SW) theory that includes the long-range dipole-dipole interactions is presented for monolayers of van der Waals (vdW) ferromagnets for which the magnetic ions lie on a two-dimensional honeycomb lattice. The dipolar interactions provide an additional anisotropy in these materials, along with the Ising exchange interaction and/or single-ion anisotropies that typically stabilize the two-dimensional magnetic ordering. Analytical results for the linearized SW energies are obtained for the ferromagnets in two geometries: complete films and finite-width stripes (or ribbons). In both cases it is found that the inclusion of the dipole-dipole interactions leads to a shift and sometimes a splitting of the magnetic modes in the vdW structure. Also, in the latter case, where the edges are assumed to be along the zigzag lattice directions, the dipole-dipole interactions are found to play a role, as well as the exchange interactions, in modifying the localized edge SWs. Numerical examples are given, including applications to the ferromagnet CrI.
本文提出了一种自旋波（SW）理论，该理论包含长程偶极 - 偶极相互作用，适用于范德华（vdW）铁磁体单层，其中磁性离子位于二维蜂窝晶格上。偶极相互作用在这些材料中提供了额外的各向异性，同时还有伊辛交换相互作用和/或通常稳定二维磁有序的单离子各向异性。针对两种几何形状的铁磁体，即完整薄膜和有限宽度条纹（或带），获得了线性化SW能量的解析结果。在这两种情况下，都发现包含偶极 - 偶极相互作用会导致vdW结构中磁模式的偏移，有时还会导致分裂。此外，在后一种情况下，假设边缘沿锯齿形晶格方向，发现偶极 - 偶极相互作用以及交换相互作用在修改局域边缘SW方面都发挥了作用。文中给出了数值示例，包括应用于铁磁体CrI的情况。
