An analytical work on intrinsic localized modes in a two-dimensional Heisenberg ferromagnet on the checkerboard lattice is presented. Taking advantage of an asymptotic method, the governing lattice dynamical equations are reduced to one (2+1) -dimensional nonlinear Schr\"odinger. In our work, we obtain two types of nonlinear localized mode solutions, namely, Brillouin zone center modes and Brillouin zone corner modes. The occurrence conditions for these intrinsic localized modes are given in detail. Especially, we find that the competition between the Dzialozinskii-Moriy interaction and the next-nearest neighbor interaction of the checkerboard ferromagnet has an effect on the local structure of the Brillouin zone corner acoustic mode.

中文翻译：

---

二维棋盘铁磁晶格中的本征局域模式

提出了对棋盘格上二维海森堡铁磁体的固有局域模式的分析工作。利用渐近方法，将控制晶格动力学方程简化为一（2+1）维非线性薛定谔。在我们的工作中，我们获得了两种类型的非线性局部模式解，即布里渊区中心模式和布里渊区角模。详细给出了这些固有局域模的发生条件。特别是，我们发现 Dzialozinskii-Moriy 相互作用与棋盘状铁磁体的下最近邻相互作用之间的竞争对局部结构有影响。布里渊区角声模式。