By introducing biquadratic together with usual bilinear ferromagnetic nearest neighbor exchange interaction in a square lattice, we find that the energy of the spin-wave mode is minimized at a finite wavevector for a vanishingly small Dzyaloshinskii–Moriya interaction (DMI), supporting a ground state with spin-spiral structure whose pitch length is unusually short as found in some of the experiments. Apart from reproducing the magnetic structures that can be obtained in a canonical model with nearest neighbor exchange interaction only, a numerical simulation of this model with further introduction of magnetic anisotropy and magnetic field predicts many other magnetic structures some of which are already observed in the experiments. Among many observed structures, nanoscale skyrmion even at vanishingly small DMI is found for the first time in a model. The model provides the nanoscale skyrmions of unit topological charge at zero magnetic field as well. We obtain phase diagrams for all the magnetic structures predicted in the model.

通过在方形晶格中引入双二次和通常的双线性铁磁最近邻交换相互作用，我们发现自旋波模式的能量在有限波矢量处最小化，用于极小的 Dzyaloshinskii-Moriya 相互作用（DMI），支持基态在一些实验中发现其螺距长度异常短的自旋螺旋结构。除了在仅具有最近邻交换相互作用的规范模型中再现磁结构外，进一步引入磁各向异性和磁场的该模型的数值模拟预测了许多其他磁结构，其中一些已在实验中观察到. 在许多观察到的结构中，首次在模型中发现了即使在极小的 DMI 下的纳米级斯格明子。该模型还提供了零磁场下单位拓扑电荷的纳米级斯格明子。我们获得了模型中预测的所有磁结构的相图。