*Article* **Magnonic Metamaterials for Spin-Wave Control with Inhomogeneous Dzyaloshinskii–Moriya Interactions**

**Fengjun Zhuo 1,2, Hang Li 1,\*, Zhenxiang Cheng 3,\* and Aurélien Manchon 4,\***


**Abstract:** A magnonic metamaterial in the presence of spatially modulated Dzyaloshinskii–Moriya interaction is theoretically proposed and demonstrated by micromagnetic simulations. By analogy to the fields of photonics, we first establish magnonic Snell's law for spin waves passing through an interface between two media with different dispersion relations due to different Dzyaloshinskii– Moriya interactions. Based on magnonic Snell's law, we find that spin waves can experience total internal reflection. The critical angle of total internal reflection is strongly dependent on the sign and strength of Dzyaloshinskii–Moriya interaction. Furthermore, spin-wave beam fiber and spinwave lens are designed by utilizing the artificial magnonic metamaterials with inhomogeneous Dzyaloshinskii–Moriya interactions. Our findings open up a rich field of spin waves manipulation for prospective applications in magnonics.

**Keywords:** spin waves; Dzyaloshinskii–Moriya interaction; ferromagnetism; spintronics
