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Reflection and refraction process of spinwave in a ferromagnet/frustrated ferromagnet junction system

Frustration introduces a nontrivial dispersion relation of spinwave even in a ferromagnetic phase in a spin system. We study the reflection and refraction process of spinwaves in the ferromagnet/frustrated ferromagnet junction system by using the Holstein-Primakoff spinwave expansion and taking the large-S limit. We discuss the relation between the incident angle and refraction angle of spinwave, namely, the Snell's low of spinwave. As concrete examples of frustrated ferromagnets, we study the fully polarized ferromagnet phases in the J1-J2 chains and the J1-J2 model on the square lattice. The interesting refraction processes, such as the splitting of the incident spinwave and the negative refraction, are discussed. We also study the transmittance and reflectance in these concrete models.