Goos-H\"{a}nchen effect of spin waves at heterochiral interfaces

We theoretically investigate the Goos-H\"{a}nchen (GH) effect of spin-wave beams reflected from the interface between two ferromagnetic films with different Dzyaloshinskii-Moriya interactions (DMIs). The formula of the GH shift as functions of the incident angle and material parameters is derived analytically. We show that the GH effect occurs only when spin waves are totally reflected at the interface and vanishes otherwise. We further explore the GH shift of spin waves by narrow DMI strips of different widths. It is found that the induced shift is independent of the strip width down to $10$ nm, offering a novel approach to measure the DMI strength of ultra-narrow magnetic strips which is out the scope of current technology. Full micromagnetic simulations compare well with our theoretical findings. Strong distortion of edge magnetizations for narrower strips however generates a width dependence of the GH shift. The results presented in this work are helpful for understanding the GH effect in chiral magnets and for quantifying the DMI parameter in magnetic strips of sub-$50$ nm scales.