  It is a conventional wisdom that a left-hand microwave cannot efficiently
excite the spin wave (SW) in ferromagnets, due to the constraint of angular
momentum conservation. In this work, we show that the left-hand microwave can
drive nonreciprocal SWs in the presence of a strong ellipticity-mismatch
between the microwave and precessing magnetization. A critical frequency is
predicted, at which the left-hand microwave cannot excite SWs. Away from it the
SW amplitude sensitively depends on the ellipticity of left-hand microwaves, in
sharp contrast to the case driven by right-hand ones. By tuning the microwave
frequency, we observe a switchable SW non-reciprocity in a ferromagnetic single
layer. A mode-dependent mutual demagnetizing factor is proposed to explain this
finding. Our work advances the understanding of the photon-magnon conversion,
and paves the way to designing diode-like functionalities in nano-scaled
magnonics.
