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We use inelastic neutron scattering to study spin waves and their correlationwith the magnetoelectric effect in Y$_{0.7}$Lu$_{0.3}$MnO$_3$. In the undopedYMnO$_3$ and LuMnO$_3$, the Mn trimerization distortion has been suggested toplay a key role in determining the magnetic structure and the magnetoelectriceffect. In Y$_{0.7}$Lu$_{0.3}$MnO$_3$, we find a much smaller in-plane(hexagonal $ab$-plane) single ion anisotropy gap that coincides with a weakerin-plane dielectric anomaly at $T_N$. Since both the smaller in-planeanisotropy gap and the weaker in-plane dielectric anomaly are coupled to aweaker Mn trimerization distortion in Y$_{0.7}$Lu$_{0.3}$MnO$_3$ comparing toYMnO$_3$ and LuMnO$_3$, we conclude that the Mn trimerization is responsiblefor the magnetoelectric effect and multiferroic phenomenon inY$_{1-y}$Lu$_{y}$MnO$_{3}$.

Doping influence of spin dynamics and magnetoelectric effect in hexagonal Y$_{0.7}$Lu$_{0.3}$MnO$_{3}$