Muon spin spectroscopy in multiferroic (Cu,Zn)$_{3}$Mo$_{2}$O$_{9}$

We present the muon spin relaxation/rotation spectra in the multiferroic compound (Cu,Zn)$_{3}$Mo$_{2}$O$_{9}$. The parent material Cu$_{3}$Mo$_{2}$O$_{9}$ has a multiferroic phase below $T_{\rm N}$ = 8.0 K, where the canted antiferromagnetism and the ferroelectricity coexist. The asymmetry time spectra taken at RIKEN-RAL pulsed muon facility show a drastic change at $T_{\rm N}$. At low temperatures the weakly beating oscillation caused by the static internal magnetic fields in the antiferromagnetic phase was observed in Cu$_{3}$Mo$_{2}$O$_{9}$ and the lightly ($0.5\%$) Zn-doped sample. From the fitting of the oscillating term, we obtain the order parameter in these samples: ferromagnetic moment in two sublattices of antiferromagnet. In the heavily ($5.0\%$) Zn-doped sample, the muon-spin oscillation is rapidly damped. The frequency-domain spectrum of this sample suggests a formation of magnetic superstructure.