Experimental study of antiferromagnetic resonance in noncollinear antiferromagnet Mn$_{3}$Al$_{2}$Ge$_{3}$O$_{12}$

We have measured antiferromagnetic resonance (AFMR) frequency-field dependences for aluminum-manganese garnet Mn$_{3}$Al$_{2}$Ge$_{3}$O$_{12}$ at frequencies from 1 to 125 GHz and at the fields up to 60 kOe. Three AFMR modes were observed for all orientations, their zero field gaps are about 40 and 70 GHz. Andreev-Marchenko hydrodynamic theory [Sov. Phys. Usp. 130, 39 (1980)] well describes experimental frequency-field dependences. We have observed hysteresis of resonance absorption as well as history dependence of resonance absorption near gap frequencies below 10 kOe in all three measured field orientations, which are supposedly due to the sample domain structure. Observation of the AFMR signal at the frequencies from 1 to 5 GHz allows to estimate repulsion of nuclear and electron modes of spin precession in the vicinity of spin-reorientation transition at H||[100].