Anomalously strong relaxation of the polarization of muons in the magnetically ordered and paramagnetic states of the TbMnO$_3$ multiferroic

An anomalously strong relaxation of the muon polarization in a magnetically ordered state in the TbMnO$_3$ multiferroic has been revealed by the method below the $\mu SR$ Néel temperature ($42$ K). Such a relaxation is due to the muon channel of relaxation of the polarization and the interaction of the magnetic moment of the muon with inhomogeneities of the internal magnetic field of an ordered state in the form of a cycloid. Above the Néel temperature, beginning with temperatures depending on the applied magnetic field, a two-phase state has been revealed where one phase has an anomalously strong relaxation of the muon polarization for a paramagnetic state. These features of the paramagnetic state are due to short-range magnetic order domains that appear in strongly frustrated TbMnO$_3$. A true paramagnetic state has been observed only at $T\geqslant150$ K.