$\mu SR$ study of the dynamics of internal magnetic correlations in Tb(Bi)MnO$_3$ multiferroic in magnetically ordered and paramagnetic states

The dynamics of internal magnetic correlations in Tb$_{0.95}$Bi$_{0.05}$MnO$_3$ multiferroic in the temperature range of $10$–$290$ K has been studied. Separation into two phases with different relaxations of the polarization of muons in the basic matrix of the crystal and the phase separation regions has been detected for the first time both in a magnetically disordered state at $T < T_N = 40\,$K and in a paramagnetic state in a transverse magnetic field of $290$ G in a temperature range of $80$–$150$ K. A muon ferromagnetic complex (Mn$^{3+}$-Mu-Mn$^{4+}$), where the hyperfine interaction in a muonium depolarizes a muon in a time less than $10^{-8}$ s, is formed at $T<40$ K in phase separation regions containing pairs of Mn$^{3+}$ and Mn$^{4+}$ ions, as well as electrons that recharge them. In the matrix of the original crystal containing only Mn$^{3+}$ ions, a muonium is formed with a broken hyperfine bond. In this case, muons are depolarized at a high rate because of their interactions with the local magnetic fields of a cycloid. At temperatures of $80$–$150$ K, one phase in the phase separation regions constitutes approximately $50\%$ and is characterized by long relaxation times about $10 \mu$s (described by the Gaussian relaxation function). The other phase is formed by Mn$^{3+}$-Mn$^{3+}$ correlations in the short-range magnetic order regions in the matrix of the original crystal, which are weakly sensitive to a magnetic field of $290$ G.