Investigation of the GdMn$_2$O$_5$ multiferroic by the $\mu$SR method

The GdMn$_2$O$_5$ multiferroic (a ceramic sample and a sample consisting of a large array of randomly oriented single crystals with linear dimensions 2–3 mm) has been studied by the $\mu$SR method within the temperature range 10–300 K. Three anomalies in the temperature behavior of the parameters of the muon polarization relaxation function, namely, close to the phase transition driven by the onset of long-range magnetic order in the manganese ion subsystem ($T_{N1}$ = 40–41 K), near the lock-in transition initiated by an abrupt change of the wave vector of magnetic order ($T_L$ = 35 K), and close to the Gd$^{3+}$ ion ordering temperature ($T_{N2}$ = 15 K), have been found. An analysis of the time spectra of muon spin precession in the internal magnetic field of the samples has revealed two positions of preferable muon localization sites in samples, which differ in precession frequencies and the character of their behavior with temperature. The lower-frequency precession driven by Mn$^{4+}$ ions, ferromagnetic Mn$^{4+}$–Mn$^{4+}$ + muonium complexes, and Gd$^{3+}$ ions is observed throughout the temperature region $T < T_{N1}$ and is practically independent of temperature. At temperatures $T < T_L$ = 35 K, a higher-frequency precession associated with Mn$^{3+}$ ions appears also. It is characterized by a temperature dependence $\sim(1-T/T_{N1})^\beta$ with the index $\beta$ = 0.39, which is typical of Heisenberg-type 3D magnets. For $T < T_{N1}$, a deficiency of the rest total asymmetry is observed. This phenomenon can probably be assigned to formation of muonium, which suggests that charge transfer processes play an important role in formation of long-range magnetic order.