## 1 Introduction  
Due to the coupling between the ferroelectric and magnetic order parameters, magnetoelectric multiferroics are considered promising for various applications involving electric field-driven modulation of magnetic properties and spin-polarized charge transport [1; 2; 3]. Bismuth ferrite (BiFeO\({}_{3}\)) is an extremely rare example of a single-phase magnetic ferroelectric exhibiting multiferroic behavior at room temperature [4; 5; 6; 7]. This perovskite-like (\(AB\)O\({}_{3}\)) compound is classified as belonging to so-called _Type-I_ multiferroics [8], a class of materials in which ferroelectricity and magnetism have different sources (in the case of bismuth ferrite, associated with the 6s electrons of Bi\({}^{3+}\) and the 3\(d\) electrons of Fe\({}^{3+}\), respectively). Although this distinction does not inherently imply a strong coupling between ferroelectric and magnetic properties [8], in the case of BiFeO\({}_{3}\), polar atomic displacements significantly influence the magnetic structure and stabilize the antiferromagnetic (AFM) spin cycloid [9; 10] instead of the G-type AFM order predicted by superexchange rules [11]. While the presence of the cycloidal modulation forbids any linear magnetoelectric effect [12], the linear magnetoelectric coupling becomes observable in phases characterized by cones-type or canted AFM order, which can be stabilized in a strong magnetic field (10-15 T at room temperature) [13]. Numerous investigations indicate that the threshold field value can be effectively reduced by partial replacement of Bi\({}^{3+}\) with rare-earth (\(RE^{3+}\)) ions [14; 15; 16]. The chemical substitution-driven decrease in the critical field inducing the cycloidal AFM structure-to-canted AFM structure transformation has also been reported for the Bi\({}_{1-y}\)Ca\({}_{y}\)FeO\({}_{3-y/2}\)[17], Bi\({}_{1-y}\)Ca\({}_{y}\)Fe\({}_{1-y}\)Ti\({}_{y}\)O\({}_{3}\)[18], and Bi\({}_{1-y}\)Ca\({}_{y}\)Fe\({}_{1-y/2}\)Nb\({}_{y/2}\)O\({}_{3}\)[19] series, to name a few. The list of solid solutions is not accidentally limited by materials in which Bi\({}^{3+}\) is replaced by Ca\({}^{2+}\): in contrast to Sr\({}^{2+}\)-, Pb\({}^{2+}\)-, and Ba\({}^{2+}\)-substituted bismuth -ferrite samples, whose magnetic properties are often affected by the presence of the ferrimagnetic impurity \(AE\)Fe\({}_{12}\)O\({}_{19}\) (\(AE\) stands for Sr\({}^{2+}\), Pb\({}^{2+}\) or Ba\({}^{2+}\)) [20; 21; 22; 23], the formation of Ca-doped BiFeO\({}_{3}\) is not accompanied by the appearance of the hexaferrite-type phase [24]. This makes Ca doping a more convenient approach to uncover the real correlations between the crystal structure, microstructure, and multiferroic behavior of bismuth iron oxide-based materials, a long-standing challenge in the study of magnetic ferroelectrics [25; 26]. The spontaneous magnetization specific to the canted AFM order (not necessarily stabilized by Ca substitution) is intrinsically small, typically less than 0.3 emu/ g [17; 18; 19; 27; 28; 29; 30]. Therefore, new doping-related approaches aimed at enhancing the multiferroic behavior of BiFeO\({}_{3}\) remain a key focus of ongoing investigations [31; 32]. One of these approaches can be implemented based on the Bi\({}_{1-y}\)Ca\({}_{y}\)Fe\({}_{1-x}\)Mn\({}_{x}\)O\({}_{3}\) systems [33; 34], where the charge imbalance introduced by the replacement of Bi\({}^{3+}\) by Ca\({}^{2+}\) is compensated by the appearance of Mn\({}^{4+}\). In this system, Mn\({}^{4+}\) coexists with Mn\({}^{3+}\) at \(x>y\), thereby providing ferromagnetic exchange coupling Mn\({}^{3+}\): t\({}_{2g}\)\({}^{3}\)e\({}_{g}\)\({}^{1-}\)O-Mn\({}^{4+}\): t\({}_{2g}\)\({}^{3}\)e\({}_{g}\)\({}^{0}\). The recent investigations indicate that the competition between this and the dominant AFM superexchange, Fe\({}^{3+}\): t\({}_{2g}\)\({}^{3}\)e\({}_{g}\)\({}^{2-}\)O-Fe\({}^{3+}\): t\({}_{2g}\)\({}^{3}\)e\({}_{g}\)\({}^{2}\), gives rise to the formation of a glassy state, which underlies the appearance of significant magnetization at low temperatures [33; 34].