## 3 Results and Discussion
Neutron diffraction measurements indicate that the antiferromagnetic order in Ca/Mn-substituted bismuth ferrites is partially frustrated, resulting in an ordered magnetic moment significantly smaller than that expected based on the electronic configurations of the interacting ions. DC magnetization and AC magnetic susceptibility measurements reveal magnetic field- and frequency-dependent behavior indicative of a glassy magnetic component. These findings are consistent with observations from  
Figure 5: Enlarged sections of the field dependencies of magnetization measured for Bi\({}_{1-y}\)Ca\({}_{y}\)Fe\({}_{1-x}\)Mn\({}_{x}\)O\({}_{3}\) samples at \(T=125\), 150, 175, 200, and 300 K: (**a**) \(y=0.1\), \(x=0.35\); (**b**) \(y=0.1\), \(x=0.4\); (**c**) \(y=0.1\), \(x=0.45\); (**d**) \(y=0.15\), \(x=0.35\); (**e**) \(y=0.15\), \(x=0.4\); (**f**) \(y=0.15\), \(x=0.45\); (**g**) \(y=0.175\), \(x=0.35\); (**h**) \(y=0.175\), \(x=0.4\); (**i**) \(y=0.175\), \(x=0.45\). Identical horizontal and vertical scales are used across all panels for direct comparability. similar systems, such as LaFe\({}_{1-x}\)Mn\({}_{x}\)O\({}_{3+\delta}\)[45] or Bi\({}_{1-y}\)_RE\({}_{y}\)Fe\({}_{1-x}\)Mn\({}_{x}\)O\({}_{3+\delta}\)[46], where the glassy component arises from spin frustration due to the coexistence of antiferromagnetic (e.g., Fe\({}^{3+}\)-O-Fe\({}^{3+}\) or Fe\({}^{3+}\)-O-Mn\({}^{3+}\)) [11] and ferromagnetic (e.g., Mn\({}^{3+}\)-O-Mn\({}^{4+}\)) [11] exchange interactions involving magnetically-active transition-metal ions in a site-disordered lattice [47]. The glassy behavior is more pronounced in samples with a higher concentration of Mn (including Mn\({}^{4+}\) ions), which participate in the ferromagnetic superexchange Mn\({}^{3+}\): \({\rm t_{28}^{3}e_{8}^{1}-O-Mn^{4+}}\): \({\rm t_{28}^{3}e_{8}^{0}}\). Figure 6: Temperature dependencies of magnetization measured for Bi\({}_{1-y}\)Ca\({}_{y}\)Fe\({}_{1-x}\)Mn\({}_{x}\)O\({}_{3}\) samples with an applied field \(H\) = 2 kOe in zero field cooling (ZFC), field-cooled cooling (FCC), and field-cooled warming (FCW) modes: (**a**) \(y\) = 0.1, \(x\) = 0.35; (**b**) \(y\) = 0.1, \(x\) = 0.4; (**c**) \(y\) = 0.1, \(x\) = 0.45; (**d**) \(y\) = 0.15, \(x\) = 0.35; (**e**) \(y\) = 0.15, \(x\) = 0.4; (**f**) \(y\) = 0.15, \(x\) = 0.45; (**g**) \(y\) = 0.175, \(x\) = 0.35; (**h**) \(y\) = 0.175, \(x\) = 0.4; (**i**) \(y\) = 0.175, \(x\) = 0.45. The insets show the behavior of the dependencies near the Néel temperature. Figure 7: Compositional dependencies of the Néel temperature for Bi\({}_{1-y}\)Ca\({}_{y}\)Fe\({}_{1-x}\)Mn\({}_{x}\)O\({}_{3}\) series. The dashed lines are guides to the eye. The most unusual feature in the temperature dependencies of magnetization for the samples containing the \"\(R3c\)\" phase is the presence of hysteresis between the curves obtained in the cycles of zero field cooling, field-cooled cooling, and field-cooled warming (Figure 6a-e,g,h). The hysteresis starts to develop immediately below the Neel point and persists down to the lowest temperature (2 K) used in the experiment. This effect is most pronounced in the structurally inhomogeneous samples (Table 1, Figure 6c,g,h). No intrinsic hysteresis was detected for the single-phase compounds with an orthorhombic structure, apart from a small instrument-related effect common to all these measurements. (Figure 6f,i). The origin of the difference in the low- and high-temperature (below the Neel point) magnetic states of the rhombohedral samples, which results in the dependence of the measured magnetization on the heating-cooling protocol, becomes clear when considering the results of neutron diffraction measurements carried out for the Bi\({}_{0.9}\)Ca\({}_{0.1}\)Fe\({}_{0.6}\)Mn\({}_{0.4}\)O\({}_{3}\) compound [48].