Analysis of the X-ray diffraction patterns showed that an increase in the iron concentration to 20 mol.% leads to a structural phase transition from the monoclinic phase (C2/с space group) to the orthorhombic phase (Pnma space group) described by the $\sqrt{2}{a}_{\mathrm{p}}·4a_{\mathrm{p}}·2\sqrt{2}{a}_{\mathrm{p}}$ metric, where a_p is the Perovskite unit cell parameter. Figure 1 shows the diffraction pattern of the BiMn_0.7Fe_0.3O₃ solid solution which suggests the presence of two phases, the predominant one remaining the monoclinic phase typical of the BiMnO₃ composition and the fraction of the orthorhombic phase being ~20%. It should be noted that the diffraction patterns of the solid solutions with x > 0 do not exhibit reflections corresponding to the monoclinic phase (Fig. 1, inset) due to the superimposition of the reflections typical of the two phases in question. Analysis of the X-ray diffraction data showed that further increase in the concentration of iron ions leads to a rapid decrease in the volume fraction of the monoclinic phase and the BiMn_0.6Fe_0.4O₃ composition has an almost single-phase structure with orthorhombic distortions of the unit cell. This concentration phase transition is accompanied by a gradual decrease in the unit cell parameters suggesting the formation of a continuous sequence of solid solutions in the entire test concentration range, which is in agreement with earlier literary data [17, 18].

Figure 1.

X-ray diffraction pattern of BiMn_0.7Fe_0.3O₃ solid solution corrected in two-phase model: top row of Bragg peaks in a bar diagram form is for monoclinic phase (C2/c), bottom row is for orthorhombic phase (Pnma). Inset: concentration evolution of reflections typical of two phases in question (the reflections ascribed to the monoclinic phase are marked by the symbol “*”)

The initial domain structure of the test specimens features a moderate number of domains from several hundreds of nanometers to 1 mm in diameter inhomogeneously distributed on the specimens surface. The specimens exhibit both vertical and lateral random polarization components. By and large, the number of the domains with predominant random polarization direction in the scanning plane is less than those with polarization in orthogonal planes. Figure 2 a–f shows images of the piezoresponse signal after repolarization with a ±20 V bias for the BiMn_1-xFe_xO₃ solid solutions with x = 0.2, 0.3 and 0.4. The polarized areas clearly show the grain boundaries with the grains having a diameter of ~5 mm, and the induced areas replicate the pattern set by the cantilever during DC voltage scanning. There is a piezoresponse signal contrast between the polarized areas. The dark and bright areas suggest opposite polarization vector directions. Analysis of piezoresponse signal phase showed that the dark areas correspond to the domains with the polarization vector directed into the depth of the ceramic surface and the bright ones, to the domains with the polarization vector oriented along the surface. After polarization a series of scans were made showing the evolution of the induced domain structure as a function of time, polarization response signal profiles were plotted and averaging over the middle parts of these images was made (Fig. 2 d–f). The induced piezoresponse magnitude decreases with time. Based on the experimental data, the polarization relaxation time was determined to be ~14 min for the BiMn_0.7Fe_0.3O₃ specimen and 7 min for the BiMn_0.8Fe_0.2O₃ specimen. The piezoresponse signal of the BiMn_0.6Fe_0.4O₃ specimen proved to be stable over 1 h of continuous scanning.

In 1 h after polarization and scanning in PFM Kelvin mode, a clear surface potential signal is also observed for the polarized areas in 2 h after polarization (Fig. 3). By analogy with piezoresponse signal images, the surface potential signal maps visualize the grain boundaries.

The results suggest that piezoelectric signal decreases dramatically at the grain boundaries in the test specimens and the coercive field magnitude increases, i.e., the 20 V bias used in the experiment proves to be sufficient to change the direction of polarization in the surface layer of grains. Noteworthy, the surface layer of grains typically exhibits a deviation of its chemical composition from the stoichiometric one due to specific features of the synthesis technique. For example, if high-pressure techniques are used, the quantity of oxygen ions decreases (due to oxidation of metallic foils used as specimen containers) resulting in the formation of oxygen vacancies and an increase in the concentration of structural defects in the surface layer which, in turn, shows itself in the observed degradation of the piezoelectric properties.

Residual piezoelectric hysteresis loops were recorded in polarization switching spectroscopy mode (Fig. 4) and also confirm polarization switching on a nanometric scale. The hysteresis loops shown in Fig. 4 are symmetrical and have an internal bias of: –0.6 V for the BiMn_0.6Fe_0.4O₃ composition, +0.17 V for the BiMn_0.7Fe_0.3O₃ composition and +3.67 V for the BiMn_0.8Fe_0.2O₃ composition. By analogy with the polarization of areas (see Fig. 2) the piezoresponse signal at –20 V is greater than at +20 V and is –3.8 and 3.5 pm/V, respectively, for the BiMn_0.6Fe_0.4O₃ composition, –6 and 5.2 pm/V, respectively, for the BiMn_0.7Fe_0.3O₃ composition and ,–2.4 and 1.6 pm/V, respectively, for the BiMn_0.8Fe_0.2O₃ composition.

Figure 2.

(a–c) Piezoresponse signal of BiMn_1-xFe_xO₃ solid solutions after polarization with ±20 V bias and (d–f) piezoresponse signal profiles for different time after polarization: (a, c): х = 0.4; (b, e): x = 0.3; (c, f): x = 0.2; (1) source signal; (2) immediately after polarization; (3) in 1 h after polarization. Dashes show grain boundaries

Figure 3.

Surface potential signal of BiMn_1-xFe_xO₃ solid solutions in 2 h after polarization with ±20 V bias: (а) BiMn_0.6Fe_0.4O₃; (b) BiMn_0.7Fe_0.3O₃; (c) BiMn_0.8Fe_0.2O₃. Dashes show grain boundries

Figure 4.

Piezoelectric hysteresis loops of BiMn_1-xFe_xO₃ solid solutions: (1) BiMn_0.6Fe_0.4O₃; (2) BiMn_0.7Fe_0.3O₃; (3) BiMn_0.8Fe_0.2O₃

The greatest number of magnetic domains and the highest amplitude of their signals were observed for the BiMn_0.8Fe_0.2O₃ composition. The locations of the ferroelectric and magnetic domains are coincident. By way of example, scans of the same regions were taken for the BiMn_0,8Fe_0,2O₃ composition specimen in PFM magnetic mode (Fig. 5).

The magnetic structure of the solid solutions changes dramatically with an increase in the concentration of iron ions due to a change in the structural state of the solid solution. It is well-known that the initial composition BiMnO₃ has a ferromagnetic state due to the orbital ordering of the Mn³⁺ ions since the 3d⁴ electron configuration of the Mn³⁺ ions causes the Jahn–Teller effect which implies splitting of the e_g energy level (the d_x2-y2 and d_z2 orbitals). In this case, the orbital ordering shows itself in that the semi-populated d_z2 orbital of one Mn³⁺ ion is directed toward the unpopulated d_x2-y2 orbital of an adjacent Mn³⁺ ion. This produces positive exchange interaction between adjacent manganese ions in accordance with the Goodenough–Kanamori–Andersen theory [22] and leads to the formation of ferromagnetic ordering. The phase transition temperature of the initial BiMnO₃ solid solution to the magnetically ordered state is T_C ~ 100 K which is in agreement with literary data [13, 18, 23].

Elevated concentration of Fe ions destructs the orbital ordering formed by the ordering of the d_z2 orbitals of the Mn³⁺ ions and thus leads to the formation of a frustrated magnetic state. Noteworthy, the decrease in the magnetization has a nonlinear pattern. For example, substitution of 20% of manganese ions for iron ions reduces the specific magnetization in a 6 T field from 64.9 to 31.6 emu/g, and for the composition with x = 0.4 the magnetization is 16.1 emu/g (Fig. 6). The field dependences of magnetization for all the compositions exhibit a clear hysteresis loop at 5 K. The coercive force of the solid solutions with x = 0 and 0.2 is less than 0.01 T which is typical of magnetically soft materials while an increase in the concentration of iron ions leads to a significant increase in the coercive force for the compositions with x = 0.3 and 0.4 to H_c = 0.4 T at 5 K.

The temperature dependences of the magnetization (see Fig. 6, inset) for all the experimental solid solution compositions suggest the presence of a phase transition to a magnetically ordered state at below 100 K. An increase in the concentration of iron ions destructs the long-range ferromagnetic order produced by the orbital ordering of the Mn³⁺ ions [19] which is accompanied by a decrease in the transition temperature to the magnetically ordered state. The composition with x = 0.4 exhibits a slight increase in the magnetic transition temperature, probably due to the formation of magnetic ordering in the Fe³⁺ ions. It should be noted that the structural state of the solid solution with x = 0.4 features predominantly the orthorhombic phase which implies the absence of orbital ordering in the Mn³⁺ ions, and an additional ferromagnetic component in the magnetic system of these compositions is caused by a noncollinear antiferromagnetic structure formed by the Fe³⁺ ions due to the Dzyaloshinskii–Moriya interaction [24].

Figure 5.

Experimental data for BiMn_0.8Fe_0.2O₃ ceramics: (a) topography; (b) vertical piezoresponse image; (c) magnetic domain structure

Figure 6.

Isothermal magnetization curves for BiMn_1-xFe_xO₃ solid solution with x = 0, 0.2, 0.3 and 0.4 at T = 5 K. Inset: temperature dependence of magnetization taken in cooling mode in a 100 Oe field