Solid-state sintering method was used to prepare ceramic materials based on bismuth ferrite, i.e., (BiFeO3)1 − x –(BaTiO3) x and Bi1 − x Nd x FeO3 solid solutions and the Aurivillius Bi5Ti3FeO15 compound. The structure of the materials was examined using X-ray diffraction, and the Rietveld method was applied to phase analysis and structure refinement. Magnetoelectric coupling was registered in all the materials using dynamic lock-in technique. The highest value of magnetoelectric coupling coefficient α ME was obtained for the Bi5Ti3FeO15 compound (α ME ~ 10 mVcm−1 Oe−1). In the case of (BiFeO3)1 − x –(BaTiO3) x and Bi1 − x Nd x FeO3 solid solutions, the maximum α ME is of the order of 1 and 2.7 mVcm−1 Oe−1, respectively. The magnitude of magnetoelectric coupling is accompanied with structural transformation in the studied solid solutions. The relatively high magnetoelectric effect in the Aurivillius Bi5Ti3FeO15 compound is surprising, especially since the material is paramagnetic at room temperature. When the materials were subjected to a preliminary electrical poling, the magnitude of the magnetoelectric coupling increased 2–3 times.

Structural and physical properties of the high-entropy alloy ${\left(\mathrm{NbTa}\right)}_{0.67}{\left(\mathrm{MoHfW}\right)}_{0.33}$ were studied by x-ray powder diffraction, energy dispersive x-ray spectroscopy, magnetization, electrical resistivity, and specific heat measurements. The experimental results were supported by theoretical calculations using two complementary approaches for electronic structure calculations: the Korringa-Kohn-Rostoker method with the coherent potential approximation (KKR-CPA) and projector augmented wave (PAW) within the density functional theory. It was found that the alloy forms with a cubic, body-centered structure (space group $Im\overline{3}m$, W-type structure) with a lattice parameter $a=3.287\left(1\right)$ Å and a random (but microscopically homogeneous) distribution of the constituent elements. At high temperature the alloy exhibits simple metallic behavior, while at low temperature it becomes a type-II superconductor with the critical temperature $T_{\mathrm{c}}\approx 4.3$ K and the upper critical field ${\mu }_0{H}_{\mathrm{c}2}\approx 1.45$ T. The electron-phonon coupling constant calculated from the PAW data, ${\lambda }_{\mathrm{el}-\mathrm{ph}}^{\mathrm{th}-\mathrm{PAW}}=0.63$, is in perfect agreement with the experimental results.

In this work, BiFeO₃ powders were synthesized by a sol–gel method. The influence of annealing temperature on the structure and magnetic properties of the samples has been discussed. X-ray diffraction studies showed that the purest phase was formed in the temperature range of 400 °C to 550 °C and the samples annealed at a temperature below 550 °C were of nanocrystalline character. Mössbauer spectroscopy and magnetization measurements were used as complementary methods to investigate the magnetic state of the samples. In particular, the appearance of weak ferromagnetic properties, significant growth of magnetization, and spin-glass-like behavior were observed along with the drop of average grain size. Mössbauer spectra were fitted by the model assuming cycloidal modulation of spins arrangement and properties of the spin cycloid were determined and analyzed. Most importantly, it was proved that the spin cycloid does not disappear even in the case of the samples with a particle size well below the cycloid modulation period λ = 62 nm. Furthermore, the cycloid becomes more anharmonic as the grain size decreases. The possible origination of weak ferromagnetism of the nanocrystalline samples has also been discussed.