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Multiferroic Ba(Ti${}_{0.80}$Zr${}_{0.20}$)O₃-0.5(Ba${}_{0.70}$Ca${}_{0.30}$)TiO₃ (BCTZ)@CoFe₂O₄ (CFO) hybrid nanofibers (NFs) were fabricated by a sol–gel electrospinning. The perovskite structure of ferroelectric BCTZ and the spinel structure of ferromagnetic CFO coexist and are homogeneously distributed, and their interface along the perovskite [110] zone axis was directly observed. The indirect magnetoelectric (ME) coupling effect was observed from the magnetization versus temperature (M–T) curves, demonstrating a distinct singularity on the dM/dT curve near the ferroelectric Curie temperature ($T$${}_C$) of 387 K. The piezocatalytic rate of BCTZ@CFO multiferroic hybrid NF (2.6 × 10${}^{-2}$min${}^{-1}$) is higher than NP (1.9 × 10${}^{-2}$min${}^{-1}$) because the piezoelectricity of the one-dimensional (1D) multiferroic NF is higher than that of NPs, beneficial for the mechanical vibration-induced localized built-in electric fields for piezocatalysis under ultrasound.

By X-ray diffraction and dielectric spectroscopy, the crystal structure, phase composition, and properties of Sr${}_{0.6}$Ba${}_{0.4}$Nb₂O₆/Ba₂NdFeNb₄O${}_{15}$/Sr${}_{0.6}$Ba${}_{0.4}$Nb₂O₆/Ba₂NdFeNb₄O${}_{15}$/SrRuO₃/MgO and Ba₂NdFeNb₄O${}_{15}$/Sr${}_{0.6}$Ba${}_{0.4}$Nb₂O₆/Ba₂NdFeNb₄O${}_{15}$/Sr${}_{0.6}$Ba${}_{0.4}$Nb₂O₆/SrRuO₃/MgO multilayer heterostructures were studied. The heterostructures were manufactured under identical conditions but differing in the layer deposition sequence. It is shown that the orientation domains are formed in each Ba₂NdFeNb₄O${}_{15}$ (BNFN) and Sr${}_{0.6}$Ba${}_{0.4}$Nb₂O₆ (SBN) layers. BNFN and SBN layers have tetragonal unit cells with tensile out-of-plane strain and compression in-plane strain. At $T=-100\dots 100^{\circ }$C both heterostructures are characterized by fairly high relative permittivity values. The reasons for the revealed regularities are discussed.

We have investigated magnetization, magneto-transport, and complex impedance spectroscopy of structurally characterized multiferroic composites xLa_0.7Sr_0.3MnO₃ (LSMO)–(1-x)ErMnO₃ (EMO) (0≤x≤1). Para- to ferromagnetic Curie temperatures for this series of composites indicate almost complete immiscibility within the mixture of those two compounds of LSMO and EMO having nearly identical chemical formula. Magnetization as a function of magnetic field curves at T=300 K exhibit an appreciable enhancement of coercive field of LSMO in the composites with increase in EMO content. This feature has been attributed to the increasing grain boundary pinning center of LSMO grains at their interfaces in the composites. Magneto-transport measurements reveal a considerable decrease in spin polarized tunneling transport with increase in EMO content in the composites. This feature is understood as a consequence of increasing grain boundary pinning centers of magnetic domains of LSMO grains in the composites. Room temperature complex impedance spectroscopy studies, i.e., -Z^′′ versus Z′ curves (Nyquist plots) for EMO, x=0.1, x=0.2, and LSMO samples reveal that relaxation time of both bulk and grain boundary increases with increase in EMO content in the composites. Slow relaxation processes of conduction electrons at both bulk and grain boundary occurs due to the proximity of highly resistive insulating EMO in the composites.

This paper discusses recent efforts to control magnetism with electric fields in single and multilayer oxides, which has great potential to improve a variety of technological endeavors, such as magnetic sensing and magnetoelectric (ME) logic. The importance of electrical control of magnetism is followed by a discussion of multiferroics and MEs, which are the leading contenders for this task. The focus of this paper is on complementary methods in understanding the ME coupling, an essential step to electrical control of magnetism. Neutron scattering, nonlinear optics and X-ray spectromicroscopy are addressed in providing key parameters in the study of ME coupling. While primarily direct (single-phase multiferroics) ME materials are used as examples, the techniques discussed are also valuable to the study of indirect (e.g., multilayers and pillars) magnetoelectrics. We conclude with a summary of the field and future directions.

Multiferroic materials are characterized by the coexistence of ferroelectric and ferromagnetic (or antiferromagnetic) orders, the coupling to lattice vibration can be invoked either through piezoelectric or piezomagnetic effects. In this paper, the polaritonic band structures of multiferroic superlattices composed of oppositely polarized domains are investigated using the generalized transfer matrix method. For the primitive cell with broken parity symmetry, the polaritonic band structure is asymmetrical with respect to the forward and backward propagation directions (nonreciprocality). In particular, the band extreme points move away from the Brillouin zone center. This asymmetry in band-gap positions and widths can be used to design compact one-way optical isolators, while the extremely slow light velocities near the asymmetrical upper edges of lower bands includes the essential ingredients for designing slow light devices.

The polycrystalline La_0.1Lu_xBi_0.9-xFeO₃(x = 0, 0.01, 0.03, 0.05, 0.1 and 0.2) compounds were synthesized by a conventional solid-state reaction method. An unusual exchange bias-like (EB-like) phenomenon was found in this system. Both horizontal shift (H_s) and vertical shift (M_s) are observed simultaneously. Moreover, the horizontal shift displays a similar trend to the vertical shift with the variation of Lu content and the variation of maximum applied magnetic field, revealing that the horizontal shift and the vertical shift are closely correlated. We propose that the horizontal shift may be related to the exchange interaction between two different canted-AFM phases and the vertical shift is related to the large anisotropy of LuFeO₃.

The magnetoelectric (ME) properties of sol–gel grown BiFe${}_{0.95}$Co${}_{0.05}$O₃ (BFCO) nanoceramics, with different sizes, were investigated at room-temperature. X-ray diffraction (XRD) measurement was performed to investigate structural properties of the samples understudy. Magnetic field-dependent dielectric permittivity has been systematically investigated in the frequency range of 20 Hz to 1 MHz. To ensure the origin of magnetodielectric response, the magnetoimpedance (MI) spectroscopy was adopted using equivalent circuit model. The a.c. conductivity was found to obey the Jonscher’s universal power law. The modifications in spiral spin structure in the BFCO nanoparticles with size less than $\sim$62 nm significantly affect the ME coupling parameters.

The multiferroic magnetoelectric materials have gained intensive research interest in the recent years due to their prospective applications. In this perspective, the thermally tunable complex impedance, dielectric behavior and room-temperature magnetoelectric coupling of xCo${}_{0.5}$Ni${}_{0.5}$Fe₂O₄–(1 - x)PbZr${}_{0.58}$Ti${}_{0.42}$O₃ (x = 0.2, 0.3 and 0.5) nanocomposites have been investigated. A series of samples have been prepared by chemical pyrophoric reaction process. The structural characterization confirms the coexistence of two different types of phases, there is no phase segregation. The temperature-controlled complex impedance analysis reveals that grain boundaries and grain of the nanocomposites are playing a dominating role. The existence of Maxwell–Wagner interfacial polarization of the nanocomposites causes a high dielectric constant at low frequency. The calculated AC conductivity values with frequency at different temperatures follow the Jonscher’s power-law. A small polaronic hopping contributes largely to the conduction process of the decorated composite. The magnetostriction properties lead to the AC and DC magnetic field-dependent magnetoelectric coupling of the nanocomposites. The magnetoelectric coupling coefficient depends on the concentration of the piezomagnetic phase of the composites.

Structural, electronic, magnetic and mechanical properties of the perovskites BiFeO₃ (BFO) and BaTiO₃ (BTO) are investigated using density functional theory (DFT). Structural and mechanical parameters are calculated using generalized gradient approximation (GGA) and the results consistent with the available literature. The stable magnetic phases are achieved by optimizing total energies versus volumes of the cells in different magnetic configurations such as nonmagnetic (NM), ferromagnetic (FM) and antiferromagnetic (AFM). BTO is found to be NM while BFO favors G-type AFM (G-AFM) phase. The electronic properties are investigated using GGA, GGA with Hubbard potential (GGA+U) and modified Becke–Johnson (GGA-mBJ) exchange–correlation functionals. BFO is found to be a direct bandgap semiconductor having gap energy value 3.0 eV whereas BTO is an indirect semiconductor with bandgap energy 2.9 eV. Spin–orbit coupling effect is dominant in BFO due to the larger size of A-site cation. The electrical polarization shows that both the compounds are ferroelectric materials with significant spontaneous polarization of 144.1 $\mu$C/cm² and 27.9 $\mu$C/cm² for BFO and BTO respectively.

The compound BaFe${}_{11.4}$In${}_{0.6}$O${}_{19}$ was synthesized in the solid phase and its chemical composition and structural properties were studied. SEM analysis showed that the size of crystallites in the resulting polycrystal is $d\approx 0.5-2$$\mu$m. When analyzing the microcomposition of the surface, 55.8% of Fe, 19.7% of O, 14.3% of Ba, and 10.0% of In atoms were determined. XRD analysis showed that the crystal structure of this compound corresponds to hexagonal (P6₃mmc) symmetry. The crystallographic parameters of the compound were determined by the Rietveld method.

Magnetoelectric composites have been synthesized by sintering mixtures of highly piezoelectric component Pb(Zr_0.52Ti_0.48)O₃, PZT and highly magnetostrictive piezomagnetic component Ni_0.93Co_0.02Mn_0.05Fe_1.95O_4-δ, NCMF. These composites with generic formula (1 - x)PZT + xNi_0.93Co_0.02Mn_0.05Fe_1.95O_4-δ, where x varies as 0.1, 0.3 and 0.5 mole fractions, were prepared from the powders of the pure components by the conventional ceramic route. The presence of two phases in multiferroic was confirmed by XRD technique. The variation of dielectric constant and dissipation factor, as a function of frequency from 100 Hz to 1 MHz and in the temperature range of 30–500°C were studied. The piezoelectric d₃₃ coefficient of these composites was also studied in these composites. The magnetoelectric (ME) output voltage was measured in terms of the dE/dH as a function of magnetic bias field. A high value of ME output (1200 mV/Oe · cm) was obtained in the composite containing 70% ferroelectric phase (PbZr_0.52Ti_0.48O₃) and 30% ferrite phase (Ni_0.93Co_0.02Mn_0.05Fe_1.95O_4-δ). These multiferroic particulate composites are used as sensors and transducers.

The formation and characterization of multiferroic Gadolinium Ferrite (GdFeO₃) nanoparticles has been demonstrated in detail. The structural, magnetic, magnetodielectric, ferroelectric, optical and electrical properties are studied at different temperature ranges. Dielectric properties, DC and AC transport properties and dielectric relaxation behavior are analyzed in electrical characterization. XRD pattern confirms the phase formation where crystallite size, lattice strain, etc. are carried out by Rietveld refinement and Williamson–Hall plot. Average particle size is 64 nm, which is calculated from TEM image. Mixed ferroic order of ferromagnetism and antiferromagnetism along with exchange bias are detected in the nanoparticles. Ferroelectric nature of the sample is confirmed by the P-E hysteresis loops. Positive magnetodielectric coupling is observed in GdFeO₃ nanoparticles, which is a signature of multifunctionality nature. Charge transport mechanism of DC and AC applied electric field is successfully analyzed with Mott’s variable range hopping (VRH) and correlated barrier hopping (CBH) theoretical models, respectively. Non-Debye type relaxation behavior is observed with activation energy of 0.37 eV. Optical band gap is calculated from the Tauc plot (2.98 eV) which confirms the semiconducting nature of the sample. Existence of ferromagnetic/antiferromagnetic (FM/AFM) and ferroelectric along with magnetodielctric coupling ensures the multiferroic property of GdFeO₃ nanoparticles, which may enhance potentiality in spintronic device applications.

The crystal structure and luminescent properties of Al-substituted ${\mathrm{\text{BaFe}}}_{12}{\mathrm{\text{O}}}_{19}$ were studied. It was found that under normal conditions, the samples are characterized by the space group P6₃/mmc. Depending on the ionic radii of the Al and Fe atoms and the concentration of Al atoms, a decrease in the distance between the atoms in the crystal structure and the lattice parameters was observed. ${\mathrm{\text{BaFe}}}_{12-x}{\mathrm{\text{Al}}}_x{\mathrm{\text{O}}}_{19}$ crystals ($x$ = 0.1–1.2) were excited by a laser with a wavelength of 375 nm and 435 nm, to study their luminescent features. From the information obtained from luminescent spectrum, it is seen that with the replacement of magnetic ${\mathrm{\text{Fe}}}^{3+}$ ions by diamagnetic ${\mathrm{\text{Al}}}^{3+}$ ions, the intensity of the spectra increases. During exciting by a laser with a wavelength of 435 nm, anti-Stokes luminescence is observed in the ultraviolet region.

Multiferroic Bi_0.95La_0.05Fe_0.7Sc_0.3O₃ (BLFS) thin films with different thicknesses have been prepared on (1 0 0) LaAlO₃ (LAO) substrates using a sol–gel process and annealed in N₂ ambient at 650°C for 5 min. From the X-ray diffraction (XRD) analysis, it was observed that BLFS thin films had (h 0 0)-preferred orientation for the film thickness 63, 125, 186, and 240 nm and became isotropic thereafter. The films developed in-plane epitaxial growth with respect to the substrate. The surface morphology became denser and the surface roughness increased as thickness increased up to 241 nm. The highest dielectric constant observed for the 241 nm thick BLFS film too. No prominent of the leakage current density observed for the film thickness up to 241 nm. However, two fold increase in the leakage current density observed for the film thickness 382 nm. For the BLFS films with thickness 241 nm, we observed the highest dielectric constant (ε) value of 1675 and remnant polarization (P_r) polarization value of 52 μC/cm² using a sol–gel spin coating process.

The insertion effect of Bi-excess layers on stoichiometric BiFeO₃ thin films prepared by chemical solution deposition is investigated. A stoichiometric BiFeO₃ thin film with both the Bi-excess top and bottom surface layers shows improved crystallinity with the remanent polarization of 65 μC/cm² at 80 K, which is larger than for BiFeO₃ film prepared by the same process using stoichiometric solution. These results are attributed to the reduction of the imperfect crystal at the interface between the BiFeO₃ film and electrode. By inserting Bi-excess layers, the saturated magnetization of all the films becomes smaller than that of the film using stoichiometric solution. Bi-excess surface layers at the top and bottom interfaces are an effective way to obtain good ferroelectric properties.

BiFeO₃ (BFO) is usually considered as a multiferroic material, which shows both ferroelectric and antiferromagnetic properties at room temperature. It is an important material having potential applications in various spintronics devices. Many studies have been done to understand the ferroelectric and magnetic responses of BFO; therefore, this work is focused on characterizing the coupling effects of electric, magnetic and mechanical field on the ferroelectric properties and surface potential of the BFO thin films. A polycrystalline BFO film (~200 nm) is deposited on the Si substrate by the Pulse Laser Deposition techniques. The Vertical Piezoresponse Force Microscopy (PFM) is used to study the ferroelectric domain structure and the hysteresis loop of as-deposited BFO film as well as the effects of the mechanical stress and magnetic field on those properties. Kelvin Probe Force Microscopy (KPFM) is used to measure the surface potential of the samples. To apply the mechanical stress on the film, micro-indentations were made on the surface of the film with two different loads (1.96 N, 2.94 N). Then the ferroelectric domain structure, strain amplitude, domain switching (hysteresis response) behavior and surface potential are measured at the locations near the side of the indentation cavity and cracks. This way, the coupling effects of electric, magnetic and stress field on BFO film are studied at nanoscale.

A multiferroic heterostructure composed of (Bi_0.875Nd_0.125)FeO₃ (BNF) are grown on (Ba_0.65Sr_0.35)TiO₃(BST) buffered Pt/Ti/SiO₂/Si(100) substrate by rf-magnetron sputtering. The heterostructure BNF/BST exhibits a quite low leakage current (3.7 × 10^-7 A/cm² at 300 kV/cm) and dielectric loss (0.0036 at 100 kHz) at room temperature. The saturated magnetization and the coercive field of the BST/BNF heterostructure are 37.7 emu/cm³ and 357.6 Oe, respectively. The low leakage current owed to the action of BST in the charge transfer between BNF and the bottom electrode, the coupling reaction between BST and BNF films. And the better crystallization in BNF/BST heterostructure thin film lead to the ferromagnetic properties enhanced.

Multiferroic composite thin films of ferroelectrics and magnets have attracted ever-increasing interest in most recent years. In this review, magnetoelectric (ME) responses as well as their underlying ME coupling mechanisms in such multiferroic composite thin films are discussed, oriented by their potential applications in novel ME devices. Among them, the direct ME response, i.e., magnetic-field control of polarization, can be exploited for micro-sensor applications (sensing magnetic field, electric current, light, etc.), mainly determined by a strain-mediated coupling interaction. The converse ME response, i.e., electric-field modulation of magnetism, offers great opportunities for new potential devices for spintronics and in data storage applications. A series of prototype ME devices based on both direct and converse ME responses have been presented. The review concludes with a remark on the future possibilities and scientific challenges in this field.

Based on density-functional calculations, we have studied possible ferroelectric switching path in monodomain single crystal of rhombohedral BiFeO₃, a prototypical multiferroic compound. By carefully studying the behaviors of FeO₆ corner-sharing double-tetrahedrons, we find abrupt changes in total energy and oxygen atomic positions, and therefore polarizations, occur in the ferroelectric switching path of rhombohedral BiFeO₃. Detailed analyses suggest that such behavior might be caused by the frustrated magnetic ordering in the paraelectric phase of rhombohedral BiFeO₃, where three O atoms and the Bi atom are in the same plane perpendicular to the polarization direction. This is supported by the fact that the ferroelectric switching for paramagnetic BiFeO₃ is smooth and has a much lower energy barrier than that of antiferromagnetic BiFeO₃.

Domain structure, ferroelectric and magnetic properties of [001]-oriented multiferroic single crystals Pb(Fe_0.5Nb_0.5)O₃–Pb(Yb_0.5Nb_0.5)O₃–PbTiO₃ (PFN–PYN–PT) with various compositions were investigated with the purpose of understanding the ferroelectric and magnetic order. The samples were determined to be rhombohedral phase or coexistence of tetragonal and rhombohedral phases by means of X-ray diffraction analysis and optical study. Furthermore, the domain configuration in tetragonal phase always takes on 90° domain wall. All samples exhibit well-developed saturated hysteresis loop, indicating no substantial increase of conductivity despite the introduction of Fe³⁺ ions. But the piezoelectric coefficients were reduced due to the introduction of PFN. In addition, the PFN–PYN–PT single crystals showed paramagnetic behavior, resulting from the –O–Fe³⁺–O–Nb/Yb/Ti–O–Fe³⁺–O– magnetic interaction. Interestingly, M–H hysteresis loops display a magnetic relaxor behavior.