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The original micromagnetism is quasi-classical since it is based on the assumption that the magnetization magnitude is unchanged in the whole magnetic system, so the theory is only strictly valid at zero temperature. To generalize its applicability to elevated temperatures, Garanin proposed the Landau–Lifshitz–Bloch equation by further considering the random fields arising from the heat effects and allowing the length variations of magnetic moments. However, the expressions for the fields and changes are usually complicated, or even impossible to be derived for materials with complex spin structures. In the present work, a quantized static micromagnetic theory is proposed and integrated with the quantum computational methods we developed before, and afterwards used to simulate the topological ferromagnetic (FM) and ferroelectric (FE) textures in the CoFeB-like multiferroic thin films consisting of spins with S = 1/2, 1, 3/2, 2, and 5/2 respectively. Consequently, both FM and FE skyrmionic lattices (SkLs) of the Néel- and Bloch-types are observed simultaneously at low temperatures, except for the case of S = 1/2 where only FM SkLs can be induced; the topological charge per FM skyrmion (SkN) is calculated to be -1.0, whereas those of FE SkNs are quantized fractional numbers; and the formation temperatures of the FM and FE SkLs are proportional to J S (S + 1). With this quantized micromagnetic theory, we are able to simulate and display FM and FE textures in mesoscopic scale at nonzero temperatures without the need to derive extra mathematic expressions, however with greatly reduced computer memory and expedited computational speed. This work possibly paves a new way for computational magnetism. • A quantized static micromagnetic theory and its computational method are proposed here. • The quantum theory and computational method can be applied at nonzero temperatures. • The computing program is used to simulate topological textures in multiferroic films. • FM and FE skyrmionic crystals in mesoscopic scale are produced at low temperatures. • The topological charges of ferroelectric skyrmions are quantized fractional numbers. [ABSTRACT FROM AUTHOR]

• The structural properties can be obtained in Tm 1− x In x FeO 3 ceramics with different doping of In. • Structural and magnetic properties was discussed in the h -Tm 1− x In x FeO 3 (x = 0.6, 0.7). • Magnetoelectric coupling effects was observed in in the h -Tm 1− x In x FeO 3 (x = 0.6, 0.7). Hexagonal rare-earth ferrites (h -RFeO 3) is a promising multiferroic materials with strong magnetoelectric coupling effect by tuning the collective tilt of FeO 5 trigonal bipyramids. However, the metastable hexagonal structure for RFeO 3 bulk materials is still pain point that needs to be solved. In this work, multiferroic h -RFeO 3 ceramic materials were designed and prepared by doping TmFeO 3 ceramics with In, which were fabricated by using the standard solid-state sintering method. Stable h -Tm 1− x In x FeO 3 (x = 0.6, 0.7) ceramics crystallized into a pure hexagonal structure with the polar space group P6 3 cm (x = 0.6) and the non-polar space group P6 3 /mmc (x = 0.7) at room temperature. Two magnetic transitions were identified in the ceramic samples, a paramagnetic to antiferromagnetic transition (T N), and spin reorientation transition (T SR). The dielectric anomalies were observed around the spin reorientation temperature (T SR), which indicates significant magnetoelectric coupling effects in the h -Tm 1− x In x FeO 3 (x = 0.6, 0.7) ceramics. Furthermore, using dielectric and pyroelectric characterization techniques, dielectric peaks were observed near 280 K for the x = 0.6 sample, which should be a weak structural transition through the analysis of XRD patterns at various temperatures. The presence of stable hexagonal structure for In-doping TmFeO 3 is enlightening the multiferroic materials in hexagonal ferrites. [ABSTRACT FROM AUTHOR]

Nonvolatile electrical control of magnetism in two-dimensional (2D) van der Walls heterostructure has sparked significant interest for both understanding the fundamental magnetoelectric physics and device application. Here, using the first-principles calculations, we propose a new multiferroic van der Waals (vdW) heterostructure C 2 N / In 2 Se 3 based on C 2 N and ferroelectric (FE) In 2 Se 3 relying on no-transition metals. Upon electron doping, C 2 N / In 2 Se 3 - P ↓ maintains nonmagnetic nature, but C 2 N / In 2 Se 3 - P ↑ changes into ferromagnetic state. Moreover, the magnetoelectric coupling is enhanced via engineering interlayer distance of C 2 N / In 2 Se 3 . The magnetic moment of C 2 N / In 2 Se 3 - P ↑ reaches 1.0 μ B /e over the electron concentration ranging from 0.1 to 0.4 e per unit cell at an interlayer distance of 3.2 Å. Our results broaden the materials design space for 2D multiferroic materials. [Display omitted] • We have designed a new multiferroic heterostructure without magnetic transition metals. • Upon electron doping, C 2 N / In 2 Se 3 displays different magnetic states. • The magnetoelectric coupling can be tuned via engineering interlayer distance of C 2 N / In 2 Se 3 . • Our results broaden the materials design space for 2D multiferroic materials. [ABSTRACT FROM AUTHOR]

• Investigated the longitudinal (α 33) and transverse(α 31) ME effect for CoFe 1.88 Dy 0.12 O 4 –K 0.5 Na 0.5 NbO 3 multiferroics. • K 0.5 Na 0.5 NbO 3 showed the d 33 of 47 pC/N having 25296 × 10-15 m2/N figure of merit. • The CFDO /KNN/ CFDO structure revealed the α 31 38.5 mV/cm·Oe at 400 Oe and -37.55 mV/cm·Oe at -400 Oe. • Significance of piezomagnetic coupling coefficients is discussed to get the correct hysteretic nature for magnetoelectric response. • The hysteretic nature is a characteristic feature of multiferroic system is verified. The magnetoelectric (ME) laminate structures of CoFe 1.88 Dy 0.12 O 4 (CFDO, ferrite) and K 0.50 Na 0.50 NbO 3 (KNN, ferroelectric/piezoelectric) phases were fabricated by silver epoxy bonding technique and tested the ME response in longitudinal (α 33) and transverse (α 31) mode. The CFDO reveals the cubic spinel structure while KNN reveals the perovskite orthorhombic crystal structures having dense microstructure. The CFDO confirms the phase segregation of the DyFeO 3 ortho -ferrite phase, while the KNN lead-free ceramic showed the Curie temperature of 416 °C, 13µC/cm2 maximum polarization, 25,296 × 10-15 m2/N figure of merit, piezoelectric charge coefficient d 33 of 47 pC/N. The longitudinal (α 33) and transverse (α 31) dynamic magnetoelectric response is studied to figure out the effective magnetic field direction to get better values of magnetoelectric voltage sensitivity i.e. α ME. Both modes revealed the hysteretic behavior i.e. lagging of ME voltage response to an applied magnetic field which evidences a true multiferroic character of CFDO/KNN laminates. Remarkably, the (CFDO /KNN/ CFDO) structure demonstrated a substantial magnetoelectric coefficient in LT (α 31) mode of approximately 38.5 mV/cm·Oe at a magnetic field of 400 Oe and −37.55 mV/cm·Oe at a magnetic field of −400 Oe. Thus, here we present the magnetoelectric laminate structure of CFDO /KNN/ CFDO phases beneficial for magnetic field sensors. [ABSTRACT FROM AUTHOR]

• In this work, our creative points are in two aspects. One is the importance of inter-chain interaction is included in our model, that is not found in literature. • Another one is our reformed method, e. g. quantum Green's functional approach [25,26] by mapping spin operator into creative or annihilate field one. • A random phase approximation (RPA) is used for quasi-particle interactions to replace the Hartree-Fock one. • Our calculations show both spin transverse fluctuation and longitudinal fluctuation are equally importance in Green's function equation of motion. [ABSTRACT FROM AUTHOR]

• we have synthesized Ni 0.5 Co 0.5 Fe 2 O 4 (NCFO) and BaTiO 3 (BTO) core–shell (12 % NCFO − 88 %BTO) multiferroic nanopowder by hydrothermal method and sol–gel method, respectively. • The core–shell like morphology is clearly observed in the SEM analysis. • The sample exhibits a notable energy storage density W (38.25 mJ/cm3), accompanied by a slightly lower energy storage efficiency η (46.50 %) and energy loss density W rec (17.78 mJ/cm3). • From the magnetic measurements it is revealed that the sample shows lower saturation magnetization (1.33 emu/g) with coercivity (430 Oe) and magneto-crystalline anisotropy of (595.7 erg/g). • A moderate magnetoelectric coefficient of 18.34 mV/cm*Oe is observed on the higher field side than the value obtained on the lower field side (32.62 mV/cm*Oe). In this report, we have synthesized Ni 0.5 Co 0.5 Fe 2 O 4 (NCFO) and BaTiO 3 (BTO) core–shell (12 % NCFO − 88 %BTO) multiferroic nanopowder by hydrothermal method and sol–gel method, respectively. The structural, morphological, ferroelectric, and magnetoelectric properties of the as- prepared sample was investigated in detail. X-ray diffraction results revealed that no secondary phase is obtained. As investigated from the scanning electron microscopy (SEM) and energy dispersive X-ray (EDX) analysis, the grains are almost spherical, which depicts the core–shell like morphology and the presence of all the constituent elements in the prepared sample. FTIR analysis gives information about the formation of two individual phases and the different chemical compositions present in the sample. The prepared core–shell composite exhibits a notable energy storage density W (38.25 mJ/cm3), accompanied by a slightly lower energy storage efficiency η (46.50 %) and energy loss density W rec (17.78 mJ/cm3). Magnetic characterization revealed that the sample shows lower saturation magnetization (1.33 emu/g) with coercivity (430 Oe) and magneto-crystalline anisotropy (595.7 erg/g). A moderate magnetoelectric coefficient of 18.34 mV/cm*Oe is observed on the higher field side, surpassing the value on the lower field side 32.62 mV/cm*Oe. Anisotropy in the system leads to varying magnetoelectric coefficients in different directions. These findings provide valuable insights for enhancing the magnetoelectric response in core–shell multiferroic composites. [ABSTRACT FROM AUTHOR]

• The influence of different Nd and PbTiO 3 compositions on the magnetic and magnetoelectric features of (1-y)Bi 1-x Nd x FeO 3-y PbTiO 3 solid solutions, were investigated. • The degree of magnetization is found to increase with increasing Nd doping due to the modification in spiral spin structure and by affecting Fe-O-Fe bending's. • The splitting of the ZFC and FC branches in M-T plots with increasing Nd doping indicate the change of antiferromagnetic to ferromagnetic behavior of solid solutions which is also confirmed by M-H characterization of solid solutions. • The splitting of the ZFC and FC branches in M-T plots with increasing Nd doping indicate the change of antiferromagnetic to ferromagnetic behavior of solid solutions which is also confirmed by M-H characterization of solid solutions. • The splitting of the ZFC and FC branches in M-T plots with increasing Nd doping indicate the change of antiferromagnetic to ferromagnetic behavior of solid solutions which is also confirmed by M-H characterization of solid solutions. Magneto-electronic devices applications of room-temperature multiferroics have been made possible by recent developments. But the potential use of pure BFO in multifunctional devices is constrained by its antiferromagnetic nature and need substitution-induced modification to improve magnetic and magnetoelectric properties. In the present paper, attempt has been made to improve the magnetic and magnetoelectric properties of the BiFeO 3 -PbTiO 3 solid solution by incorporating Bismuth cation with Lead(II) ion and Ferric cation with Titanium cation into the formulation of Nd doped,(1- y)Bi 1- x Nd x FeO 3 - y PbTiO 3 where x = 0.05,0.10,0.15,0.20 and y = 0.1, 0.2,0.3 and 0.4. The impact of different PbTiO 3 and Nd compositions on magnetoelectric and magnetic characteristics of solid solution has been investigated. The results showed that, degree of magnetization continuously increases with increasing Nd doping by affecting Fe-O-Fe angles. However, the magnetization drops as the volume of PbTiO3 rises, that may be attributed to a rise in the tetragonal phase of solid solutions. The improvement of the magnetoelectric coupling coefficient and change of antiferromagnetic behaviour to ferromagnetic behaviour of solid solutions has been observed with increasing Nd doping. This enhance the ferromagnetic behaviour of the compound. [ABSTRACT FROM AUTHOR]

• Mixing of electric and magnetic field frequencies was observed in a heterostructure. • Nonlinearity of converse ME effect arises due to nonlinearity of magnetoelasticity. • A theory describing converse ME effects in composite structures has been developed. Nonlinear magnetoelectric effects in a disk-like heterostructure composed of a layer of amorphous ferromagnet (FeBSiC) mechanically coupled to a layer of piezoelectric ceramics (lead zirconate titanate) were studied both experimentally and theoretically. The structure was excited by alternating electrical and magnetic fields far from its acoustic resonance frequency. This induced changes in the magnetic induction within the heterostructure which were recorded using an electromagnetic coil. The experiments were performed for excitations with electric and magnetic fields up to 250 V/cm and 6 Oe, respectively, and bias permanent magnetic fields up to 60 Oe. For large excitation fields, a generation of the second harmonic and harmonics corresponding to the sum and difference frequencies were observed. The coefficient of the frequency doubling for the converse magnetoelectric effect and the coefficient of mixing of electrical and magnetic field frequencies were found to be 4.6∙10−6 G cm2/V2 and ∼1∙10−2 G cm/(Oe∙V), respectively. A simple theoretical model qualitatively describing the experimental findings was proposed. It was shown that the nonlinearity in the converse magnetoelectric effect arises due to the nonlinear dependence of magnetic induction in the ferromagnetic layer on mechanical stress. [ABSTRACT FROM AUTHOR]

• La 1− x Y x FeO 3 had been synthesized by a combustion method using citric acid. • Structural and microstructural have been studied using XRD and Rietveld method. • The estimated values of crystallite size from HRTEM and XRD data were coincident. • LYFO crystals are canted antiferromagnets with room temperature weak ferromagnetism. • Magnetization versus temperature M(T) and M(H) hysteresis loop were analyzed. In this work, the structural and magnetic properties of multiferroic La 1 - x Y x FeO 3 perovskites, (x = 0.00, 0.05, 0.10, 0.15, 0.20, 0.25 and 0.30) synthesized through Sol-gel auto-combustion technique were investigated.The room temperature synchrotron X-ray diffraction (XRD) analysis revealed that the all the synthesized samples consisted of the polycrystalline orthorhombic structure perovskites (space group pnma), and tolerance factor confirmed the phase stability of the prepared perovskite system.The Williamson-Hall plots based on synchrotron XRD data were employed to estimate the average particle diameter and vary from 18.8 nm to 37.5 nm.For a deeper insight into the crystal structure, high-resolution transmission microscopy imaging (HRTEM) was performed.The estimated values of crystallite size from HRTEM and synchrotron XRD data were coincident.Many of crystallographic parameters and electron density measurements were calculated by Rietveld refinement of synchrotron XRD data. La 1 - x Y x FeO 3 perovskite crystals are canted antiferromagnets with a weak ferromagnetism at room temperature.Selected Area Electron Diffraction (SAED) patterns of the investigated samples exhibited spotty ring patterns, confirming the polycrystalline character.The magnetic properties were gotten through analyzing the magnetization versus temperature M(T) and M(H) hysteresis loop which characterized by a vibrating sample magnetometer (VSM). The orthoferrite La 1 - x Y x FeO 3 crystals are a promising candidate for optical device applications in broad temperature range and high power system. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • Investigated materials are ferri- or antiferromagnetic materials. • Investigated materials present good ferroelectric properties. • Investigated materials present magneto-crystalline anisotropy and anisotropic ferroelectric response. • The effect of double magnetism on multiferroism of R3c structure was evaluated. • The PbFeO 3 materials present half-metallic behavior as a consequence of spin contamination on Pb atoms. Abstract Multiferroic materials, such as the BiFeO 3 , have been investigated as emergent material to technological purposes. Other multiferroic materials reported in literature are PbNiO 3 , NiTiO 3 and FeTiO 3. In this work, we decide to investigate a new series of multiferroic materials composed by Fe3+ in A and B sites of R3c structures, resulting in AlFeO 3 , FeAlO 3 , FeVO 3 , BiFeO 3 and PbFeO 3. Therefore, a DFT/B3LYP investigation was employed to evaluate the structural, electronic, topological analysis, ferroelectric and magnetic properties, as well as the magnetoelectric coupling. Our results indicates that the multiferroism were theoretically evidenced in these materials since a magnetic resultant is oriented along [1 1 1] direction of unit cell (as ferromagnetic as antiferromagnetic materials) while the ferroelectricity is oriented along z [0 0 1] direction. In all materials, it was observed a D 3d distortion on clusters and its characteristic energy levels pattern for t 2g and e g. In particular, the electronic structure of PbFeO 3 material indicates that Pb atoms presents a spin contamination caused by unpaired electrons from Fe in the structure and also suggesting a half-metallic ferromagnetism pointing it as important alternatives to spintronic devices development. The results for energetic stability suggest that all materials are stable under high pressures and room conditions. [ABSTRACT FROM AUTHOR]

Highlights • The Fe 48 Rh 52 magnetic film with a thickness of 50 nm was grown on a piezoelectric substrate by magnetron sputtering. • Magnetic measurements of the FeRh film helped to observe an AFM-FM phase transition around 305 K (B = 0.1 T) in heating with a 27 K hysteresis, which is broader than in bulk alloys. • A maximum of direct and converse magnetoelectric coefficients near the temperature of the AFM-FM transition was found during magnetoelectric measurements. Abstract The Fe 48 Rh 52 magnetic film with a thickness of 50 nm was grown on a piezoelectric substrate by magnetron sputtering. The chemical composition and crystalline structure were examined by energy dispersive X-ray spectroscopy and X-ray diffraction, respectively. Two types of structural phases were detected: a bcc phase chemically ordered to the CsCl-type (B2 or α′) and an fcc γ-phase. Magnetic measurements of the FeRh film helped to observe an antiferromagnetic-ferromagnetic phase transition around 305 K (B = 0.1 T) in heating with a 27 K hysteresis, which is broader than in bulk alloys. A maximum of direct and converse magnetoelectric coefficients around the temperature of the antiferromagnetic-ferromagnetic transition was found during magnetoelectric measurements; they correlate with the results of magnetic measurements. [ABSTRACT FROM AUTHOR]

Highlights • Possible change of metal ions and organic blocks in layered metal-organic perovskites. • Magnetic anisotropy and transitions from Heisenberg 2D to 3D and to Ising 3D magnet. • Changes of magnetization at temperatures of structural transformations. Abstract Metal organic compound (C 2 H 5 NH 3) 2 CuCl 4 belongs to the family of layered perovskite multiferroic materials. It consists of ferromagnetic layers of corner sharing [CuCl 4 ]2− octahedra connected by organic ions (two layers of [C 2 H 5 NH 3 ]+). In this work we have studied magnetic properties of (C 2 H 5 NH 3) 2 CuCl 4 using SQUID magnetometer and AC susceptometer. Temperature dependence of magnetization showed existence of the antiferromagnetic transition at 10.2 K which changes to ferromagnetic with the application of moderate magnetic field. Near structural transition temperatures the anomaly of magnetization was observed. Hysteresis loops showed ferromagnetic behaviour for T < T N and existence of anisotropy. Results of AC measurements showed no frequency dependence of the susceptibility and obtained temperature dependence of nonlinear susceptibility can be interpreted as a result of successive crossovers between different regimes. [ABSTRACT FROM AUTHOR]

Highlights • In this work, the standard and straightforward method of solid-state reaction and direct mixing of ferrite and ferroelectric phases were used to prepare high-quality magnetoelastic multiferroic composites, (x)NiFe 2 O 4 + (1 − x)BaTiO 3. • The significant change in temperature-dependent magnetization curves of NiFe 2 O 4 -BaTiO 3 composite multiferroics at structural phase transitions of BaTiO 3 is a clear signature of the strain-mediated converse magnetoelectric effect. • The NiFe 2 O 4 -BaTiO 3 composite system will be a potential candidate for future low-power consumption device applications at room temperature. Abstract The room-temperature magnetoelastic coupling has been demonstrated in (x)NiFe 2 O 4 + (1 − x)BaTiO 3 (where x = 0–1 with a difference of 0.1) composite system by investigating its structural, magnetic and ferroelectric properties. The samples were prepared by the standard solid-state reaction method and characterized by x-ray diffraction, backscattered scanning electron microscopy and energy dispersive x-ray spectroscopy techniques. The temperature dependent magnetization data clearly show significant jumps in magnetization curves at structural phase transitions of BaTiO 3 , signifying the strain-mediated converse magnetoelectric (CME) coupling in NiFe 2 O 4 -BaTiO 3 multiferroic system. The substantial changes observed in the obtained parameters from structural, magnetic and ferroelectric properties clearly ensure the strain-mediated magnetoelectric (ME) as well as CME effects in this system. The present investigation indicates that the NiFe 2 O 4 -BaTiO 3 composite system will be a potential candidate for the future low-power consumption device applications at room temperature. [ABSTRACT FROM AUTHOR]

Highlights • Phase transitions in multiferroic superlattice with two order parameters studied. • The ground state is calculated by minimizing energy with steepest descent method. • ME interaction parameter J C mf = - 3.7 separates two types of phase transition. Abstract In this paper, we study the phase transitions in superlattice with two order parameters by the use of Monte Carlo simulation. We have studied the effects of temperature, external magnetic field, magnetoelectric coupling and interface effects on the multiferroic superlattice. Our multiferroic superlattice is formed by interleaved ferromagnetic and ferroelectric layers. Ferromagnetic layers are modelled as simple cubic lattice with Heisenberg spins. Electrical polarization of (0, ±1) was randomly assigned at each simple cubic lattice site in the ferroelectric layers in the direction perpendicular to the plane of layers. The effect of magnetoelectric coupling between ferroelectric and ferromagnetic layers of the system on the critical temperature, the order parameters, the susceptibility, the internal energy, the surface magnetization of the system have been considered in detail. The layer magnetizations as functions of temperature are shown for various interaction and field parameters. [ABSTRACT FROM AUTHOR]

Highlights • ATiO 3 (A = Mn, Fe, Ni) surfaces were investigated from DFT calculations. • The relation between morphology for these materials and magnetism is highlighted. • Enhanced superficial magnetism was founded for the different surfaces. • Multiferroic properties can be tunned by morphological modulations. Abstract Magnetic materials are of great interest due to their widespread applications in various technologies. Precise control of different aspects of the morphology and magnetic properties is a key aspect in establishing their relationship with material shapes and sizes. In this work, the density functional theory (DFT) is applied to investigate the surface structure and magnetic properties of low-index (1 1 0), (1 0 1), (1 0 0), (0 0 1), (1 1 1), (0 1 2) surfaces of ATiO 3 (A = Mn, Fe, Ni) multiferroic materials. In particular, a theoretical approach, based on the Wulff construction and magnetization density (M) index, is applied to infer the relationship between the morphology and surface magnetism. The results indicate that the magnetic properties of ATiO 3 materials can be controlled by the presence of exposed surfaces. In particular, the (0 0 1) and (1 1 1) surfaces are found to be adequate to enhance the superficial magnetism. The underlying reasons behind such mechanism are discussed from the perspective of uncompensated spins and charge-transfer processes along the exposed surfaces. This investigation suggests that the morphology-oriented ATiO 3 materials are good candidates for superior multiferroic applications. [ABSTRACT FROM AUTHOR]

Highlights • Multiferroic YMn 0.5 Cr 0.5 O 3 possesses a multicaloric effect. • YMn 0.5 Cr 0.5 O 3 displays a second-order magnetic phase transition. • The nearest neighboring exchange integral J 12 of 10−4 eV has been derived from the spin wave picture. Abstract We have studied magneto- and electro-caloric effects in multiferroic YMn 0.5 Cr 0.5 O 3 compound, which has a ferrimagnetic transition at T N ∼73 K. Two peaks in the temperature dependence of isothermal magnetic entropy change Δ S M can be observed at T N and lower T 0 , respectively. While the first maximum of Δ S M corresponds to the ferrimagnetic transition as expected, the second one might be related to a metamagnetic transition. Using the Maxwell's relation, an electric field driven entropy change (−Δ S E) has also been obtained at temperatures around T N , revealing the multicaloric effect in the YMCO sample. Temperature dependence of the specific-heat confirms the second-order feature for the ferrimagnetic transition in YMCO. By fitting the specific-heat and magnetization data at low temperatures according to the spin-wave excitation model, the nearest neighboring exchange integral J 12 has been estimated to be around 10−4 eV, which is in agreement with the value gained from the molecular field theory. [ABSTRACT FROM AUTHOR]

Highlights • We provide a theoretical description of frustrated helimagnet MnI 2 at low temperature. • Competition of two multiferroic orders is successfully described. • Evolution of electric polarization with magnetic field is explained qualitatively. Abstract We provide a theoretical description of frustrated multiferroic MnI 2 with a spiral magnetic ordering in magnetic field h. We demonstrate that subtle interplay of exchange coupling, dipolar forces, hexagonal anisotropy, and the Zeeman energy account for the main experimental findings observed recently in this material (Kurumaji et al., Phys. Rev. Lett. 106 (2011) 167206). We describe qualitatively the non-trivial evolution of electric polarization P upon h rotation, changing P direction upon h increasing, and disappearance of ferroelectricity at h > h c , where h c is smaller than the saturation field. [ABSTRACT FROM AUTHOR]

Highlights • Low temperature neutron diffraction data reveal non-collinear magnetic structure in Co 4 Ta 2 O 9. • Neutron diffraction data fit best to a non-centro-symmetric crystal structure below Neel temperature. • Correlation between magnetic structure and improper ferroelectricity is analyzed for Co 4 Ta 2 O 9. • Co-existing large magnetoelectric coupling is determined in the spin-flop phase of Co 4 Ta 2 O 9. Abstract We study magnetocapacitance (MC) effect and magnetoelectric (ME) coupling in spin-flop driven antiferromagnet Co 4 Ta 2 O 9. Powder neutron diffraction data reveal that the magnetic structure corresponds to a non-collinear arrangement along with a non-centrosymmetric crystal structure below Néel Temperature. Electric polarization is achieved below Néel temperature only when the sample is cooled in the presence of external magnetic field. The magnetocapacitance data at high magnetic fields are analyzed by phenomenological Ginzburg-landau theory of ferro-electromagnets and it is found that change in dielectric constant is proportional to the square of magnetization. The saturation polarization and magnetoelectric coupling are estimated to be 52 µC/m2 and γ = 1.4 × 10−3 (emu/g)−2 respectively at 6 Tesla. Strong magnetoelectric coupling and ferroelectric phase in the anti-ferromagnetic Co 4 Ta 2 O 9 are correlated to magnetic structure as derived from neutron diffraction data. [ABSTRACT FROM AUTHOR]

• A systematic study of Ni–Mn–Ga substituted by elements from Cr to Cu is presented. • Transformation temperatures vary non–trivially with valence electron number. • Saturation magnetization at 10 K seems to follow Slater–Pauling curve. • Complex behavior of magnetocrystalline anisotropy is observed. Heusler Ni–Mn–Ga alloys with martensitic transformation being multiferroic materials exhibit magnetic shape memory (MSM) phenomena and moreover, these are touted for magneto– and multi–caloric effect (MCE). MCE benefits from high saturation magnetization and also large variability and sensitivity of transformation temperatures on alloying. In contrast, MSM phenomena are limited by low temperatures of both ferromagnetic and ferroelastic transformations. In an attempt to increase or modify the transformation temperatures and to understand the physical fundamentals beyond transformation variations and magnetic ordering, we experimentally investigate the magnetic and transformation properties in Ni 2 MnGa alloyed with transitional elements spanning from Cr to Cu. These elements are consecutively substituted on Ni, Mn, and Ga sites, to establish the effect of chemical substitution and elemental evolution. The elemental dependence of saturation magnetization, magnetocrystalline anisotropy, Curie temperature, and martensitic transformation temperatures are compared with (non–)stoichiometric Ni–Mn–Ga Heusler compounds. The observed behavior is complex and there are no clear trends of transformation temperatures as a function of the number of valence electrons or of non–bonding electrons per atom. The saturation magnetization at 10 K seems to follow the Slater–Pauling curve particularly for Ni substitution. Obtained results can serve as useful rectification for the theoretical prediction of new Ni–Mn–Ga–X Heusler alloys. [ABSTRACT FROM AUTHOR]

Highlights • The dynamic magnetization model of the magnetic moment flipping under the stress is established. • The results show that the nanomagnets with different tilt angles have clock sensitivity differences. • After applying a bias magnetic field, the tilted nanomagnets can complete the 180° switching under stress regulation and still have the differences of clock sensitivity. • The tilting nanomagnet has great advantages in fabrication process and numerical calculation. Abstract In this paper, the dynamic magnetization model of multiferroic elliptical nanomagnets with different tilt angles is established. Simulation of dynamic magnetization is performed through micromagnetic method. The results show that the clock sensitivities are different for nanomagnets with different tilt angles. For tilt angles below 9°, the larger the tilt angle is, the smaller the stress required for the nanomagnet to flip to the "Null" state is. Encouragingly, 180° switching of tilted nanomagnet can be achieved by applying a bias magnetic field together with stress, even if the nanomagnet is at a high aspect ratio (2:1). However, nanomagnet with excessively large tilt angle (>10°) tends to yield a vortex process during switching. As a consequence, stress duration will be longer, and larger bias magnetic field will be required for 180° switching. Therefore, nanomagnets inclined more than 10° should be avoided in magnetic design. These findings can provide important guidance for the design of multiferroic nanomagnetic logic as well as memory storage. [ABSTRACT FROM AUTHOR]

Highlights • This work presents a development of the general thermodynamic framework used to investigate metamagnetoelectric effect in multiferroic materials. The model used is a quasi-two dimensional frustrated spin chain externally controlled by a static electric field in y-direction and magnetic field in z-direction. • The entropy behavior is similar to that of the magnetic susceptibility. While the magnetic susceptibility characterizes the variations of magnetization, accordingly emphasizes the ferroic transition points of this order, the points highlight a muddle occurring due to a rearrangement of magnetic moments which is accurately described in terms of entropy. The loop of the entropy at the transition points oppose that of the heat capacity, which is strengthened during the transition process but weakened at the transition point itself. • The temperature dependance of the magnetoelectric coupling highlights how it is continuously weakened beyond the transition and accordingly assigns a continuous death to the metamagnetoelectric effect. The critical temperature value is then defined according to the corresponding electric and magnetic fields values. • The phase diagram for this model in the temperature-field plane has been investigated and the plot highlights how the heat capacity can behave as a function of applied field for different phases. • The results obtained in this work from the system constructed, could be certainly promising for the understanding of the metamagnetoelectric effect, which could be crucial for design of new mechanism in magnetoelectric spintronics. Abstract Magnetoelectric coupling in multiferroics gives rise to various properties such as metamagnetoelectric effect since external fields act. In this study, a general thermodynamic framework is developed to investigate metamagnetoelectric effects in multiferroic materials. The model used is a quasi-two dimensional frustrated spin chain controlled by a static electric field in y -direction and magnetic field in z -direction. The effects of metamagnetoelectric transitions on entropy, heat capacity and on the linear magnetoelectric coupling factor are assessed using Fermi-Dirac statistics of quantum gases and the Landau theory. The entropy behavior is shown to be similar to that of the magnetic susceptibility. In fact, while the magnetic susceptibility characterizes the variations of magnetization and accordingly emphasizes the ferroic transition points of this order, the intrinsic physics of these transition points highlights a muddle occurring due to a rearrangement of magnetic moments in the system, and this is accurately described in terms of entropy. The transition effects due to this rearrangement described in terms of entropy at the corresponding critical points show different loop to that of the heat capacity. The opposite loop showed by the heat capacity compared to the entropy is its weakening at the exact transition point in spite of its strengthening during the transition process. It is also recorded only a few ranges of the electric field which allows the effect provided. The temperature dependence of the magnetoelectric coupling highlights how it is continuously weakened by the increase of temperature, leading to a second order transition from the metamagnetoelectric state. [ABSTRACT FROM AUTHOR]

Highlights • The nanostructural growth of BaTiO 3 -CoFe 2 O 4 composite by hydrothermal method. • The compressive lattice strain in the composite via 75% of CoFe 2 O 4 with BaTiO 3. • The oriented growth of BaTiO 3 is hindered with CoFe 2 O 4 concentration. • The ferromagnetism of CoFe 2 O 4 is influenced with inversion degree and bond angles between A and B-site atoms. • Ferroelectric polarization and magnetoelectric coupling are enhanced. Abstract Magnetoelectric (ME) nanocomposites is a topic of intensive research due to their superficial potential in spintronic applications. In the present work, the magnetic field controlled electrical polarization is studied in hydrothermally synthesized multiferroic 0.25BaTiO 3 -0.75CoFe 2 O 4 (BTO-CFO) nanocomposite. This multiferroic heterostructure is combined ferrimagnetic (CFO) with ferroelectric/piezoelectric (BTO) and achieved strain-mediated ME effect, which can effectively mediate magnetic anisotropy. The X-ray diffraction pattern confirmed polycrystalline phases of spinel CFO and tetragonal BTO, for which the compressive lattice strain is made. The microstructural study has evaluated BTO-CFO nanoparticles formation and the value of d -lattice spacing is calculated. The room temperature magnetic hysteresis is arising which depends on CFO inversion degree, and the change in bond-angle/length along A and B-sites. The ferroelectric hysteresis is measured at room temperature, which changed with applied magnetic field, i.e. , the phenomenon of reduction in domain wall pinning related with oxygen vacancies and grain boundaries effect. The magnetic field is also influenced impedance spectra to induce magnetoimpedance effect and the positive value of magnetoresistance is obtained. A giant magnetodielectric coefficient up to −27% is obtained at 1 kOe of field. A strain mediated ME coupling enhancement is obtained. [ABSTRACT FROM AUTHOR]

Multiferroics, in which off-center magnetic ions induced ferroelectricity, are believed to exhibit enhanced magnetoelectric (ME) or magnetodielectric (MD) effects because their ferroelectricity and ferromagnetism are driven by the same originations. In this paper, multiferroics with off-center Mn ions were obtained in hexagonal manganite-barium titanate solid solutions. As an external magnetic field (H) was applied, intermediate and high frequency MD effects were observed. The MD (MD(%) = ( ε (H  =  3.5 kOe)  −  ε (H = 0 Oe) ) ×  100/ε (H = 0 Oe) ) values at 10 MHz frequency were 3.37%, 3.21% and 2.65% for the three samples, respectively. The further discussion indicated that the MD effects did not originate from some extrinsic source such as grain boundary magnetoresistance (MR) and contributions from the electrode, but mainly attributed to the intrinsic ME coupling such as magnetic-field-induced variations of asymmetric hopping. The first-principles calculations also confirmed that the asymmetry of coplanar octahedrons aggravated when Mn ions occupied the off-center site in the hexagonal phases, especially in 0.1La 0.7 Ca 0.3 MnO 3  − 0.9BaTiO 3 solid solutions. [ABSTRACT FROM AUTHOR]

Highlights • Investigated materials are ferro- or weak-ferromagnetic materials. • Investigated materials present high ferroelectric properties. • Magnetoelectric coupling was theoretically evidenced. • The influence of structural distortion on magnetic ground state was evidenced. • The degeneration profile for 3d Ni orbitals is different for ferromagnetic and antiferromagnetic materials. Abstract Multiferroic materials have been investigated as emergent materials to application on new technologies, mainly BiFeO 3 material, the most important multiferroic material actually. Others materials reported for multiferroic applications are NiTiO 3 and NiPbO 3. Therefore, we decide investigate a new series of materials from atoms with d0 and d10 orbitals to avoid magnetic coupling between [NiO 6 ] and [BO 6 ] clusters and to keep a high ferroelectric property. In this manuscript, a DFT/B3LYP investigation was employed to discuss new candidates to multiferroic materials based on NiBO 3 (B = Ti, Ge, Zr, Sn, Hf and Pb) compounds in R3c structure. Our results describe as antiferromagnetic states as ferromagnetic states evidencing modifications very interesting on [NiO 6 ] magnetic cluster from perturbation of t 2g and e g degenerated energy levels controlled by chemical modifications in [BO 6 ] clusters. The originality of our manuscript is the theoretical evidence that non-magnetic clusters can control the magnetic state of a material from perturbation on energy levels of the magnetic clusters. More amazing is these non-magnetic clusters are also responsible by a high spontaneous polarization naturally found in R3c structures. At end, the multiferroic effect in NiBO 3 materials is clarified from coupling between magnetic and ferroelectric properties oriented along z and x directions, respectively. [ABSTRACT FROM AUTHOR]

Exchange bias in the bilayer of half-metallic La 0.7 Sr 0.3 MnO 3 and multiferroic BiFeO 3 has been applied for the electric field control of magnetization, which is strongly limited by the much low blocking temperature of about 100 K (Phys. Rev. Lett. 105 , 027201 (2010)). One possible solution is to strengthen the interfacial exchange coupling, thus another half-metallic oxide Sr 2 FeMoO 6 is selected. Tetragonal-like BiFeO 3 has been successfully fabricated on (0 0 1) SrTiO 3 substrate using Sr 2 FeMoO 6 as buffer layer. By replacing the exchange coupling between Fe and Mn ions in BiFeO 3 /La 0.7 Sr 0.3 MnO 3 bilayer, stronger exchange couplings between Fe and Fe ions are established at the interface, and the blocking temperature has been significantly increased to 160 K. A second blocking temperature at 110 K due to the exchange coupling between Fe and Mo ions is also observed. Detailed magnetization measurements confirm the conventional mechanism of exchange coupling between ferromagnetic and antiferromagnetic layers and exclude the contribution from surface spin glass. Furthermore, BiFeO 3 still retains excellent ferroelectric properties with Sr 2 FeMoO 6 acting as ferromagnetic conducting electrode, which may have important applications in multiferroic spintronics devices. [ABSTRACT FROM AUTHOR]

Magnetoelectric properties of ferrite garnets are of great interest due to possibility of electric control of micromagnetic structures at room temperatures promising for applications in advanced technologies. However, the governing mechanisms underlying magnetoelectric coupling and origin of ferroelectricity in these materials remain under discussion. In this article, we appeal to polar mechanism related to electric dipole moments of Fe 3+ and rare earth ions in order to explain ferroelectricity of epitaxial ferrite garnet film. We show that existence of electric dipole moments of ‘ d ’ (Fe 3+ ) ions and ‘ f ’ (rare earth) ions is allowed by the local symmetry of the environments and calculate electric polarization related to electric dipole moments of the ‘ d ’ and the ‘ f ’ ions in inhomogeneously magnetized ferrite garnet film. Our results suggest that magnetoelectricity of iron garnets is attributed to polarizability of Fe 3+ and rare earth ions; the conducted calculations demonstrate the difference between polarization impacts given by electric dipole moments of rare earth and iron ions. Polarization depend on ground state of the ions, local symmetry of the ions environments and the type of magnetic inhomogeneity. [ABSTRACT FROM AUTHOR]

Ferrite-ferroelectric core-shell nanoparticles were prepared by deoxyribonucleic acid (DNA) assisted self-assembly and the strained mediated magneto-electric (ME) interactions between the ferroic phases were studied. The nanoparticle type and size were varied and the DNA linker sequence was also varied. Two kinds of particles, one with 600 nm barium titanate (BTO) core and 200 nm nickel ferrite (NFO) shell and another with 200 nm BTO core and 50 nm nickel cobalt ferrite (NCFO) shell were prepared. The particles were linked by three different oligomeric DNA containing 19, 18 or 30 base pairs. The core–shell structure was evident from electron microscopy and scanning microwave microscopy images. Films and disks of the core-shell particles were assembled in a magnetic field and used for measurements of low frequency ME voltage coefficient (MEVC) and magnet-dielectric effect. The MEVC data on films indicate that particles assembled with DNA with 30 base pairs exhibit the strongest ME coupling suggesting a more fully integrated heterogenous nanocomposite and the weakest interaction for DNA with 18 base pairs. These results indicate that the longer linker region in DNA is the key factor for forming better composites. This result may be due to the irregular shape of the nanoparticles. Longer DNA strands would be able to bridge better generating more linkages. Shorter strands would not able to bridge the irregularly shaped particles as well and therefore result in linkages and less heterogeneity in the composites. [ABSTRACT FROM AUTHOR]

We studied the multiferroic property of Ca 1-x La x Ti 1-x Fe x O 3 (0.0 ≤  x  ≤ 0.5) perovskite. We showed that multiferroic property can be triggered by strain mediation due to different ion doping. The prepared samples were characterized by X-ray to check for its phase purity. Increasing the La 3+ ion concentration is found to induce a crystal distortion. A pseudo-tetragonal phase is found at the highest La 3+ ion concentration. The changes in crystal symmetry induce different effects on the electrical polarization that can be seen in the electrical hysteresis of the perovskite. The correlation between magnetic and electric ordering reduces as the concentration of La 3+ ion increases in which the lattice symmetry are more close to space invariant. The changes in the vibrational bands due to changes in the crystal structure were investigated by FTIR. [ABSTRACT FROM AUTHOR]

Pure-phased orthorhombic RMn 0.5 Fe 0.5 O 3 (R = Tb, Dy, and Ho) were successfully synthesized via the low-temperature hydrothermal technique. The nucleation and crystal growth of RMn 0.5 Fe 0.5 O 3 (R = Tb, Dy, and Ho) were influenced mainly by medium alkalinity, reaction temperature and time. All the three samples are of orthorhombic structure with +3 valences of Mn and Fe. They present morphologies of spheres that are assembled by smaller tabular crystals. Spin reorientation transitions were observed in RMn 0.5 Fe 0.5 O 3 (R = Tb, Dy, and Ho), and magnetization reversal was observed in TbFe 0.5 Mn 0.5 O 3 . The spin reorientation temperatures show a linear relation with the magnetic field intensity, and the spin reorientation and magnetization reversal disappear when the applied field is big enough. Antiferromagnetic transition of R 3+ was observed in TbFe 0.5 Mn 0.5 O 3 and DyFe 0.5 Mn 0.5 O 3 at lower temperatures. All the three samples show the characteristics of spiral magnetic ordering at 2 K and show residual magnetism at both 2 K and 300 K. [ABSTRACT FROM AUTHOR]

The effect of magnetic and electric fields on the electrical and magnetic properties of BiMnO 3 films within the framework of Landau-Ginzburg theory had been investigated. We also calculated and discussed the hysteresis loops of polarization and magnetization as a function of electric and magnetic fields. The results reveal that, the possibility of electric-field control of magnetization switching, and vice versa. By decreasing the film thickness of BiMnO 3 film, it is shown that the coercive fields and remnant order parameters are suppressed. [ABSTRACT FROM AUTHOR]

High performance lead-free multiferroic composites with strong magnetoelectric coupling effect are desired to replace lead-based ceramics in multifunctional device applications due to increasing environmental issues. We report crystal structure, ferroelectric, magnetic, dielectric and magnetoelectric properties of (1-x)Ba 0.85 Ca 0.15 Ti 0.90 Zr 0.10 O 3 -(x)CoFe 2 O 4 (BCTZ-CFO) lead-free composites with x = 0.1, 0.3, 0.5, 0.7 and 0.9 synthesized by chemical solution method. BCTZ power was synthesized by sol-gel method while CFO was prepared by metallo-organic decomposition (MOD) method. The XRD results confirm successful formation of the BCTZ-CFO composites without presence of any impurity phase. At room temperature, the BCTZ-CFO composites show multiferroic behavior characterized by ferroelectric and ferromagnetic hysteresis curves. The composite having 10 wt% of CFO exhibited maximum polarization, remnant polarization and coercive field of P s  ∼ 5.1 µC/cm 2 , P r  ∼ 1.4 µC/cm 2 and E c  ∼ 11.6 kV/cm respectively. The BCTZ-CFO composite with 90 wt% of CFO incorporation exhibits improved ferromagnetic properties with M s  ∼ 32 emu/g, M r  ∼ 11.7 emu/g and H c  ∼ 504 Oe. Mӧssbauer spectra analysis show two sets of six-line hyperfine patterns for BCTZ-CFO composites, indicating the presence of Fe 3+ ions in both A and B sites. Increasing BCTZ content was found to decrease the hyperfine field strength at both sites and is consistent with the decreasing magnetic moment observed for the samples. The maximum dielectric constant value ε′ ∼ 678 is obtained at 1 MHz for composite with 10 wt% of CFO phase. The results indicate that the BCTZ-CFO composites are potential lead-free room temperature multiferroic systems. [ABSTRACT FROM AUTHOR]

Neutron and X-ray diffraction, magnetic susceptibility, and specific heat measurements have been used to investigate the magneto-structural phase transitions in 20% Cu substituted multiferroic CoCr 2 O 4 spinel. The Jahn-Teller active Cu 2+ ion in the tetrahedral A -site of the spinel configuration induces the Jahn-Teller distortion slightly above the Néel temperature. In this compound, we observe a Jahn-Teller distortion of the crystal structure at 90 K. It was further observed that the high temperature cubic ( Fd 3 ‾ m ) structure coexists with the low temperature orthorhombic ( Fddd ) structure till the lowest temperature of measurement. [ABSTRACT FROM AUTHOR]

We present a theoretical calculation of magnetoelectric properties in a quasi-two dimensional spin chain externally controlled by a static electric field in y -direction and magnetic field in z -direction. Given the diversity of properties in functional materials and their applications in physics, the multiferroic model is investigated. By using the Fermi–Dirac statistics of quantum gases and the Landau theory, we assess the effects of the Dzyaloshinskii-Moriya interaction and the electric polarization on the magnetoelectric coupling that induces at low temperature the “metamagnetoelectric” effet, and likewise affects the ferroelectricity induced through symmetry mechanisms and magnetic properties of the multiferroic system. In fact, the variation of the induced polarisation due to spin arrangement through the Dzyaloshinskii-Moriya interaction gives rise to a multistep interdependent metamagnetic and metaelectric transitions which are settled up by the corresponding Dzyaloshinskii-Moriya parameter and the system then exhibits a spin gap that results from an electric and a magnetic demagnetization field range. This metamagnetoelectric effect observed in these multiferroic materials model is seem to be highly tunable via the external electric and magnetic fields and thus can be crucial in the design of new mechanisms for the processing and storage of data and other spintronic applications. [ABSTRACT FROM AUTHOR]

Nanostructures of complex oxides [BiFe x Mn 2−x O 5 (x = 0, 1, 2)] have been designed to study their structural, optical and magnetic behaviour. X-ray diffraction data (XRD) revealed orthorhombic phase with Pbam space group. Noticeable expansion in unit cell parameters has been found from BiMn 2 O 5 (x = 0) to BiFe 2 O 4.5 (x = 2). The observed structural changes via tuning of B-site (x = 0–2) played an important role in overall magnetic properties. Transmission electron microscopic images confirm that the average particle size of all the materials are in nano domain range with different morphologies. From optical studies, it has been found that the observed energy band gap values are strongly related to 3d electron numbers. These values appear to be larger than that reported for bulk. Isothermal magnetization plots (at 5 K) show increase in coercivity (H c ) from x = 0 to x = 2. Temperature dependent magnetization studies implied anti-ferromagnetic interactions for BiMn 2 O 5 , frustrated magnet for BiFeMnO 5 and ferromagnetic behaviour for BiFe 2 O 4.5 . Ferromagnetic state of nanostructured BiFe 2 O 4.5 is in contrast with its bulk counterparts. [ABSTRACT FROM AUTHOR]

Multiferroic ceramics of Bi 0.99 Y 0.01 Fe 1 - x Ni x O 3 with 0.01 ⩽ x ⩽ 0.05 were synthesized by using a modified solid state reaction method. The crystalline structure and the morphology of the samples were investigated by X-ray diffraction (XRD) and by scanning electron microscopy (SEM). The addition of Y and Ni to the bismuth ferrite (BiFeO 3 ) was found to decrease the average grain size. Ac magnetic susceptibility and the zero-field-cooled (ZFC) and field-cooled (FC) magnetizations were measured for temperatures in the range 5 ⩽ T ⩽ 300  K. Hysteresis loops and an irreversible behavior in the temperature dependence of the magnetization not present in pure BiFeO 3 were observed in the doped samples. However, the ferromagnetism was found more likely to be due to the presence of small amounts of magnetite. Nevertheless, the determination of the amount of Fe 3 O 4 in these composite materials is important because it influences the magnetoelectric coupling which is important for some technological applications. [ABSTRACT FROM AUTHOR]

Magnetic excitations and exchange interactions in multiferroic NdFe 3 (BO 3 ) 4 were studied by inelastic neutron scattering in the phase with commensurate antiferromagnetic structure. The observed spectra were analyzed in the frame of the linear spin-wave theory. It was shown that only the model, which includes the exchange interactions within eight coordination spheres, describes satisfactorily all observed dispersion curves. The calculation showed that the spin-wave dynamics is governed by the strongest antiferromagnetic intra-chain interaction and three almost the same inter-chain interactions. Other interactions, including ferromagnetic exchange, appeared to be insignificant. The overall energy balance of the antiferromagnetic inter-chain exchange interactions, which couple the moments from the adjacent ferromagnetic layers as well as within a layer, stabilizes ferromagnetic arrangement in the latter. It demonstrates that the pathway geometry plays a crucial role in forming of the magnetic structure. [ABSTRACT FROM AUTHOR]

[Display omitted] • Ferroelectric and magnetic properties were enhanced significantly in BFO-BTO/BaM composites. • Magnetic domain structure changed from multi-domain to single-domain with increasing BaM content. • Electric-induced magnetic changes were observed in BFO-BTO/BaM composites. The 0–3 type (1- x)(0.75BiFeO 3 -0.25BaTiO 3)/ x BaFe 12 O 19 (BFO-BTO/BaM) multiferroic composites were successfully prepared by a solid-state reaction sintering process. The coexistence of perovskite BFO-BTO phase and hexagonal BaM phase was confirmed for all BFO-BTO/BaM composites. Due to the large leakage current, the breakdown electric field decreased with increasing BaM content. Nevertheless, the ferroelectric properties of the composite ceramics have also been significantly improved, mainly as the increase of remanent polarization and the decrease of coercive field, where Pr = 19.79 μC/cm2, Ec = 30 kV/cm at x = 0.075. Meanwhile, the magnetic properties of BFO-BTO phase were enhanced, and the remanent magnetization linearly increased with increasing BaM content. The single domain magnetic structure was obtained for all BFO-BTO/BaM composite ceramics, and the magnetic properties changed after electric poling, which indicated the electric field controlled magnetic properties. The electric-controlled magnetic behavior was attributed to the structural phase transition. The magnetoelectric coupling coefficient α ME of the composite material has been improved, with a maximum value of 0.61 mV/cm.Oe. Thus, the BFO-BTO/BaM magneto-electric composite system is a promising multiferroic system in information technology and sensing fields. [ABSTRACT FROM AUTHOR]

[Display omitted] • Facile synthesis of (1–x)[Bi 0.8 La 0.2 FeO 3 ] + x[Zn 0.5 Co 0.5 Fe 2 O 4 ] multiferroic composites using a cost-efficient method. • Diffraction analysis confirmed the development of the desired crystalline phases and development of phase pure composites. • Optimization to maximize recoverable energy density, maximum magnetization and remanence magnetization. Multiferroic materials has brought evolutionary impact in multifunctional devices that are exclusively based on magnetoelectric coupling. In this work, a bi-phasic composite series of the form; (1–x)[Bi 0.8 La 0.2 FeO 3 ] + x[Zn 0.5 Co 0.5 Fe 2 O 4 ] was prepared using sol–gel auto–combustion. The X-ray diffraction analysis confirmed the rhombohedrally distorted cubic structure of BiFeO 3 and normal spinel cubic structure of Zn 0.5 Co 0.5 Fe 2 O 4 having R 3 c and Fd -3 m space group symmetry, respectively. A reduction in average crystallite size was observed by gradually enhancing the substituent spinel contents (x). Energy dispersive X-ray confirmed the presence of all the constituent elements in accordance with stoichiometrically calculated values. Mostly the particles having spherical shapes were observed via micro-graphical analysis. At x = 0.2, the composite sample showed the highest value of recoverable energy density as 7.2 × 10-2 mJ/cm3 with the highest value of % efficiency ∼ 88.83 %. A clear enhancement in saturation magnetization was observed from 0.16 to 19.87 emu/g. The remanent magnetization also increased from 0.018 to 6.363 emu/g by enhancing the spinel phase contents. Furthermore, coercivity also increased significantly from 672.98 Oe to 841.89 Oe in the composite samples. The highest squareness ratio M r : M s was observed at x = 0.3. These distinctive properties of the nanocomposites lead toward potential applications in multiferroic and spintronic devices. [ABSTRACT FROM AUTHOR]

• New model for frustrated magneto-ferroelectric bilayers. • The magnetic frustration induces creation of skyrmions and a skyrmion lattice at moderate values of Dzyaloshinskii-Moriya interaction and interface magnetoelectric coupling. • Effects of magneto-ferroelectric coupling and compass-type anisotropy on the ground state. • Monte Carlo simulation of the phase transition as a function of compass-type anisotropy. • Shifting of the critical temperature is found depending on the coupling strength. In this paper, we study phase transitions in a magnetoelectric bilayer with two order parameters using Monte Carlo simulation. We investigate the effects of temperature, magnetoelectric coupling, and anisotropy in the multiferroic bilayer formed by a frustrated antiferromagnetic layer with Heisenberg spins and a triangular lattice ferroelectric layer. We show that magnetic frustration induces creation of skyrmions and a skyrmion lattice at moderate values of Dzyaloshinskii-Moriya interaction and interface magnetoelectric coupling with adjacent ferroelectric layer. The skyrmion crystal is stable up to relatively high temperatures. The effect of anisotropy is to cause only a shift of the critical temperature without changing the type of the phase transition. The phase of the skyrmion lattice becomes more resistant and stable to temperature fluctuations in the case of a highly anisotropic frustrated film. [ABSTRACT FROM AUTHOR]

• Model for electric field induced magnetization reversal in FM-MF bi-layer is developed. • Magnetic states in FM-MF nanoelement are calculated. • Electric field induced transformations of magnetic states in FM-MF nanoelement are explored. The development of new computing technologies has given a new stimulus in the study of multiferroics. The use of multiferroics allows the realization of competitive energy efficient scalable logic and storage devices. The low - power consumption in Magneto Electric – Spin Orbital logics [1] and Magnetic Random Access Memory components is provided by magnetoelectric switching in multiferroic – based systems using a low-energy electric field. Our work concerns the modelling of the Magneto Electric – Spin Orbital elements with an emphasis on the magnetoelectric component and simulation of magnetization reversal processes in a model system. The use of the proposed approach makes it possible to analyze the influence of dimensional factors (film thicknesses, transverse dimensions, sample shape) affecting the magnetic states of multiferroic nanoelements; taking into account interfacial interactions (magnetic anisotropy and interlayer exchange); energy-efficient external influences that allow switching magnetic states using magnetic and electric fields. [ABSTRACT FROM AUTHOR]

• The linear magnetoelectric and flexomagnetic effects coexist in antiferromagnets. • The ferrovalley in vdW magnets couples antiferromagnetic vector to electric polarization. • The spin cycloid in curved vdW magnets is a flexoelectricity in spin subsystem. • The flexomagnetic effect is enhanced in vdW antiferromagnetic bilayers. In this short review the coupling of various subsystems of crystal in van der Waals magnetic materials are considered: the magnetoelectric effect mediated by antisymmetric antiferromagnetic ordering, the ferrovalley-mediated coupling of antiferromagnetism and electric polarization as well as the effects induced by flexural deformations: the spin flexoelectric effect as a curvature induced Dzyaloshinskii-Moriya interaction and flexomagnetic effect as a curvature-induced decompensation of layer magnetization in antiferromagnetic bilayers. [ABSTRACT FROM AUTHOR]

• Theoretical study on the magnetic-mechanical-electric multiphysics coupling behavior of semiconductor/magnetostrictive composites for the first time. • The coupled among polarization charge and magnetic field dependent variables for composites are solved using an iterative finite difference program. • Theoretical study on the magnetoelectric effect of magnetoelectric composites using semiconductor materials as piezoelectric layers for the first time. • Polarization charge and strain distributed of magnetoelectric composites is investigated comprehensively. A magnetoelectric composites is designed and investigated, which combines GaN-based semiconductor and magnetostrictive Terfenol-D. In this work, we study the polarization charge and strain of the multilayer composites under an applied magnetic field and prestress. In order to quantitatively describe the response of composites under different loading environments, a nonlinear magneto-electric self-consistent coupling model is established based on nonlinear constitutive equation, Schrodinger equation, and Poisson equation. The validity of this model is well-proven by comparing experimental data and numerical results under different magnetic fields. The results demonstrate that the giant magnetostriction effect of Terfenol-D offered large tensile strain to decrease the polarization charge and strain in GaN-based semiconductor layer. These conclusions will be of great help to the basic research of piezomagnetic composite materials as well as guidance for the future device design. [ABSTRACT FROM AUTHOR]

Single-phase multiferroic Bi 1− x La x FeO 3 ( x  = 0.00, 0.10, 0.20, 0.30, and 0.40) ceramics were studied by positron annihilation lifetime spectroscopy and the effect of the cation vacancies on the magnetism were investigated. Positron lifetime measurements and density-functional theory calculation of positron lifetimes identified the presence of Bi and Fe vacancies. It was observed that when x  > 0.20 the Bi monovacancies disappeared gradually and some larger vacancy clusters begin to appear. Magnetic property measurements showed that the remnant magnetization increases greatly when x  > 0.20. It is found that the enhanced magnetization is not only due to the suppressed spin cycloid structure, but the variation of cation defects also contributes. [ABSTRACT FROM AUTHOR]

We report an experimental study of single-phase Bi 0.85−x La 0.15 Ho x FeO 3 nanoparticles (BLH x FO-NPs) that synthesized by a sol–gel method. The Rietveld refinement of X-ray diffraction pattern of BLH x FO samples indicate a phase transition from rhombohedral (space group R3c) to orthorhombic (space group Pbnm) structure with increasing Ho content. The bond lengths and angles for all samples were determined which supports the magnetic and electrical results. The average particles size of BLH x FO-NPs has been estimated from field emission scanning electron microscopy (FESEM) images and using a standard log-normal distribution equation. The remnant magnetisation in BLH x FO-NPs increase from 0.09 emu/g for x = 0–0.35 emu/g for x = 0.25 sample at 5 K. In order to clarify origin of magnetisation behaviour in BLH x FO-NPs, a systematic investigation has been performed on the magnetisation of all samples. The frequency ( f ) and composition (x) dependence of relative dielectric constant (ε) and dielectric loss (tan δ) have been studied for BLH x FO nanoparticles at room temperature. The dielectric properties indicates a local maximum in sample with x = 0.25 while maximum magnetodielectric coefficient occurs in x = 0.35. Simultaneous enhancement in magnetic and dielectric properties can play an important role for the practical applications. [ABSTRACT FROM AUTHOR]

We present a first-principles study of electronic structures and magnetic properties in Ni-doped BiFeO 3 using the density functional theory + U methods. The BiNi x Fe 1-x O 3 (x = 0.125, 0.25, 0.5) multiferroic ceramics represent ferromagnetic properties due to the ferrimagnetic order in Ni-O-Fe, and the magnetic moment rises with increase in Ni doping concentration agreeing well with experimental results. Ni atoms prefer to occupy the diagonal positions in the quasi-plane Ni-O-Fe eight-membered ring. Charge transfer from Bi 6 s state to Ni 3 d state through O 2 p orbital lead to the 2+ oxidation state of Ni, indicating high Néel temperatures of BiNi x Fe 1-x O 3 , and the electronic state of the system can be described as Bi 4+ x Bi 3+ 1-x Ni 2+ x Fe 3+ 1-x O 3 . The spin polarization of Bi 6 s state and O 2 p state near the Fermi level contributes to the total magnetic moment. A spin-polarized acceptor level of about 0.4 eV constituted by Bi 6 s state and O 2 p state is found, which is responsible for the increase in leakage current of Ni-doped BiFeO 3 . [ABSTRACT FROM AUTHOR]

Latent magnetization in the multiferroics can be achieved via the structural distortion with respect to particle size and destroying the spiral spin structure, which plays the vital role in high-performance applications. In this investigation, multifunctional single phase Bi 1−x La x Fe 1−y Co y O 3 nanomaterials were synthesized by co-precipitation technique. The chemical composition, phase genesis, morphology and thermal characteristics of the Bi 1−x La x Fe 1−y Co y O 3 were studied by FTIR, XRD, SEM/EDS, TEM and TGA. XRD studies confirmed single phase distorted rhombohedral structure in Bi 1−x La x Fe 1−y Co y O 3 . The novelty in magnetic behavior of the Bi 0.85 La 0.15 Fe 0.75 Co 0.25 O 3 multiferroic at room temperature showed both ferro and anti-ferromagnetic nature with higher order remanent magnetization among other nanocomposites in this study. This magnetic anomaly in Bi 0.85 La 0.15 Fe 0.75 Co 0.25 O 3 is due to doping and size effects on the crystal structure that leads to spin-orbit interactions. Besides, Bi 0.85 La 0.15 Fe 0.75 Co 0.25 O 3 integrated graphene oxide (GO) nanocomposite has shown the change in the magnetic hysteresis that indicates the effect of the semiconducting behavior of GO on the ordered magnetic moments in the multiferroic. This kind of magnetic anomaly could form advanced multiferroic devices. [ABSTRACT FROM AUTHOR]

The effect of sintering time on the evolution of structural and magnetic phases has been studied in Bi 0.8 Nd 0.2 FeO 3 multiferroic. These multiferroics were prepared by normal solid state reaction technique. XRD, NPD and VSM characterizations were performed to explore the structural and magnetic properties and correlation between these. The refinement of the XRD patterns using FullProf program show, mixed phase having rhombohedral (R3c) + orthorhombic (Pnma) symmetry in sample sintered for 1 h. For sample sintered for two hours, crystal structure was found to be mixed phase with rhombohedral (R3c) + orthorhombic (Pbam) symmetry and the sample sintered for three hours, it crystallized in pure orthorhombic (Pbam) symmetry. The octahedral tilting is thus found to be changing systematically with the variation of sintering time. The refinement of the neutron diffractions patterns confirms the XRD results of structural evolution with sintering time. The magnetic moment undergoes change in the direction of their preferential alignment from c-axis to along a-axis in the 3 h sintered sample. The M-H loops shows significant enhancement in magnetization from 0.17455 emu/g to 0.35872 emu/g with increase in sintering time from 1 to 3 h. The enhancement in the magnetization is attributed to increase in the canting angle between magnetic spins. Also, the observation of exchange bias effect with discontinuous variation in exchange bias field indicates the presence of magnetic anisotropy. The magnetic moments obtained through the magnetic refinement of NPD patterns are found to decrease from 4.6 μ B to 3.8 μ B with increase in sintering time from 1 to 3 h. [ABSTRACT FROM AUTHOR]

The lattice parameters, electronic structure, magnetism and multiferroicity of compound BiMn 3 Fe 4 O 12 were investigated by using the first-principle calculations. The total energy calculations indicated that BiMn 3 Fe 4 O 12 was a G-type antiferromagnetic insulator. The ferroelectricity was induced by magnetism and originated from the hybridization between Fe and Mn ions. The electric polarization was predicted to be around 39 μC/m 2 along 〈1 1 1〉 orientation. It was sensitive to the lattice distortion such as Fe ion shift of FeO 6 octahedron and a great improvement in electric polarization could be possibly achieved by strain engineering or inducing chemical pressure. Furthermore, the effects of on-site Coulomb repulsion on electronic structure, magnetism, and ferroelectricity were also discussed. It was showed that with increasing U the spin splitting increased, resulting in an increased ban-gap and hybridization between Fe and Mn ions, and then electric polarization. [ABSTRACT FROM AUTHOR]

Nanomagnetic memory and logic are currently seen as promising candidates to replace current digital computing architectures due to its superior energy-efficiency, non-volatility and propensity for highly dense and low-power applications. In this work, we investigate the use of shape engineering (concave and diamond shape) to introduce biaxial anisotropy in single domain nanomagnets, giving rise to multiple easy and hard axes. Such nanomagnets, with dimensions of ∼100 nm × 100 nm, double the logic density of conventional two-state nanomagnetic devices by encoding more information (four binary bits: “00”, “11”, “10”, “01”) per nanomagnet and can be used in memory and logic devices as well as in higher order information processing applications. We study reliability, magnetization switching coherence, and show, for the first time, the use of voltage-induced strain for the clocking of magnetization in these four-state nanomagnets. Critical parameters such as size, thickness, concavity, and geometry of two types of four-state nanomagnets are also investigated. This analytical study provides important insights into achieving reliable and coherent single domain nanomagnets and low-energy magnetization clocking in four-state nanomagnets, paving the way for potential applications in advanced technologies. [ABSTRACT FROM AUTHOR]