Multiferroics are the class of crystalline materials in which, at least, two of three order parameters exist simultaneously: ferromagnetic or antiferromagnetic, ferroelectric, and ferroelastic degrees of freedom . Multiferroics are classified on heterogeneous (composite) and homogeneous (single-phase) compounds. A study of magnetic properties of heterogeneous and homogeneous multiferroics and their evolution with temperature, stresses, radiation, electrical, magnetic fields and so on are necessary to shed light on the origin of a magnetoelectric effect. This effect allows controlling the polarization of a material using an external magnetic field and vice versa – a change of the magnetization with an electrical field. According to a phenomenological theory, the magnetoelectric response in a single-phased material is limited by dielectric constant and magnetic permeability . Search of materials with high ferromagnetic and ferroelectric properties is actual task now. A magnetoelectric effect in composite multiferroics is significantly higher in its value than that in homogeneous materials . Due to large magnetoelectric effect, such multiferroics have good perspective for application as magnetic sensors, capacity electromagnets, elements of magnetic memory, logic elements of information processing systems etc. [4, 5]. In single-phase multiferroics a value of interaction between magnetic and ferroelectric degrees of freedom relates with a spin-orbital couple, and so, depends on crystal state and magnetic structure of a sample. Therefore, for understanding mechanism of magnetoelectric effect in composite and single-phase multiferroics it is important to determine structure and magnetic characteristics and their evolution with temperature and concentration of doping elements.
The aim of the paper is studying crystal and magnetic structures of some multiferroics by X-ray and neutron diffraction.
Composite multiferroics (x)MFe2O4 + (1-x)BaTiO3, with x = (0.2; 0.3; 0.4) and M = (Ni or Co), have been synthesized from the spinel NiFe2O4 (or CoFe2O4) and barium titanate (BaTiO3). Mixing components in the desired ratio, we made pellets of the (x)MFe2O4 + (1-x)BaTiO3 samples, which were heat-treated at 1150 μC for 4 hours. High resolution X-ray powder diffractions (XRD) patterns were recorded at room temperature (RT) using Bruker D8 diffractometer with Cu K α radiation (wavelength λ = 1.54056 μ). Patterns were obtained in the range scattering (10 – 120) degrees. Neutron powder diffraction (NPD) patterns have been recorded at 293 K using the D2 diffractometer installed on a horizontal channel of the RWW-2M reactor (Zarechny, Russia). We used neutron length was λ = 1.805 μ.
Powder samples of Ni3− y Co y V2O8 with y = (0.1; 0.3; 0.5) were synthesized using a solid-state reaction method with NiO, Co3O4, and V2O5 as starting materials. Reagents were mixed in the desired ratio and heated in Al2O3 crucibles. Samples were annealed in air at 800 ∘C. The XRD measurements were performed at RT with an X-ray diffractometer (Philips X'PERT MPD) using Cu K α radiation. The NPD patterns were recorded in temperature range from 2.8 K up to 9.0 K with the HRPD diffractometer, installed at the HANARO reactor in the Korea Atomic Energy Research Institute. The wavelength of the incident beam was λ = 1.837 μ.
The sample Bi0.9Ba0.1Fe0.9Ti0.1O3 was synthesized by crystallization in a solution. The NPD patterns have been recorded with the high resolution powder diffractometer B1 mounted on a horizontal channel of the reactor in Institute of Laue-Lanjevine (Grenoble, France). The neutron wavelength was λ = 1.5395 μ; measurements have been carried out in the range (300 – 1000) K and the scattering interval (10 – 130) degrees.
The analysis of all XRD and NPD patterns was performed using the software package “Fullprof” .
Fig. 1a shows observed and calculated XRD patterns of composite multiferroic 0.2(NiFe2O4) + 0.8(BaTiO3) at RT. The XRD patterns of x(MFe2O4) + (1-x)BaTiO3 composites with x = (0.3 and 0.4), and M = (Ni and Co) are similar to patterns, presented in Fig. 1. The NiFe2O4 (or CoFe2O4) is a magnetic component of composites and it crystallizes in the cubic structure (space group Fd-3m), in which Fe-ions occupy the half of the 8a and 81 % of 16d sites, respectively. The Ni-ions occupy 50 % of the 8a and 19 % of 16d positions, respectively. The BaTiO3 is a ferroelectric component; its crystal structure is tetragonal structure and belongs to P4mm space group. Crystal unit cells of magnetic and ferroelectric components of composite multiferroic are presented in Fig. 1b.
Fig. 2a represents observed and calculated NPD patterns of the composites 0.2(NiFe2O4) + 0.8(BaTiO3) at RT; a spin ordering in magnetic component is presented in Fig. 2b. The magnetic structure is described by the propagation vector k = 0. Magnetic moments of Ni/Co- and Fe-ions are antiparallel and their values are given in Table 1. A difference between magnetic moment values at the 8a and 16d positions is caused by a distinction of the Fe- and Ni/Co-ion moment magnitudes. As one can see in Table 1, the Fe-ion magnetic moment is by the factor 1.8 more than Ni-ion moment. An average magnetic moment increases slowly in the 8a position and decreases in the 16d site with a rise of the concentration x, pointing to a displacement of the Ni-ions from the 16d position to the 8a site. Therefore, a presence of the BaTiO3 in the composite multiferroics induces a driving force to move the Ni-ions and decrease a degree of inverse spinel structure.
Fig. 3 shows observed and calculated NPD patterns of the Ni2.9Co0.1V2O8 multiferroic at 2.85 K (a), 4.85 K (b), and 7.40 K (c). Fig. 4 presents observed and calculated NPD patterns of the Ni2.5Co0.1V2O8 at 2.83 K (a), 4.20 K (b), and 7.30 K (c). Both samples crystallize in the orthorhombic structure, described by the space group Cmca. They belong to frustrated Kagome-staircase structures . The structure is characterized by edge-sharing MO6 octahedra, which are isolated by nonmagnetic vanadium ions. The Ni/Co-ions form buckled planes, containing two inequivalent positions the 4a and 8e.
We have refined a magnetic structure of these multiferroics and have determined that it is like a longitudinal spin wave with the vector k = (δ, 0, 0), where δ = 0.283 and 0.348 at 7.4 K for y = 0.1 and 0.5, respectively. Magnetic moments are predominantly oriented along the a-axis. Magnetic structures of the Ni2.9Co0.1V2O8 at 2.85 K, 4.85 K, and 7.40 K as well as of the Ni2.5Co0.5V2O8 at 2.83 K, 4.20 K, and 7.30 K are given in Fig. 3 and Fig. 4.
Fig. 5 presents temperature dependences of the propagation vector and the magnetic moment value at the 8e position for the Ni3− y Co y V2O8 samples with y = 0.1 and 0.5. As it is seen, the temperature evolution of the vector k for y = 0.1 is very weak, that confirms literature data, showing a substitution of 3.5 % Ni-ions by cobalt suppresses the explicit temperature dependence of the vector k, which is observed in the parent compound. However, we found that the vector k for y = 0.5 exhibited the definite temperature dependence, that differed from a dependence of the k in the undoped sample. For y = 0.5 the Ni/Co-ion magnetic moment decreases from 1.8 μ B at 2 K down to zero at 9 K.
Fig. 6a shows NDP patterns of the Bi0.9Ba0.1Fe0.9Ti0.1O3 multiferroic at 300 K. A crystal structure of this multiferroic is rhombohedral up to about 1100 K and belongs to the R3c space group. The Ba-ions are placed in the Bi-sublattice and the Ti-ions partly occupy the Fe-sublattice of the BiFeO3 structure (see Fig. 6b).
To refine a magnetic structure of the Bi0.9Ba0.1Fe0.9Ti0.1O3 we used the magnitude of the vector k = (0.0045, 0.0045, 0) from Ref. . The magnetic structure is described as the cycloidal spiral. The Fe-ion moments are oriented ferromagnetically in planes perpendicular to the  direction and antiferromagnetically in adjacent planes. Fig. 6 presents also the temperature dependence of Fe-ion magnetic moments. As one can see, moments decrease almost linear with temperature from (3.46 ± 0.05) μ B down to (2.38 ± 0.08) μ B over region (300 – 500) K. The temperature dependence of the moments becomes abrupt over region (500 – 600) K and they vanish then at 600 K by a magnetic phase transition of second order.
The X-ray and neutron diffraction experiments have been carried out on the multiferroics (x)MFe2O4 + (1-x)BaTiO3 (with x = 0.2, 0.3, and 0.4; M = Ni and Co), Ni3− y Co y V2O8 (with y = 0.1, 0.3, and 0.5) as well as Bi0.9Ba0.1Fe0.9Ti0.1O3.
In the composite multiferroic (x)MFe2O4 + (1-x)BaTiO3 the magnetic component has the ferrimagnetic structure that is described by the propagation vector k = 0. The value of the Ni/Fe-ion magnetic moment increases at 8a position and decreases at the 16d sites, when the concentration x arises. Incommensurate magnetic structure of the Ni3− y Co y V2O8 oxides with y = (0.1, 0.3, and 0.5) is described by vector k = (δ, 0, 0), where δ = 0.283 and 0.348 at 7.4 K for y = 0.1 and 0.5, respectively. The Fe-spins are predominantly oriented along the a-axis. The Ni/Co-ion magnetic moment decreases from 2.4 μ B at 2 K down to zero at 9 K for y = 0.1 and from 1.8 μ B down to zero for y = 0.5. The Bi0.9Ba0.1Fe0.9Ti0.1O3 multiferroic has a modulated magnetic structure with the propagation vector k = (0.0045, 0.0045, 0). The Fe-ion moments are oriented ferromagnetically in planes perpendicular to the  direction and antiferromagnetically in adjacent planes. The value of the Fe-ion moment decreases with temperature from 3.46(5) μ B at 300 K and vanishes at 600 K.
This research was supported by the State contract No. 1362 between UrFU and the Minobrnauka. Work was partially carried out in neutron center of IMP and supported by the FASO of Russia (theme “Flux” No. 01201463334). The equipment of Ural Center for Shared Use “Modern Nanotechnology” UrFU has been used.