THE INVESTIGATION OF CRYSTAL AND MAGNETIC STRUCTURES OF SOLID SOLUTIONS BaFe12-xDxO19 (D= In AND Ga\; x= 0.1 – 1.2)

The influence of partially substituted of barium ferrites by diamagnetic In and Ga ions with neutron diffraction method was studied. The substitution of Fe by In ions leads to increase of volume of unit cell while replacing with Ga ions insignificantly change the lattice parameters. The concentration dependence of the Tc Curie temperature as well as the magnetization is constructed. The refinement of the magnetic structure was carried out within the framework of Gorter’s model. The microstructural parameters of solid solutions BaFe12−xDxO19 (D= In and Ga; x = 0.1–1.2) were determined by the high-resolution neutron diffraction method.


Introduction
The crystalline structure of barium ferrites and their solid solutions has a structure of magnetoplumbit PbFe 12 O 19 which was first studied by Adelskold [1] in 1938. As a rule, it is well described in the framework of the space group P6 3 /mmc (No. 194) with a hexagonal unit cell a = b ≈ 5.90Å, c ≈ 23.30Å containing two formula units. Iron ions are localized in five nonequivalent crystallographic positions: 2a, 4 f VI and 12k -with octahedral, 2b -with trigonally bipyramidal and 4 f IV -with a tetrahedral oxygen environment.
In order to improve functional properties of barium ferrites for their application use the substitution of iron ions with diamagnetic ions Al, Sc, Ga, etc. [2,3], which change the number of bonds between magnetoactive ions. The replacement of iron ions in certain crystallographic positions influences on valence angles and interatomic distances in Fe-O-Fe [4] bonds, and consequently, affects to the pair exchange integral and the magnitude of the sublattice exchange [5].
In this paper, the effect of partial replacement of magnetoactive Fe ions by diamagnetic In and Ga ions on the crystal and magnetic structures of BaFe 12−x D x O 19 in a wide range of concentrations (D= In and Ga; x = 0.1-1.2) was studied by neutron diffraction method. The substitution of solid solutions BaFe 12−x D x O 19 by diamagnetic ions D= In and Ga allows research the influence of appearing chemical pressure on distortions of unit cell parameters and on the value of bond length Fe/In/Ga-O and determine the influence to magnetic properties (temperature e-mail: turchenko@jinr.ru of magnetic phase transition, value of magnetic moments, etc). Concentration range of diamagnetic substitution (x= 0.1-1.2) was determined due to the preservation of optimal magnetic characteristics in doped Ba-hexaferrites. For concentration more than 10 at.% is high risk of observation some magnetic anomalious like frustration of magnetic structure [6] instead of collinear ferrimagnetic structure. Another feature of the work is the use of a high-resolution diffractometer for the measurement of neutron diffraction patterns BaFe 12−x D x O 19 (D= In and Ga; x = 0.1-1.2), which made it possible to obtain information about both the crystalline and magnetic structures and the microstructure of the samples studied.

Experimental Details
Solid solutions of BaFe 12−x D x O 19 (D= In and Ga; x = 0.1-1.2) have been prepared from high purity Fe 2 O 3 and In 2 O 3 and Ga 2 O 3 oxides and carbonate BaCO 3 using 'two-steps' topotactic reactions (conventional solid reaction method). Oxides and carbonate have been mixed with design ratio and synthesized at 1200 o C (6 h) and at 1300 o C (6 h) in air. After synthesis the sample has been slowly cooled (100 o C/h).
The powder neutron investigations of sample was performed by neutron time-of-flight method at High Resolution Fourier Diffractometer (HRFD, Dubna) at room temperature. The refining of crystal and magnetic structures was performed by Rietveld analysis [7], using the FullProf [8] software program. The resolution of diffractometer is ∆d/d 0 ≈ 0.001% and lattice parameters were defined more exactly at standard Al 2 O 3 powder (standard SRM-676 of NIST, USA).
Field dependences of specific magnetization were measured at 10-730 K by Liquid Helium Free High Field Measurement System (VSM) [9]. The "ferrimagnetparamagnet" phase transition temperature for the BaFe 12−x D x O 19 (D= In and Ga; x = 0.1-1.2) has been defined as the inflection point in the temperature dependence of the specific magnetization.  essary to note that doping of diamagnetic ions In and Ga leads to reducing of the number of neighbors of magnetic iron cations and so that the magnetic order is destroyed at lower temperatures [10]. Therefore the Curie temperature decreases as the doping of In or Ga ions is increased whereas for the un-doped BaFe 12 O 19 the Curie temperature is equal 740 K [11].

Crystal structure
According to neutron data all investigated polycrystalline samples possesses a hexagonal structure with space group (P6 3 /mmc) with two formula units (Z = 2). The powder neutron diffraction patterns for the BaFe 10.8 D 1.2 O 19 (D= In and Ga) are presented in Fig. 2.
The high resolution of diffractometer and, correspondingly, the large number of well-separated peaks provided the good convergence of the minimization process. Fig-ures of merit (R wp , R exp , χ 2 ) that quantify the quality of the refinement using the Rietveld method are in range: R wpfrom 14.8% to 16.9%, R exp -from 10.0% to 11.9%, χ 2from 2.2 to 2.0. The dependencies of lattice parameters of unit cells versus temperature are shown in Fig. 3. Volumes of unit cells of solid solution of barium hexaferrite increase as the concentration of In ions is increased because of significant difference of ionic radii between In 3+ (r = 0.94Å) and Fe 3+ (r = 0.645Å) [12]. The increase of concentration of Ga 3+ (r= 0.62Å) ions leads to insignificant decreasing of volume of unit cell.

Magnetic structure
In hexaferrites the magnetic Fe 3+ ions are located in positions which have octahedral (Fe1-2a, Fe4-4 f VI and Fe5-12k), tetrahedral (Fe3-4 f IV ) and bipyramidal (Fe2-2b) oxygen environment. Therefore, partially replacement of iron ions by diamagnetic In or Ga ions that are distributed statistically equivalent for all positions of the magnetic lattice are able to change in the values of the magnetic moments in corresponding positions.  Fig.4. The substitution of iron by diamagnetic cation breaks the exchange interactions between the magnetic positions and sublattices that leads to a decrease in the value of their magnetic moments, as it was previously shown in Ref. [14]. The total magnetic moment M total per formula unit for the barium hexaferrite (BaFe 12 O 19 ) at T temperature can be calculated according to the formula [15]: where m i is the magnetic moment of Fe 3+ ion in the i-th sublattice. If the magnetic moment of Fe 3+ ion at 0 K is equal 5µ B then magnetic moment of pure BaFe 12 O 19 ferrite will be equal to 20µ B per formula unit. Less values of magnetic moments are explained by influence of diamagnetic ions and thermal factor causing the disorientation of the magnetic moments in space due to the increase of the thermal fluctuations of the ions forming the crystal lattice. The dependencies of total magnetic moment per formula unit for the barium hexaferrite versus temperature are shown in Fig. 4.

Microstructure
The high resolution of Fourier Diffractometer allowed making analysis of influence the concentration of diamagnetic ions to microstructural parameters, which were determined from broadening of powder neutron peaks. The presence of microstresses and variation of average size of coherent blocks have different effect on the width of the diffraction peaks, which makes it possible to split their contributions. The widths of the diffraction peaks W hkl of the tested samples have the following dependence from d hkl [16]: 4 (3) where C 1 , C 2 , C 3 , C 4 -refining constants; W -full width at half maximum of diffraction peak; (C 1 + C 2 · d 2 ) -resolution function of HRFD obtained from standard Al 2 O 3 (SRM-676 of NIST, USA); C 3 · d 2 -contribution determined by size effect; C 4 ·d 4 -contribution determined by microstraine effect.
The contribution of true physical line broadening of powder neutron peaks for the BaFe 12−x D x O 19 (D= In and Ga; x = 0.1-1.2) was determined by FullProf software calculated as difference of widths among experimental samples and standard Al 2 O 3 . In our case, the line broadening is connected with only microstresses factor. In ferrimagnetic crystals, the separate sublattices give different contributions to general deformation. Besides, the local environment symmetry of magnetic ions in ferrimagnetic crystals differs from macroscopic symmetry. This leads to increase of the microscopic parameters number in comparison with macroscopic. The slope of approximated function increases with temperature decreasing. This behavior indicates that the microstress increases in crystallites. It is shown in Fig. 5 the experimental points correspond to different combinations of Miller indices, which indicates the absence of explicit anisotropic effects in the broadening of diffraction peaks.  Fig. 6. The calculation of microstresses has been carried out for isotropic approximation i.e. (L > 3000 A) size effect is absent. The increase in the microscopic microstress with the concentration of diamagnetic ions increasing is associated with rising of the system disorder, as a result of the statistical distribution of indium or gallium in magnetic sublattices, which can make different contributions to the total deformation.

Conclusions
The behavior of crystal and magnetic structures of barium ferrites doped by diamagnetic ions was investigated by neutron diffraction method with high resolution. The refinement of crystal structure of solid solutions of BaFe 12−x D x O 19 (D= In and Ga; x= 0.1 -1.2) has been performed in frames of space group P6 3 /mmc (No. 194). Larger volume of unit cell of barium ferrites doped with In ions is explained by the larger value of ionic radii of In 3+ unlike of Ga 3+ ions. The magnetic structure of BaFe 12−x D x O 19 (D= In and Ga; x= 0.1 -1.2) is well described by the Gorter model: according to which the magnetic moments of the Fe 3+ ions are oriented along the hexagonal axis that is the axis of easy magnetization. Microstresses in crystallites increase as the concentration of In ions is increased whereas the rising of concentration of Ga ions decreases microstresses. This behavior was explained by different distortion of crystal sublattices due to diference of ionic radii of indium and gallium ions at substitution of iron ions.