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We use first-principles total-energy calculations based on density functional theory to study the site occupancy and magnetic properties of Al-substituted $M$-type strontium hexaferrite SrFe$_{12-x}$Al$_{x}$O$_{19}$ with $x=0.5$ and $x=1.0$. We find that the non-magnetic Al$^{3+}$ ions preferentially replace Fe$^{3+}$ ions at two of the majority spin sites, $2a$ and $12k$, eliminating their positive contribution to the total magnetization causing the saturation magnetization $M_s$ to be reduced as Al concentration $x$ is increased. Our formation probability analysis further provides the explanation for increased magnetic anisotropy field when the fraction of Al is increased. Although Al$^{3+}$ ions preferentially occupy the $2a$ sites at a low temperature, the occupation probability of the $12k$ site increases with the rise of the temperature. At a typical annealing temperature ($> 700,^{circ}{rm C}$) Al$^{3+}$ ions are much more likely to occupy the $12k$ site than the $2a$ site. Although this causes the magnetocrystalline anisotropy $K_1$ to be reduced slightly, the reduction in $M_s$ is much more significant. Their combined effect causes the anisotropy field $H_a$ to increase as the fraction of Al is increased, consistent with recent experimental measurements.
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The site preference and magnetic properties of Zn, Sn and Zn-Sn substituted M-type strontium hexaferrite (SrFe$_{12}$O$_{19}$) have been investigated using first-principles total energy calculations based on density functional theory. The site occupancy of substituted atoms were estimated by calculating the substitution energies of different configurations. The distribution of different configurations during the annealing process at high temperature was determined using the formation probabilities of configurations to calculate magnetic properties of substituted strontium hexaferrite. We found that the magnetization and magnetocrystalline anisotropy are closely related to the distributions of Zn-Sn ions on the five Fe sites. Our calculation show that in SrFe$_{11.5}$Zn$_{0.5}$O$_{19}$, Zn atoms prefer to occupy $4f_1$, $12k$, and $2a$ sites with occupation probability of 78%, 19% and 3%, respectively, while in SrFe$_{11.5}$SnO$_{19}$, Sn atoms occupy the $12k$ and $4f_2$ sites with occupation probability of 54% and 46%, respectively. We also found that in SrFe$_{11}$Zn$_{0.5}$Sn$_{0.5}$O$_{19}$, (Zn,Sn) atom pairs prefer to occupy the ($4f_1$, $4f_2$), ($4f_1$, $12k$) and ($12k$, $12k$) sites with occupation probability of 82%, 8% and 6%, respectively. Our calculation shows that the increase of magnetization and the reduction of magnetic anisotropy in Zn-Sn substituted M-type strontium hexaferrite as observed experimentally is due to the occupation of (Zn,Sn) pairs at the ($4f_1$, $4f_2$) sites.
We study the site occupancy and magnetic properties of Zn-Sn substituted M-type Sr-hexaferrite SrFe$_{12-x}$(Zn$_{0.5}$Sn$_{0.5}$)$_x$O$_{19}$ with x = 1 using first-principles total-energy calculations. We find that in a ground-state configuration Zn-Sn ions preferentially occupy $4f_1$ and $4f_2$ sites unlike the model previously suggested by Ghasemi et al. [J. Appl. Phys, textbf{107}, 09A734 (2010)], where Zn$^{2+}$ and Sn$^{4+}$ ions occupy the $2b$ and $4f_2$ sites. Density-functional theory calculations show that our model has a lower total energy by more than 0.2 eV per unit cell compared to Ghasemis model. More importantly, the latter does not show an increase in saturation magnetization ($M_s$) compared to the pure $M$-type Sr-hexaferrite, in disagreement with the experiment. On the other hand, our model correctly predicts a rapid increase in $M_s$ as well as a decrease in magnetic anisotropy compared to the pure $M$-type Sr-hexaferrite, consistent with experimental measurements.
Hexaferrite materials are highly demanded to develop and manufacture electronic devices operating at radio- and microwave frequencies. In the light of the prospects for their use in the forthcoming terahertz electronics, here, we present our results on the terahertz and infrared dielectric response of a typical representative of hexaferrites family, lead-substituted M-type barium hexaferrite doped with aluminum, Ba0.2Pb0.8AlxFe12-xO19, x(Al)=0.0, 3.0, and 3.3. We studied uniquely large and high-quality single crystals of the. Systematic and detailed investigations of the dependences of terahertz-infrared (frequencies 8 - 8000 cm-1) spectra of complex dielectric permittivity on the temperature, 4 - 300 K, and on the chemical composition, x(Al)=0.0, 1.2, 3.0, 3.3, were performed for polarizations of the electric field E-vector of the probing radiation normal and parallel to the crystallographic c-axis. A number of resonance absorption bands are discovered at infrared-terahertz frequencies and assigned to polar phonons and transitions between energy levels of the fine-structured ground state of Fe2+ (5E) ions. In contrast to undoped BaFe12O19, no softening of the lowest frequency A2u phonon is observed, indicating suppression of a displacive phase transition in substituted compounds. Basing on dielectric data and detailed X-ray experiments, we find that for all concentrations of Al3+ ions, x(Al)=0.0, 1.2, 3.0, and 3.3, they mainly occupy the 2a and 12k octahedral site positions and that the degree of substitution of iron in tetrahedral positions is not substantial. Along with fundamental findings, the obtained data on broad-band dielectric properties of Ba0.2Pb0.8AlxFe12-xO19 crystals provides the information that can be used for development and manufacture of electronic devices with operating frequencies lying in the terahertz spectral band.
We examined the formation mechanisms of magnetic bubbles in an M-type hexaferrite via Lorentz microscopy. When magnetic fields were perpendicularly applied to a thin sample of BaFe$_{12-x-0.05}$Sc$_x$Mg$_{0.05}$O$_{19}$ ($x = 1.6$), Bloch lines, which were identified as reversals of domain-wall chirality, appeared, and magnetic bubbles were formed when the magnetic stripes were pinched off at these Bloch lines. The number of Bloch lines increased with the amount of Sc in BaFe$_{12-x-0.05}$Sc$_x$Mg$_{0.05}$O$_{19}$ probably because of the reduction in magnetic anisotropy. A Lorentz microscopic observation revealed that Bloch lines with high magnetostatic energy may play an important role in the formation of magnetic bubbles.
Ti-substituted perovskites, La0.7Sr0.3Mn1-xTixO3, with x between 0 to 0.20, were investigated by neutron diffraction, magnetization, electric resistivity, and magnetoresistance (MR) measurements. All samples show a rhombohedral structure (space group R3c) from 10 K to room temperature. At room temperature, the cell parameters a, c and the unit cell volume increase with increasing Ti content. However, at 10 K, the cell parameter a has a maximum value for x = 0.10, and decreases for x greater than 0.10, while the unit cell volume remains nearly constant for x greater than 0.10. The average (Mn,Ti)-O bond length increases up to x=0.15, and the (Mn,Ti)-O-(Mn,Ti) bond angle decreases with increasing Ti content to its minimum value at x=0.15 at room temperature. Below the Curie temperature T_C, the resistance exhibits metallic behavior for the x _ 0.05 samples. A metal (semiconductor) to insulator transition is observed for the x_ 0.10 samples. A peak in resistivity appears below T_C for all samples, and shifts to a lower temperature as x increases. The substitution of Mn by Ti decreases the 2p-3d hybridization between O and Mn ions, reduces the bandwidth W, and increases the electron-phonon coupling. Therefore, the TC shifts to a lower temperature and the resistivity increases with increasing Ti content. A field-induced shift of the resistivity maximum occurs at x less than or equal to 0.10. The maximum MR effect is about 70% for La0.7Sr0.3Mn0.8Ti0.2O3. The separation of TC and the resistivity maximum temperature Tmax enhances the MR effect in these compounds due to the weak coupling between the magnetic ordering and the resistivity as compared with La0.7Sr0.3MnO3.
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