Magnetocrystalline anisotropy of La- and Co-substituted $\mathrm{M}$-type strontium ferrites: Role of ${\mathrm{Co}}^{2+}$ and ${\mathrm{Fe}}^{2+}$

We have systematically investigated the magnetic properties of ${\mathrm{La}}_{}$- and ${\mathrm{Co}}_{}$-substituted ${\mathrm{Sr}}_{}{\mathrm{Fe}}_{12}{\mathrm{O}}_{19}$ using single crystals. By utilizing the traveling solvent floating zone technique, we have grown single crystals over a wide range of substitution content, and examined their saturation moments and magnetocrystalline anisotropy. With increasing content of ${\mathrm{La}}_{}$ and ${\mathrm{Co}}_{}$, the saturation moment at $300\mathrm{K}$ monotonically increases. The increment of magnetocrystalline anisotropy is almost proportional to the content of Co. In addition, further La substitution also enhances magnetocrystalline anisotropy, which demonstrates that ${\mathrm{Fe}}^{2+}$ plays an important role to enhance magnetocrystalline anisotropy. We have analyzed magnetocrystalline anisotropy energy as a function of substitution content, and elucidate the effects of ${\mathrm{Co}}^{2+}$ and ${\mathrm{Fe}}^{2+}$.

Figure 1

Nominal and measured compositions of single-crystal samples of ${\mathrm{Sr}}_{1\text{−}x}{\mathrm{La}}_x{\mathrm{Fe}}_{12\text{−}y}{\mathrm{Co}}_y{\mathrm{O}}_{19}$. Crosses indicate nominal compositions, which is the same value as that of the starting materials. Squares and circles indicate compositions obtained using WDX and those using ICP, respectively. The insets are pictures of cleaved surfaces of obtained single crystals with nominal compositions of $(x,y)=(0.7,0.7)$ and $(0.8,0.4)$.

Figure 2

The variations of $T_{\mathrm{C}}$, the lattice constants and the unit cell volume of ${\mathrm{Sr}}_{1\text{−}x}{\mathrm{La}}_x{\mathrm{Fe}}_{12\text{−}y}{\mathrm{Co}}_y{\mathrm{O}}_{19}$ as a function of ${\mathrm{La}}_{}$ content $x$. In the region of $x\le 0.4$, the ${\mathrm{Co}}_{}$ content $y$ is equal to $x$. For $x\ge 0.4$, we fix $y=0.4$. The lines in the graphs are the results of linear fittings.

Figure 3

The variation of saturation magnetization $M_{\mathrm{s}}$ per formula unit as a function of ${\mathrm{La}}_{}$ content $x$. As is the same as before, the ${\mathrm{Co}}_{}$ content $y$ is equal to $x$ for $x\le 0.4$, and we fix $y=0.4$ for $x\ge 0.4$. Upper and lower panels are the results measured at 5 and $300\mathrm{K}$, respectively. The filled circles indicate the measured value and the bars scale experimental errors. The lines are guides to the eyes. The inset shows the temperature dependence of $M_{\mathrm{s}}$ for $x=0,0.4,1$, which was measured at $1\mathrm{T}$ for $H\parallel c$.

Figure 4

The magnetization of ${\mathrm{Sr}}_{1\text{−}x}{\mathrm{La}}_x{\mathrm{Fe}}_{12\text{−}y}{\mathrm{Co}}_y{\mathrm{O}}_{19}$ where the magnetic field is applied perpendicular to the $c$ axis. The effective magnetic field $H_{\mathrm{eff}}$ is obtained by subtracting the demagnetization field. The upper panel shows magnetization curves measured at 5 K, and the lower panel shows those at 300 K. The inset displays temperature dependence of magnetic susceptibility under magnetic field of $0.1\mathrm{T}$ in cooling process, which indicates the initial slopes of $M\text{−}{\mu }_{0}H$ curves.

Figure 5

The main panel shows the angle dependence of the magnetocrystalline anisotropy energy $E_{\mathrm{a}}$ of the $x=y=0.4$ sample, ${\mathrm{Sr}}_{0.6}{\mathrm{La}}_{0.4}{\mathrm{Fe}}_{11.6}{\mathrm{Co}}_{0.4}{\mathrm{O}}_{19}$. The experimentally obtained $E_{\mathrm{a}}\text{−}{sin}^2\theta$ curve, which displayed as a dashed line, is fitted using two formulas that are described in the figure. The lower panel shows the difference between experimental data and fitted ones. The inset displays the temperature dependence of ${\mu }_0{H}_{\mathrm{A}}$.

Figure 6

The variations of two terms $2C_2/M_{\mathrm{s}}$ and $C_1/M_{\mathrm{s}}$ and the sum of them, which were obtained from the fittings of $E_{\mathrm{a}}$ at $5\mathrm{K}$. This figure includes also ${\mu }_0{H}_{\mathrm{A}}=M_{\mathrm{s}}/\chi \left(0.1\mathrm{T}\right)$ at 5 and $300\mathrm{K}$.