Different mechanisms for dielectric, magnetic, and magnetodielectric properties in $M$-type $\mathrm{Ba}{\mathrm{Fe}}_{12}{\mathrm{O}}_{19}$ hexaferrite by ${\mathrm{Ga}}^{3+}$ and ${\mathrm{In}}^{3+}$ doping

An $M$-type hexaferrite is a material with rich physical characteristics, such as magnetism, the dielectric property, and the magnetodielectric (MD) effect. In this paper, we systematically investigated the magnetic, dielectric, and MD properties of $\mathrm{Ba}{\mathrm{Fe}}_{12-x}{\mathrm{Me}}_x{\mathrm{O}}_{19}$ ($\mathit{Me}$ = Ga and In; $x=0.0$, 1.2, 1.8, and 2.4) ceramics prepared by a solid-state reaction method. The ${\mathrm{Ga}}^{3+}$ cations with a smaller radius preferentially substitute the ${\mathrm{Fe}}^{3+}$ ions in $\mathrm{Fe}{\mathrm{O}}_6$ octahedra, while the ${\mathrm{In}}^{3+}$ cations with a larger radius tend to replace the ${\mathrm{Fe}}^{3+}$ ions in $\mathrm{Fe}{\mathrm{O}}_5$ bipyramids of $R$ blocks, inducing different physical characteristics. The pure $\mathrm{Ba}{\mathrm{Fe}}_{12}{\mathrm{O}}_{19}$ and Ga-doped samples show ferrimagnetism in the temperature range from 10 to 300 K. The In-doped samples exhibit a transition from noncollinear magnetism to collinear ferrimagnetism at 39, 128, and 144 K for the doping amounts of $x=1.2$, 1.8, and 2.4, respectively. The dielectric decrease of pure $\mathrm{Ba}{\mathrm{Fe}}_{12}{\mathrm{O}}_{19}$ at $\sim 10–175\mathrm{K}$ is attributed to the quantum paraelectric state, and the shoulder peaks of tan $\delta$ at ∼140–200 K are from electron hopping. The dipole glass state is responsible for the dielectric peak of Ga-doped samples at $\sim 20–40\mathrm{K}$. The dielectric increase and plateau of In-doped samples are mainly ascribed to the electron hopping at low temperatures. Their dielectric properties at high temperatures are all attributed to the interfacial polarization caused by the Maxwell-Wagner effect. The MD effect also has different origins for the various samples at low temperatures. For pure $\mathrm{Ba}{\mathrm{Fe}}_{12}{\mathrm{O}}_{19}$, the negative MD effect at extremely low temperatures and the positive MD effect after warming are ascribed to spin-phonon coupling and field-dependent electron hopping, respectively. The positive MD effect in Ga-doped hexaferrites results from the field-dependent electric dipoles inside $\mathrm{Fe}{\mathrm{O}}_5$ bipyramids. For the In-doped samples, the negative MD effect and subsequent transformation to the positive MD effect originate from the field-dependent noncollinear spin ordering and electron hopping, respectively. The MD effect at high temperatures is attributed to the combination of magnetoresistance and Maxwell-Wagner effects. These research results are helpful for understanding the relationship among doped ions, spin order, dielectric property, and the MD effect in $M$-type hexaferrites.

Figure 1

(a) Schematic of $\mathrm{Ba}{\mathrm{Fe}}_{12}{\mathrm{O}}_{19}$ crystal structure, (b) magnetic structure of cross-section view in (110) plane, and (c)–(e) schematics of noncollinear spin order for the $M$-type hexaferrite under different magnetic fields. ${\mathbf{e}}_{ij}$ is the unit vector connecting the adjacent basic magnetic units.

Figure 2

(a) X-ray diffraction (XRD) patterns of $\mathrm{Ba}{\mathrm{Fe}}_{12-x}{\mathrm{Me}}_x{\mathrm{O}}_{19}$ ($\mathit{Me}$ = Ga and In; $x=0$, 1.2, 1.8, and 2.4) ceramics and their subtle patterns around the main peaks. (b) Dependence of lattice parameters and cell volume on the doping amount.

Figure 3

Raman spectra of $\mathrm{Ba}{\mathrm{Fe}}_{12-x}{\mathrm{Me}}_x{\mathrm{O}}_{19}$ ($\mathit{Me}$ = Ga and In; $x=0$, 1.2, 1.8, and 2.4) ceramics.

Figure 4

X-ray photoelectron spectroscopy (XPS) spectra of (a) Ba $3d$, (b) In $3d$, (c) Ga $2p$, (d) Fe $2p$, and (e) O $1s$ for $\mathrm{Ba}{\mathrm{Fe}}_{12-x}{\mathrm{Me}}_x{\mathrm{O}}_{19}$ ($\mathit{Me}$ = Ga and In; $x=0$, 1.2, 1.8, and 2.4) ceramics.

Figure 5

Thermomagnetic curves of $\mathrm{Ba}{\mathrm{Fe}}_{12-x}{\mathrm{Me}}_x{\mathrm{O}}_{19}$ ($\mathit{Me}$ = Ga and In; $x=0$, 1.2, 1.8, and 2.4) ceramics. The testing field is 100 Oe, and the field-cooling (FC) field is also 100 Oe.

Figure 6

(a)–(g) Hysteresis loops of $\mathrm{Ba}{\mathrm{Fe}}_{12-x}{\mathrm{Me}}_x{\mathrm{O}}_{19}$ ($\mathit{Me}$ = Ga and In; $x=0$, 1.2, 1.8, and 2.4) ceramics at various temperatures. The insets show the initial magnetization curves and hysteresis loops at 10 K. (h) and (i) Temperature dependence of ceramic coercivity. The inset shows the blown-up patterns. (j) and (k) Temperature dependence of saturation magnetization.

Figure 7

Temperature dependence of dielectric permittivity of $\mathrm{Ba}{\mathrm{Fe}}_{12-x}{\mathrm{Me}}_x{\mathrm{O}}_{19}$ ($\mathit{Me}$ = Ga and In; $x=0.0$, 1.2, 1.8, and 2.4) ceramics with different frequencies. The insets in (a)–(d) show the temperature dependence of inverse dielectric permittivity and lines fitted by the Curie-Weiss law. The insets in (e)–(g) show blown-up patterns.

Figure 8

(a)–(g) Temperature dependence of dielectric permittivity, dielectric loss (tan $\delta$), and imaginary of the complex electric modulus ($M^{\prime \prime }$) of $\mathrm{Ba}{\mathrm{Fe}}_{12-x}{\mathrm{Me}}_x{\mathrm{O}}_{19}$ ($\mathit{Me}$ = Ga and In; $x=0.0$, 1.2, 1.8, and 2.4) ceramics at different frequencies. (h)–(j) Arrhenius plots from $M^{\prime \prime }$. The inset in (a) shows the blown-up pattern of dielectric loss in exponential form.

Figure 9

Impedance complex plots of $\mathrm{Ba}{\mathrm{Fe}}_{12-x}{\mathrm{Me}}_x{\mathrm{O}}_{19}$ ($\mathit{Me}$ = Ga and In; $x=0.0$, 1.2, 1.8, and 2.4) ceramics at room temperature. The insets show blown-up patterns at low impedance.

Figure 10

(a)–(g) Magnetic field dependence of magnetodielectric (MD) coefficient under various temperatures at 100 kHz for the $\mathrm{Ba}{\mathrm{Fe}}_{12-x}{\mathrm{Me}}_x{\mathrm{O}}_{19}$ ($\mathit{Me}$ = Ga and In; $x=0.0$, 1.2, 1.8, and 2.4) ceramics. (h)–(n) Their blown-up patterns at low magnetic fields. The blue curves show the MD change from 50 to −50 kOe, while the red curves show a reverse change. The different vertical axes show the MD values clearly.

Figure 11

Temperature dependence of the magnetodielectric (MD) coefficient gathered from the isothermal MD curves. The MD coefficients collected at MD maximum and at zero field share close values.

Figure 12

Dielectric difference as a function of the square of magnetization for the pure $\mathrm{Ba}{\mathrm{Fe}}_{12}{\mathrm{O}}_{19}$ at 10 K. The inset shows the magnetic field-dependent dielectric difference and square of magnetization, where two curves overlap together in a large magnetic field range.

Figure 13

Magnetic field dependence of (a) magnetodielectric (MD) coefficient and (b) magnetization for the $\mathrm{Ba}{\mathrm{Fe}}_{9.6}{\mathrm{Ga}}_{2.4}{\mathrm{O}}_{19}$ sample at 10 K.

Figure 14

Temperature dependence of magnetodielectric (MD) coefficient and dielectric permittivity at different frequencies for the In-doped $\mathrm{Ba}{\mathrm{Fe}}_{12-x}{\mathrm{In}}_x{\mathrm{O}}_{19}$ samples with (a) and (b) $x=1.2$, (c) and (d) $x=1.8$, and (e) and (f) $x=2.4$. The MD coefficient is calculated by the dielectric permittivity at 0 and 50 kOe.