Different mechanisms for dielectric, magnetic, and magnetodielectric properties in M-type BaFe12O19 hexaferrite by Ga3+ and In3+ 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 $\mathrm{Ba}{\mathrm{Fe}}_{12\ensuremath{-}x}{\mathrm{Me}}_{x}{\mathrm{O}}_{19}$ ($\mathit{Me}$ = 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 $\ensuremath{\sim}10--175\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ is attributed to the quantum paraelectric state, and the shoulder peaks of tan $\ensuremath{\delta}$ at \ensuremath{\sim}140--200 K are from electron hopping. The dipole glass state is responsible for the dielectric peak of Ga-doped samples at $\ensuremath{\sim}20--40\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. 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.