Coexistence of large negative and positive magnetodielectric response in Bi1−xCaxFe1−yTiyO3−δ nanoparticle ceramics

Magnetodielectric (MD) properties of as-prepared (AP) and air-annealed ${\\mathrm{Bi}}_{1\\ensuremath{-}x}{\\mathrm{Ca}}_{x}{\\mathrm{Fe}}_{1\\ensuremath{-}y}{\\mathrm{Ti}}_{y}{\\mathrm{O}}_{3\\ensuremath{-}\\ensuremath{\\delta}}$ nanoparticle ceramics made by spark plasma sintering process are investigated as a function of temperature. Aliovalent ${\\mathrm{Ca}}^{2+}$ substitution at ${\\mathrm{Bi}}^{3+}$ site creates oxygen vacancies (${\\mathrm{V}}_{\\mathrm{O}}$) in the lattice disrupting the intrinsic spin cycloid of ${\\mathrm{BiFeO}}_{3}$, which are suppressed when the charge compensating ${\\mathrm{Ti}}^{4+}$ is co-substituted. In addition, cation substitution reduces the grain size and increases surface oxygen vacancies. These lattice and surface ${\\mathrm{V}}_{\\mathrm{O}}$ defects play a significant role in enhancing the magnetic properties. Zero-field-cooled magnetization curves of all AP samples show a sharp Verwey-like transition at \\ensuremath{\\sim}120 K, which weakens on air-annealing. A coexistence of positive and negative MD [MD = $\\frac{\\mathrm{\\ensuremath{\\Delta}}\\ensuremath{\\varepsilon}(H)}{\\ensuremath{\\varepsilon}(H=0)}$; $\\mathrm{\\ensuremath{\\Delta}}\\ensuremath{\\varepsilon}(H)=\\ensuremath{\\varepsilon}(H)\\ensuremath{-}\\ensuremath{\\varepsilon}(H=0)$] response is observed, with the former dominating at 300 K and the latter at 10 K. As-prepared 5 at.% (10 at.%) Ca and Ca-Ti substituted ${\\mathrm{BiFeO}}_{3}$ ceramics exhibit a maximum MD response of --10% (\\ensuremath{\\sim}+3%) at 10 K (300 K). Negative MD response diminishes for air-annealed ${\\mathrm{Bi}}_{1\\ensuremath{-}x}{\\mathrm{Ca}}_{x}{\\mathrm{Fe}}_{1\\ensuremath{-}y}{\\mathrm{Ti}}_{y}{\\mathrm{O}}_{3\\ensuremath{-}\\ensuremath{\\delta}}$ ceramics due to the reduction in ${\\mathrm{V}}_{\\mathrm{O}}$ concentration. Samples exhibiting dominant positive MD response show a similar trend for MD $vs$ H and ${M}^{2}$ vs H plots. This agreement between ${M}^{2}$ and $\\mathrm{\\ensuremath{\\Delta}}\\ensuremath{\\varepsilon}(H)$ demonstrates a strong inherent MD coupling. On the contrary, negative MD does not follow this trend yet shows a linear relationship of MD vs ${M}^{2}$, suggesting a strong coupling between the magnetic and dielectric properties. Temperature-dependent MD studies carried out at 5 T show a gradual change from negative to positive values. Negative MD at low temperatures could be activated by the spin-lattice coupling, which dominates even at high frequency (1 MHz) under the applied field. Other contributions, including Verwey-like transition, magnetoresistance, and Maxwell-Wagner effects, do not influence the observed MD response. A prominent role of oxygen vacancies in altering the MD behavior of ${\\mathrm{BiFeO}}_{3}$ is discussed in detail.