Coexistence of large negative and positive magnetodielectric response in ${\mathrm{Bi}}_{1-x}{\mathrm{Ca}}_x{\mathrm{Fe}}_{1-y}{\mathrm{Ti}}_y{\mathrm{O}}_{3-\delta }$ nanoparticle ceramics

Magnetodielectric (MD) properties of as-prepared (AP) and air-annealed ${\mathrm{Bi}}_{1-x}{\mathrm{Ca}}_x{\mathrm{Fe}}_{1-y}{\mathrm{Ti}}_y{\mathrm{O}}_{3-\delta }$ 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 ∼120 K, which weakens on air-annealing. A coexistence of positive and negative MD [MD = $\frac{\mathrm{\Delta }\varepsilon \left(H\right)}{\varepsilon \left(H=0\right)}$; $\mathrm{\Delta }\varepsilon \left(H\right)=\varepsilon \left(H\right)-\varepsilon \left(H=0\right)$] 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% (∼+3%) at 10 K (300 K). Negative MD response diminishes for air-annealed ${\mathrm{Bi}}_{1-x}{\mathrm{Ca}}_x{\mathrm{Fe}}_{1-y}{\mathrm{Ti}}_y{\mathrm{O}}_{3-\delta }$ 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 $\mathrm{\Delta }\varepsilon \left(H\right)$ 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.

Figure 1

Magnetodielectric response of (a), (c) as-prepared (AP) and (b), (d) air-annealed (AA) ${\mathrm{Bi}}_{1\text{–}x}{\mathrm{Ca}}_x{\mathrm{Fe}}_{1\text{–}y}{\mathrm{Ti}}_y{\mathrm{O}}_{3\text{–}\delta }$ ceramics at (a), (b) 10 K and (c), (d) 300 K. The insets show the magnified plots.

Figure 2

Magnetization (M) $vs$ applied magnetic field (H) curves for (a), (b) as-prepared (AP) and (c), (d) air-annealed (AA) ${\mathrm{Bi}}_{1\text{–}x}{\mathrm{Ca}}_x{\mathrm{Fe}}_{1\text{–}y}{\mathrm{Ti}}_y{{\mathrm{O}}_{3\text{–}\delta }}_{}$ ceramics. M-H curves are shown at two different temperatures (a), (c) 20 K and (b), (d) 300 K for AP and AA pellets. Magnified region of M-H curves near center are shown in the inset of corresponding figure. BFO, BC5FO, BC10FO, BC5FT5O, and BC10FT10O correspond to $x=y=0$, $x=0.05$; $y=0$, $x=0.1$; $y=0$, $x=y=0.05$ and $x=y=0.1$, respectively.

Figure 3

Zero-field-cooled (ZFC) and field-cooled (FC) plots for (a) as-prepared (AP) and (b) air-annealed (AA) ${\mathrm{Bi}}_{1\text{–}x}{\mathrm{Ca}}_x{\mathrm{Fe}}_{1\text{–}y}{\mathrm{Ti}}_y{{\mathrm{O}}_{3\text{–}\delta }}_{}$ ceramics. BFO, BC5FO, BC10FO, BC5FT5O, and BC10FT10O correspond to $x=y=0$, $x=0.05$; $y=0$, $x=0.1$; $y=0$, $x=y=0.05$ and $x=y=0.1$, respectively.

Figure 4

(a), (b) Resistivity $vs$ temperature curves for (a) BC5FT5O-AP and (b) BC10FT10O-AP ceramics with and without field. Insets show the derivative of the log of resistivity $vs$ temperature plot. (c), (d) Change in magnetoresistance with the variation of temperature for (c) BC5FT5O-AP and (d) BC10FT10O-AP ceramics. (e), (f) Change in resistivity with the variation of the magnetic field at temperatures 80 and 300 K for (e) BC5FT5O-AP and (f) BC10FT10O-AP ceramics.

Figure 5

Temperature-dependent normalized MD response of (a) as-prepared and (b) air annealed ceramics. Normalization is done with respect to the MD values found at 10 K temperature.

Figure 6

(a), (c), (e) Overlap plots of squared magnetization and modulus of MD response as a function of the magnetic field and (b), (d), (f) MD response [Δε(H)/ε(H = 0)] as a function of squared magnetization ($M^2$) (H) of (a), (b) BC5FO-AA at 300 K (c), (d) BC5FO-AP at 10 K and (e), (f) BC10FT10O-AA at 300 K. (b), (d), (f) Open symbols show the measured data and solid lines are the linearly fitted curves.