Scaling behavior of dynamic hysteresis in Bi_3.15Nd_0.85Ti₃O₁₂ ceramics

Abstract

The scaling behavior of dynamic hysteresis was investigated in Bi_3.15Nd_0.85Ti₃O₁₂ bulk ceramics at a frequency of 1–1000 Hz and an external electric field amplitude of 79–221 kV/cm. The scaling behavior at low amplitude (E ₀ ≤ 114 kV/cm) takes the form of $\langle A \rangle \propto f^{ - 0.013} E_{0}^{0.7}$ for low frequency (f ≤ 200 Hz) and $\langle A \rangle \propto f^{ - 0.013} E_{0}^{0.22}$ for high frequency (f > 200 Hz), where $\langle A \rangle$ is the area of hysteresis loop and f and E ₀ are frequency and amplitude of external electric field, respectively. At high amplitude (E ₀ > 114 kV/cm), we obtain $\langle A \rangle \propto f^{0.011} E_{0}^{1.163}$ at low frequency and $\langle A \rangle \propto f^{ - 0.015} E_{0}^{0.7}$ at high frequency. At low E ₀, the contribution to the scaling relation mainly results from reversible domain switching, while at high E ₀ reversible and irreversible domain switching concurrently contribute to the scaling relation.