Scaling behavior of dynamic hysteresis in Bi3.15Nd0.85Ti3O12 ceramics

The scaling behavior of dynamic hysteresis was investigated in Bi3.15Nd0.85Ti3O12 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.