Fig. 1: Comparison of the various properties for pristine, Fe-doped, and Mn-doped KTN crystals.

A–C Dielectric constant ε_r as a function of temperature and frequency, D–F strain–electric field (S–E) loops at 1 Hz, G–I polarization–electric field (P–E) loops, current–electric field (J–E) loops at 1 Hz, J dielectric losses tan δ at 100 kHz, K internal bias fields, E_int, extracted from P–E loops, and L lateral-mode mechanical quality factors, Q_m, for pristine, Fe-doped, and Mn-doped KTN crystals, respectively. The orthorhombic–tetragonal phase transition temperatures of 50 °C are marked in (A–C), and the insets show the corresponding low-temperature dielectric properties in the range of −150 to 0 °C. The arrow in (C) inset indicates a frequency dependence of dielectric maxima at the rhombohedral-to-orthorhombic phase transition, showing a typical relaxor behavior. The insets in (D–F) are the photos giving the results of quasi-static d₃₃ tests. In the S–E, P–E, and Q_m measurements, the samples poled along the [001]_C crystallographic direction were used. The magnitude of E_int is determined by E_int = (E₊ + E₋)/2, where E₊ and E₋ are the intersections of polarization loop with positive and negative electric field axis.