Ferroelectric hysteresis loops and switching current were collected from the current density–voltage (J–V) curves via the double-wave method in a physical properties measurement system (PPMS-9, Quantum Design)39 (link),40 (link). Dielectric measurements were carried out using an Impedance analyzer (E4990A). The temperature was controlled by a Linkam Scientific Instruments HFS600E-PB4 system. The magnetodielectric effects were measured using an Agilent 4980 A LCR meter in a cryogen-free superconducting magnet system (Oxford Instruments, TeslatronPT). For the ferroelectric, dielectric, and magnetodielectric measurements, Pt top electrodes with an area of 8 × 10−4 cm2 and the VAN films grown on Nb-STO substrates were used. The magnetic measurements were carried out using a PPMS-9 and a superconducting quantum interface device magnetometer (SQUID, Quantum Design).
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