Pressure effect on ferroelectricity of multiferroic Ho$_{0.5}$Nd$_{0.5}$Fe$_{3}$(BO$_{3}$)$_{4}$

Ho$_{0.5}$Nd$_{0.5}$Fe$_{3}$(BO$_{3}$)$_{4}$ becomes multiferroic below 33 K where it enters into the AFM1 phase and gives rise to a ferroelectric polarization along the a-axis. At 9.5 K, the polarization drops sharply and remains finite value of $\sim$ 40 $\mu$C/m$^2$. This is due to the spin rotation from the a-b plane into the c-axis and gives rise to the AFM2 phase. The application of pressure suppresses the AFM2 phase and moves the spin rotation transition from 9.5 K to 4.8 K up to pressure of 18.8 kbar which is observed in both dielectric and pyroelectric measurements. The change in magnetic anisotropy of rare-earth moments and Fe ions under pressure drives the spin rotation transition of rare-earth at lower temperature.