Effect of crystal field local distortions on terahertz spectra of Pr$^{3+}$ in langasite Pr$_3$Ga$_5$SiO$_{14}$

The rare earth langasite Pr$_3$Ga$_5$SiO$_{14}$ (PGS) was studied using terahertz time-domain spectroscopy (TDS) at temperatures of 5–300 K. In the frequency range of 5–40 cm$^{-1}$, a non-uniformly broadened absorption line was detected in the transmission and phase shift spectra of transmitted radiation, identified as a magnetic dipole transition between the levels of the ground quasi-doublet of the Pr$^{3+}$ ion split by the crystal field. Strong non-uniform broadening is caused by random distortions of the local crystal field near rare earth ions. Consistent modeling of transmission spectra and static magnetic properties was carried out, which made it possible to establish the nature of the distribution of local distortions of the crystal field and determine the contribution of magnetic dipole transitions. Static magnetic properties are highly sensitive to the presence of local positions of Pr$^{3+}$ ions with small splitting of the main quasi-doublet, while the main contribution to the terahertz resonance properties is made by ions with splitting near the maximum of the distribution and above.