Effect of local distortions on magnetic and magnetoelectric properties of paramagnetic Pr3Ga5SiO14 langasite

Magnetic-field-induced electric polarization has been observed in trigonal noncentrosymmetric paramagnetic ${\mathrm{Pr}}_3{\mathrm{Ga}}_5{\mathrm{SiO}}_{14}$ langasite. We detected quadratic electric polarization along the $a$ axis in the basal $ab$ plane for various magnetic field orientations. Electric polarization along the $c$ axis is only evident starting from the fourth power of magnetic field, in accordance with the trigonal symmetry. The magnetic properties of ${\mathrm{Pr}}_3{\mathrm{Ga}}_5{\mathrm{SiO}}_{14}$ primarily stem from the local anisotropic magnetic moment of the two lowest $\mathrm{P}{\mathrm{r}}^{3+}$ singlets (quasidoublet) in the crystal electric field. The random distribution of Ga/Si in the $2d$ positions leads to a local distortion of the $C_2$ symmetry and to a distribution of the quasidoublet splitting. By considering the interactions of local moments among different $\mathrm{P}{\mathrm{r}}^{3+}$ positions within a phenomenological approach for the allowed magnetoelectric coupling, we derive the electric polarization in terms of symmetry-allowed combinations of local magnetic susceptibilities and field components. The magnetic field dependence of electric polarization in the basal plane, $P_{a,b*}$, is mainly determined by the accumulation of effective local susceptibilities, exhibiting similar behavior in low fields, while polarization along the $c$ axis, $P_c$, arises from the nonequivalence of local effective magnetic susceptibilities in different $\mathrm{P}{\mathrm{r}}^{3+}$ positions. Our findings suggest that the temperature dependencies of magnetic and magnetoelectric susceptibilities are highly sensitive to the distribution of the quasidoublet splitting, which reflects the local symmetry breaking.