The effect of local distortions on magnetic and magnetoelectric properties of paramagnetic Pr3Ga5SiO14 langasite

Magnetic field-induced electric polarization has been observed in trigonal non-centrosymmetric paramagnetic Pr3Ga5SiO14 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 Pr3Ga5SiO14 primarily stem from the local anisotropic magnetic moment of the two lowest Pr3+ singlets (quasi-doublet) in the crystal electric field. The random distribution of Ga/Si in the 2d positions leads to a local distortion of C2 symmetry and to a splitting distribution of the quasi-doublet. By considering the interactions of local moments among different Pr3+ 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 non-equivalence of local effective magnetic susceptibilities in different Pr3+ positions. Our findings suggest that the temperature dependencies of magnetic and magnetoelectric susceptibilities are highly sensitive to the distribution of the quasi-doublet splitting, which reflects the local symmetry breaking.