Magnetic-field-induced electric polarization has been observed in trigonal noncentrosymmetric paramagnetic

\Pr_{3} {Ga}_{5} {SiO}_{14}

langasite. We detected quadratic electric polarization along the

a

axis in the basal

a b

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

\Pr_{3} {Ga}_{5} {SiO}_{14}

primarily stem from the local anisotropic magnetic moment of the two lowest

P r^{3 +}

singlets (quasidoublet) in the crystal electric field. The random distribution of Ga/Si in the

2 d

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

P 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

P 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.

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