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We demonstrate that parity nonconserving interaction due to the nuclear weakcharge Q_W leads to nonlinear magnetoelectric effect in centrosymmetricparamagnetic crystals. It is shown that the effect exists only in crystals withspecial symmetry axis k. Kinematically, the correlation (correction to energy)has the form H_PNC ~ Q_W (E,[B,k])(B,k), where B and E are the externalmagnetic and electric fields. This gives rise to magnetic induction M_PNC ~ Q_W{k(B,[k,E]) + [k,E](B,k)}. To be specific we consider rare-earth trifluoridesand, in particular, dysprosium trifluoride which looks the most suitable forexperiment. We estimate the optimal temperature for the experiment to be of afew kelvin. For the magnetic field B = 1 T and the electric field E = 10 kV/cm,the expected magnetic induction is 4 \pi M_PNC = 0.5 * 10^-11 G, six orders ofmagnitude larger than the best sensitivity currently under discussion.Dysprosium has several stable isotopes, and so, comparison of the effects fordifferent isotopes provides possibility for precise measurement of the Weinbergangle.Comment: 7 pages, 1 figure, 2 tables; version 2 - added discussion of neutron  distribution uncertaint

Possibility for precise Weinberg-angle measurement in centrosymmetric crystals with axis