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

Abstract

We demonstrate that parity-nonconserving interaction due to the nuclear weak charge ${Q}_{W}$ leads to a nonlinear magnetoelectric effect in centrosymmetric paramagnetic crystals. It is shown that the effect exists only in crystals with special symmetry axis $\mathbf{k}$. Kinematically, the correlation (correction to energy) has the form ${H}_{\mathrm{PNC}}\ensuremath{\propto}{Q}_{W}\mathbf{E}∙[\mathbf{B}\ifmmode\times\else\texttimes\fi{}\mathbf{k}](\mathbf{B}∙\mathbf{k})$, where $\mathbf{B}$ and $\mathbf{E}$ are external magnetic and electric fields. This gives rise to the magnetic induction ${\mathbf{M}}_{\mathrm{PNC}}\ensuremath{\propto}{Q}_{W}{\mathbf{k}(\mathbf{B}∙[\mathbf{k}\ifmmode\times\else\texttimes\fi{}\mathbf{E}])+[\mathbf{k}\ifmmode\times\else\texttimes\fi{}\mathbf{E}](\mathbf{B}∙\mathbf{k})}$. To be specific, we consider rare-earth-metal trifluorides and, in particular, dysprosium trifluoride which looks the most suitable for experiment. We estimate the optimal temperature for the experiment to be of a few kelvin. For the magnetic field $B=1\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ and the electric field $E=10\phantom{\rule{0.3em}{0ex}}\mathrm{kV}∕\mathrm{cm}$, the expected magnetic induction is $4\ensuremath{\pi}{M}_{\mathrm{PNC}}\ensuremath{\sim}0.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}\mathrm{G}$, six orders of magnitude larger than the best sensitivity currently under discussion. Dysprosium has several stable isotopes, and so comparison of the effects for different isotopes provides the possibility for precise measurement of the Weinberg angle.