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Second harmonic generation (SHG) on the pyrochlore metal Cd2Re2O7 indicatesthe presence of three order parameters setting in below an inversion breakingtransition. Here, we explore a possible structural explanation and relate itnot only to the SHG data, but also to neutron and x-ray diffraction, where wefind that such a structural scenario can explain certain reflection extinctionsobserved in single crystal x-ray data. From this analysis, we suggest futureexperiments that could be done to resolve this matter. Finally, we comment onthe Landau-violating nature of the inversion breaking transition and itsrelation to similar phenomena observed in improper ferroelectrics.

Crystal structure of the inversion-breaking metal Cd2Re2O7