Fig. 3: Temperature dependence of the dielectric constant of PbCuTe₂O₆.

Dielectric constant of single crystal sc #5(b) (black squares), with electric field E applied along the [110] direction, and a pressed-powder sample pd #Ι(b) (orange spheres). Similar measurements on the single crystals #1(a) and #4 reveal essentially the same results albeit with a somewhat reduced peak height, see Supplementary Fig. 9 and Note 6. The inset gives details of the data for sc #5(b) in a narrow temperature range around 1 K. Inset a, showing 1/(ε’ − ε’_b) vs. T, reflects a Curie–Weiss-like behavior on approaching the maximum in ε’ from both sides. The slopes of the linear regimes differ by a factor of about −1.9. This factor is very close to −2, expected for a mean-field second-order ferroelectric transition⁴³, but strongly departs from −8 seen at first-order ferroelectric transitions^25,44. The lower inset b shows ε’ vs. T for varying frequencies as indicated in the figure. The small shift of the background dielectric constant ε’_b, visible for the data at highest frequency, indicates some contribution from extrinsic factors.