Fig. 2: Spontaneous and antiparallel polarization in α-Ag₂Se.

a In the Se-Ag tetrahedron, the basic structural unit of α-Ag₂Se, the center of Ag⁺-cations deviates from the Se²⁻ anion position, inducing a localized polarization. b Projection of α-Ag₂Se along the [100] zone axis showing the arrangement of the polarizations in a unit cell. c Pairs of oppositely oriented polarizations with vectors of [\(01\bar{4}\)]/[0\(\bar{1}\)4] and [014]/ [\(0\bar{1}\bar{4}\)] are formed, like a regular arrangement of antiparallel dipoles. d HAADF STEM image of the [100] oriented α-Ag₂Se, in which the Ag⁺-tetrahedra are outlined and the localized and antiparallel dipoles can be experimentally measured, as indicated by the arrowheads. e Analysis of the map of polarizations shows that the displacement vectors pointing upward (close to the [001] direction) have an average length of ~54 pm, which is shorter than those pointing downward (close to the [00-1] direction) with an average length of ~68 pm. Also the alternatively clockwise and anticlockwise vortexes formed by the dipoles can be seen. The scale bar is 1 nm.