Theory of electric, magnetic, and toroidal polarizations in crystalline solids with applications to hexagonal lonsdaleite and cubic diamond

The spontaneous electric polarization in bulk crystals like wurtzite defies a naive definition using classical electromagnetism, and its measurable signatures have remained unclear. It was also bulk wurtzite for which Emmanuel Rashba discovered in 1959 what is called today the Rashba effect. The authors argue that the Rashba effect is the long-sought hallmark of a spontaneous electric polarization in polar crystals like wurtzite. Beyond that, they develop a comprehensive theory of multipolar order in crystals. Treating electric and magnetic order on equal footing, they identify five categories of polarized matter that are characterized by distinct observable signatures.