# Can a bulk crystal have a spontaneous quadrupole moment?

Crystals of polar space groups e.g. ferroelectrics can have a spontaneous electric dipole moment. Is it possible for a crystal to have a spontaneous electric quadrupole moment (and higher order terms of the multipole expansion)? If so, what are the symmetry requirements for such moments to arise?

• For example: the unit cell of $\mathrm{Na}\,\mathrm{Cl}$ should have an uncompensated octupole moment, so a defectless table salt cube should have a fairly substantial electric octupole moment. – Sean E. Lake Mar 30 '17 at 5:19
• A friend found this paper on arXiv: arxiv.org/pdf/1611.07987.pdf . I'll look more into it tomorrow, but it seems like it has what I'm looking for. – Tess Mar 30 '17 at 7:18