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?

  • $\begingroup$ 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. $\endgroup$ – Sean E. Lake Mar 30 '17 at 5:19
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    $\begingroup$ 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. $\endgroup$ – Tess Mar 30 '17 at 7:18

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