Abstract
We introduce a mechanism in which coupling between fluctuating spin magnetic dipole moments and polar optical phonons leads to a non-zero ferroic ordering of quasi-static magnetoelectric multipoles. Using first-principles calculations within the LSDA$+U$ method of density functional theory, we calculate the magnitude of the effect for the prototypical cuprate superconductor, HgBa$_2$CuO$_4$. We show that our proposed mechanism is consistent, to our knowledge, with all experimental data for the onset of the pseudo-gap phase and therefore propose the quasi-static magnetoelectric multipole as a possible pseudo-gap order parameter. Finally, we show that our mechanism embraces some key aspects of previous theoretical models, in particular the description of the pseudo-gap phase in terms of orbital currents.
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