$A$-cation control of magnetoelectric quadrupole order in $A$(TiO)Cu${}_4$(PO${}_4$)${}_4$ ($A$ = Ba, Sr, and Pb)

Abstract

Ferroic magnetic quadrupole order exhibiting macroscopic magnetoelectric activity is discovered in the novel compound $A$(TiO)Cu${}_4$(PO${}_4$)${}_4$ with $A$ = Pb, which is in contrast with antiferroic quadrupole order observed in the isostructural compounds with $A$ = Ba and Sr. Unlike the famous lone-pair stereochemical activity which often triggers ferroelectricity as in PbTiO${}_3$, the Pb${}^{2+}$ cation in Pb(TiO)Cu${}_4$(PO${}_4$)${}_4$ is stereochemically inactive but dramatically alters specific magnetic interactions and consequently switches the quadrupole order from antiferroic to ferroic. Our first-principles calculations uncover a positive correlation between the degree of $A$-O bond covalency and a stability of the ferroic quadrupole order.

7 pages, 4 figures