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

TL;DR

This study reveals how the choice of $A$-cation in $A$(TiO)Cu$_4$(PO$_4$)$_4$ influences magnetic quadrupole order, with Pb inducing a ferroic state through altered magnetic interactions, unlike Ba and Sr.

Contribution

It demonstrates that $A$-cation selection controls magnetic quadrupole order, highlighting the role of $A$-O covalency in stabilizing ferroic states in this compound family.

Findings

Pb cation induces ferroic quadrupole order.

$A$-O covalency correlates with ferroic stability.

Contrast between Pb and Ba/Sr compounds.

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.