Magnetic Structural Unit with Convex Geometry: a Building Block Hosting an Exchange-striction-driven Magnetoelectric Coupling

We perform a combined experimental and theoretical study of a magnetic-field ($B$) induced evolution of magnetic and ferroelectric properties in an antiferromagnetic material Pb(TiO)Cu$_4$(PO$_4$)$_4$, whose structure is characterized by a staggered array of Cu$_4$O$_{12}$ magnetic units with convex geometry known as square cupola. Our experiments show a $B$-induced phase transition from a previously reported low-$B$ linear magnetoelectric phase to a new high-$B$ magnetoelectric phase, which accompanies a 90$^\circ$ flop of electric polarization and gigantic magnetodielectric effect. Moreover, we observe a $B$-induced sign reversal of ferroelectric polarization in the high-$B$ phase. Our model and first-principles calculations reveal that the observed complex magnetoelectric behavior is well explained in terms of a $B$-dependent electric polarization generated in each Cu$_4$O$_{12}$ unit by the so-called exchange striction mechanism. The present study demonstrates that the materials design based on the magnetic structural unit with convex geometry deserves to be explored for developing strong magnetoelectric couplings.