We perform a combined experimental and theoretical study of a magnetic-field $\left(B\right)$-induced evolution of magnetic and ferroelectric properties in an antiferromagnetic material $\mathrm{Pb}\left(\mathrm{TiO}\right){\mathrm{Cu}}_4{\left({\mathrm{PO}}_4\right)}_4$, whose structure is characterized by a staggered array of ${\mathrm{Cu}}_4{\mathrm{O}}_{12}$ 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 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 ${\mathrm{Cu}}_4{\mathrm{O}}_{12}$ 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.

• Received 26 July 2018

DOI:https://doi.org/10.1103/PhysRevMaterials.2.104415