Magnetic charges and magnetoelectricity in hexagonal rare-earth manganites and ferrites

Magnetoelectric (ME) materials are of fundamental interest and show broad potential for technological applications. Commonly the dominant contribution to the ME response is the lattice-mediated one, which is proportional to both the Born electric charge $Z^{\rm e}$ and its analogue, the dynamical magnetic charge $Z^{\rm m}$. Our previous study has shown that exchange striction acting on noncollinear spins induces much larger magnetic charges than those that depend on spin-orbit coupling. The hexagonal manganites $R$MnO$_3$ and ferrites $R$FeO$_3$ ($R$ = Sc, Y, In, Ho-Lu) exhibit strong couplings between electric, magnetic and structural degrees of freedom, with the transition-metal ions in the basal plane antiferromagnetically coupled through super-exchange so as to form a 120$^\circ$ noncollinear spin arrangement. Here we present a theoretical study of the magnetic charges, and of the spin-lattice and spin-electronic ME constants, in these hexagonal manganites and ferrites, clarifying the conditions under which exchange striction leads to an enhanced $Z^{\rm m}$ values and anomalously large in-plane spin-lattice ME effects.