  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.
