  Magnetoelectric (ME) materials are of fundamental interest and have been
investigated for their broad potential for technological applications. The
search for, and eventually the theoretical design of, materials with large ME
couplings present challenging issues. First-principles methods have only
recently been developed to calculate the full ME response tensor $\alpha$
including both electronic and ionic (i.e., lattice-mediated) contributions. The
latter is proportional to both the Born dynamical electric charge $Z^{\rm e}$
and its analogue, the dynamical magnetic charge $Z^{\rm m}$. Here we present a
theoretical study of the magnetic charge $Z^{\rm m}$ and the mechanisms that
could enhance it. Using first-principles density-functional methods, we
calculate the atomic $Z^{\rm m}$ tensors in $\rm{Cr_2O_3}$, a prototypical
magnetoelectric, and in KITPite, a fictitious material that has previously been
reported to show a strong ME response arising from exchange striction effects.
Our results confirm that in $\rm{Cr_2O_3}$, the $Z^{\rm m}$ values and
resulting ME responses arise only from spin-orbit coupling (SOC) and are
therefore rather weak. In KITPite, by contrast, the exchange striction acting
on the non-collinear spin structure induces much $Z^{\rm m}$ values that
persist even when SOC is completely absent.
