  Control of magnetization and electric polarization is attractive in relation
to tailoring materials for data storage and devices such as sensors or
antennae. In magnetoelectric materials, these degrees of freedom are closely
coupled, allowing polarization to be controlled by a magnetic field, and
magnetization by an electric field, but the magnitude of the effect remains a
challenge in the case of single-phase magnetoelectrics for application. We
demonstrate that the magnetoelectric properties of the mixed-anisotropy
antiferromagnet LiNi$_{1-x}$Fe$_x$PO$_4$ are profoundly affected by replacing a
fraction of the Ni$^{2+}$ ions with Fe$^{2+}$ on the transition metal site.
This introduces random site-dependent single-ion anisotropy energies and causes
a lowering of the magnetic symmetry of the system. In turn, magnetoelectric
couplings that are symmetry-forbidden in the parent compounds, LiNiPO$_4$ and
LiFePO$_4$, are unlocked and the dominant coupling is enhanced by two orders of
magnitude. Our results demonstrate the potential of mixed-anisotropy magnets
for tuning magnetoelectric properties.
