We present a new member of the multiferroic oxides, Lu$_2$MnCoO$_6$, which we have investigated using X-ray diffraction, neutron diffraction, specific heat, magnetization, electric polarization, and dielectric constant measurements. This material pos
sesses an electric polarization strongly coupled to a net magnetization below 35 K, despite the antiferromagnetic ordering of the $S = 3/2$ Mn$^{4+}$ and Co$^{2+}$ spins in an $uparrow uparrow downarrow downarrow$ configuration along the c-direction. We discuss the magnetic order in terms of a condensation of domain boundaries between $uparrow uparrow$ and $downarrow downarrow$ ferromagnetic domains, with each domain boundary producing a net electric polarization due to spatial inversion symmetry breaking. In an applied magnetic field the domain boundaries slide, controlling the size of the net magnetization, electric polarization, and magnetoelectric coupling.
