Magnetoelectric domain engineering from micrometer to Ångstrøm scales
The functionality of magnetoelectric multiferroics depends on the formation, size, and coupling of their magnetic and electric domains. Knowing the parameters guiding these criteria is a key effort in the emerging field of magnetoelectric domain engineering. Here we show, using a combination of piezoresponse-force microscopy, non-linear optics, and x-ray scattering, that the correlation length setting the size of the ferroelectric domains in the multiferroic hexagonal manganites can be engineered from the micron range down to a few unit cells under the substitution of Mn$^{3+}$ ions with Al$^{3+}$ ions. The magnetoelectric coupling mechanism between the antiferromagnetic Mn$^{3+}$ order and the distortive-ferroelectric order remains intact even at substantial replacement of Mn$^{3+}$ by Al$^{3+}$. Hence, chemical substitution proves to be an effective tool for domain-size engineering in one of the most studied classes of multiferroics.