| الملخص: | 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, nonlinear 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.
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