Hena Das, Aleksander L. Wysocki, Craig J. Fennie
The interplay of improper structural ferroelectricity (trimerization) and geometrically frustrated spins in the hexagonal RMnO$_3$ rare-earth manganites lead to a network of topologically protected defects that create strongly coupled structural and magnetic vortices. This unusual vortex structure is responsible for a significant domain wall magnetoelectric effect and magnetization, $M$, neither of which, however, occurs in the bulk. Here we demonstrate from a combination of first-principles calculations, group-theoretic techniques, and spin models that this structural trimerization not only exists in a family of hexagonal RFeO$_3$ ferrites, but also induces a bulk $M$, leading to a bulk coupling of ferroelectric and ferromagnetic domains such that if the polarization, $P$, reverses so does $M$. We show how this trimer distortion mediates an trilinear-coupling of $P$, $M$, and antiferromagnetic order, which is a universal feature of the hexagonal ferrites.
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http://arxiv.org/abs/1302.1099
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