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Magnetic ordering in the crystal lattice arises from exchange interactions between partially filled d or f shells of transition metal or rare-earth ions. For a collinear spin alignment, the Heisenberg exchange interaction is of main importance, whereas in spiral spin order, the magnetic frustration related to spin-orbit coupling accounts for these fascinating spin formations.1,2,3 A few basic magnetic structures are: ferromagnetic (FM), antiferromagnetic (AFM), ferrimagnetic (FiM) and helical (Figure on the left).
The understanding of the underlying microscopic mechanisms that lead to magnetoelectric coupling is essential for the engineering of novel single-phase magnetoelectric multiferroics, since the ones already existing in nature are very limited. Complex interactions related to magnetic, ionic and electronic contributions may occur in the majority of the multiferroic materials, however one can distinguish two main types of coupling mechanisms: spin-orbit and spin-lattice.
The main difference between the two mechanisms is that in the former, the magnetically-induced polarization is related to the direction of the magnetic moments, thus the magnetic easy axis or plane, whereas in the latter, the polarization emerges as a result of the crystal symmetry. In addition, usually spiral magnetic order corresponds to spin-orbital coupling, whereas collinear magnetic order to spin-lattice coupling. Naturally, combination of the two operations may occur, which might hinder the efforts of clear understanding of the origin of magnetoelectric coupling in particular materials.
1. K.F. Wang, J.-M. Liu, and Z.F. Ren, Adv. Phys. 58, 321 (2009).2. S. Dong, J.-M. Liu, S.-W. Cheong, and Z. Ren, Adv. Phys. 64, 519 (2015).3. D. Khomskii, Physics (College. Park. Md). 2, 20 (2009).
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