page_title: Antisymmetric exchange
section_title: Material examples
hierarchical_section_title: Antisymmetric exchange / Material examples
caption_attribution_description: Corundum crystal structure named after the crystalline form of aluminum oxide (Metal ions in red, oxygen ions in blue). Displays R3c space group symmetry, and also displays the crystal forms of α-Fe2O3 and α-Cr2O3
context_page_description: Antisymmetric exchange, also known as the Dzyaloshinskii–Moriya interaction, is a contribution to the total magnetic exchange interaction between two neighboring magnetic spins, and. Quantitatively, it is a term in the Hamiltonian which can be written as. In magnetically ordered systems, it favors a spin canting of otherwise parallel aligned magnetic moments and thus, is a source of weak ferromagnetic behavior in an antiferromagnet. The interaction is fundamental to the production of magnetic skyrmions and explains the magnetoelectric effects in a class of materials termed multiferroics.
context_section_description: The image at right displays a coordinated heavy metal-oxide complex that can display ferromagnetic or antiferromagnetic behavior depending on the metal ion. The structure shown is referred to as the corundum crystal structure, named after the primary form of Aluminum oxide (Al
  ₂O
  ₃), which displays the R3c trigonal space group. The structure also contains the same unit cell as α-Fe₂O₃ and α-Cr₂O₃ which possess D⁶3d space group symmetry. The upper half unit cell displayed shows four M³⁺ ions along the space diagonal of the rhombohedron. In the Fe₂O₃ structure, the spins of the first and last metal ion are positive while the center two are negative. In the α-Cr₂O₃ structure, the spins of the first and third metal ion are positive while the second and fourth are negative. Both compounds are antiferromagnetic at cold temperatures (<250K), however α-Fe₂O₃ above this temperature undergoes a structural change where its total spin vector no longer points along the crystal axis but at a slight angle along the basal (111) plane. This is what causes the iron-containing compound to display an instantaneous ferromagnetic moment above 250K, while the chromium-containing compound shows no change. It is thus the combination of the distribution of ion spins, the misalignment of the total spin vector, and the resulting antisymmetry of the unit cell that gives rise to the antisymmetric exchange phenomenon seen in these crystal structures.
caption: Corundum crystal structure displaying the crystal forms of α-Fe2O3 and α-Cr2O3 (Metal ions in red, oxygen ions in blue)
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