Antisymmetric exchange

The antisymmetric exchange is a contribution to the total magnetic exchange interaction between two neighboring magnetic spins, ${\displaystyle \mathbf {S} _{i}}$ and ${\displaystyle \mathbf {S} _{j}}$. It was first postulated by Igor Dzyaloshinskii on the grounds of phenomenological considerations based on Landau theory. Toru Moriya identified the spin-orbit coupling as the microscopic mechanism of the antisymmetric exchange interaction. It can be written as ${\displaystyle H_{DM}=\mathbf {D} _{ij}\cdot (\mathbf {S} _{i}\times \mathbf {S} _{j})}$. This term is also called the Dzyaloshinskii-Moriya interaction. In magnetically ordered systems, it favors a spin canting of otherwise (anti)parallel aligned magnetic moments and thus, e.g., is a source of weak ferromagnetic behavior in an antiferromagnet.

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