Antisymmetric exchange

In Physics, antisymmetric exchange, also known as the Dzyaloshinskii–Moriya interaction (DMI), is a contribution to the total magnetic exchange interaction between two neighboring magnetic spins, ${\displaystyle \mathbf {S} _{i}}$ and ${\displaystyle \mathbf {S} _{j}}$. Quantitatively, it is a term in the Hamiltonian which can be written as

${\displaystyle H_{i,j}^{\rm {(DM)}}=\mathbf {D} _{ij}\cdot (\mathbf {S} _{i}\times \mathbf {S} _{j})}$.

In magnetically ordered systems, it favors a spin canting of otherwise parallel or antiparallel 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.