DzyaloshinskiiMoriya

The Dzyaloshinskii–Moriya interaction (DMI) is an antisymmetric exchange interaction between neighboring spins that arises in magnetic systems with strong spin–orbit coupling and broken inversion symmetry. It favors canting of adjacent spins and stabilizes chiral, noncollinear spin textures, contrasting with the symmetric Heisenberg exchange that tends to align spins parallel or antiparallel.

Mathematically, the interaction is written as H_DM = sum over neighboring pairs D_ij · (S_i × S_j), where D_ij is a vector fixed by the local crystal or interface symmetry. Moriya’s rules determine the direction and magnitude of D_ij based on the bonding geometry and symmetry operations. In bulk non-centrosymmetric crystals, DMI can produce helical spin order or weak ferromagnetism; in centrosymmetric magnets, it can still appear at surfaces or interfaces where inversion symmetry is broken, often driven by heavy elements with strong spin–orbit coupling.

Materials and textures governed by DMI include bulk chiral magnets such as MnSi, FeGe, and Cu2OSeO3, which host helical or conical spin states and, under magnetic fields, skyrmion lattices. At thin-film interfaces, interfacial DMI arises in structures like Pt/Co, Ta/CoFeB, or W/CoFeB, enabling chiral domain walls and nanoscale skyrmions in ultrathin layers.

Experimentally, DMI is probed by neutron scattering, Lorentz transmission electron microscopy, spin-polarized scanning tunneling microscopy, and Brillouin light scattering. Its presence is central to spintronics concepts such as chiral domain walls, skyrmion-based racetrack devices, and low-power magnetic logic, by enabling controlled, stable chiral spin textures. The interaction is named for Igor Dzyaloshinskii and Toru Moriya, who described it in the late 1950s and early 1960s.