helimagnetism

Helimagnetism is a magnetic order in which the direction of the magnetization rotates as one moves through a crystal, forming a helical structure along a propagation direction. This type of order commonly arises in materials with broken inversion symmetry, where the antisymmetric Dzyaloshinskii–Moriya (DM) interaction competes with the symmetric Heisenberg exchange. In a simple description the magnetization can be written as a spiral with a fixed pitch: M(r) = M0 [cos(Q·r) e1 + sin(Q·r) e2], yielding a helix with period λ = 2π/|Q|.

The helix results from the competition between exchange, which favors alignment, and the DM interaction, which favors canting of neighboring spins. The balance fixes the helix wavevector Q, with |Q| proportional to the DM strength D relative to the exchange J. In bulk crystals lacking inversion symmetry, such as MnSi, FeGe, and Fe1−xCoxSi (B20-type compounds), helimagnetism occurs below a magnetic transition temperature Tc. Similar helicoidal order can arise in thin films and at interfaces where interfacial DM interactions are present. The helix can be suppressed by temperature and external magnetic fields, giving way to a conical ferromagnetic state or, at high enough fields, to a fully polarized paramagnetic state.

Experimental signatures include neutron scattering, which reveals Bragg peaks at ±Q, and real-space imaging methods such as Lorentz transmission electron microscopy. Magnetic phase diagrams typically show helimagnetic, conical, and paramagnetic regions, and, in many materials near Tc, the same DM interaction stabilizes skyrmion lattices in a narrow field–temperature window.

Significance lies in the study of chiral magnetism and topological spin textures, with potential applications in spintronics and magnonics.