Phenomenology of chiral Dzyaloshinskii-Moriya interactions in strained materials

We use phenomenological symmetry arguments to demonstrate that while chiral magnetic (Dzyaloshinskii-Moriya) interactions are conventionally restricted by symmetry to appear in a limited set of noncentrosymmetric materials, they may arise in a material with any symmetry when coupled to a strain field. We derive point-group specific free-energy functionals that capture the relationship between an applied strain field and chiral magnetic couplings, demonstrating how strain may offer highly selective control over magnetic textures. Finally, we discuss several examples of common strain configurations that may lead to out-of-plane modulation in the magnetic moment of a quasi-two-dimensional film as required for applications in magnetic devices.

Figure 1

(a) Helicoid and cycloid spin textures comprising the two variants of cDM interactions in total magnetization $m$. (b) A map of cDM interactions in materials across all 32 point groups. Point groups where cDM interactions are intrinsically allowed are denoted by ovals and color-coded by whether symmetry allows for helicoidal (green) or cycloidal (brown) cDM terms in the free energy, or both (black). Point groups where cDM interactions are enabled by a strain field are denoted by rectangles and color-coded by whether cDM interactions couple to homogeneous strain (blue) or only strain gradients (red). The connections between point groups indicate group-subgroup relationships and illustrate which point groups can be reached by symmetry-breaking operations. (c,d) The couplings between elastic strains and strain gradients and cDM interactions which yield a modulation in $m_z$ (the out-of-plane component of total magnetization) of a $m\overline{3}m$ or $6/mmm$ material, for out-of-plane and in-plane gradients in strain respectively. (e) Couplings between homogeneous strain and cDM interactions yielding a modulation in $m_z$ for a $\overline{4}3m$ material.