Dzyaloshinsky-Moriya interactions

Microscopically, this type of anisotropy in metallic spin glasses is linked to the existence of Dzyaloshinsky-Moriya interactions (see sec. 3.2). This interpretation has been stimulated by hysteresis studies of ternary CuMn spin glasses by Prejean et al. (1980) where the third component is a nonmagnetic impurity of concentration X, Whereas and are found to be independent on x, the width of the hysteresis and hence the anisotropy constant K increases linearly with x (fig. 36). By taking different impurities the authors demonstrate that the spin-orbit interaction is responsible for the anisotropy. 

The pure RKKY interaction is isotropic, and the canonical spin glass systems are therefore often referred to as Heisenberg spin glasses. However, some anisotropy is also present in those systems originating from dipolar interaction and interaction of the Dzyaloshinsky-Moriya (DM) type [73]. The latter is due to spin-orbit scattering of the conduction electrons by non-magnetic impurities and reads... 

Kagome lattice leads to Dzyaloshinsky-Moriya (DM) interactions, the in-plane components of which can give rise to magnetic polarizations in the out-of-plane directions with canted vectors of magnetic moments.16 It is interesting to... 

Departures from Equation (15) observed on single-crystal samples of Cdi Mn Se have been ascribed to Dzyaloshinski-Moriya (DM) interactions within noncentrosymmetric couples of manganese(II) ions. The DM interactions (Equation (16)) are indeed able to mix the spin wave functions near thus leading to a rounding of the steps. 

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