of the exchange interaction concept leads to a spin-spin interaction that is too strong, as the relevant energy scale is the atomic scale, or roughly $100,000\,{\text K}$. Many-body and band-structure effects renormalize this scale and bring it down to the observed ferromagnetic scale of rougly $1,000\,{\text{K}}$ or lower.[@Lonzarich_Taillefer_1985] This is still much larger than the dipole-dipole scale, and the latter is often neglected in the discussion of ferromagnets. When it is considered, e.g., for its influence on the critical behavior,[@Aharony_Fisher_1973; @Frey_Schwabl_1994; @Ma_1976] it is usually added phenomenologically to models that describe the exchange interaction. Another spin-spin interaction that has been of interest lately is the Dzyaloshinsky-Moriya (DM) interaction.[@Dzyaloshinsky_1958; @Moriya_1960] It results (in systems with suitable lattice structures) from the spin-orbit interaction, has been derived from microscopic models, and is believed to be responsible for the helical magnetic order observed in MnSi and FeGe.[@Bak_Jensen_1980] Rough estimates show that the DM interaction and the dipole-dipole interaction are of about the same strength, and should thus be considered together.[@Maleyev_2006] Furthermore, in weak ferromagnets, which order only at low temperatures, all three interactions can be comparable in strength, which can make the dipole-dipole and DM interactions crucial.

In this paper we provide a comprehensive 