Domain-period method for determination of the energy of the Dzyaloshinskii-Moriya interaction in [Co/Pd(111)]5 superlattices

Determination of the energy of the interface Dzyaloshinskii-Moriya interaction (DMI) along with a definition of the basic magnetic characteristics in ferromagnetic/nonmagnetic multilayered systems are both required for the construction of a magnetic skyrmion recording medium. A method for estimating the energy of the effective DMI, which compares the periods of micromagnetically simulated and experimentally measured demagnetized domain structures, is widely used for investigations of heavy metal/ferromagnetic superlattices. In the present paper, the applicability of this method was tested on a series of symmetric epitaxial ${[\mathrm{Co}\text{/}\mathrm{Pd}(111)]}_{5}$ superlattices with Co layers of varying thickness. We examined the problem of ambiguous determination of the DMI energy, which is related to the dependence of the periodicity of the domain structure, experimentally measured in a sample on the direction of a demagnetizing field. The Co thickness dependencies of the effective and surface DMI constants, obtained using in-plane and out-of-plane demagnetized structures and fixed micromagnetic parameters, were qualitatively and quantitatively different. Having analyzed the Co thickness dependencies of the DMI energies in the entire series of samples, we found that the DMI energies obtained using in-plane rather than out-of-plane demagnetized domain structures are more acceptable. Of greatest importance for the accurate determination of the DMI energy in an investigated system is the knowledge of the exchange interaction constant. The applicability of the method in the case of variable micromagnetic parameters and the reliability of the results obtained from the samples with different magnetic parameters are discussed.