Measurement of interfacial Dzyaloshinskii-Moriya interaction from static domain imaging

Abstract

Perpendicularly magnetized thin films with a strong Dzyaloshinskii-Moriya interaction (DMI) exhibit chiral spin structures such as N\'eel domain walls and skyrmions. These structures are promising candidates for next-generation magnetic memory devices. Determining the magnitude of the DMI accurately is key to engineering materials for such applications. Existing approaches are based on quantities extracted either from magnetization dynamics, which present experimental and theoretical challenges, or from measurements of quasistatic domain spacing, which so far have been analyzed using incomplete models or prohibitively slow micromagnetic simulations. Here, we use a recently developed analytical model of stripe domain widths in perpendicularly magnetized multilayers to extract the DMI from domain images combined with magnetometry data. Our approach is tested on micromagnetically simulated domain patterns, where we achieve a 1% agreement of the extracted DMI with the DMI used to run the simulation. We then apply our method to determine the thickness-dependent DMI in two experimental materials, one with (${[\mathrm{Pt}(2.5--7.5\phantom{\rule{0.28em}{0ex}}\mathrm{nm})/{\mathrm{Co}}_{60}{\mathrm{Fe}}_{20}{\mathrm{B}}_{20}(0.8\phantom{\rule{0.28em}{0ex}}\mathrm{nm})/\mathrm{MgO}(1.5\phantom{\rule{0.28em}{0ex}}\mathrm{nm})]}_{13}$) and one without (${[\mathrm{Pt}(2.5--7.5\phantom{\rule{0.28em}{0ex}}\mathrm{nm})/\mathrm{Co}(0.8\phantom{\rule{0.28em}{0ex}}\mathrm{nm})/\mathrm{Pt}(1.5\phantom{\rule{0.28em}{0ex}}\mathrm{nm})]}_{13}$) inversion symmetry breaking. We discuss the means to obtain realistic error bars with our method. Our results demonstrate that analytical domain spacing analysis is a powerful tool to extract the DMI from technologically relevant multilayer materials.