Determination of interfacial Dzyaloshinskii-Moriya exchange interaction from static domain size imaging

Dzyaloshinskii-Moriya interaction (DMI) has been identified [1-2] as a necessary ingredient for the formation of chiral spin structures such as skyrmions and N\'{e}el domain walls in perpendicularly magnetized thin films. Various simulation and experimental studies have tried to quantify DMI from domain wall [2] and skyrmion [3-4] motion with applied currents and magnetic fields. Here, a means to quantify DMI in multilayer films using only static magnetic characterizations is proposed. Static domain structure is observed using magnetic force microscopy (MFM) in multilayer stacks of [Pt(2.5-7.5nm)/CoFeB(0.8nm)/MgO(1.5nm)]$_{15}$ where the thickness $t_{pt}$ of the Pt layer is systematically varied from 2.5 nm to 7.5 nm. A variation of domain size from \textasciitilde 300 nm to \textasciitilde 70 nm is seen in the labyrinthine demagnetized state as $t_{pt}$ is decreased. It is shown that the domain size as a function of $t_{pt}$ can be well-fitted analytically by a model in which the domain wall energy is the sole free parameter. Additional measurements of magnetic anisotropy of the film reveal the significant contribution of interfacial DMI (\textasciitilde 1.4 mJ/m$^{2})$ to the domain wall energy. Ref: 1.Fert et al., \textit{Nat. Nanotech}., 8, 152-156 (2013); 2. S. Emori et al., \textit{Nature Materials} 12,611--616 (2013); 3. S. Woo et al., arXiv:1502.07376;~4.W. Jiang et al., arXiv:1502.08028v1