Scaling of Dzyaloshinskii-Moriya interaction with magnetization in Pt/Co(Fe)B/Ir multilayers

Magnetic multilayers with perpendicular anisotropy and an interfacial Dzyaloshinskii-Moriya interaction (DMI) contain chiral domain walls and skyrmions that are promising for applications. Here, we measure the temperature dependence of the DMI in Pt/CoFeB/Ir and Pt/CoB/Ir multilayers by means of static domain imaging. First, the temperature dependences of saturation magnetization $({M}_{\mathrm{S}})$, exchange stiffness $(A)$, and intrinsic perpendicular anisotropy $({K}_{\mathrm{u}})$ are determined. Then the demagnetized domain pattern in each multilayer is imaged by wide-field Kerr microscopy in the temperature range 9--290 K, and the characteristic domain period at each temperature is determined. We calculate the DMI constant $D$ from an analytical expression for the domain wall energy density that treats the multilayer as a uniform medium. Scaling laws for ${K}_{\mathrm{u}}$ and $D$ with the magnetization are established from the experiments. While the scaling of ${K}_{\mathrm{u}}$ is consistent with Callen-Callen theory, we find that the scaling of $D$ is like that of $A$ predicted theoretically $(\ensuremath{\sim}1.8)$.