Experimental correlation of Interfacial Dzyaloshinskii-Moriya interaction amplitude and Work Function in magnetic multilayers and its relation with Rashba effect at metallic interfaces.

Abstract

Magnetic multilayers (MML) with large perpendicular magnetic anisotropy (PMA) and Dzyaloshinskii-Moriya interaction (DMI) have attracted great attention in recent years owing to the possibility of stabilizing non-collinear magnetic textures such as chiral domain walls (DW) [1], spin spirals [2] or skyrmions [3-4] with chiral Neel magnetization rotation. The latter are promising candidates as carriers of information for next-generation race-track magnetic memories or logic devices. The accurate experimental determination of the DMI is an important challenge as it is necessary to tailor the properties of future devices. The determination of the effective DMI amplitude D is still a current subject of active research since the origin of the DMI is not well known. Beyond the three-sites Fert-Levy model [5], first principle calculations for the common Pt|Co|M systems were carried out [6], aiming at finding a simple relation between the DMI and the intrinsic properties of the metallic element that would be easily accessible to the experimentalist, providing guidance to design systems with a required D value.In this study, we perform thorough measurements to determine DMI strength by asymmetric expansion of domains in the presence of an in-plane magnetic field, using Kerr microscopy [7-8]. Results are shown in Figure 1 for all the different materials selected to build asymmetric trilayers with the general structure is Pt|Co|M, with M = Ni, Pd, Ru, Al, Al|Ta and MoSi. The symmetric (asymmetric) expansion of Néel-type bubble without (under the presence of) an external in-plane magnetic field of Pt|Co|Al trilayer is displayed in panel (a). In panels b-g are plotted the expansion velocities of the up and down domain branches as function of the in-plane field for all the studied systems. The minima of the plotted curves correspond to the field which compensates HDMI, which is related to D by , is the DW parameter.From the D, we estimate the effective interfacial DMI (summing Pt and M contributions), Ds = D*t, with t the Co thickness. We look for correlation between Ds and three material properties in Fig. 2. In Fig. 2a is presented in log-log scale the absolute value of Ds as function of atomic number (Z). As DMI is proportional to spin-orbit coupling, Z scales with different power laws e.g. Z2 and Z4 for 3d and 4d elements, becoming more complex for the heaviest elements. Fig. 2b shows Ds as function of Pauling electronegativity (χ) [6]. Here we found a linear correlation in good agreement with theoretical calculations (Pearson-r dispersion index of 0.74). Finally, in panel c is presented Ds as a function of the work function difference (ΔΦ) [9] at the Co|M interfaces. We find a striking linear relationship between Ds and ΔΦ (Pearson-r dispersion index of 0.93). This strong correlation points to Rashba-like interfacial fields, leading to the modulation of the effective interfacial DMI. **