Interaction of chiral domain walls with pinning disorder in thin ferromagnetic films

Abstract

Despite numerous recent studies focusing on the dynamics of pinned chiral magnetic textures [1-6], their interactions with weak pinning disorder is far from being understood. Basic issues such as the length-scale and the strength of interaction between domain walls (DWs) and defects in magnetic materials remain open. Our works [7] evidence a strong correlation between controlled variations of DW width and the characteristic length of pinning. The DW-disorder interaction strength is also shown to depend on DW energy and width. These findings should be also relevant for a wide variety of elastic interfaces moving in weak pinning disordered media.We explore the magnetic field-driven motion of domain walls with different chiralities in thin ferromagnetic films made of Pt/Co/Pt, Au/Co/Pt, and Pt/Co/Au. The displacement of DWs was observed by polar Kerr microscopy. An in-plane magnetic field Hx was used to control the magnetization direction in the DW, as well as its width. A pulse out-of-plane field H was used to move DW. The measured velocity corresponds to the ratio between the measured DW displacement and the pulse duration. The velocity curves obtained for Pt/Co/Au with different values of Hx are reported in Fig. 1. Their analysis with the self-consistent description of the universal creep and depinning regimes [8] was used to extract parameters (depinning field Hd and temperature Td) characterizing the interaction between domain wall and weak random pinning disorder of the films. Surprisingly, the values of Hd and Td vary (not-shown) with the in-plane magnetic field Hx, which strongly suggests that the pinning properties of DWs depend on their magnetic texture, in contrast to the usual assumption found in the literature [1-6].To predict accurately the variation of DW energy and structure with in-plane and DMI fields, we have calculated the orientation of the magnetization M (x) for a DW plane perpendicular to Hx, from numerical micromagnetic calculations (MuMax3), using the micromagnetic parameters of the three samples (not-shown). For the DW width, we both use the geometrical Hubert and dynamic Thiele definitions. Upon varying Hx away from the magnetic field H_DMI associated to the Dzyaloshinskii-Moriya interaction (DMI), the magnetization within the DW progressively switches from Bloch to Néel configuration, and the DW width increases due to the Zeeman contribution, as expected. The DW surface energy decreases as Hx departs fromH_DMI, in qualitative agreement with the predictions of simplified models [3-5].In order to discuss the DW pinning at microscopic scale as a function of in-plane field Hx, we use standard scaling arguments [8] based on the variation of the energy produced by the deformation of a DW. The DW energy is assumed to be controlled by the gain of Zeeman energy due to magnetization reversal, the elastic energy produced by the increase of DW length, and the pinning energy due to the fluctuations of DW energy produced by the weak disorder. From scaling arguments, we obtain the relations which link the characteristic range and force of the interaction between DW and pinning defects, to the measured depinning field Hd(Hx), temperature Td(Hx), and the predicted DW surface energy. For a comparison (see Fig. 2) with the predicted variations of the DW width, the values of the pinning range were rescaled with a constant factor, which is the only adjustable parameter. As it can be observed, there is a strong correlation between the variations of the pinning range and the DW width. This strong correlation suggests that the variations of domain wall structure, controlled by an in-plane field, modify the characteristic lengthscale of pinning, whatever the DW chirality and the interaction strength between domain wall and pinning defects. **