Estimation of Dzyaloshinskii-Moriya interaction and domain wall damping in ultrathin nanostripes

Asymmetric ultrathin magnetic thin films represent intriguing materil platforms, which support emerging fundamentals effects, such as skyrmion and topological [1] Hall effects and fast motion of chiral magnetic non-collinear textures [2], that underlie prospective memory and logic devices based on spin-orbit torques. Such asymmetric stacks can provide strong perpendicular magnetic anisotropy and Dzyaloshinskii-Moriya interactions (DMI), which is necessary for the sabilization of chiral non-collinear magnetic textures. As the performance of spin-orbitronic devices is determined by the static and dynamic micromagnetic parameters [3], it is crucial to determine all internal micromagnetic parameters for the particular layer combination and sample geometry. In particular, the speed of a domain wall (DW) based racetrack is determined by the DMI constant, $D$, and the DW damping parameter, $\alpha$. The necessity of having strong DMI requires the utilization of ultrathin magnetic (~1 nm) layers, which implies polycrystalinity and compromized structural quality, that substantially enhances the magnetic damping compared to bulk. Accessing this parameters typically requires dynamic experiments, whose interpretations are cumbersome due to the creep regime.
Here, we present the experimental and theoretical investigation of tilted DWs in perpendicularly magnetized asymmetric //CrOx/Co/Pt layer stacks with the surface-induced DMI. We will discuss two possible theoretical mechanism for the appearance of titled DWs: (I) A unidirectional tilt could appear in equilibrium as a result of the competition between the DMI and additional in-plane easy-axis anisotropy, which breaks the symmetry of the magnetic texture and introduce tilts [4]. (II) A static DW tilt could appear due to the spatial variation of magnetic parameters, which introduce pinning centers for DWs [5]. A moving DW can be trapped in a tilted state after the external driving field is off. Based on these theoretical approaches, we perform a statistical analysis of the DW tilt angles obtained in staticts after the external magnetic field used for the sample demagnetization was off. We found that the second approach confirms the experimental observations and allows to determine self-consistently the range of DW damping parameters and DMI constants for the particular layer stack. Using two reference fields, which provide two characteristic tilt angles, allow us to retrieve the range of DMI strength $D \geq 0.8$ mJ/m2 and DW damping parameters $\alpha \geq 0.1$. The upper limit for the DMI constant agrees with an independent transport-based measurement giving $D=0.90 \pm 0.13$ mJ/m2, which further refines our estimate of the damping parameter $\alpha=0.13 \pm 0.02$. Thus, the combination of the proposed method with standard metrological techniques opens up opportunities for the quantification of both static and dynamic micromagnetic parameters based on static measurements of the DW morphology.
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[4] O. V. Pylypovskyi, V. P. Kravchuk, O. M. Volkov, J. Fassbender, D. D. Sheka and D. Makarov, “Unidirectional tilt of domain walls in equilibrium in biaxial stripes with Dzyaloshinskii–Moriya interaction”, J. Phys. D: Appl. Phys. 53, 395003 (2020).
[5] O. M. Volkov, F. Kronast, C. Abert, E. Se. Oliveros Mata, T. Kosub, P. Makushko, D. Erb, O. V. Pylypovskyi, M.-A. Mawass, D. Sheka, S. Zhou, J. Fassbender and D. Makarov, “Domain-Wall Damping in Ultrathin Nanostripes with Dzyaloshinskii-Moriya Interaction”, Phys. Rev. Appl. 15, 034038 (2021).