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Domain Walls in Antiferromagnetic Samples With non-Trivial Surface Topography
Antiferromagnets (AFMs) have regained strong attention from the magnetism community especially with the advent of antiferromagnetic spintronics . The key operational element of spintronic devices is represented by information carriers, such as domain walls (DWs) and skyrmions. The simplest AFM DW separates two regions with the opposite orientation of the Neel order parameter. Although highly relevant, the experimental studies of AFM DWs (visualization, dynamics, mechanics) are challenging because of strict requirements on measurement techniques to access their properties. Here, we overcome these limitations and conduct detailed, quantitative studies of the mechanics and the nanoscale properties of individual, antiferromagnetic DWs in a single crystal Cr2O3 – a room-temperature, magnetoelectric, insulating AFM . Our results reveal a remarkably pristine DW behaviour, which is governed by DW energy minimization and boundary conditions, but largely unaffected by pinning or disorder – a “textbook example” of antiferromagnetic DW physics. In our experiment, the crystal’s (0001) surface is patterned by a grid of mesas with mean thickness and width t=166 nm and w=2400 nm, respectively. The DW is nucleated by means of magnetoelectric field cooling by inverting the electric bias field over opposite halves of the sample. The DW may also be dragged through the mesa pattern by a focused laser spot. The magnetic texture is imaged using Nitrogen Vacancy (NV) magnetometry . We find that the DW mimics an elastic surface with specific mechanical properties, determined by the interaction with the topographic features of the sample where the DW is (i) deflected from the straight plane crossing the mesa; (ii) bent around mesa corners. To address the DW behaviour theoretically, we perform large-scale spin-lattice simulations with GPU speed-up . The analytical Ansatz is developed based on the numerically-obtained, three-dimensional DW profile. All main features of the DW behaviour can be determined taking into account the nearest-neighbour exchange and uniaxial anisotropy for a general model of a bipartite AFM. Crossing the mesa, the DW experiences an S-shaped distortion observed at the mesa surface, which is the result of exchange-driven boundary conditions at the side faces of the mesa, see Fig. 1. Below the top surface, the DW possesses a twist to match this distortion with the straight plane far below the sample’s surface. We find that the DW surface is deflected from the plane over a characteristic depth of 0.34w. Comparison of the equilibrium DW direction in bulk and at the mesa’s top surface allows us to derive an effective Snell’s law for the DW behaviour at the sample’s surface with the given incidence and refraction angles θ1 and θ2. The effective refraction coefficient is determined by the analytical energy minimization and reads neff = 1 + 3.1t/w + O(θ1). Controlled manipulation via laser not only enables DW dragging through the mesa, but also pinning at mesa corners. The shape of the DW surface is governed by its intrinsic elasticity. In terms of mechanics of an elastic ribbon, the corresponding tension coefficient is determined by the temperature-dependent exchange stiffness and anisotropy coefficient. This allows for curved DW states in which it is pinned at the opposite mesa sides. Using mesas as bistable pinning sites, we propose a potential DW-based AFM memory concept. Here, the memory state “0” or “1” is associated with the direction of the Neel order parameter at the mesa surface. We have realized such pinning sites experimentally and have shown manipulation of the state via laser dragging. In summary, we realize engineered DW potentials and control over DW trajectories by topographic structuring and manipulation of the DW position by means. The physics of AFM DWs in a single crystal with non-trivial surface topography is described theoretically by means of spin-lattice simulations and analytical model. A novel nanoscale AFM memory architecture is suggested.
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Keywords: Cr2O3; NV magnetometry; topography; surface; domain wall
IEEE International Magnetic Virtual Conference INTERMAG21, 26.-30.04.2021, Online, Online