The interfacial Dzyaloshinskii-Moriya Interaction is a critical property of magnetic thin films for the stabilization of chiral magnetic objects, including skyrmions, for use in future spintronic applications.[1] However, direct measurement of the strength of this interaction remains an experimental challenge.[2] Here, we present a technique for direct extraction of the interfacial Dzyaloshinskii-Moriya Interaction using a tapered c-shape (herein referred to as a nanohorn). A schematic of this idea is shown in figure 1. The nanohorn is designed to provide a driving force for the DW to propagate in the counter-clockwise direction driven by a reduction in the overall length of the DW itself. An in-plane magnetic field coupled with the interfacial DMI provides a driving force for propagation in the clockwise direction. This is due to the Zeeman energy associated with the DW’s internal magnetization and the magnetic field. The balance of these forces results in an energy minimum in wall position that depends directly on the strength of iDMI. In short, the rest position of the DW can be read like the needle of an analog meter to determine the strength of DMI. A series of micromagnetic calculations using Mumax3 were performed using the gradient descent approach to determine the energy of the DW as a function of its position along the nanohorn radius. Here, we use material parameters A = 15pJ/m, Keff = 598 kJ/m3, Ms = 800 kA/m for a film thickness of 2nm. The width of the magnetic nanohorn ranges from ~100-200nm although larger dimensions are not expected to significantly impact the results. The sides of this horn follow the two polar equations r = a+b-cθ, r = a-b+cθ. This produces a shape with a circular arc of radius a along its center and radial width increasing symmetrically from this arc in a linear rate 2c. We note that there are a range of parameters where there is no energy minima, which is not useful experimentally. However, the degree of horn tapering can be designed to work for material systems with different strengths of DMI. In the presentation, comparison with semi-analytical calculations will be presented, which show minimal differences in the equilibrium wall position likely due to dipolar interactions and slight tilting of the DW. Challenges associated with experimental realization of this technique will be discussed along with ways to mitigate them as evidenced by additional micromagnetic modeling. Most notably, there are dynamic limitations with driving the wall to its equilibrium, which can be addressed through increased statistics (simultaneously examining many nanohorns of different dimensions) and exciting the DW with AC magnetic fields to overcome edge pinning. Prospects for the experimental use of this technique for different materials systems will be discussed.

**References:**

[1] Thiaville, A., Rohart, S., Jué, É., Cros, V. and Fert, A., 2012. Dynamics of Dzyaloshinskii domain walls in ultrathin magnetic films. EPL (Europhysics Letters), 100(5), p.57002. [2] Lau, D., Pellegren, J.P., Nembach, H.T., Shaw, J.M. and Sokalski, V., 2018. Disentangling factors governing Dzyaloshinskii domain-wall creep in Co/Ni thin films using Pt x Ir 1− x seed layers. Physical Review B, 98(18), p.184410.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/fb0a86c9ee7547974d3ed351125b5c6f.jpg)
Figure 1: Schematic of the coordinate system and example micromagnetic output for a nanohorn with D = 1.6 mJ/m2 and μ0Hx = 150mT. Orange arrows show the DW internal magnetization direction. Tick marks along the circumference indicate the equilibrium position (θMIN) of the domain wall for a range of other DMI strengths.

![](https://assets.underline.io/uploads/markdown_image/1/image/ac305d09aeeebe7e5935ed137942f415.jpg)
Figure 2: Domain wall energy vs wall position (θ) normalized to the energy minima for varying DMI strengths. The lines shown are empirical fits to the micromagnetic energy output. Inset: Equilibrium wall position (θMIN) vs DMI strength.

 Magnetic Nano-horns for measurement of the interfacial Dzyaloshinskii-Moriya Interaction

*Session Chair: See-Hun Yang, International Business Machines Corp*

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Magnetic Nano-horns for measurement of the interfacial Dzyaloshinskii-Moriya Interaction

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