Exercise - Domain wall pair conversion

We want to simulate a domain wall conversion in a two-dimensional thin film sample with:

• exchange energy constant $A = 15 \,\text{pJ}\,\text{m}^{-1}$,
• Dzyaloshinskii-Moriya energy constant $D = 3 \,\text{mJ}\,\text{m}^{-2}$,
• uniaxial anisotropy constant $K = 0.5 \,\text{MJ}\,\text{m}^{-3}$ with $\hat{\mathbf{u}} = (0, 0, 1)$ in the out of plane direction,
• gyrotropic ratio $\gamma = 2.211 \times 10^{5} \,\text{m}\,\text{A}^{-1}\,\text{s}^{-1}$, and
• Gilbert damping $\alpha=0.3$.

Please carry out the following steps:

1. Create the following geometry with discretisation cell size $(2 \,\text{nm}, 2 \,\text{nm}, 2 \,\text{nm})$.

   <img src="dw_pair_conversion_geometry.png",width=500>

2. Initialise the magnetisation so that when relaxes, a domain pair is present in the narrower part of the geometry.

3. Relax the system. Is a domain wall pair contained in the constrained part?

4. Apply the spin polarised current in the positive $x$ direction with velocity $\mathbf{u} = (400, 0, 0) \,\text{m}\,\text{s}^{-1}$, with $\beta=0.5$.

5. Evolve the system over $0.2 \,\text{ns}$. What did you get? [1]

References

[1] Zhou, Y., & Ezawa, M. (2014). A reversible conversion between a skyrmion and a domain-wall pair in a junction geometry. Nature Communications 5, 8. https://doi.org/10.1038/ncomms5652

Solution