Analysis of magnetization reversal in ferromagnetic nanodots of different shapes with dimension in the range of 100 nm in the presence of Dzyaloshinskii-Moriya Interaction (DMI) is extremely important for technological application 1. Though a few studies have explored the effect of DMI on the magnetization reversal mechanism in nanostructures, to disentangle the influence of shape and DMI requires further systematic studies 2-4. Here, we investigate the effect of DMI (D) and in-plane bias field (H) on magnetization reversal in perpendicularly magnetized isolated square, circular, and triangular nanodot using the micromagnetic simulation Mumax³ 5. The side length/diameter of the nanodot is chosen as 128 nm and the thickness as 1 nm and the material parameters of Co is selected. Our results indicate that the coercive field monotonically decreases as the strength of D increases and loop becomes asymmetric in the presence of both D and H in all three shapes. Interestingly, for D = 0 and H ≠  0, nucleation of the reverse domain occurs at the central region of the nanodot (Figs. 1(a-c)), and in case of D ≠  0 and H ≠  0 chiral nucleation occurs at the far edge (Figs. 1(d-f)). Due to lateral asymmetry of the triangular nanodot, the total energy value is smaller for the triangular nanodots (for -100 mT < H < +100 mT, and -1 mJ/m² < D < + 1 mJ/m²) thereby making it preferred for energy efficient magnetization reversal as compared to other two shapes. However, at sufficiently higher value of the magnitude of H (> 200 mT) and D (> 1 mJ/m²), due to the laterally symmetric sides of the square the energy barrier for the magnetization reversal reduces drastically (cf. Fig.1(f)). These findings indicate that the effect of D and H in lowering the energy barrier for the magnetization reversal is intricately related to the symmetry associated with the shape of the nanodots.

References
1 F. Hellman, A. Hoffmann, Y. Tserkovnyak et al., Rev. Mod. Phys., Vol.89, p.025006 (2017)
2 S. Pizzini, J. Vogel, S. Rohart et al., Phys. Rev. Lett., Vol.113, p.047203 (2014)
3 D.-S. Han, N.-H. Kim, J.-S. Kim et al., Nano Lett., Vol.16, p.4438 (2016)
4 Syamlal S K, Hari Prasanth Perumal, and Jaivardhan Sinha., Mater. Lett., Vol.303, p.130492 (2021)
5 A. Vansteenkiste, J. Leliaert, M. Dvornik et al., AIP Adv., Vol.4, p.107133 (2014)

Figure 1: Snapshot of the spin configuration for square, circular and triangular nanodot during down to up (D-U) switching at H = -100 mT and D = 0 (a-c), H = -100 mT and D = 3 mJ/m² (d-f). (g) Variation of total energy as a function of in-plane bias field for square, circular, and triangular nanodots at different value of D is plotted during D-U switching.