Formation and stability of metastable skyrmionic spin structures with various topologies in an ultrathin film

We observe metastable localized spin configurations with topological charges ranging from $Q=-3$ to $Q=2$ in a (${\mathrm{Pt}}_{0.95}{\mathrm{Ir}}_{0.05}$)/Fe bilayer on a $\mathrm{Pd}\left(111\right)$ surface by performing spin dynamics simulations, using a classical Hamiltonian parametrized by ab initio calculations. We demonstrate that the frustration of the isotropic exchange interactions is responsible for the creation of these various types of skyrmionic structures. The Dzyaloshinsky-Moriya interaction present due to the breaking of inversion symmetry at the surface energetically favors skyrmions with $Q=-1$, distorts the shape of the other objects, and defines a preferred orientation for them with respect to the underlying lattice.

Figure 1

Metastable localized spin configurations with different topological charges: (a) skyrmion with $Q=-3$, (b) skyrmion with $Q=-2$ [17, 36, 37], (c) skyrmion with $Q=-1$, (d) chimera skyrmion with $Q=0$, (e) antiskyrmion with $Q=1$, and (f) antiskyrmion with $Q=2$ [40]. The value of the external field is $B=2.35\mathrm{T}$ in part (a) and $B=0.23\mathrm{T}$ in parts (b)–(f); the ground state is field-polarized for $B>0.21\mathrm{T}$ [43]. The colors indicate the directions of the spin vectors, illustrated on the right edge of the figure.

Figure 2

Metastable localized spin configurations with topological charges (a) $Q=-3,$ (b) $Q=-2,$ (c) $Q=-1,$ (d) $Q=1$, and (e) $Q=2$. Compared to Fig. 1, only the isotropic part of the exchange tensors was kept. The value of the external field is $B=0.23\mathrm{T}$.

Figure 3

Preferred orientation angle $\delta$ of the topological objects in Fig. 1 with respect to the underlying lattice. (a) $\delta =\pi /3$ for $Q=-3$, (b) $\delta =\pi /6$ for $Q=-2$, (d) $\delta =5\pi /6$ for $Q=0$, (e) $\delta =5\pi /6$ for $Q=1$, and (f) $\delta =2\pi /3$ for $Q=2$. Skyrmions with $Q=-1$ in (c) are cylindrically symmetric, and they are characterized by the helicity $\gamma =\pi$ instead.