Skyrmion magnetic structure of an ordered FePt monolayer deposited on $\mathrm{Pt}(\mathrm{111})$

The effect of the Dzyaloshinsky-Moriya interaction on the magnetic structure of an ordered FePt monolayer deposited on the $\mathrm{Pt}(\mathrm{111})$ surface has been investigated. In the ground state, the pronounced anisotropic geometry of the FePt layer with alternating Fe and Pt chains gives rise to a helimagnetic structure with a strong difference in the helicity period along the chains and perpendicular to them. In the presence of an external magnetic field, the region of stable Skyrmion magnetic structures in the B-T phase diagram has been demonstrated via Monte Carlo simulations using the parameters obtained within first-principles electronic structure calculations. The present study demonstrates clearly that the ratio of the exchange coupling parameters $J/D$ for a deposited magnetic film—being of central importance for the formation of Skyrmions—can be manipulated by growing an overlayer of 2-dimensional compounds with the atoms carrying spontaneous magnetic moments separated by the atoms of nonmagnetic elements.

Figure 1

(a) Geometry of the system and directions of in-plane components of DM exchange interactions (shown by the arrows) between Fe1 and Fe2 atoms, Fe1 and Fe3 atoms, etc. (b) Calculated exchange coupling parameters: isotropic, $J_{ij}$, for Fe-Fe (circles) and Fe-Pt (diamonds) (top panel), and $D_{ij}^x$, $D_{ij}^y$ and $D_{ij}^z$ components of DM interactions between Fe atoms for FePt/$\mathrm{Pt}(\mathrm{111})$.

Figure 2

Helimagnetic structure in FePt/$\mathrm{Pt}(\mathrm{111})$. The arrows represent the magnetic moments of Fe atoms.

Figure 3

Magnetic moment distribution within the Skyrmion. Yellow and blue colors in (a) represent schematically the region giving gain and loss of Zeeman energy in the presence of a magnetic field; blue color in (b) shows the region giving loss of the exchange energy contributed by in-plane components of magnetic moments. (c) and (d): Structure of single Sk obtained with the contributions of the Fe-Pt exchange interactions taken into account [the same color code as in (a) and (b)]. Long arrows show the spontaneous magnetic moments on Fe atoms; short arrows indicate the induced magnetic moments on Pt atoms.

Figure 4

(a) Low-temperature part of $B$-$T$ phase diagram calculated for FePt/$\mathrm{Pt}(\mathrm{111})$; (b)–(g) representative magnetic structures of the phase diagram regions indicated in (a) obtained at $B=0.0$ T, $T=3.0$ K (b), $B=2.5$ T, $T=3.0$ K (c), $B=7.5$ T, $T=3.0$ K (d), $B=12.5$ T, $T=3.0$ K (e), $B=1.0$ T, $T=22.0$ K (f), $B=3.5$ T, $T=17.0$ K (g).

Figure 5

Temperature-dependent magnetization $M\left(T\right)$ (diamond), susceptibility $\chi \left(T\right)$ (triangles), and heat capacity $c_v\left(T\right)$ functions represented for three different magnetic fields: $B=12$ T (top panel), $B=8$ T (middle panel), and $B=4$ T (bottom panel).