Probing the Nano-Skyrmion Lattice on Fe/Ir(111) with Magnetic Exchange Force Microscopy

We demonstrate that the magnetic nano-Skyrmion lattice on the Fe monolayer on Ir(111) and the positions of the Fe atoms can be resolved simultaneously using magnetic exchange force microscopy. Thus, the relation between magnetic and atomic structure can be determined straightforwardly by evaluating the Fourier transformation of the real space image data. We further show that the magnetic contrast can be mapped on a Heisenberg-like magnetic interaction between tip and sample spins. Since our imaging technique is based on measuring forces, our observation paves the way to study Skyrmions or other complex spin textures on insulating sample systems with atomic resolution.

Figure 1

(a) Overview noncontact AFM image of the Fe/Ir(111) sample system with a coverage of 0.7 ML. Parameters: $\mathrm{\Delta }f=-12.0\mathrm{Hz}$, $A=2.3\mathrm{nm}$, $k_c=147.1{\mathrm{Nm}}^{-1}$, $U_{\mathrm{bias}}=+0.1\mathrm{V}$. (b) Atomic resolution image of the Fe ML in the constant-height mode recorded with a nonmagnetic tip. The hexagonal lattice demonstrates that the Fe ML grows pseudomorphically on Ir(111). The inset shows the 2D FT of the image data with the six spots corresponding to the hexagonal atomic lattice. Parameters: $A=1.2\mathrm{nm}$, $k_c=148.3{\mathrm{Nm}}^{-1}$, $U_{\mathrm{bias}}=+0.9\mathrm{V}$.

Figure 2

Left: MExFM image of the Fe ML on Ir(111) recorded with an Fe-coated tip in constant-height mode. An applied magnetic field of $B=4\mathrm{T}$ ensures an out-of-plane magnetized tip. In addition to the hexagonal atomic structure (white hexagon) the magnetic structure of the nano-Skyrmion lattice (red square) is visible as well. The dashed lines indicate the principal crystallographic directions of the substrate. Right: overlaid Fourier-filtered image generated by taking only the atomic and magnetic peaks of the 2D FT. The atomic lattice has been reproduced by a hexagonal arrangement of white circles. Inset: the 2D FT of the raw image data clearly reveals that the atomic and magnetic structure are incommensurate. Parameters: $A=0.8\mathrm{nm}$, $k_c=147.2{\mathrm{N}\mathrm{m}}^{-1}$, $U_{\mathrm{bias}}=+1.1\mathrm{V}$, $B=4\mathrm{T}$.

Figure 3

(a) Commensurate approximation of the spin texture on top of the hexagonal arrangement of atoms that is closest to the real incommensurate nano-Skyrmion lattice (adapted from Ref. [8]). The polar and azimuthal angles of the cones represent the orientation of the canted spins with respect to the surface plane. (b) Magnetic contrast obtained after removing the atomic contribution using Fourier filtering and subsequent unit cell averaging. The image is tiled from several unit cells to match the size of the model in (a). The line indicates the [11] direction of the square lattice, which is parallel to [$1\overline{1}0$] direction of the substrate. Black dots mark the positions of the Fe atoms. (c) Line section as indicated in (b). The black circles represent the expected behavior of the magnetic signal according to the Heisenberg model assuming an out-of-plane magnetized tip. Below the curve, the cones in the spheres indicate the varying angle between the spin and surface plane.

Figure 4

MExFM images (a) and (b) show two rotational domains of the Skyrmion lattice. They were recorded in close proximity to each other using the same constant-height mode imaging parameters. As visible in the corresponding 2D FT displayed below the images, only the magnetic contrast pattern is rotated. Parameters: $B=3\mathrm{T}$, $A=0.5\mathrm{nm}$, $k_c=147.1{\mathrm{Nm}}^{-1}$, $U_{\mathrm{bias}}=+0.1\mathrm{V}$.