Element-specific soft x-ray spectroscopy, scattering, and imaging studies of the skyrmion-hosting compound ${\mathrm{Co}}_8{\mathrm{Zn}}_8{\mathrm{Mn}}_4$

A room-temperature skyrmion-hosting compound ${\mathrm{Co}}_8{\mathrm{Zn}}_8{\mathrm{Mn}}_4$ has been examined by means of soft x-ray absorption spectroscopy, resonant small-angle scattering, and extended reference holography. An element-selective study was performed by exciting the $2p$-to-$3d$ transitions near Co and Mn $L_{2,3}$ absorption edges. By utilizing the coherence of soft x-ray beams the element-specific real-space distribution of local magnetization at different temperatures has been reconstructed using iterative phase retrieval and holography with extended reference. It was shown that the magnetic moments of Co and Mn are ferromagnetically coupled and exhibit similar magnetic patterns. Both imaging methods provide a real-space resolution of 30 nm and allowed us to record a magnetic texture in the temperature range between $T=20$ K and $T=120$ K, demonstrating the elongation of the skyrmions along the principal crystallographic axes at low temperatures. Micromagnetic simulations have shown that such deformation is driven by a decreasing ratio of symmetric exchange interaction to antisymmetric Dzyaloshinskii-Moriya interaction in the system and effect of the cubic anisotropy.

Figure 1

Sketch of the (a) XMCD, (b) RSXS and (c) HERALDO experiments. (d) SEM image of the RSXS sample aperture. (e) Thin plate of the ${\mathrm{Co}}_8{\mathrm{Zn}}_8{\mathrm{Mn}}_4$ fixed onto the membrane. (f) SEM image of the sample aperture and the reference slit drilled in the 1-$\mu \mathrm{m}$-thick gold plate for the HERALDO experiment. (g) ${\mathrm{Co}}_8{\mathrm{Zn}}_8{\mathrm{Mn}}_4$ thin plate fixed onto a gold plate by tungsten contact. The strong white/black contrast in the top/bottom parts of (d)–(g) corresponds to the Au wires sputtered onto the membrane [49], which is irrelevant for this study.

Figure 2

(a) XAS spectra of the bulk ${\mathrm{Co}}_8{\mathrm{Zn}}_8{\mathrm{Mn}}_4$ near the Co and Mn $L_{2,3}$ absorption edges: measured points are shown as the solid lines; calculated spectra are shown as the dashed lines. (b) XMCD signal. The measurements were performed at temperature $T=130$ K at applied magnetic field $B=0.5$ T.

Figure 3

(a) Schematic phase diagram of ${\mathrm{Co}}_8{\mathrm{Zn}}_8{\mathrm{Mn}}_4$ and the procedure of the resonant soft x-ray scattering (RSXS) measurements. The sample is field cooled (FC) in the applied magnetic field $B=70$ mT from room temperature down to 25 K (indicated by the blue arrow) and then warmed back to 300 K in the same field (indicated by the red arrow). Coherent RSXS speckle patterns measured for the ${\mathrm{Co}}_8{\mathrm{Zn}}_8{\mathrm{Mn}}_4$ sample at $E=779$ eV corresponding to the $L_3$ absorption edge of Co at different temperatures (b) $T=25$ K, (c) $T=120$ K, and (d) $T=150$ K and applied field $B=70$ mT. White scale bar corresponds to 0.05 ${\mathrm{nm}}^{-1}$.

Figure 4

Temperature dependence of the modulation vector of skyrmion lattice $q_{\text{Sk}}$. Inset shows magnetic field dependence of $q_{\text{Sk}}$ measured at $T=25$ K and $T=50$ K.

Figure 5

Differential scattering patterns between LCP and RCP x rays of energies (a) $E=779$ eV and (b) $E=640.5$ eV taken at $T=20$ K. The color bar is given for both patterns in arbitrary units. Note that the strong linear patterns inclined upward right should be due to the incomplete subtraction of the charge scattering from the reference slit. (c) Fourier transform of (a) after applying linear differential filter and rotation of the image by ${39}^{\circ }$. (d) and (e) Magnetic texture recorded at Co and Mn $L_3$ edges, respectively. The color bar is given for both images in arbitrary units. The region outside the field of view is filled with the black background manually for clarity. (f) Fourier ring correlation analysis of the reconstructed images for Co and Mn. The orange line represents a calculated half-bit threshold and the dashed line indicates a irreversible cross point between the FRC function and half-bit threshold.

Figure 6

Real-space magnetic textures imaged at the Co $L_3$ edge ($E=779$ eV) at temperatures (a) $T=20$ K, (b) $T=100$ K, and (c) $T=120$ K and applied magnetic field $B=70$ mT.

Figure 7

Reconstruction of coherent RSXS patterns at (a) $T=25$ K, (b) $T=55$ K, and (c) $T=120$ K collected at the Co ${\mathrm{L}}_3$ edge. The color bar for intensity ($z$ scale) is given in arbitrary units. (d) Magnification of the region highlighted by the blue square in (a) is shown for the the different temperatures.

Figure 8

Micromagnetic simulations of ${\mathrm{Co}}_8{\mathrm{Zn}}_8{\mathrm{Mn}}_{4}10\times 10$ $\mu {\mathrm{m}}^2$ thin plate: $z$ projection of the magnetic texture is shown for various exchange from stiffness parameters $A_{\text{ex}}=9.2\times {10}^{-12}$ J/m (a), $5.8\times {10}^{-12}$ J/m (b), and $3.2\times {10}^{-12}$ J/m (c). Bottom panels show magnification of the rectangular regions highlighted by the corresponding red boxes.

Figure 9

Measured dependence of $q_{\text{Sk}}$ over temperature (symbols) and calculated dependence of $q_{\text{Sk}}$ over the exchange stiffness ($A_{\text{ex}}$) parameter.

Figure 10

Magnetic field evolution of the $z$ projection of magnetization derived from the micromagnetic simulation of ${\mathrm{Co}}_8{\mathrm{Zn}}_8{\mathrm{Mn}}_4$ thin plate in magnetic field $B=150$ mT (a), $B=250$ mT (b), $B=300$ mT (c), $B=350$ mT (d), $B=400$ mT (e), and $B=450$ mT (f) showing the hexagonal SkX restoration.