Depth-dependent magnetic crossover in a room-temperature skyrmion-hosting multilayer

Skyrmion-hosting multilayer stacks are promising avenues for applications, although little is known about the depth dependence of the magnetism. We address this by reporting the results of circular dichroic resonant elastic x-ray scattering (CD-REXS), micromagnetic simulations, and low-energy muon-spin rotation (LE-${\mu }^{+}\mathrm{SR}$) measurements on a stack comprising $[\mathrm{Ta}$/CoFeB/${\mathrm{MgO}]}_{16}$/Ta on a Si substrate. Energy-dependent CD-REXS shows a continuous, monotonic evolution of the domain-wall helicity angle with incident energy, consistent with a three-dimensional hybrid domain-wall-like structure that changes from Néel-like near the surface to Bloch-like deeper within the sample. LE-${\mu }^{+}\mathrm{SR}$ reveals that the magnetic field distribution in the trilayers near the surface of the stack is distinct from that in trilayers deeper within the sample. Our micromagnetic simulations support a quantitative analysis of the ${\mu }^{+}\mathrm{SR}$ results. By increasing the applied magnetic field, we find a reduction in the volume occupied by domain walls at all depths, consistent with a crossover into a region dominated by skyrmions above approximately 180 mT.

Figure 1

CD-REXS patterns of the multilayered sample, measured at room temperature in zero magnetic field. (a) Energy-dependent CD-REXS patterns measured at $\theta ={12}^{\circ }$. The individual patterns at the energies at which a helicity angle could be extracted are shown in Ref. [17]. (b), (c) CD-REXS patterns measured at $\theta ={32}^{\circ }$ and ${35}^{\circ }$, respectively, using a photon energy of 707.8 eV (at the Fe $L_3$ edge). (d) Energy dependence of the measured helicity angle ${\chi }_{\text{m}}$ across the $L_3$ absorption edge.

Figure 2

(a) A diagram of the multilayer sample used in this work, with a demonstration of how this has been converted to a micromagnetic model in (b). (c) The helicity of the multilayer system, $\chi$, changes from Néel-type twisting at the top and bottom surfaces, to Bloch-like in the center of the stack.

Figure 3

(a), (b) Muon stopping profiles: (a) implantation energy dependence; (b) the proportion of muons stopping in each layer type. (c) Typical ZF ${\mu }^{+}\mathrm{SR}$ spectra $A\left(t\right)$ with parameters extracted from fitting shown as points in (d) and (e). The dashed lines in (d) and (e) show the results from micromagnetic simulations of a ferromagnetic and a skyrmion-like state.

Figure 4

(a) Energy dependence of parameters from fitting TF ${\mu }^{+}\mathrm{SR}$ at 10 mT, with a conversion to average muon penetration depth in (b). Error bars in (b) represent the asymmetric range in which two-thirds of the muons stop according to the calculations in Fig. 3. (c), (d) Field-dependent parameters from fitting TF ${\mu }^{+}\mathrm{SR}$ data, showing (c) the amplitude $a_{\text{I}}$, and (d) the ratio of $B$ to the applied field $B_{\text{ext}}$. Dashed lines are guides to the eye.