Electrical Detection of Domain Walls and Skyrmions in Co Films Using Noncollinear Magnetoresistance

A large noncollinear magnetoresistance (NCMR) is observed for $\mathrm{Rh}/\mathrm{Co}$ atomic bilayers on Ir(111) using scanning tunneling microscopy and spectroscopy. The effect is 20% at the Fermi energy and large in a broad energy range. The NCMR can be used to electrically detect nanometer-scale domain walls and skyrmions directly in the tunnel current without the need for a differential measurement. The NCMR results from changes in the density of states of noncollinear spin textures with respect to the ferromagnetic state. Density functional theory calculations reveal that they originate from spin mixing between majority $d_{xz}$ and minority $p_z$ states.

Figure 1

(a) Constant-current STM image colorized with the spin-resolved $dI/dU$ signal of a sample of about 0.4 atomic layers of Rh on 0.6 atomic layers of Co on Ir(111). The hcp-stacked Rh islands can be identified by their blue color, thin lines indicate DWs between oppositely oriented out-of-plane FM domains. The red circle highlights a skyrmion observed in the hcp-$\mathrm{Rh}/\mathrm{Co}$ atomic bilayer. The corresponding color bar is shown below. (b) and (c) $dI/dU$ maps of identical sample areas imaged with spin-averaging and spin-resolving tip, respectively; the bright roughly triangular-shaped objects on the hcp-$\mathrm{Rh}/\mathrm{Co}$ are small islands of Rh on top of the film. Images (a)–(c) were taken at $T=4.2\mathrm{K}$, $U=-250\mathrm{mV}$, and $I=0.8\mathrm{nA}$ with a Cr bulk tip. (d) Line profile across a modeled magnetic skyrmion with a diameter of 5 nm and corresponding STM simulations of (e) the TMR signal with a canted tip magnetization, (f) the NCMR signal, and (g) a combination of both.

Figure 2

(a) Spin-resolved $dI/dU$ map of $\mathrm{Rh}/\mathrm{Co}/\mathrm{Ir}(111)$ with three FM domains separated by two DWs measured at $-250\mathrm{mV}$. (b) Spin-averaged $dI/dU$ spectra obtained by averaging the spectra taken at the color-coded points in (a), feedback switched off at $-1\mathrm{V}$ and 1 nA; see also Ref. [21]. (c) NCMR calculated according to Eq. (1) using the two spectra in (b). (d) Calculated vacuum LDOS 3 Å above the film of $\mathrm{Rh}/\mathrm{Co}/\mathrm{Ir}(111)$ for the FM state (gray curve) and for spin spirals with different nearest-neighbor angles $\theta$ (colored curves). The zero line is aligned with that in (b). The inset shows a sketch of the hexagonal atomic lattice with the spin spiral propagation direction given by $\mathbf{q}$ and the angle $\theta$ between spins on neighboring sites. (e) NCMR calculated from the FM and spin spiral vacuum LDOS for different $\theta$. (f) Peak position ($E_P$) relative to $E_F$ (black points) and peak intensity relative to the main peak of the FM state at $E_F+0.04\mathrm{eV}$ (red points) for the calculated spin spiral curves as a function of $\theta$.

Figure 3

Orbital and spin decomposition of the local density of states (LDOS) at the Rh atom. (a) LDOS of the majority $d_{xz}$ (upper panel) and minority $p_z$ states (lower panel) obtained from DFT calculations for spin spiral states with an angle $\theta$ between adjacent spins as given in the legend. (b) LDOS of the states obtained within a simplified two-state tight-binding model (see text for details).