Impact of the skyrmion spin texture on magnetoresistance

We investigate the impact of the local spin texture on the differential conductance by scanning tunneling microscopy. In the focus is the previously found noncollinear magnetoresistance (NCMR), which originates from spin mixing effects upon electron hopping between adjacent sites with canted magnetic moments. In the present work, NCMR is studied with lateral resolution both for the zero magnetic field spin spiral state as well as for individual magnetic skyrmions at different magnetic field values. We analyze in detail the response of the differential conductance and find different dependencies of peak energy and peak intensity on the local properties of the noncollinear spin texture. We find that in the center of a skyrmion, the peak energy and intensity scale roughly linearly with the angle between nearest-neighbor moments. Elsewhere in the skyrmion, where the noncollinearity is not isotropic and the magnetization quantization axis varies, the behavior of the peak energy is more complex.

Figure 1

Sketches of different MR effects. (a) The conductance/MR between two magnetic electrodes depends on the relative alignment of their magnetization directions. (b) The spatial resolution of STM grants access to magnetic structures down to the atomic scale. (c) Using a nonmagnetic probe electrode, the conductance/MR depends on the quantization axis of magnetization due to the TAMR. (d) A nonmagnetic probe electrode is also sensitive to the noncollinearity of a spin texture due to the NCMR. This figure has been adapted from Ref. [4].

Figure 2

(a) Pseudo-3D STM topography of a typical sample of Pd/Fe on Ir(111), colorized with the $dI/dU$ signal. (b) $dI/dU$ map of the area indicated by the black rectangle in (a) showing NCMR contrast for the spin spiral ground state in both stackings of the Pd/Fe. (c) $dI/dU$ map of the same area as in (b) in applied magnetic field with individual magnetic skyrmions imaged by NCMR. (d),(e) $dI/dU$ spectra of the different magnetic states as color coded in (b),(c) for both stackings of Pd/Fe. Measurement parameters for (a)–(c) are $U=+0.7$ V, $I=1$ nA, $U_{\mathrm{mod}}=40$ mV, and for (d) and (e) are $U_{\mathrm{stab}}=-1$ V, $I_{\mathrm{stab}}=1$ nA, $U_{\mathrm{mod}}=7$ mV; all $T=4.2$ K.

Figure 3

(a) $dI/dU$ map of a single skyrmion in Pd/Fe on Ir(111) at $B=-1.75$ T measured with a W tip ($U=+0.7$ V, $I=1$ nA, $U_{\mathrm{mod}}=20$ mV, $T=8$ K). (b) $dI/dU$ spectra taken at different positions within the skyrmion [see labels in (a); $U_{\mathrm{stab}}=-0.3$ V, $I_{\mathrm{stab}}=0.2$ nA, $U_{\mathrm{mod}}=20$ mV, $T=8$ K]. (c) Sketch of a skyrmion at $-1.75$ T; the cones represent atomic magnetic moments, their directions point in the direction of magnetization, and the color scale indicates the out-of-plane magnetization component (red down, blue up). (d)–(g) Magnetic-field-dependent properties of individual magnetic skyrmions in Pd/Fe as a function of distance from the skyrmion center: (d) the polar angle of the spins in a skyrmion, (e) the mean angle between a spin and its six neighbors and (f) standard deviation of this mean angle, (g) the magnetic quantization axis, which varies from out of plane in the center of a skyrmion via in plane back to out of plane in its surrounding.

Figure 4

(a) Spatially resolved $dI/dU$ spectra across a skyrmion at $B=-1.75$ T measured with a W tip ($U_{\mathrm{stab}}=-0.3$ V, $I_{\mathrm{stab}}=0.2$ nA, $U_{\mathrm{mod}}=20$ mV, $T=8$ K); the dashed line indicates the skyrmion center. (b) Evolution of the peak energy as a function of distance from the skyrmion center for different magnetic fields $\left|B\right|$ as labeled with the same W tip; all data points are also mirrored at the skyrmion center. Lines are guides to the eye. (c) Same as (b), but for the peak intensity. The empty circles at the bottom indicate data points that are considered unreliable due to a defect.

Figure 5

(a) Evolution of the peak energy (data of Fig. 4) as a function of mean angle at the respective position in the skyrmion. Solid line is a linear fit to the data at the skyrmion centers; dashed lines are guides to the eye. (b) Same as (a), but for the peak intensity. The empty circles at the bottom mark data points that are considered unreliable due to a defect.

Figure 6

Data as in Fig. 5 together with the evolution of (a) the degree of inhomogeneity ${\sigma }_{\overline{\alpha }}$ and (b) the quantization axis ${\cos }^2\left(\theta \right)$ in addition to the mean angle. Insets show the separate contributions of ${\sigma }_{\overline{\alpha }}$ and ${\cos }^2\left(\theta \right)$ as a function of the mean angle.