Magnetic Sensitivity Distribution of Hall Devices in Antiferromagnetic Switching Experiments

We analyze the complex impact of the local magnetic spin texture on the transverse Hall-type voltage in device structures utilized to measure magnetoresistance effects. We find a highly localized and asymmetric magnetic sensitivity in the eight-terminal geometries that are frequently used in current-induced switching experiments, for instance, to probe antiferromagnetic materials. Using current-induced switching of antiferromagnetic $\mathrm{Ni}\mathrm{O}/\mathrm{Pt}$ as an example, we estimate the change in the spin Hall magnetoresistance signal associated with switching events based on the domain-switching patterns observed via direct imaging. This estimate correlates with the actual electrical data after subtraction of a nonmagnetic contribution. Here, the consistency of the correlation across three measurement geometries with fundamentally different switching patterns strongly indicates a magnetic origin of the measured and analyzed electrical signals.

Figure 1

Device layout and measurement scheme of devices utilized in antiferromagnetic switching experiments. In the four-terminal Hall cross in (a), current pulses (arrows) and read-out measurements use the same channels. In the eight-terminal Hall star in (b), separate (smaller) channels serve as read-out lines. Orientation of pulse arrows and read-out is displayed here for the example of $\mathrm{Ni}\mathrm{O}(001)/\mathrm{Pt}$ bilayers, i.e., with respect to the crystallographic axes of $\mathrm{Ni}\mathrm{O}$ indicated by the coordinate system.

Figure 2

Simulations of the local magnitude of the Hall response in bar geometry obtained from a scan with a localized magnetic field. At Hall coefficients $R_H=-0.24\times {10}^{-10}{\mathrm{m}}^3/\mathrm{C}$ (left column) and $-1\times {10}^{-5}{\mathrm{m}}^3/\mathrm{C}$ (right column), the magnitude of the Hall resistance for a current from left to right (black arrow) and into-the-plane field is shown in (a),(b), while inverting current and field direction results are shown in simulations (c),(d), respectively. For higher $R_H$, adding (b) and (d) yields the total magnetic sensitivity map displayed in (f), which compares to individual simulations (a),(c) for a lower $R_H$, as well as their sum, as displayed in (e). Simulations performed with comsol Multiphysics [23].

Figure 3

Verification of the simulated Hall sensitivity distribution. (a) Analytical solution for a Hall bar geometry, based on a previous work [25]. Simulations performed with comsol Multiphysics [23] in a similar geometry yield the magnetic sensitivity map displayed in (b), which compares to the analytical solution in (a). (a) Adapted from Ref. [26] with permission from the author.

Figure 4

(a),(b) Simulations of read-out properties of the two measurement configurations in eight-terminal Hall devices (Hall stars). (c),(d) Respective current-density distributions of the I = 210 µA reading current. (e),(f) Sensitivity of transverse-resistance read-out to local magnetic signals. Simulations are carried out using comsol Multiphysics [23].

Figure 5

Estimate of the SMR signal based on difference images of domain-switching events. Detection of changes visible in a difference image (a) yields the number of pixels affected by switching. Definition of an appropriate threshold singles out the switched domains (b). After aligning the images to a uniform orientation [see insets (a) and (b)], the threshold image (b) is weighted with the Hall sensitivity distribution [inset (c)]. Sum of the intensity levels visible in (c) is an estimation of the impact of domain switching on the average SMR signal.

Figure 6

Imaging and electrical measurements of current-induced switching in different geometries on $\mathrm{Ni}\mathrm{O}(001)/\mathrm{Pt}$. (a)–(c) Changes of the domain structure caused by the application of a current pulse, as denoted by arrows in the difference image between the initial and final-state domain image. Column on the right of (a)–(c) includes the difference images after setting a threshold and weighting the difference with the magnetic sensitivity distribution of the electrical read-out, as displayed in the corresponding insets. Transverse-resistance data in (d) are measured simultaneously and are displayed after the subtraction of a linear contribution in each pulse direction. Correlation of the estimated SMR signal change from the difference images with actual electrical data is displayed in (e), which includes data for multiple sequences at different pulse current densities in each geometry.