Field-free manipulation of magnetization alignments in a Fe/GaAs/GaMnAs multilayer by spin-orbit-induced magnetic fields

We investigate the process of selectively manipulating the magnetization alignment in magnetic layers in the Fe/GaAs/GaMnAs structure by current-induced spin-orbit (SO) magnetic field. The presence of such fields manifests itself through the hysteretic behavior of planar Hall resistance observed for two opposite currents as the magnetization in the structure switches directions. In the case of the Fe/GaAs/GaMnAs multilayer, hystereses are clearly observed when the magnetization switches direction in the GaMnAs layer, but are negligible when magnetization transitions occur in Fe. This difference in the effect of the SO-field in the two magnetic layers provides an opportunity to control the magnetization in one layer (in the presence case in GaMnAs) by a current, while the magnetization in the other layer (i.e., Fe) remains fixed. Owing to our ability to selectively control the magnetization in the GaMnAs layer, we are able to manipulate the relative spin configurations in our structure between collinear and non-collinear alignments simply by switching the current direction even in the absence of an external magnetic field.

Magnetic anisotropy fields of the GaMnAs layer obtained by this fitting process for six current values are shown in Table S1. The results show that the cubic anisotropy field H c rapidly decreases with increasing magnitude of the applied current, while the uniaxial anisotropy field H u is less sensitive to the current. This anisotropy behaviour is closely similar to that observed with increasing temperature, indicating effects of Joule heating as discussed in Supplementary Material 3. Device temperatures Td corresponding to the applied currents, as obtained in Supplementary Material 3, are shown in the second column of Table   S1.

Supplementary 2
In order to achieve full rotation of magnetization in both GaMnAs and Fe layers, we used a larger magnetic field (sufficient to overcome the energy barriers in the Fe film) to achieve complete magnetization reversals in both layers. Magnetizations of both the A and B device were initialized using a strong magnetic field at the same orientation as that used for

Supplementary 4
In order to see the current dependence of the SOI field, we performed magnetization reversal experiment by using several difference currents, from which the strength of the SOI field was then determined. Figure S5 shows the data summary for the SOI field as a function of current density. The data in insets show PHR hystereses formed by currents of opposite polarity at two representative current densities. It is clear that the width of the hysteresis is larger for the larger current, indicating an increase of the SOI field with increasing current.
The data in Fig. S5 also shows a linear dependence of the SOI field on the current density.

Supplementary 5
We performed magnetization switching experiments as a function of applied current in a constant background field of H = 20 Oe applied along the 11 0 direction. Figure S7 shows the PHR data measured while the applied current was scanned between -3.0 mA and +3.0 mA. The data show a clear hysteresis, indicating a reorientation of magnetization as the current is swept. The PHR is seen to switch sign near 2.9 mA, which corresponds to a critical current that produces the reorientation of magnetization in the GaMnAs layer. As seen from the presence of intermediate values of PHR within the transition region, in that region the GaMnAs layer is characterized by a multi-domain landscape. mA|.

Supplementary 6
The presence of interlayer exchange coupling can be verified by minor loop scan experiments, in which the magnetization of only one layer switches, while that of the other layer remains unchanged. Figure S8 shows PHR data obtained from major (black squares) and minor loop scans (open and solid red circles for CW and CCW rotations of the applied field, respectively). As seen from the directions of magnetization shown by arrows, the hysteresis in the minor loop scan arises from the reorientation of magnetization only in the GaMnAs layer, while that of Fe layer is fixed. If an exchange coupling between Fe and GaMnAs layers were present, the hysteresis would shift. 7,8 However, the observed hysteresis does not show shift, as seen in Fig. S8, thus indicating the absence of noticeable interlayer exchange coupling between the Fe and GaMnAs layers.