Anisotropic Magnetoresistance Zero-Field Domain Wall Depinning in Cylindrical Nanowires

Abstract

Investigations the current-driven domain wall (DW) motion in cylindrical nanowires (CNWs) are more valuable if performed at zero applied external field for their use in prospective electronic devices. Here, we present an all-magnetoelectrical method to pin DWs in multi-segmented CNWs, maintain them pinned at zero field and de-pin them using current pulses. We test this in compositionally modulated nickel/cobalt (~ [10/14] μm) and nickel/cobalt/nickel (~ [3/7/3] μm) CNWs of c.a. 150 - 190 nm diameter where DWs can be pinned in a predictable and reproducible way and their soft/hard magnetic texture has been fairly studied [1]–[3]. Furthermore, we perform micromagnetic simulations to interpret and study the behavior of the magnetoresistance as a function of segment length.The method is based on the anisotropic magneto-resistance (AMR) measurement of a CNW with a pinned DW [4] for which we show the relevant range of one branch in Figure 1 (solid line). This branch starts from a saturated magnetization state in the “right” direction (3000 Oe, not shown) and moves to a saturated state in the “left” direction (-3000 Oe, not shown), as indicated by the arrow at the bottom. The CNW’s long axis is parallel to the applied field.Simplifying, AMR gives an overall measure of the portion of the CNW’s magnetization that is not along the direction of the applied electrical current: at ±3000 Oe, most of the CNW’s magnetization is in the same direction as the electrical current, i.e., along the CNW’s long axis, resulting in a saturated high resistance state. As the field decreases, magnetization vortexes appear at the ends of the CNW, driving magnetization away from the axial direction and resulting in a low resistance state. When the field is ramped in the opposite direction, a DW propagates from one of the ends and is pinned at some point within the nickel segment [1], increasing the axial component of the magnetization as indicated by the rapid increase in resistance in Figure 1 (“Domain wall pinning”). Finally, when the field is further increased, the DW de-pins and propagates to the opposite end from where it was initially nucleated leaving most of the magnetization in the axial direction, as indicated by the second resistance change in Figure 1 (“Domain wall de-pinning”). Note that pinned DWs and vortexes at the ends of the CNW lower the resistance as they are mainly composed of magnetization textures out of axis.To test current-driven DW motion at zero field, a DW has to be pinned first by saturating the magnetization to +3000 Oe, decreasing the field, inverting it and increasing it only until the first resistance jump is reached (red, open squares in Figure 1). After this, the field is reduced to 0 (blue, open triangles in Figure 1), at which point current pulses are applied. To verify whether the DW is still pinned after reducing the field to zero and/or that a current pulse has de-pinned it, the field is ramped up again in the negative direction (towards -3000 Oe). If the DW had de-pinned as a consequence of reducing the field, the CNW’s magnetization would return to a “right” state and the domain wall pinning resistance jump would be registered again, which we never observed. If the DW remained pinned, even after the application of a pulse, only the DW de-pinning resistance jump was observed, as seen in Figure 2 (solid red squares), where a current pulse of 9.21x1011 A/m2 and 10 ns width was applied. On the other hand, if a current pulse de-pinned the DW, neither of the resistance jumps would be observed, as seen in Figure 2 (solid blue triangles), where a pulse of 1.38x1012 A/m2 and 20 ns width was used.This method resembles recent ones in the sense that the state of the CNW is known after the current pulse is sent, for example using MFM [5] or TEM [6]. As the DW is de-pinned at high enough current densities, the width of the pulse can be used to estimate the DW speed by successively reducing the pulse width until no de-pining event is found. With this, the velocity is estimated as the length of the cobalt segment over the current pulse width.We find that the de-pinning event is dependent on the direction of the applied current and that the magnetoresistance value for pinned domain walls increases as the length of the segments increases, which is consistent with our simplified view of AMR. This suggests that, for long enough CNWs, the DW width remains constant as the segment length increases, which we also confirmed with micromagnetic simulations.We believe this method can be used to study current-induced DW de-pinning at zero applied field in soft/hard magnetic CNWs with known magnetic configurations. **