Main

The current-controlled motion of domain walls along magnetic nanowires promises the development of novel memory-storage devices with high density, performance and endurance at a very low cost per bit1. The fundamental principle underlying such devices lies in the possibility of moving a series of closely spaced domain walls back and forth along the nanowire using spin torques generated within the bulk2,3,4 or at the surfaces of the nanowires interfacing with neighbouring metal or insulating layers5,6,7. In contrast, an applied magnetic field drives adjacent domain walls in exactly opposite directions; this is the main reason why the manipulation of domain walls with spin currents is so useful1. Why all the domain walls move in the same direction is easy to understand when bulk spin transfer torque (STT) dominates, because the spin polarization of the current arises from spin-dependent scattering within the interior volume of the magnetic domains. This takes place over a very short length scale compared to the extent of a typical domain wall. However, why the domain walls move in the same direction when driven by interface-derived spin–orbit torques is more difficult to explain. Indeed, the Rashba8,9,10 and the spin Hall effect (SHE)11,12,13,14 mechanisms that have been proposed, give rise, respectively, to a magnetic field, whose direction, and a spin current15,16, whose polarization, are in plane and perpendicular to the current direction. Most importantly, these phenomena do not depend on the direction of magnetization of successive domains.

The Rashba effect arises from discontinuity in the electronic structure at an interface, here the Co/Pt interface, which is transformed via a relativistic spin–orbit interaction into a magnetic field acting on the conduction electrons17. This magnetic field acts on the magnetization through an s–d exchange interaction between the sp conduction electrons and the localized 3d electrons18,19. The SHE acts in the Pt layer to convert charge current to pure spin currents, which flow perpendicular to the electrical current. The spin currents diffuse across the Pt/Co interface to generate a STT that acts on the magnetization11. The form of this SHE-STT is the same as that generated in spin valves and magnetic tunnel junctions20, where the polarization of the spin current in Pt plays the role of the reference layer (that is, the polarizer) in the latter devices4,20. Both the Rashba field and the SHE-STT are directly proportional to the current density13,21.

Several theoretical models have been developed to describe how the Rashba field and the SHE-STT influence domain-wall motion10,12. Although these models can predict the high-speed motion of domain walls along the current direction (that is, opposite to conventional bulk STT), they find that this occurs only for limited ranges of current or for special domain-wall configurations. More recently, numerical models have suggested that a combination of SHE and a Dzyaloshinskii–Moriya interaction (DMI)22,23,24,25,26,27,28 could lead to fast domain-wall motion as a result of stabilization of a particular domain-wall configuration by the DMI interaction29,30.

In this article, we show that the current-driven motion of domain walls in perpendicularly magnetized Co/Ni/Co trilayers with interfaces to Pt under- and/or overlayers is strongly affected by magnetic fields applied along directions perpendicular to the direction of magnetization, that is, in the plane of the nanowires. In the absence of current, these fields do not drive the domain walls along the nanowire. By comparing these data with the well-established one-dimensional analytical model of current- and field-induced domain-wall dynamics31, which includes both STT and spin–orbit torques32,33, we find that the model can only account for our observations if we introduce into the model a phenomenological effective longitudinal magnetic field acting on the domain walls, the direction of which alternates between successive domain walls (that is, at the boundaries between adjacent up/down (↑↓) and down/up (↓↑) magnetic domains). This chiral effective field, which is independent of the current (in contrast to the Rashba and SHE mechanisms), is consistent in direction and sign with a DMI at the Pt/Co interface that imposes a handedness to the domain walls26,27,29,30. It is the combination of the DMI and SHE-STT that results in the observed domain-wall dynamics. Furthermore, we can vary these two phenomena independently by engineering the Co/Pt interfaces at the top and bottom of the Co/Ni/Co stack and can thereby control the direction of domain-wall motion.

Identification of chiral internal local magnetic field

Experiments were performed on nanowires patterned by ultraviolet photolithography and argon ion milling in Co/Ni/Co films that had been deposited by magnetron sputtering (Fig. 1a). All the films considered here exhibited well-defined perpendicular magnetic anisotropy (PMA), with their remanent state fully magnetized in the direction perpendicular to the substrate. A domain wall, either ↑↓ or ↓↑ , was first introduced into the nanowire by applying a sequence of magnetic fields along the magnetic easy axis, after which these fields were reduced to zero. Current-driven domain-wall motion was then studied by applying a series of current pulses of length tP to the nanowire in the presence of a static magnetic field. This field was applied either along the direction perpendicular to the wafer plane (Hz, along the magnetization easy axis) or in the plane of the wafer, either in the longitudinal (Hx, parallel to the current) or transverse (Hy, perpendicular to the current) directions. In the following, we define positive and negative quantities with respect to the x-axis as defined in Fig. 1a. Optical Kerr microscopy in differential mode34 was used to image the position of the domain wall as it was moved along the nanowire in response to the current pulses. The domain-wall position was determined from these images by automated analysis of the Kerr contrast along the nanowire. The domain-wall velocity vDW was then determined, assuming that the domain wall moved only during the current pulses, and using a linear fit of the domain-wall position versus the integrated current pulse length, tCP. The standard deviation of the differential velocity values calculated for all points of the domain-wall position versus tCP curves was used to determine the error bars of the measured velocity.

Figure 1: Current-driven domain-wall motion in the presence of a magnetic field.
figure 1

Domain-wall motion versus current density in response to sequences of 5 ns current pulses in the presence of external magnetic fields applied along, perpendicular and transverse to the nanowire. a, Optical image of a typical device. Devices comprise a nanowire (length, 50 µm; width, 2 µm), connected at both ends to wider regions that are used as bond pads for electrical connections. Domain-wall motion and current directions are along the x-axis. Positive values are defined with respect to this axis. b, Domain-wall velocity for fields applied in the z-direction for Hz = 5 Oe (red squares), 0 Oe (black diamonds) and −5 Oe (blue circles). c,d, Data for ↓↑ (c) and ↑↓ (d) domain walls in the presence of transverse fields Hy of −2.8 kOe (red squares), 0 kOe (black diamonds) and +2.8 kOe (blue circles). e,f, Data for ↓↑ (e) and ↑↓ (f) domain walls in the presence of longitudinal fields Hx of −2.8 kOe (red squares), −1.3 kOe (green triangles), 0 kOe (black diamonds), +1.3 kOe (orange triangles) and +2.8 kOe (blue circles). The error bars in b–f represent the standard deviation.

Full size image

The results of typical velocity measurements are shown in Fig. 1b–f as a function of the current density J for different values of the external field applied in the x-, y- and z-directions. The structure of the film used in these experiments was as follows: 20 Å TaN/15 Å Pt/3 Å Co/7 Å Ni/1.5 Å Co/50 Å TaN. The current pulses were 5 ns long. Without an applied field (Fig. 1b–f, black diamonds), the domain walls move along the direction of the current flow. The effect of an applied field depends strongly on its orientation. When the magnetic field is applied along the easy axis its magnitude is limited to values smaller than the domain-wall propagation field, which is typically ∼10 Oe for these devices. The resulting vDW versus J curves are simply offset by a constant value that is approximately proportional to the magnitude and sign of Hz (Fig. 1b). This behaviour can be readily understood because Hz favours either ↑ or ↓ domains, depending on its sign. Note that this behaviour is quite distinct from that observed for domain-wall motion driven by bulk STT in the adiabatic limit, where vDW has been found to be independent of Hz for a wide range of values35.

When the field is applied in the plane along either the x- or y-directions, much larger fields can be applied without causing any motion of the domain wall when no current is applied. Surprisingly, however, when the current is applied we find that the field has a remarkably strong influence on the domain-wall velocity, with very different results for fields applied along the x- and y-directions. Along y (Fig. 1c,d) the effect of the field is independent of domain-wall configuration (that is, whether ↑↓ or ↓↑) but depends on the current direction. For positive current, vDW increases for positive fields and decreases for negative fields, whereas for negative currents the effects are reversed. Along x the influence of the field is even more dramatic (Fig. 1e,f) and the effects are opposite for the two different domain-wall configurations. Moreover, whereas along y, the direction of domain-wall motion remained the same for all fields, along x the direction of domain-wall motion can even be reversed by application of the field (Fig. 1e,f). To understand the origin of this remarkable behaviour, in Fig. 2 we replot the data from Fig. 1 as a function of the applied field, for constant values of current density. These plots reveal the distinct symmetries and functional dependencies of vDW on Hx and Hy. In particular, vDW varies linearly on Hx with a slope that increases with the magnitude of the current density (Fig. 2a,c) and a sign that depends on the current direction, that is vDW(Hx, J) = −vDW(Hx, −J). As can be clearly seen from Fig. 2a for ↓↑ domain walls, all the vDW versus Hx curves intersect at a single point where vDW = 0 at a particular crossing field HCR ≈ −1.9 kOe. Similar behaviour is found for ↑↓ domain walls, but whereas HCR has the same magnitude it has the opposite sign. In contrast, the dependence of vDW on Hy is nonlinear (Fig. 2b,d) but we find that vDW(Hy, J) = −vDW(−Hy, −J).

Figure 2: Chiral internal longitudinal field.
figure 2

Dependence of domain-wall motion on the configuration of the domain wall versus strength and direction of the external magnetic field. a,c, Data as a function of longitudinal field Hx for ↓↑ (a) and ↑↓ (c) domain walls. b,d, Results as a function of transverse field Hy. From top to bottom, the different curves correspond to current densities of 2.5 A cm−2 (red triangles), 1.5 A cm−2 (blue triangles), 1 A cm−2 (green triangles), −1 A cm−2 (green circles), −1.5 A cm−2 (blue circles) and −2.5 × 108 A cm−2 (red circles). e,f, Domain-wall velocity versus Hx (e) and Hy (f). Blue and red symbols represent ↓↑ and ↑↓ domain walls, respectively. Triangular and circular symbols correspond to positive and negative currents, respectively. The current density is ∼1.5 × 108 A cm−2. The error bars in all panels represent the standard deviation.

Full size image

A detailed comparison of ↑↓ and ↓↑ domain walls is given in Fig. 2e,f. As discussed above, in the absence of an external field, both ↑↓ and ↓↑ domain walls move in the same direction with current. This is still the case with a field applied along y, but is no longer true with the field applied along x. We find for the ↑↓ and ↓↑ domain walls that vDW(↑↓, Hx, J) = vDW(↓↑, −Hx, J). Most importantly, although the crossing fields for ↑↓ and ↓↑ domain walls are identical, they have opposite signs.

Similar results are obtained for Ir and Pd underlayers, although the domain walls in these cases move much more slowly than for Pt underlayers. However, a completely different result is found for Au underlayers (Supplementary Section S1 and Fig. S1). In this case, domain-wall motion is along the direction of electron flow and is consistent with the conventional bulk STT mechanism. Furthermore, the role of the longitudinal and transverse fields is completely different from that we find for Pt, Ir and Pd underlayers. For the case of Au underlayers, vDW decreases slightly with increasing field, irrespective of the orientation of the field along x or y or indeed its polarity (positive or negative), and irrespective of domain-wall configuration ( ↑↓ or ↓↑ ).

One-dimensional model of domain-wall dynamics

To understand the origin of these results we used the one-dimensional model of domain-wall dynamics, including SHE-STT as well as longitudinal and transverse applied fields. For simplicity we did not include a Rashba field, which, in any case, can be simply described by a field along y that has a magnitude proportional to the current. Moreover, a Rashba field cannot account for the crossing fields that we find along x. Indeed, we rely on the one-dimensional model not to provide a quantitative fit to our data, but rather to provide insight into the key physical phenomena underlying our experimental observations. In the one-dimensional model, the Landau–Lifshitz–Gilbert equation is solved assuming that the static domain-wall profile is preserved during its motion. Within this approximation, the domain-wall dynamics can be described by using only two variables, the position of the domain-wall centre of mass q and a domain-wall tilt angle ψ, which plays the role of a conjugate momentum. The equations of motion are presented in Supplementary Section S2. The key parameters of the model are of two types. The first parameters are magnetic quantities, and include saturation magnetization MS, domain-wall width Δ and in-plane anisotropy field HK (which is distinct from the PMA field). HK arises from magnetostatic interactions, which lift the degeneracy between Bloch and Néel-type domain walls (for which the magnetization rotates in the plane perpendicular or parallel to the nanowire). The second parameters are spin-transport parameters, and include the spin torque parameter u, which is proportional to the current density J and the spin polarization of the current, and the spin Hall angle θSHE. The SHE-STT is proportional to JθSHE. These parameters, and the values used in the one-dimensional model, are discussed in Supplementary Sections S2–S4 and Figs S2–S4.

The results of the model are presented in Fig. 3. The domain-wall velocity is shown as a function of the longitudinal field for positive and negative currents (triangles and circles, respectively) and for ↑↓ and ↓↑ domain walls (red and blue symbols, respectively). Figure 3a,b shows results for positive and negative values of θSHE, respectively. Closely resembling the experimental results, vDW varies linearly with Hx, with a slope that changes sign for positive and negative currents and also for ↑↓ and ↓↑ domain walls. The slope is also reversed when the sign of θSHE is reversed. However, there is a major discrepancy with the experimental results: in the absence of any applied field, ↑↓ and ↓↑ domain walls move along the direction of electron flow, contrary to the experimental findings. The domain walls move at Hx = 0 only because of the conventional volume STT that we included in the model. Without any volume STT we find that the domain walls do not move at Hx = 0, but the slope of vDW versus Hx is not affected because it does not depend on the volume STT term (Supplementary Section S2). To reconcile the experimental data with the model, we must include an effective longitudinal field acting on the domain wall, the sign and magnitude of which are such that the direction of domain-wall motion is reversed from electron to current direction at Hx = 0. Furthermore, this offset field must have the same amplitude but opposite sign for ↑↓ and ↓↑ domain walls in order that the two domain-wall configurations move in the same direction at Hx = 0 (Fig. 3a,b). Indeed, it is easy to see from Fig. 3a that if the same offset field were applied to both ↑↓ and ↓↑ domain walls, these domain walls would move at different velocities and may even move in opposite directions at Hx = 0. For the purposes of illustration, Fig. 3c,d shows the same results as in Fig. 3a,b, but with the curves for ↑↓ and ↓↑ domain walls offset by ±2.5 kOe, respectively. The resulting curves are now in excellent qualitative agreement with the experimental results shown in Fig. 2e. (Note that the sign of the offset field is reversed when θSHE changes sign.) The model also reproduces qualitatively the transverse field dependence of the domain-wall velocity (Supplementary Fig. S4).

Figure 3: One-dimensional model of domain-wall dynamics.
figure 3

An analytical one-dimensional model is used to calculate the current-driven domain-wall velocity as a function of longitudinal fields Hx in the presence of SHE-STT. a,b, Results for opposite signs of the spin Hall angle. Red and blue symbols represent ↑↓ and ↓↑ domain walls, respectively. Triangles and circles correspond to positive and negative currents. These results reproduce most features of our experiments, with the major difference that domain walls move along the electron flow in zero external field. c,d, To mimic the experimental data, an internal longitudinal offset field of ±2.5 kOe is included. This offset field has opposite signs for ↑↓ and ↓↑ domain walls. The sign of the offset field is also reversed when the sign of the spin Hall angle is reversed. These offset fields favour Néel domain walls, that is, with their magnetization along the nanowires. e, They also favour one chiral rotation direction for both ↑↓ and ↓↑ domain walls, as shown schematically. The chiral nature of the two neighbouring Néel domain walls shown is preserved by the change in direction of the longitudinal moment (purple) within the domain walls.

Full size image

We now show that a DMI at the Co/Pt interface can account for these offset fields. The DMI is an antisymmetric exchange interaction that is produced by a spin–orbit interaction in structures with broken inversion symmetries. Evidence for DMI has been found, for example, in very thin Fe films deposited on W27. In the context of domain walls, it has been shown that DMI favours not only the domain-wall structure, whether Néel or Bloch, but also the magnetization rotation direction within the domain wall, that is, the domain wall's chirality (Fig. 3e)27. In the framework of the one-dimensional model, the DMI plays the role of a longitudinal field Hx, the direction of which is reversed for ↑↓ and ↓↑ domain walls.

Role of proximity-induced magnetic moment

To further our understanding of the mechanism of domain-wall motion, we explored the role of material parameters on the dependence of vDW on Hx. First, we varied the thickness of the Pt layer to tune the strength of the PMA constant. Figure 4a,b shows results for two devices with 10- and 30-Å-thick Pt underlayers, respectively. Qualitatively, the dependences of vDW on Hx are similar, but the values of HCR and the slopes of the vDW versus Hx curves are significantly different: HCR increases with increasing Pt thickness, whereas the slope decreases. Both these quantities, as well as the PMA constants, are shown in Fig. 4c–e as a function of Pt layer thickness. Interestingly, the dependences of HCR and PMA are closely related. In contrast, the slope is inversely related to the PMA, in good agreement with the one-dimensional model, which predicts that the slope is proportional to the domain-wall width Δ, and thus should vary as 1/K1/2, consistent with our experimental results (Supplementary Section S2). The DMI originates from the Pt/Co interface and is intimately tied to the proximity-induced magnetic moment (PIM) in Pt. The role of the Co/Pt interface is shown very directly by inserting a thin Au spacer layer at this interface, which suppresses the PIM in Pt. We find that HCR decreases rapidly as the thickness of the Au layer is increased, to nearly zero for a Au layer only ∼4 Å thick. Again, the variations of the PMA field and HCR are closely related (Fig. 4f–h).

Figure 4: Role of underlayer.
figure 4

The influence of the underlayer on current-driven domain-wall motion is investigated by varying the thickness of the Pt underlayer and by introducing a thin Au spacer layer between the Pt and Co. a,b, Data for Pt layers with thicknesses of 10 and 30 Å, respectively. Red and blue symbols represent ↑↓ and ↓↑ domain walls, respectively. Triangles and circles correspond to positive and negative currents. The current density used here is ∼2.0 × 108 A cm−2. c–e, Slope of the vDW versus Hx curves, the crossing field HCR and the perpendicular anisotropy constant K, as derived from magnetization measurements of blanket films, as a function of the thickness of the Pt layer. f–h, The same quantities as a function of the thickness of a Au spacer layer inserted between the Pt layer (thickness, 15 Å) and the Co layer (thickness, 3 Å). The error bars in a and b represent the standard deviation. The error bars in c,d and f,g represent the standard deviation of the linear fits to each of the four datasets in a and b, respectively.

Full size image

Influence of SHE and DMI from top and bottom interfaces

According to our model, it should be possible to separately vary the SHE-STT and the DMI to adjust the domain-wall dynamics. In the structure discussed above, both the SHE-STT and the DMI originate from the bottom Pt/Co interface. By capping the stack with another Pt layer and by adjusting the thicknesses of the bottom and top Pt layers, we can change the sign of the SHE-STT14. The data shown in Fig. 5 were obtained using a structure in which the capping Pt layer was 20 Å thick and the bottom Pt layer was only 5 Å thick. Accordingly, most of the SHE-induced spin current should originate from the top Pt layer and the sign of the SHE-STT should be reversed. Indeed, we find that the slopes of the vDW versus Hx curves are reversed compared with our previous results. When the thickness of the Co layer at the bottom Pt/Co interface is larger than that of the top Co layer (Fig. 5a), the DMI interaction originates from the bottom Pt/Co, and HCR has the same sign as in the data discussed above. Thus, because HCR is unchanged and the slope is reversed, the direction of domain-wall motion is reversed compared with the previous data, and the domain walls move along the direction of electron flow at Hx = 0. In contrast, when the top Co layer is the thickest (Fig. 5b), the DMI interaction arises primarily from the top Co/Pt interface. As a result, both HCR and the slopes are reversed, such that the direction of domain-wall motion at Hx = 0 remains along the current flow. From these data, we conclude that for Pt/Co interfaces, domain-wall motion is along the current flow when both the DMI and the SHE-STT originate predominantly from the same interface, irrespective of whether this interface is at the top or bottom of the stack. In contrast, domain-wall motion is along the direction of electron flow if the DMI and the SHE-STT originate from opposing interfaces (Fig. 5c).

Figure 5: Symmetry breaking at top and bottom interfaces.
figure 5

By tuning the thicknesses of the Pt and Co layers in the magnetic stack, both the SHE-STT and the DMI interaction can be adjusted independently, thereby enabling the direction of domain-wall motion to be determined. a,b, Data for two different PMA stacks, with their detailed structures shown schematically. Thicknesses of the layers are given in Å. Red and blue symbols represent ↑↓ and ↓↑ domain walls, respectively. Triangles and circles correspond to positive and negative currents. The current density used is ∼1.8 × 108 A cm−2. Interfaces that are dominant for SHE and DMI are indicated by an arrow and a dark grey bar, respectively. Because the top Pt layer is much thicker than the bottom one, the SHE-STT originates predominantly from the top interface. As a result, the slopes of the vDW versus Hx curves are reversed compared with the cases shown in Figs 2 and  4. Depending on the thicknesses of the top and bottom Co layers, the DMI field arises primarily from the top (a) or bottom (b) interface. c, The direction of domain-wall motion at zero external field depends on both the SHE-STT and DMI fields, as indicated in the ‘truth table’. The error bars in a and b represent the standard deviation.

Full size image

Conclusions

We have shown that domain walls are driven by current in ultrathin PMA nanowires by a combination of two phenomena, both derived from spin–orbit coupling. Most importantly, we find compelling evidence that the domain walls are subjected to an effective local longitudinal magnetic field that arises from a PIM in Pt at the Co/Pt interfaces. One possible origin of this effective field is the Dzyaloshinskii–Moriya interaction, which, by symmetry, must be of opposite sign at the top and bottom Pt/Co and Co/Pt interfaces, respectively. This interaction locks the chirality of the domain walls so that successive domain walls along the nanowire have the same handedness. The handedness of the domain walls will be determined by which of the top and bottom interfaces is the dominant one. The SHE-STT thus drives all the domain walls along the nanowire in the same direction, which would not otherwise be the case were the chirality of the domain walls not locked. Because the sign of the SHE-STT is also opposite for the top and bottom Co/Pt interfaces, the direction of domain-wall motion depends on which of these interfaces is dominant. The combined effects of the DMI and SHE-STT at the top and bottom nanowire interfaces are summarized in the truth table in Fig. 5c.