Domain-wall step motors: Controlling the motion of magnetic domain walls using patterned magnetic films

Magnetic domain walls can move when driven by an applied magnetic field. This motion is important for numerous devices, including magnetic recording read/write heads, transformers, and magnetic sensors. A magnetic film with a sawtooth profile localizes magnetic domain walls in discrete positions at the narrowest parts of the film. We propose a controllable way to move these domain walls between these discrete locations by applying magnetic-field pulses. A similarly patterned magnetic film attached to a larger magnetic element at one end of the film can operate as an XOR logic gate.

Figure 1

(Color online) (a) 3D sketch of the sample, indicating the height $l\left(x\right)$ and width $s$. Since the sample is mirror-symmetric along the $x$ direction, hereafter we only draw the top part, to save space. (b) Schematic diagram of a magnetic domain wall (red dashed vertical line) moving in a triangular-patterned film (here we only show its upper half). The magnetic domain wall separates regions having different orientations of the magnetization (shown by the up and down arrows). This wall can be shifted from one minimum-thickness location to another one by applying an external magnetic-field pulse. This domain-wall motion is easily controllable and robust to small variations of the magnetic-field pulse, e.g., possible errors in either the duration $\Delta t$ or the amplitude $H_0$ of the pulses (see text). These pulses can be generated by an external solenoid magnet (not shown here).

Figure 2

Controllable discrete shift of a domain-wall location vs the duration of the applied driving pulse, calculated using Eqs. (7, 10). The long flat plateaus indicate the robustness of the proposed magnetic domain-wall step motor to errors in the applied pulse time $\Delta t$ and intensity $h_0$.

Figure 3

(Color online) Schematic diagram of a magnetic logic gate. When applying a magnetic field, the entire patterned magnetic sample can be set to either its “0” or “1” state. This structure can work as an XOR gate if both ac and dc magnetic fields are applied: $H_{\mathrm{dc}}+H_{\mathrm{ac}}\left(t\right)$. The inputs of the XOR gate are (i) an applied dc field and (ii) the magnetization of the larger part of the structure. Then an ac field is added to start the XOR operation. The output can be either 0 (no domain wall) or 1 (a domain wall is nucleated in the sample and oscillates). This MDW oscillation corresponds to the “1” output state and can generate a voltage in a pick-up coil. Thus, the moving domain wall exists either for $H_{\mathrm{dc}}<0$ and state “1” or $H_{\mathrm{dc}}>0$ and state “0.”