Electric field induced domain-wall dynamics: Depinning and chirality switching

We theoretically study the equilibrium and dynamic properties of nanoscale magnetic tunnel junctions (MTJs) and magnetic wires, in which an electric field controls the magnetic anisotropy through spin-orbit coupling. By performing micromagnetic simulations, we construct a rich phase diagram and find that, in particular, the equilibrium magnetic textures can be tuned between Néel and Bloch domain walls in an elliptical MTJ. Furthermore, we develop a phenomenological model of a quasi-one-dimensional domain wall confined by a parabolic potential and show that, near the Néel-to-Bloch-wall transition, a pulsed electric field induces precessional domain-wall motion which can be used to reverse the chirality of a Néel wall and even depin it. This domain-wall motion controlled by electric fields, in lieu of applied current, may provide a model for ultralow-power domain-wall memory and logic devices.

Figure 1

The MTJ stack modeled by micromagnetic simulations: The free layer/insulator interface gives rise to an interfacial anisotropy $K^{\perp }$ with vertical easy axis, controlled by a voltage $V$.[4] Pinned layer is kept fixed to point along $-x$.

Figure 2

Schematics of the relevant equilibrium configurations: (a) In-plane state with canted edges, (b) perpendicular state, (c) Néel domain wall, (d) Bloch domain wall, and (e) the intermediate domain wall where $\varphi$ is the angle of magnetization at the center of the ellipse with respect to the $x$ axis. The lower right hand frame (f) depicts the domain-wall width, i.e., the central region delineated with vertical lines, much larger (top) and smaller (bottom) than the semiminor axis of the ellipse corresponding to a Néel and Bloch wall, respectively.

Figure 3

The dependence of energy of equilibrium configurations on the interfacial perpendicular anisotropy: The vertical lines mark approximate boundaries between regions marked I-IV. Region I has only an in-plane state with canted edges [schematically shown in Fig. 2] as a stable state, region II has both Néel domain wall [schematically shown in Fig. 2] and perpendicular (monodomain) states, with domain walls having lower energy. In region III perpendicular states become lower in energy, whereas in region IV the Néel domain wall starts transforming into Bloch form (referred as Bloch-like wall with its micromagnetic configuration, corresponding to $K^{\perp }=9.4$ Merg/cc, also shown in region IV). Here the red and blue colors represent magnetization pointing along positive and negative $z$ axis, respectively, while the white arrows show the magnetization direction in the domain-wall region.

Figure 4

Comparison between micromagnetics and 1D model: (Top panel) The maximum deviation of domain wall from the center $X_{\max }^{\mathrm{DC}}$ obtained for the electric field applied in a steplike fashion. (Bottom panel) The dynamical approach to a Bloch-like wall from the initial configuration of a Néel wall, for the same electric field magnitude in micromagnetic simulations (bottom left) and 1D model (bottom right). Here solid lines depict the position ($X$) while the dashed lines show the angle ($\varphi$) of the domain wall.

Figure 5

Pulse width dependence of maximum domain-wall deviation and depinning: (Top panel) Oscillatory enhancement of maximum deviation of domain wall from center, obtained from micromagnetics for electric field $E=0.65$ V/nm. The dash-dotted horizontal line depicts the long-time maximum deviation ($X_{\max }^{\mathrm{DC}}$) for the same electric field as reference. (Bottom panel) Phase plot depicting the dependence of depinning on the pulse width as obtained within the 1D model for $E=0.65$ V/nm. The extent of the parabolic potential $X_C=50$ nm is marked by the horizontal dash-dot lines while the trajectory for which the pulse is on and off is marked by a dashed and a solid line, respectively. Depinning occurs when the pulse is turned off for $\varphi$ close to 90${}^{\circ }$ (bottom right panel), whereas no depinning occurs when the pulse is turned off for $\varphi$ close to 0${}^{\circ }$ (bottom left panel).

Figure 6

Chirality switching: (Top panel) Switching from state 0, having resistance of $R_{AP}$, to state 1, having a resistance of $R_P$ (along with the respective domain-wall configurations in free layer depicted schematically), obtained via micromagnetic simulation for a pulsed electric field $E=0.65$ V/nm of duration 75 ns. (Bottom panel) Switching trajectory in phase space from 1D model for the switching between state 0 and state 1 for the same electric field.