Domain wall dynamics in easy-cone magnets

We theoretically and numerically investigate magnetic domain wall dynamics in a nanowire of an easy-cone magnet. The easy-cone domain wall exhibits several distinguishing dynamic features in comparison to the easy-axis domain wall. They are related to the generation of additional chiral spin textures due to the domain wall precession, which occurs commonly for various driving sources such as magnetic fields and spin-transfer torque. We envision that the unique easy-cone domain wall dynamics can enrich the study of magnetic domain walls both for fundamental interest and for device applications.

Figure 1

Easy-cone state and its wall profile. (a) Phase diagram of magnetic state as a function of effective first-order anisotropy $K_{1,\mathrm{eff}}$ and second-order anisotropy $K_2$. (b) Schematic illustration of conically magnetized nanowire. Regions I and III are uniform domain parts where the equilibrium polar angles of magnetization are $\theta ={sin}^{-1}\sqrt{-\frac{K_{1,\mathrm{eff}}}{2K_2}}\mathrm{and}\pi -{sin}^{-1}\sqrt{-\frac{K_{1,\mathrm{eff}}}{2K_2}}$, respectively, whereas region II is domain wall part. (c) Wall profile represented as normalized $M_z$ component of easy-cone (blue open symbols) and PMA (black open symbols) domain wall.

Figure 2

Field-induced domain wall motion in a conically magnetized nanowire. (a) Domain wall velocity (bottom panel) and the number of sub-domain walls (SDs) (top panel) as a function of applied magnetic field. (b) Schematic illustration of easy-cone domain wall profile in the absence (top) and presence (bottom) of magnetic field. (c) Top view of magnetization configuration for $|{\mathit{H}}_{\mathrm{z}}|=60\mathrm{Oe}$. Color code represents the $z$ component of magnetization, $M_z$.

Figure 3

Spin-transfer torque induced domain wall motion in a conically magnetized nanowire. (a) Domain wall velocity as a function of applied current for various nonadiabaticities $\beta =0,\alpha ,\mathrm{and}2\alpha$. (b) Top view of magnetization configuration (top panel) and time evolution of domain wall velocity and the number of SD (bottom panel) for $J_e=5\times {10}^8\mathrm{A}/\mathrm{c}{\mathrm{m}}^2$ and $\beta =0$. Color code represents the $z$ component of magnetization, $M_z$. We use the same parameters of Fig. 1 and $P=0.3$.

Figure 4

Domain wall motion in a conically magnetized nanowire, induced by local spin injection. (a) Schematic illustration of local spin injection in a conically magnetized nanowire. (b) Domain wall velocity as a function of time for various current densities. Easy-cone DW moving (c) away from the injection source (positive velocity) for $j_{\mathrm{inj}}=10.5\times {10}^7\mathrm{A}/\mathrm{c}{\mathrm{m}}^2$ and (d) towards the source (negative velocity in average) for $j_{\mathrm{inj}}=11.5\times {10}^7\mathrm{A}/\mathrm{c}{\mathrm{m}}^2$. Color code represents the $M_z$ component of magnetization.