Achiral tilted domain walls in perpendicularly magnetized nanowires

Perpendicularly magnetized nanowires exhibit distinct domain wall types depending on the geometry. Wide wires contain Bloch walls, and narrow wires Néel walls. Here, the transition region is investigated by direct imaging of the wall structure using high-resolution spin-polarized scanning electron microscopy. An achiral intermediate wall type is discovered that is unpredicted by established theoretical models. With the help of micromagnetic simulations, the formation of this wall type is explained.

Figure 1

(a) Scanning electron micrograph of a 70-nm-wide ferromagnetic “bowtie” nanowire. The spin polarization micrographs show the magnetization component along the (b) $z$, (c) $x$, (d) $y$ direction. The black/white contrast shows the direction of the magnetization, as indicated by the arrows. A domain wall is found at the narrowest part of the wire, where also the wire width of $70\mathrm{nm}$ is measured. The wall has magnetization components in both in-plane directions. In addition, a slight canting of the domain wall is observed. Images (c) and (d) were Gaussian filtered to improve visibility.

Figure 2

The magnetization profiles $m_i\left(x\right)$ ($i=x,y,z$) of the 70-nm-wide nanowire as a function of the distance from the center of the wall. The perpendicular and in-plane magnetization components were fitted with the 1D domain wall model and considering the finite resolution of the microscope.

Figure 3

(a) Azimuthal angle $\psi$ vs nanowire width extracted from micromagnetic simulations. Without DMI, the domain wall type is Néel ($\psi =0^{\circ }$) for wires up to $60\mathrm{nm}$, whereas for wires starting from $98\mathrm{nm}$, the type is Bloch ($\psi ={90}^{\circ })$. In the transition region $\psi$ changes continuously. By introducing DMI, Néel walls are stabilized, shifting the start of the transition to $68\mathrm{nm}$ and preventing pure Bloch walls even in 500-nm-wide wires. Our measured domain walls from Table 1 are included as data points. (b) Normalized energy difference vs $\psi$ for a 70-nm-wide wire. $\psi$ was fixed along a line in the $y$ direction in the center of the domain wall (inset) and varied between $0^{\circ }$ and ${90}^{\circ }$ in steps of $1^{\circ }$. The length $l$ of the line of fixed spins varied from $70\mathrm{nm}$ (entire wire width) down to $1\mathrm{nm}$ (only cell at center). The energy is plotted as the difference to the Néel wall and normalized by the energy of a single domain wire.

Figure 4

(a) Top view of a simulated intermediate domain wall in a 70-nm-wide perpendicularly magnetized wire. The out-of-plane component is indicated by color graduation from blue ($+z$) to red ($-z$). The domain wall is slightly wider in the center than at the edges of the wire. (b) Cross-section view at $x=0$. The corresponding magnetization direction is indicated with arrows. At the wire edges, a rotation of the $z$ component of the magnetization is observed. It is opposite for opposite edges, leading to a slight canting and an $\mathsf{S}$-shaped appearance of the wall. Overall, the wall is inclined by $\sim 3^{\circ }$ with respect to the wire's cross section. Since no chiral interaction is involved, an inclination in the opposite direction is equally well possible, provided that the magnetization tilt is also mirrored at the $yz$ plane.