Enhanced spin transfer torque effect for transverse domain walls in cylindrical nanowires

Abstract

Recent studies have predicted extraordinary properties for transverse domain walls in cylindrical nanowires: zero depinning current, the absence of the Walker breakdown, and applications as domain wall oscillators. In order to reliably control the domain wall motion, it is important to understand how they interact with pinning centers, which may be engineered, for example, through modulations in the nanowire geometry (such as notches or extrusions) or in the magnetic properties of the material. In this paper we study the motion and depinning of transverse domain walls through pinning centers in ferromagnetic cylindrical nanowires. We use (i) magnetic fields and (ii) spin-polarized currents to drive the domain walls along the wire. The pinning centers are modelled as a section of the nanowire which exhibits a uniaxial crystal anisotropy where the anisotropy easy axis and the wire axis enclose a variable angle ${\ensuremath{\theta}}_{\mathrm{P}}$. Using (i) magnetic fields, we find that the minimum and the maximum fields required to push the domain wall through the pinning center differ by $30%$. On the contrary, using (ii) spin-polarized currents, we find variations of a factor 130 between the minimum value of the depinning current density (observed for ${\ensuremath{\theta}}_{\mathrm{P}}={0}^{\ensuremath{\circ}}$, i.e., anisotropy axis pointing parallel to the wire axis) and the maximum value (for ${\ensuremath{\theta}}_{\mathrm{P}}={90}^{\ensuremath{\circ}}$, i.e., anisotropy axis perpendicular to the wire axis). We study the depinning current density as a function of the height of the energy barrier of the pinning center using numerical and analytical methods. We find that for an industry standard energy barrier of $40\phantom{\rule{0.28em}{0ex}}{k}_{\mathrm{B}}T$, a depinning current of about $5\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{A}$ (corresponding to a current density of $6\ifmmode\times\else\texttimes\fi{}{10}^{10}\phantom{\rule{0.28em}{0ex}}\mathrm{A}/{\mathrm{m}}^{2}$ in a nanowire of $10\phantom{\rule{0.28em}{0ex}}\mathrm{nm}$ diameter) is sufficient to depin the domain wall. We reveal and explain the mechanism that leads to these unusually low depinning currents. One requirement for this depinning mechanism is for the domain wall to be able to rotate around its own axis. With the right barrier design, the spin torque transfer term is acting exactly against the damping in the micromagnetic system, and thus the low current density is sufficient to accumulate enough energy quickly. These key insights may be crucial in furthering the development of novel memory technologies, such as the racetrack memory, that can be controlled through low current densities.