Dynamics of vortex nucleation in nanomagnets with broken symmetry

We investigate the dynamics of magnetic vortex nucleation in sub-100-nm mesoscopic magnets with the aim of establishing an independent control of vortex polarity and chirality. We consider the dynamic behavior of the vortex spin structure in an object with broken symmetry—a Pacman-like nanomagnet shape—proposing a model based on classical electrodynamics and providing a proof by conducting micromagnetic calculations. The model provides evidence that the desired vortex chirality and polarity could be established by applying solely quasistatic in-plane magnetic field along specific directions with respect to the structure's asymmetry. We identify the modes of vortex nucleation that are robust against external magnetic field noise. These vortex nucleation modes are common among a wide range of sub-100-nm magnets with broken rotational symmetry. The results could lead to the practical realization of high density magnetic memories based on magnetic vortices.

Figure 1

Geometry of Pacman-like nanomagnet. The structure is symmetric with respect to reflection plane ${\sigma }_y$.

Figure 2

(a) The magnetization of the Pacman-like nanomagnet is a superposition of the uniform magnetization of a full disk (red arrows) and the magnetization of the missing sector that is equal and opposite to the one of the full disk. (b) The sum of the compensation moments in the sector creates a dipole $m_{\text{cut}}$ which asymmetrically interacts with the local magnetization in the nanomagnet.

Figure 3

Top: Angular dependence of vortex nucleation field. Direction of the nucleated vortex polarity and chirality are also indicated for each quadrant. Bottom: Two different processes of vortex nucleation depending on the initial magnetization direction with respect to PL's symmetry plane ($\varphi ={15}^{\circ }\text{and}\varphi ={75}^{\circ }$). From the uniform magnetization state ($U$) the magnetization transitions to $S$-shape (dots) or $C$-shape (stars) configurations and equilibrates to a vortex state ($V$) with specific polarity and chirality. The snapshot of the intermediate state ($I$) shows the position of vortex core nucleation.

Figure 4

Angular dependence of the in-plane vortex nucleation field $B_{\text{nuc}}$ and threshold out-of-plane field $B_{\text{z}}$ necessary to reverse the polarity of the entering vortex.