Magnetization process of chiral magnet: creation and annihilation of skyrmions and anti-skyrmions

By applying a magnetic field to the single-$q$ helical state in the chiral magnet, the skyrmions appear. The topology of the skyrmion is characterized by the skyrmion number $N_{sk}$ defined as $N_{sk} = \int \frac{d^2 r}{4 \pi} {\vec n}_{\vec r} \cdot [ ({ \partial {\vec n}_{\vec r}}/{\partial x})\times ({ \partial {\vec n}_{\vec r}}/{\partial y}) ],$ where ${\vec n}_{\vec r}$ is the unit vector along magnetic moment at ${\vec r}$, assuming the two-dimensional configuration. The single-$q$ helical state is a topologically trivial magnetic texture, i.e., $N_{sk}=0$. Therefore, within the continuous deformation, there is no way to realize the skyrmions from the single-$q$ helical state. We find, by a numerical simulation of Landau-Lifshitz-Gilbert equation, the pair nucleation of skyrmion and anti-skyrmion occurs, and they annihilate to reach the skyrmion crystal-like state or the ferromagnetic state. We show the lives of skyrmion and anti-skyrmion in the dynamics of a quenched chiral magnet.