Field-driven evolution of chiral spin textures in a thin helimagnet nanodisk

The magnetic field-driven evolution of chiral spin textures in a thin helimagnet nanodisk with varied size is investigated by means of Monte Carlo simulation. It is demonstrated that the complex spin texture may simply be regarded as the superposition of the edged state with the in-plane spin orientation perpendicular or parallel to the edge and the bulk state with features similar to two-dimensional chiral magnetic films. With the increase of the external field, the proportion of the parallel spins of the edge state increases, and the spin textures finally transfer into the edged magnetic vortex. The arrangement of skyrmions strongly depends on the disk size. In addition, the uniaxial anisotropy and dipolar coupling in certain ranges are able to stabilize a special magnetic vortex with the skyrmionic core, while the disk size is comparable to the wavelength of helix state.

Figure 1

(a) The normalized magnetization $m_z$ and chirality $\tau$ of the disk for $R=10$ as a function of magnetic field $H$, discontinuous curves $m_z\left(H\right)$ and $\tau \left(H\right)$, indicating different spin textures; the corresponding snapshots of out-of-plane magnetization $m_z$ are shown for each function. The full spin orientation for three typical magnetic fields: (b) for zero field $H=0$, the complex spin textures may be regarded as the superposition of the edged state with in-plane spin orientation perpendicular or parallel to the edge and bulk state with the features of helix; (c) for moderate field $H=0.24$, the edged state and helix state transferred into the edged vortex and bimeron, respectively; and (d) for high field $H=0.8$, the skyrmions in the center of the disk transferred into the ferromagnetic state, while the edged vortex still exists.

Figure 2

(a) The phase diagram as the functions of the external field $H$ and disk size$R$ based on the normalized curves$\tau (H,R)$. (b) The dependence of the arrangements of skrymions on the disk size, while $R\le 5$, with no skyrmions formed. With increasing $R$, the skyrmion number increases discontinuously and sensitively depends on the disk size. For comparison, the spin arrangement of skyrmions in 2D films is also displayed $(L=40,H=0.4)$.

Figure 3

(a) The magnetic phase diagram as the functions of $d$ and $K$ for fixed $D$ and $J$ and $R=7$. It is composed of four regions: (I) distorted helix state, (II) chiral soft magnetic vortex for stronger dipolar couplings, (III) chiral stripe domain for stronger uniaxial anisotropy, and (IV) special magnetic vortex with skyrmion core. The corresponding snapshots of spin arrangements are shown for each function. (b) The dependence of existing magnetic intervals of skyrmions on the dipolar coupling constant $d$. (c) Typical evolution of spin textures in region (IV). The magnetic phase diagram as the functions of $d$ and $K$ for fixed $D$ and $J$ for (d) $R=10$ and (e) $R=15$, with increasing $R$; the region (IV) shrinks.