Supercurrent-induced skyrmion dynamics and tunable Weyl points in chiral magnet with superconductivity

Recent studies show superconductivity provides new perspectives on spintronics. We study a heterostructure composed of an $s$-wave superconductor and a cubic chiral magnet that stabilizes a topological spin texture, a skyrmion. We propose a supercurrent-induced spin torque, which originates from the spin-orbit coupling, and we show that the spin torque can drive a skyrmion in an efficient way that reduces Joule heating. We also study the band structure of Bogoliubov quasiparticles and show the existence of Weyl points, whose positions can be controlled by the magnetization. This results in an effective magnetic field acting on the Weyl quasiparticles in the presence spin textures. Furthermore, the tilt of the Weyl cones can also be tuned by the strength of the spin-orbit coupling, and we propose a possible realization of type-II Weyl points.

Figure 1

Heterostructure composed of a chiral magnet and an $s$-wave superconductor.

Figure 2

Dependence of $K_{xx}$ and $K_{zz}$ on the parameter ${\alpha }_{so}$ for $t=1.0,JM=2.0,\mathrm{\Delta }=0.2,\mu =-4.8$, when the direction of the localized spin is $\mathit{n}=(0,0,1)$. Both $K_{xx}$ and $K_{zz}$ increase monotonically as ${\alpha }_{so}$ increases. In the limit of ${\alpha }_{so}/JM\ll 1$, the magnitude of $K_{xx}$ is suppressed compared to $K_{zz}$, which is in agreement with the asymptotic form given by Eq. (21).

Figure 3

Dependence of $K_{xx}$ and $K_{zx}$ on the directional angle $\theta$ that parametrizes the localized spin as $\mathit{n}=(sin\theta ,0,cos\theta )$. The parameters are set as $t=1.0,JM=2.0,\mathrm{\Delta }=0.2,\mu =-4.8$, and ${\alpha }_{so}=0.2$. The diagonal component $K_{xx}$ has an offset value that is independent of $\theta$, and it is well fitted by $K_{xx}=0.118n_x^2+0.150$. The off-diagonal component $K_{xy}$ is fitted by $K_{xy}=0.112n_x{n}_y$.

Figure 4

Phase diagram of Weyl points as a function of chemical potential $\mu$ and the SO-coupling coefficient ${\alpha }_{so}$ with the parameters $t=1.0,JM=2.0,\mathrm{\Delta }=0.2$. In phases denoted by type-I (type-II) Weyl points, a pair of type-I (type-II) Weyl points exists.

Figure 5

Energy spectrum for the parameters $t=1.0,\mathrm{\Delta }=0.2,JM=2.0,\mu =-4.8$, and $\mathit{n}=(0,0,1)$. The Weyl points are at $k=(0,0,\pm k_0)$. (a) and (b) are the energy spectrum in $k_x=k_y=0$ and in the $k_z{k}_x$ plane with the parameter ${\alpha }_{so}=0.6$. A pair of type-I Weyl cones exists in the bands of quasiparticles. (c) and (d) are the energy spectrum in $k_x=k_y=0$ and in the $k_z{k}_x$ plane with the parameter ${\alpha }_{so}=0.8$. A pair of type-II Weyl cones exists.