Chirality-dependent spin-transfer torque and current-induced spin rotation in helimagnets

We have built a theory of the spin-transfer torque (STT) effect in a conductive chiral helical magnet (CHM). It is shown that the STT effect induced by a spin current flowing through CHM leads to the rotation of the CHM magnetization spiral around its axis. The frequency of such rotation of the CHM magnetization is found. The former is expressed in terms of the parameters of the quantum-exchange Hamiltonian that specifies helical magnetic ordering in a conductive crystal. We have showcased that both the direction of rotation of the CHM magnetization and the direction of changes in the shape of the magnetic spiral are determined by the electron flow direction and the chirality of the magnet. The theory developed accounts for the generation of an electromagnetic field when rotating the magnetic spiral in the CHM subjected to an electric current flowing through the helimagnet.

Figure 1

Scheme of the spatial configuration of a simple magnetic spiral of a helimagnet with a chirality vector k in the absence of a magnetic field: (a) a right-handed spiral, chirality is $K=+1$; (b) a left-handed spiral. Chirality is $K=-1$.

Figure 2

Stable conical magnetic spiral formed in a helimagnet subjected to an external magnetic field, the direction of which is given by the unit vector $\mathbf{b}={\mathbf{B}}_{\ell }/|B_{\ell }|$: (a) right-handed spiral, b is parallel to k; (b) right-handed spiral, b is antiparallel to k; (c) left-handed spiral, b is antiparallel to k; and (d) left-handed spiral, b is parallel to k.

Figure 3

Scheme of configurations of a conical magnetic spiral of a helimagnet with chirality k, rotating under the action of an electron flow, the direction of which is given by a unit vector i, in the absence of a magnetic field: (a) right-handed spiral, i is parallel to k; (b) right-handed spiral, i is antiparallel to k; (c) left-handed spiral, i is antiparallel to k; and (d) left-handed spiral, i is parallel to k.

Figure 4

Parameter space plot showing the boundary between two regions corresponding to scenarios I and II, for the case $a>>1$. Region I is in green, and region II is in yellow. The red curve stands for the function ${\overline{\nu }}_D^{(-)}\left({\overline{\nu }}_S\right)$ and the blue curve represents the function ${\overline{\nu }}_D^{(+)}\left({\overline{\nu }}_S\right)$.

Figure 5

Illustration of two scenarios of the behavior of the rotation frequency of the spin spiral with changing the drift velocity of electrons using FeGe as an example. Curve I: ${\overline{\nu }}_S=1$, represents scenario I; curve II: ${\overline{\nu }}_S=0.05$, represents scenario II; dashed curve: ${\overline{\nu }}_S=0.09$, corresponds to the boundary of the regions of existence of scenarios I and II. For all three curves $a=1$ and ${\overline{\nu }}_D=0.05$.

Figure 6

The highest values of the rotation frequency ${\omega }_d$ for the spin spiral (a), (b) and conicity angle ${\theta }_d$ (c), (d) for metallic helimagnets FeGe, MnSi, ${\mathrm{CrNb}}_3{\mathrm{S}}_6$, Dy: (a), (c) $\alpha =0.01$; (b), (d) $\alpha <<\chi \mathrm{\Lambda }$.