Magnon current generation by dynamical distortion

The interaction between spin and nanomechanical degrees of freedom attracts interest from the viewpoint of basic science and device applications. We study the magnon current induced by the torsional oscillation of ferromagnetic nanomechanical cantilever. We find that a finite Dzyaloshinskii-Moriya (DM) interaction emerges by the torsional oscillation, which is described by the spin gauge field, and the DM interaction leads to the detectably large magnon current with frequency the same as that of the torsional oscillation. Our theory paves the way for studying torsional spin-nanomechanical phenomena by using the spin gauge field.

Figure 1

Schematic setup of our theory. Considering that an external force excites the torsional oscillation mode, which is described by $\chi (z,t)$, we show that the magnon current ${\mathit{j}}_m\left(t\right)$ is induced by the torsional oscillation.

Figure 2

(a) Schematic description of the magnetic anisotropy vector ${\widehat{n}}_i$ changing by the torsional distortion. The gray dotted lines with arrows represent the coordinate axis in the laboratory frame, the blue lines with arrows describe the coordinate axis fixed in the cross section of the sample, and each red arrow stands for the projection of the anisotropy vector into each cross section of the sample. The red arrows do not change in the coordinate fixed in the sample but are modulated in the laboratory frame. (b)–(e) The spatial profile of the torsional oscillation angle $\chi (\mathit{r},t)$ of (b) the lowest, (c) second lowest, and (d) third lowest modes at a certain time, with (e) the schematic configuration of the sample ferromagnet. We can see that the torsional oscillation angle depends only on the length direction, not on the width direction.

Figure 3

Temperature dependence of the function $F\left(\beta \mathrm{\Delta }\right)$ with the gap $\mathrm{\Delta }/k_{\mathrm{B}}\simeq 0.67\mathrm{K}$ for YIG [40].

Figure 4

(a) Schematic description of the possible experimental setup, where a nanomechanical beam structure of ferromagnetic insulator is attached by a piezoelectric actuator and by a heavy metal in which the spin Hall angle is large. The piezoelectric actuator excites the torsional oscillation of the beam, which induces the magnon current and then the inverse spin Hall current is detected in the heavy metal. (b) Spatial profile of the torsional oscillation angle, and (c) the corresponding spatial profile of the magnon current generated by the torsional oscillation, where $L$ is the length of the beam. We note that the magnon current takes a maximum value at the edge of the sample.