Left-handed polarized spin waves in ferromagnets induced by spin-transfer torque

Polarization is a fundamental property of waves that refers to the orientation of the oscillations. It has been widely used to encode information in photonics and phononics. However, the polarization of spin waves is rarely used yet in magnonics. The reason for this is that only the right-handed polarized spin waves can be accommodated in ferromagnets. Here, we report that stable left-handed polarized spin waves can be introduced into ferromagnets if a spin-polarized electrical current is presented. The right-handed and left-handed polarized spin waves coexist when the current density is larger than a critical value while the system stays stable. The results are confirmed by micromagnetic simulations. This work provides playgrounds to study spin waves and points to findings for future experimental studies.

Figure 1

Dispersion relations of spin waves at different current. The curves 1, 2, and 3 correspond to the $c_j=0,-323$ and $-808\mathrm{m}/\mathrm{s}$, respectively. The dotted lines represent the analytical results calculated from Eqs. (5) and (6). $f=\omega /2\pi$.

Figure 2

Phase diagram for the RPSW and LPSW and the spin-wave stability.

Figure 3

Waveforms and the spatial Fourier transformation at $t=50\mathrm{ns}$. (a), (d) for $c_j=-323\mathrm{m}/\mathrm{s},f=1\mathrm{GHz}$; (b), (e) for $c_j=-808\mathrm{m}/\mathrm{s},f=1\mathrm{GHz}$; (c), (f) for $c_j=-808\mathrm{m}/\mathrm{s},f=5\mathrm{GHz}$. (g) Presentation of the trajectories of the magnetization precession at different sites when $c_j=-808\mathrm{m}/\mathrm{s}$ and $f=1\mathrm{GHz}$.

Figure 4

Waveforms for $m_x$ and $m_y$ components at $t=50\mathrm{ns}$ excited by field $h_x={h_x}_0\cos (2\pi ft-ky)$ with ${h_x}_0=0.05\mathrm{mT},f=1\mathrm{GHz}$, and $k=k_{-}=0.022\mathrm{n}{\mathrm{m}}^{-1}$ (a); $k=k_{+}=-0.003\mathrm{n}{\mathrm{m}}^{-1}$ (c). The precession trajectories of the magnetization at $y=5000\mathrm{nm}$ when $k=k_{-}=0.022\mathrm{n}{\mathrm{m}}^{-1}$ (b) and $k=k_{+}=-0.003\mathrm{n}{\mathrm{m}}^{-1}$ (d).

Figure 5

Time dependence of the average oscillation amplitude of magnetization.