Terahertz spin dynamics driven by an optical spin-orbit torque

Spin torques are at the heart of spin manipulations in spintronic devices. Here, we examine the existence of an optical spin-orbit torque, a relativistic spin torque originating from the spin-orbit coupling of an oscillating applied field with the spins. We compare the effect of the nonrelativistic Zeeman torque with the relativistic optical spin-orbit torque for ferromagnetic systems excited by a circularly polarized laser pulse. The latter torque depends on the helicity of the light and scales with the intensity, while being inversely proportional to the frequency. Our results show that the optical spin-orbit torque can provide a torque on the spins, which is quantitatively equivalent to the Zeeman torque. Moreover, temperature-dependent calculations show that the effect of optical spin-orbit torque decreases with increasing temperature. However, the effect does not vanish in a ferromagnetic system, even above its Curie temperature.

Figure 1

ZT and OSOT for a single spin (big red arrow) excited by an elliptically polarized laser pulse. The fields and torques are represented by yellow and blue arrows, respectively. Due to the presence of elliptical polarization, the ZF and ZT are drawn as blurry.

Figure 2

The dynamical effects of ZT and OSOT for Fe at a maximum applied field of 10 T. The calculations include (a) only ZT, (b) only OSOT, and (c) both ZT and OSOT. The first row shows the applied ZF which has $y$ and $z$ components, the second row represents the induced OSOF which has only an $x$ component. The other three rows show the change in magnetization along $x$, $y$, and $z$ components, respectively.

Figure 3

Maximum of the magnetization change as a function of applied Zeeman field for the application of circular polarized THz pulses (absolute values). Lines are fits to the data according to a single (double) power law, see Table 1 for coefficients.

Figure 4

OSOT effects at finite temperature. Top panel: The OSOT-induced field. Bottom panel: The corresponding spin dynamics for the change of $m_y$ at $T=0$ and $T=0.73\times T_{\text{C}}$ (0 K and 1000 K).

Figure 5

Temperature dependence of OSOT, by the difference between the maximum changes of $m_y$ due to right and left polarized light pulses at maximum Zeeman field amplitude of 10 T. For comparison, the right axis shows the equilibrium magnetization.

Figure 6

The dynamical effects of ZT and OSOT have been calculated for Fe including the uniaxial anisotropy at an applied field of 10 T. The calculations have been performed accounting (a) only Zeeman effect, (b) only OSOT effect and (c) both Zeeman and OSOT effects. In all plots, the first row represents the induced spin-orbit field which has only $x$ component, and rows two and three show the applied ZF which has $y$ and $z$ components. The other three rows show the change in magnetization along $x$, $y$, and $z$ components, respectively. The orange and blue colors represent the action of right- and left-circular pulses.