Laser-induced torques in metallic ferromagnets

We study laser-induced torques in bcc Fe, hcp Co, and $L{1}_0$ FePt based on first-principles electronic structure calculations and the Keldysh nonequilibrium formalism. We find that the torques have two contributions, one from the inverse Faraday effect (IFE) and one from the optical spin-transfer torque (OSTT). Depending on the ferromagnet at hand and on the quasiparticle broadening the two contributions may be of similar magnitude, or one contribution may dominate over the other. Additionally, we determine the nonequilibrium spin polarization in order to investigate its relation to the torque. We find the torques and the perpendicular component of the nonequilibrium spin polarization to be odd in the helicity of the laser light, while the spin polarization that is induced parallel to the magnetization is helicity independent. The parallel component of the nonequilibrium spin polarization is orders of magnitude larger than the perpendicular component. In the case of hcp Co we find good agreement between the calculated laser-induced torque and a recent experiment.

Figure 1

A circularly polarized light pulse propagates in the $x$ direction and hits a Co/Pt bilayer. The magnetization direction $\widehat{\mathit{M}}$ is along the $z$ axis. The laser-induced torque $\mathit{T}$ has two components: (a) The in-plane component ${\mathit{T}}_{\mathrm{ip}}$ can be attributed to an effective magnetic field ${\mathit{B}}_x^{\mathrm{eff}}$ in the $x$ direction. ${\mathit{T}}_{\mathrm{ip}}$ leads to an initial in-plane tilt of $\widehat{\mathit{M}}$. (b) The out-of-plane component ${\mathit{T}}_{\mathrm{oop}}$ can be attributed to the $y$ component ${\mathit{B}}_y^{\mathrm{eff}}$ of a laser-induced effective magnetic field and leads to an initial out-of-plane tilt of $\widehat{\mathit{M}}$.

Figure 2

Laser-induced effective magnetic fields $B_x^{\mathrm{eff}}$ (left column) and $B_y^{\mathrm{eff}}$ (right column) in Fe, Co, and FePt as a function of broadening $\mathrm{\Gamma }$ at $I=10$ GW/${\mathrm{cm}}^2$. $\widehat{\mathit{M}}$ is in the $z$ direction. $\lambda =+$ and $\lambda =-$ denote left- and right-circularly polarized light, respectively. In the case of Co, results are shown for the $c$ axis in the $z$ direction $\left(c\parallel z\right)$ and the $c$ axis in the $x$ direction $\left(c\parallel x\right)$.

Figure 3

Laser-induced effective magnetic fields $B_x^{\mathrm{eff}}$ (left) and $B_y^{\mathrm{eff}}$ (right) in Fe as a function of SOI scaling factor $\xi$ at $I=10$ GW/${\mathrm{cm}}^2$. $\widehat{\mathit{M}}$ is in the $z$ direction. $\lambda =+$ and $\lambda =-$ denote left- and right-circularly polarized light, respectively.

Figure 4

Laser-induced spin polarization $\delta S_x$ (left column) and $\delta S_y$ (right column) in Fe, Co, and FePt as a function of broadening $\mathrm{\Gamma }$ at $I=10$ GW/${\mathrm{cm}}^2$. $\widehat{\mathit{M}}$ is in the $z$ direction. $\lambda =+$ and $\lambda =-$ denote left- and right-circularly polarized light, respectively. In the case of Co, results are shown for the $c$ axis in the $z$ direction $\left(c\parallel z\right)$ and the $c$ axis in the $x$ direction $\left(c\parallel x\right)$.

Figure 5

Laser-induced spin polarization $\delta S_z$ in Fe, Co, and FePt as a function of broadening $\mathrm{\Gamma }$ at $I=10$ GW/${\mathrm{cm}}^2$. $\widehat{\mathit{M}}$ is in the $z$ direction. $\lambda =+$ and $\lambda =-$ denote left- and right-circularly polarized light, respectively. In the case of Co, results are shown for the $c$ axis in the $z$ direction $\left(c\parallel z\right)$ and the $c$ axis in the $x$ direction $\left(c\parallel x\right)$.