Unifying Ultrafast Magnetization Dynamics

We present a microscopic model that successfully explains the ultrafast equilibration of magnetic order in ferromagnetic metals at a time scale ${\tau }_M$ of only a few hundred femtoseconds after pulsed laser excitation. It is found that ${\tau }_M$ can be directly related to the so-called Gilbert damping factor $\alpha$ that describes damping of GHz precessional motion of the magnetization vector. Independent of the spin-scattering mechanism, an appealingly simple equation relating the two key parameters via the Curie temperature $T_C$ is derived, ${\tau }_M\approx c_0\hslash /k_B{T}_C\alpha$, with $\hslash$ and $k_B$ the Planck and Boltzmann constants, respectively, and the prefactor $c_0\sim \frac{1}{4}$. We argue that phonon-mediated spin-flip scattering may contribute significantly to the sub-ps response.

Figure 1

Main: experimental development of the induced perpendicular component of $\overrightarrow{M}$ [$\Delta M_z(t)/M_z(0)$] after laser heating a nickel thin film at $t=0$, and starting with $\overrightarrow{M}$ canted out of plane by applying an external field ${\overrightarrow{B}}_{\mathrm{appl}}$. A sub-ps quenching of $M$ is observed followed by a recovery via $e\mathrm{\text{−}}p$ relaxation, and finally, at $t>100\mathrm{ps}$ a damped precession of the magnetization. Insets: precession of an individual spin in the exchange field (left) and of $\overrightarrow{M}$ in the effective field (right).

Figure 2

Temperature dependence of the magnetization within the Weiss model (a), and the function $F(T)$ (b) that scales with ${\tau }_M$ as expressed by (4). (c)–(e) Evolution of electron (blue dashed line), lattice (green dotted line), and spin (red line) temperature for the impurity model (c), and the phonon-mediated model in two limiting cases ${\tau }_M\ll {\tau }_E$ (d) and ${\tau }_M\gg {\tau }_E$ (e), showing the construction of ${\tau }_M$ in the respective cases.