Femtosecond Laser Excitation Drives Ferromagnetic Gadolinium out of Magnetic Equilibrium

The temporal evolution of the exchange-split ${\Delta }_2$-like $\Sigma$ valence bands of the $4f$-ferromagnet gadolinium after femtosecond laser excitation has been studied using angle-resolved photoelectron spectroscopy based on high-order harmonic generation. The ultrafast drop of the exchange splitting reflects the magnetic response seen in femtosecond magnetic dichroism experiments. However, while the minority valence band reacts immediately, the response of the majority counterpart is delayed by 1 picosecond and is only half as fast. These findings demonstrate that laser excitation drives the valence band structure out of magnetic equilibrium.

Figure 1

Magnetic coupling (left) and calculated exchange-split valence band structure [31] of gadolinium (right). Majority spin band: blue, up arrows. Minority spin band: red, down arrows. The dashed line is the $5d_{z^2}$ majority spin surface state. Bands not seen in ARPES at 36 eV photon energy have been omitted.

Figure 2

Inset: ARPES of Gd at 100 K, taken around normal emission with a photon energy of 35.6 eV. Data were integrated over $k_{\parallel }=\pm 0.15{\AA }^{-1}$ around the $\Gamma$ point (highlighted). Main figure: PE spectra at 3 pump-probe delays fitted with the indicated spectral features. The surface state, the $4f$ level, and the majority (blue) and minority (red) spin components of the valence band are represented as Lorentzians. A linear background accounts for elastic electron scattering from degenerate points in the Brillouin zone. Fitted spectra were convolved with a 150 meV Gaussian instrument function dominated by the XUV spectrum.

Figure 3

(a) Binding energies of the majority and minority spin valence bands and majority surface state as a function of pump-probe delay. Solid lines are sigmoid fits to the initial changes. (b) $\Delta E_{\mathrm{ex}}$ and electron temperature as a function of pump-probe delay. Before the pump pulse the sample was at 100 K and the valence band $\Delta E_{\mathrm{ex}}=740\pm 30\mathrm{meV}$, in agreement with published data [20, 21, 28]. The inset axis shows the change of the electronic temperature extracted from the Fermi edge. Solid lines are exponential fits; error bars show 2 standard deviations; dashed lines mark scale changes.

Figure 4

Laser-driven versus thermal effects in the minority (red, down triangles, right axis) and majority (blue, up triangles, left axis) spin components of the valence band of Gd. During the first 2 ps, the system follows the lower path of each loop to smaller $\Delta E_{\mathrm{ex}}$. The electrons and lattice are then in thermal equilibrium, where they remain until the $4f$ electrons and the lattice equilibrate at $\approx 50\mathrm{ps}$. Between 50 ps and 500 ps, with the electrons, lattice, and spins all in thermal equilibrium, $\Delta E_{\mathrm{ex}}$ recovers as the system cools, moving along the upper paths to the starting position. Arrows show the direction of increasing pump-probe delay.