Ultrafast Spin Density Wave Transition in Chromium Governed by Thermalized Electron Gas

The energy and momentum selectivity of time- and angle-resolved photoemission spectroscopy is exploited to address the ultrafast dynamics of the antiferromagnetic spin density wave (SDW) transition photoexcited in epitaxial thin films of chromium. We are able to quantitatively extract the evolution of the SDW order parameter $\mathrm{\Delta }$ through the ultrafast phase transition and show that $\mathrm{\Delta }$ is governed by the transient temperature of the thermalized electron gas, in a mean field description. The complete destruction of SDW order on a sub-100 fs time scale is observed, much faster than for conventional charge density wave materials. Our results reveal that equilibrium concepts for phase transitions such as the order parameter may be utilized even in the strongly nonadiabatic regime of ultrafast photoexcitation.

Figure 1

(a) Schematic pump-probe experiment of the Cr(110) thin film. (b) Schematic Fermi surface and surface Brillouin zone of Cr. Electron pockets are contained within solid black lines while hole pockets are colored cyan. The hexagon marks the (110) surface projected Brillouin zone. (c) Electronic structure of Cr(110) thin film measured along the dotted arrow in Fig. 1. The spin density wave (SDW) band is marked by a white arrow.

Figure 2

ARPES images obtained with 40 eV probe energy (a) in thermal equilibrium at a delay of $-200\mathrm{fs}$ (XUV probe pulse before pump pulse) and (b) following optical excitation at 200 fs delay. The dotted box highlights the area considered in the simulation as presented in Fig. 4. (c) Difference image between the images shown in (a) and (b). In the false color plot red and blue marks intensity increase and decrease, respectively. (d) Transient rigid shift of the energy distribution curves (EDCs). The solid black line is a guide to the eye.

Figure 3

(a) Fermi distribution extracted from region SR indicated in Fig. 2 at various pulse delays. (b) Electronic temperature extracted from the Fermi distribution as a function of pulse delay. The solid black line is a guide to the eye. (c) Electronic temperature (solid black line) and associated order parameter (red markers) calculated as a function of pulse delay. The dotted line marks the SDW transition temperature. (d) Dynamics of the normalized SDW band intensity in the region marked SDW in Fig. 2 for both experiment (markers) and simulation (solid line). An arrow marks the point at which $\mathrm{\Delta }$ transitions from 0 to a finite value. The color background in (c) and (d) highlights the region where the SDW is in the ground (blue) and excited (orange) state.

Figure 4

Snapshots of the simulated electronic structure at $-200$, 50, and 500 fs in the region highlighted in Fig. 2. Following pump excitation both the order parameter and the rigid shift ($\delta \epsilon$) change transiently, leading to a reduction of spectral weight in the analyzed region. Initial excitation leads to the transition to the paramagnetic phase (50 fs), which relaxes into the SDW phase once $T_e<T_{\mathrm{SDW}}$ (500 fs). Dotted lines in the bottom left panel are guides to the eye following the dispersion in both branches of the renormalized dispersion. The difference image between $-200$ and 50 fs highlights the redistrubution of intensity as observed in the experiment [Fig. 2].