Depth-resolved magnetization dynamics in Fe thin films after ultrafast laser excitation

Abstract

We performed time-resolved x-ray resonant magnetic reflectivity measurements on a laser-excited ferromagnetic Fe thin film to simultaneously probe the transient structural and magnetic depth profiles with nanometer spatial and femtosecond temporal resolution. Our results show that during the first picoseconds after optical excitation, the magnetization of the Fe layer is strongly inhomogeneous, especially in the vicinity of the buried interface. By comparing our experimental results to predictions based on the microscopic three-temperature model and simulations of laser-induced spin-currents, we demonstrate that local and non-local angular momentum transfer phenomena take place simultaneously. After a few picoseconds, the magnetization relaxes back to equilibrium while the total thin film thickness starts oscillating periodically, with a maximum dilation of approximately 1.3% of the entire thin film thickness due to laser-induced stresses.

Figures (4)

• Figure 1: Schematic of the time-resolved magnetic reflectivity (tr-XRMR) experiment and derived magnetic profile. The x-ray probe pulses with linear polarization are shown in blue, and the pump pulse in red. Both impinge on the sample at an incidence angle $\theta$. A transverse magnetic field is applied perpendicularly to the scattering plane. The top panel shows the derived magnetic profile for the unpumped sample (blue) and 300 fs after the excitation (orange).
• Figure 2: Fitting results with respective out-of-plane deformation and magnetic depth profile for different time delays. (a) Experimental (points) normalized reflectivity, $R_\text{n}$ (top panel) and normalized magnetic asymmetry $A_\text{n}$ (bottom panel) for different delays (see legend) with the corresponding best fit (lines) (b) Derived out-of-plane deformation (pumped thickness minus unpumped thickness) in Å for the different layers of the sample as a function of each delay $\Delta t$. The background colour represents the different delays $\Delta t$ plotted in (a). (c) Magnetic moments $m$ of the Fe layer are shown on the horizontal axis as a function of the sample depth, $z$, on the vertical axis, where, on the left, the sample structure is shown. Derived depth magnetic profile for 4 different delays with the unpumped profile equal to that of Fig. \ref{['fig1']}. The dotted vertical lines represent the mean of the magnetization, $\langle m_\text{p} \rangle$ and $\langle m_\text{up} \rangle$, through the entire Fe layer.
• Figure 3: Laser-induced total out-of-plane deformation as a function of time delay, extracted from the $R_n$ fits of Fig. \ref{['fig3']} a, in red points. The black line is the total deformation calculated using the udkm1Dsim toolbox and rescaled with a constant prefactor.
• Figure 4: Extracted laser-induced magnetization profile and calculations based on the m3TM and superdiffusive simulations. (a) Normalized mean magnetization, $\langle m_\text{p} \rangle/ \langle m_\text{up}\rangle$, as a function of time delay (red points), with a double exponential fit (black line SupMat). (b) 2D-map of the normalized magnetization $m_\text{p}/m_\text{up}$, extracted from the fit of our experimental data (Fig. \ref{['fig3']} a), as a function of the depth, $z$ (vertical axis) and time delay $\Delta t$ (horizontal axis). The red vertical dotted lines indicate the measured $\Delta t$. (c) 2D-map of the normalized magnetization $m_\text{p}/m_\text{up}$ for the m3TM model, calculated for our sample structure using the udkm1Dsim toolbox schick_udkm1dsim_2024. (d) 2D-map of the relative magnetization $\Delta m = m_\text{p}-m_\text{up}$ for the superdiffusive spin model in a 15 nm thick Ni sample, adapted from eschenlohr_ultrafast_2013 with the permission of the authors.