Stoner versus Heisenberg: Ultrafast exchange reduction and magnon generation during laser-induced demagnetization

Understanding how the electronic band structure of a ferromagnetic material is modified during laser-induced demagnetization on femtosecond time scales has been a long-standing question in condensed matter physics. Here, we use ultrafast high harmonics to measure time-, energy-, and angle-resolved $M$-edge magnetic asymmetry spectra for Co films after optical pumping to induce ultrafast demagnetization. This provides a complete data set that we can compare with advanced ab initio magneto-optical calculations. Our analysis identifies that the dominant mechanisms contributing to ultrafast demagnetization on time scales up to several picoseconds are a transient reduction in the exchange splitting and the excitation of ultrafast magnons. Surprisingly, we find that the magnon contribution to ultrafast demagnetization is already strong on subpicosecond time scales, while the reduction in exchange splitting persists to several picoseconds.

Figure 1

(a) Setup for time-, energy-, and angle-resolved T-MOKE. (b) Transient average normalized magneto-optic response. (c) Evolution of the electron and lattice temperatures estimated from the three-temperature model (lines). The inset illustrates the microscopic mechanisms behind laser-induced demagnetization dynamics: Ultrafast magnons (top), and exchange reduction and thermal smearing (middle panels).

Figure 2

(a) Ab initio calculations of the spin-dependent density of states in Co at elevated electron temperatures (700, 1100, 3000, and 4600 K), (b) with reduced exchange splitting ${\varepsilon }_{{}_{\mathrm{Ex}}}$, and (c) reduced exchange splitting in combination with an elevated electron temperature of 1100 K.

Figure 3

Comparison of the (a) experimental and (d) theoretical angle- and energy-resolved T-MOKE asymmetries before laser excitation. Comparison of the (b), (c) experimental and (e), (f) theoretical differential asymmetry spectra at 0.7 and 3 ps. The measured differential spectra (b) and (c) at both delay times exhibit distinct qualitative differences from the spectrum at time zero (a). (e) and (f) show specific examples of calculated spectra near the optimal values determined from the least-squares fit. Last row (g)–(i): Contour plots of quadratic fits to rms residues resulting from independent fitting of ab initio calculated spectra to measured spectra. It can be clearly seen how the Co film is excited by a femtosecond laser pulse from (g) <0 ps to (h) 0.7 ps and how it relaxes back towards equilibrium from (h) 0.7 ps to (i) 3 ps. In (g), $\mathrm{\Delta }{m}_t=0.008$ is based on Ref. [44].