The role of ultrafast magnon generation in the magnetization dynamics of rare-earth metals

Abstract

Ultrafast demagnetization of rare-earth metals is distinct from that of 3d ferromagnets, as rare-earth magnetism is dominated by localized 4f electrons that cannot be directly excited by an optical laser pulse. Their demagnetization must involve excitation of magnons, driven either through exchange coupling between the 5d6s-itinerant and 4f-localized electrons or by coupling of 4f spins to lattice excitations. Here, we disentangle the ultrafast dynamics of 5d6s and 4f magnetic moments in terbium metal by time-resolved photoemission spectroscopy. We show that the demagnetization time of the Tb 4f magnetic moments of 400 fs is set by 4f spin-lattice coupling. This is experimentally evidenced by a comparison to ferromagnetic gadolinium and supported by orbital-resolved spin dynamics simulations. Our findings establish coupling of the 4f spins to the lattice via the orbital momentum as an essential mechanism driving magnetization dynamics via ultrafast magnon generation in technically relevant materials with strong magnetic anisotropy.

Fig. 1. Comparison of 5d6s and 4f spin dynamics in Gadolinium and Terbium.

Upper panels: Orbital-resolved spin model. The yellow arrows represent the energy flow from the laser-excited electrons into the lattice (G_ep) and to the 5d and 4f spin systems. Note the different 4f spin–to–lattice couplings α_4f in (A) Tb (J = L + S = 6, L = 3) and (B) Gd (J = S = 7/2, L = 0). In contrast, inter- and intra-atomic exchange constants (J_ij and J_intra) are of comparable magnitude. Lower panels: Illustration of 5d6s and 4f spin dynamics about 1 ps after laser excitation. While in (B), the 4f spins (yellow arrows) are strongly excited by lattice motions and tilted with respect to M_z, in (A), they remain cold and aligned along the magnetization direction M_z. The 5d6s spins (red arrows) are additionally coupled to the optically excited valence electrons α_5d and thus quiver around the 4f moments.

Fig. 2. Valence band photoemission spectra and MLD of Tb at 90 K.

ARPES spectra probed with p-polarized light for opposite in-plane magnetization directions (red and blue, see inset) at normal emission ϑ = 0^∘. The gray backfilled difference spectrum highlights the MLD, which was evaluated for the ⁸S_7/2 spin component. The binding energy of minority (↓) and majority (↑) spin 5d valence bands (VB) and the exchange splitting were extracted at ϑ = 8^∘ (see text).

Fig. 3. Magnetization dynamics of itinerant 5d and localized 4f moments in the rare earth metals Gd and Tb.

The upper panels show the response of the 5d valence band exchange splitting, and the lower panels show the transient MLD of the 4f level for (A) Gd and (B) Tb, respectively. Error bars on the last data points show 2 SDs. The solid lines result from our orbital-resolved spin dynamics simulations using ab initio input parameters for J_ij and J_intra. In the lower panels, the calculated reduced magnetization is shown. In the upper panels, the calculated dynamics of 5d magnetic moments is converted into the transient exchange splitting via first principles calculations (see the Supplementary Materials).