Disparate ultrafast dynamics of itinerant and localized magnetic moments in gadolinium metal

Abstract

The Heisenberg-Dirac intra-atomic exchange coupling is responsible for the formation of the atomic spin moment and thus the strongest interaction in magnetism. Therefore, it is generally assumed that intra-atomic exchange leads to a quasi-instantaneous aligning process in the magnetic moment dynamics of spins in separate, on-site atomic orbitals. Following ultrashort optical excitation of gadolinium metal, we concurrently record in photoemission the 4f magnetic linear dichroism and 5d exchange splitting. Their dynamics differ by one order of magnitude, with decay constants of 14 versus 0.8 ps, respectively. Spin dynamics simulations based on an orbital-resolved Heisenberg Hamiltonian combined with first-principles calculations explain the particular dynamics of 5d and 4f spin moments well, and corroborate that the 5d exchange splitting traces closely the 5d spin-moment dynamics. Thus gadolinium shows disparate dynamics of the localized 4f and the itinerant 5d spin moments, demonstrating a breakdown of their intra-atomic exchange alignment on a picosecond timescale.

Figure 1. Couplings of the gadolinium spin system.

(a) The interaction of the different heat baths in an extended three-temperature model. After infrared laser excitation of the valence electrons, the whole system equilibrates by exchanging energy and momentum, indicated by the double arrows. The 5d and 4f spin systems couple via inter- and intra-atomic exchange, where the intra-atomic exchange J_int=130 meV is much larger than the largest (nearest neighbour) inter-atomic exchange J_ij=5.9 meV. In thermal equilibrium, the combination of inter- and intra-atomic exchange interactions mediates spin order in the 4f system via the delocalized 5d valence bands. Upon femtosecond laser excitation, the dynamics of the 5d spin system is dominated by the coupling α_e to the hot valence electrons described by temperature T_e, while the localized 4f spins couple only to the phonon bath at temperature T_p via α_p. (b) The binding energy versus parallel momentum map E_B(k_||) of Gd recorded with higher-order harmonic radiation (photon energy 36.8 eV) in time- and angle-resolved photoemission gives simultaneously access to the transient exchange splitting of the 5d minority and majority spin bands (↓ and ↑, respectively) and the magnetic linear dichroism of the localized 4f state. Data are plotted on the displayed normalized false colour scale.

Figure 2. Transient 5d exchange splitting and 4f linear magnetic dichroism of gadolinium.

(a) The blue and red spectra show the Gd ARPES spectrum as a function of pump–probe delay recorded with p-polarized light in normal emission with a photon energy of 36.8 eV for the two opposite in-plane magnetization directions. Clearly visible are the exchange-split (5d) valence bands at 2 eV binding energy and the 4f core level at 8 eV, in addition to the surface state. The fitted majority and minority spin valence bands are indicated by grey peaks below the actual spectra, the peak positions are marked by black ticks. The inset depicts the experimental geometry for both magnetization directions M as indicated by the blue and red arrows. The angle of incidence of the pump and probe beams (bold black arrow) is 30° off the surface plane and the electrons (e⁻) are recorded in Γ–M direction ±13° with respect to the surface normal. The probe beam polarization, E_ph, is indicated by the thin double-headed black arrow. (b) The magnetic linear dichroism (MLD) of the 4f electrons is obtained by integrating the absolute value of the difference of two spectra recorded for opposite in-plane magnetizations. Comparison of the signal at three different delays (−1, 1 and 40 ps as indicted by the colour scale) illustrates the slow, picosecond dynamics of the 4f magnetic moment.

Figure 3. Orbital-resolved spin dynamics in gadolinium.

Measured exchange splitting of the 5d bulk bands (red circles, right ordinate) and (normalized) magnetic linear dichroism of the 4f level (black circles, left ordinate) are shown as a function of pump–probe delay recorded with 100-fs XUV pulses. The position of the minority and majority spin valence band was extracted at ±0.1 Å⁻¹ around Γ using the fit procedure described in ref. . The MLD contrast is evaluated over the 4f photoemission peak with an angular resolution of 0.5° and integrated across the full detection range of ±13° to improve statistics. The error bars show two s.d. The error of the exchange splitting is obtained from the fits of the corresponding bands. The error of the MLD signal is given by the statistical noise of the spectral area at the 4f binding energy. Solid black and blue lines are the (normalized) 4f and 5d magnetic moments calculated with our orbital-resolved spin Hamiltonian. The red solid line is the exchange splitting computed ab initio with the calculated 4f and 5d magnetic moments of the spin dynamics simulations as input. Within the first few picoseconds after laser excitation, the dynamics of the exchange splitting and the 5d orbital momentum are synchronous. The decoupling of the intra-atomic exchange is demonstrated by the significantly different demagnetization times of the 5d and 4f spin system. Single exponential fits give time constants of 0.8 and 14 ps, respectively. Note that after 3.5 ps, the dynamics are displayed on a logarithmic scale to cover the cooling back to the initial sample temperature of 90 K.