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State-resolved ultrafast charge and spin dynamics in [Co/Pd] multilayers

We use transient absorption spectroscopy with circularly polarized x-rays to detect laser-excited hole states below the Fermi level and compare their dynamics with that of unoccupied states above the Fermi level in ferromagnetic [Co/Pd] multilayers. While below the Fermi level an instantaneous and significantly stronger demagnetization is observed, above the Fermi level the demagnetization is delayed by 35+/-10 fs. This provides a direct visualization of how ultrafast demagnetization proceeds via initial spin-flip scattering of laser-excited holes to the subsequent formation of spin waves.

1 arXiv:2110.15615v1 [cond-mat.mtrl-sci] 29 Oct 2021 State-resolved dynamics in CoPd We use transient absorption spectroscopy with circularly polarized x-rays to detect laserexcited hole states below the Fermi level and compare their dynamics with that of unoccupied states above the Fermi level in ferromagnetic [Co/Pd] multilayers. While below the Fermi level an instantaneous and significantly stronger demagnetization is observed, above the Fermi level the demagnetization is delayed by 35 ± 10 fs. This provides a direct visualization of how ultrafast demagnetization proceeds via initial spin-flip scattering of laser-excited holes to the subsequent formation of spin waves.
2 State-resolved dynamics in CoPd Femtosecond optical excitation of magnetic materials and heterostructures leads to strongly non-equilibrium conditions displaying many novel phenomena that are absent in equilibrium physics (for reviews see Refs. 1 and 2 and references therein). Discoveries such as all-optical magnetization reversal [3][4][5][6] , superdiffusive spin transport [7][8][9][10][11][12][13][14] and optically induced spin transfer effect 15,16 not only challenge our fundamental understanding but also provide future perspectives for information storage and processing. It is generally accepted that laser excitation initially leads to a highly non-equilibrium electron system while conserving the total electron spin polarization. [17][18][19] Subsequently, electronic thermalization and magnetization dynamics set in that distribute the deposited laser energy over the system's electron, spin and orbital degrees of freedom and ultimately to the lattice. [17][18][19][20][21][22] While such dynamics can be described by a phenomenological three temperature model, the underlying physics at play remain hidden behind ad hoc coupling constants. 23 For understanding the angular momentum flow during ultrafast demagnetization it is important to disentangle the influence of magnetic interactions such as exchange and spin-orbit coupling in the non-equilibrium dynamics. While the exchange interaction leads to processes that conserve spin such as angular momentum transfer between magnetic sub-systems 24 and the excitation of spin waves [25][26][27][28] , spin-orbit coupling can cause electronic spin-flips where the corresponding change in angular momentum is transferred to phonons. 29 Such Elliott-Yafet type spinflip scattering on phonons has been investigated and is considered a key ingredient of ultrafast demagnetization. 20,23,30,31 Flipping electron spins also leads to the excitation of spin waves 32 via exchange scattering. However, the direct observation of spin waves in momentum space and in the time-domain remains challenging. 33 Several studies reported ultrafast excitation of spin waves for instance via a delayed onset of demagnetization. [34][35][36] This situation is visualized in Fig. 1(a) where the initial spin-conserving laser excitation and subsequent spin-flip processes are depicted.
The decay of a flipped electron spin (top of Fig. 1(a)) into spin waves (top of Fig. 1(b)) is thought to take a characteristic time of several 10 fs. [34][35][36] Here we use time-resolved x-ray absorption spectroscopy (XAS) and x-ray magnetic circular dichroism (XMCD) to follow these processes as they evolve in real time in [Co/Pd] multilayers.
We show that 2p → 3d core-valence transitions can directly probe the spin-polarization of laserinduced holes below the Fermi level. These states display an instantaneous response to fs laser excitation. Surprisingly, 2p → 3d transitions into unoccupied states above the Fermi level show a demagnetization dynamics that is delayed by 35 ± 10 fs. In addition, laser-induced hole states below the Fermi level display a much stronger demagnetization. These observations are consistent 3 State-resolved dynamics in CoPd with the notion that spin-orbit scattering in strong ferromagnets is the driving force for ultrafast demagnetization.
Experiments were performed at the SXR instrument of the Linac Coherent Light Source (LCLS) at the SLAC National Accelerator Laboratory. The experimental setup is described in detail in Ref. 37. X-ray absorption spectra were measured in transmission. The incident X-ray intensity was measured via the x-ray fluorescence from a Si 3 N 4 membrane placed in the beam before the sample and detected with an microchannel plate (MCP). The transmitted X-ray intensity behind the sample was recorded by a fast charge coupled device (CCD) detector. XAS spectra over the L 3 absorption edge corresponding to 2p 3/2 → 3d transitions were acquired by varying the x-ray energy via the LCLS electron beam energy. A 250 meV x-ray bandwidth was selected by the beamline monochromator using a 100 lines per mm grating resulting in an effective resolving power of 3000 at 780 eV 38 . Circularly polarized X-ray pulses were produced using the "Delta" afterburner undulator 39 , enabling the measurement of XAS and XMCD spectra by alternating the magnetic field saturating the sample along the beam direction and computing sum and difference for XAS and XMCD, respectively. Time-resolved XAS and XMCD data were acquired by scan- into completely occupied majority (spin "up") and partially occupied minority spin (spin "down") channels which are shifted in energy by the exchange splitting.  30,31 where an electron from the majority spin fills the hole in the minority spin, as depicted in Fig. 1(a). This flipped spin could then decay into spin waves as illustrated in Fig. 1(b), which induces a band mirroring in the nearby atoms where the quantization axis has now changed. By using time-resolved XAS and XMCD we aim at uncovering the different timescales and energies of the different processes involved.

5
State-resolved dynamics in CoPd Fig. 2 shows transient XAS and XMCD of laser-induced holes belwo and above the Fermi level. XAS ( Fig. 2(a)) and XMCD spectra ( Fig. 2(b) E-E F . Below E F the curves display initial increases in the XAS intensity followed by subsequent decays on timescales longer than several 100 fs. Above E F the transient XAS changes are negative while directly at E F a more complex behavior emerges. In the following we describe these observations in terms of changes in the hole population, ∆N, at state of energy E-E F . The small contribution due to spin-orbit coupling of the state-resolved XAS intensity 42,43 will be neglected here. It is important to emphasise that ∆N can also include time dependent changes in the electronic structure. 44 It is apparent in Fig. 2(a) that such electronic structure changes indeed occur.
For instance at E-E F near 4 eV, i.e. much higher than the pump photon energy, the observed variations of ∆N are unlikely to be caused by the population dynamics of electrons in these states.
The curves for ∆N in Fig. 3(a) were fitted with a double exponential to describe an excitation and a relaxation process. The fit parameters are summarized in Table II in  The XMCD spectra can be described as being proportional to the product of state-dependent population, N and a polarization term, P. The latter contains both spin and orbital polarization with the orbital contribution being significantly smaller than the spin polarization as shown in the sum rule analysis detailed in the supplementary information. 42,43 Similar to conventional sumrule-analysis of time-resolved XMCD spectra, the magnetic dipole term can be neglected for our poly-crystalline samples 45,46 and was found to be negligible in similar samples. 47 Using the re- sults for ∆N from Fig. 3(a) we can separate the state polarization from state-dependent charge dynamics. The time-resolved polarization dynamics, normalized to the ground-state polarization of the respective states, are shown in Fig. 3(b). The individual experimental results (symbols) are shifted vertically for clarity and are compared to exponential polarization decays that include the magnitude of the decay, ∆P, the decay time constant, τ, and a delayed demagnetization onset, ∆t, as fit parameters. All parameters are summarized in Table II in the supplementary information.
To highlight the difference between the curves below and above the Fermi level, the same relative polarization dynamics for E-E F = 0.88 eV is shown as a dashed grey curve together with each trace. This allows two visual observations. Firstly, the amount of demagnetization is not the same State-resolved dynamics in CoPd at each value of E-E F . Clearly, the demagnetisation is significantly stronger below E F than above.
Secondly, there is a time delay, ∆t, apparent in the response, with faster dynamics for states below E F . The complete fitting model and analysis of the uncertainties on the fitted values is presented in Table II in the supplementary information. In Fig. 4 the relative change in polarization ∆P/P 0 and the time lag ∆t are shown as function of E-E F . We stress here that this time lag ∆t is determined by the delayed apparent response of the relative change in polarization ∆P/P 0 with respect to the charge dynamics ∆N, for the same given photon energy. It can also be visualized by comparing the relative change in polarization ∆P/P 0 at different photon energy but this is not how we extracted it.
The data we presented in this letter conclusively demonstrate a vastly different magnetization dynamics above and below the Fermi level for Co 3d levels in [Co/Pd] multilayers. Below E F , the ultrafast drop in magnetic polarization is up to 32% larger than above (see Fig. 4). This is clearly outside any experimental uncertainty as demonstrated in Fig. 3(b). Moreover, the onset of the polarization dynamics occurs simultaneously to the charge dynamics, i.e. ∆t = 0±10 fs. This is the behavior expected for individual electrons/holes being scattered between different electronic states as depicted in Fig. 1(a). This also leads to Stoner excitations where electrons/holes are scattered between the spin up and down states. 28 In strong ferromagnets such as [Co/Pd] multilayers, spinflip scattering can only occur for states below E F where spin up and down states are hybridized via spin-orbit coupling. 31 The same Elliot-Yaffet-type spin-flip scattering processes are thought to also transfer spin angular momentum to the lattice. [29][30][31] However, for ultrafast demagnetization to occur, the flipped spins of individual electrons/holes need to be transferred to the whole electronic system. This usually takes place via the formation of collective spin excitations, i.e. spin waves. In the Heisenberg model, spin waves lead to slight changes of the atomic spin quantization axis and result in a mixing of spin up and down states as observed in photoemission spectroscopy. 48 This situation is depicted in Fig. 1(b). Since the formation of spin waves takes time 34 we expect a characteristic time delay relative to the instantaneous demagnetization of individual electrons/holes. We assign the observed delayed onset of demagnetization above E F of ∆t = 35 ± 10 fs (see Fig. 4) to this effect. This is observable above the Fermi level since there the majority of unoccupied states reflects the atomic magnetic moments. 49,50 In summary, taking advantage of the high FEL brightness and improved I 0 normalization scheme, we were able to show that time-resolved XAS and XMCD spectroscopy can provide detailed information in the microscopic mechanism at play during ultrafast laser excitation. In particular we report on different dynamics of the spin system below and above the Fermi level. This is manifested by both a 32% larger change in spin dynamics below the Fermi level and a 9 State-resolved dynamics in CoPd 35 ± 10 fs delayed response above it. Both of these effects suggest a scenario for a strong ferromagnet where spin-flips occur preferentially below the Fermi level where spin up and down states are hybridized. Moreover, we also report on initial evidence that indicates effects beyond a simple electronic redistribution and demagnetization with changes in XAS observed 4 eV above the Fermi level, suggestive of band structure dynamics. With ever improved normalization schemes and higher repetition rate FELs, transient near-edge soft X-ray spectroscopy promises to be a valuable tool in understanding out-of-equilibrium phenomena.

DATA AVAILABILITY STATEMENT
The data that support the findings of this study are available from the corresponding author upon reasonable request.