Research ArticlePHYSICS

Critical behavior within 20 fs drives the out-of-equilibrium laser-induced magnetic phase transition in nickel

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Science Advances  02 Mar 2018:
Vol. 4, no. 3, eaap9744
DOI: 10.1126/sciadv.aap9744
  • Fig. 1 Schematic of the critical behavior of ultrafast demagnetization in Ni.

    (A) After excitation by a femtosecond laser pulse above the critical fluence (Fc), the transient electron temperature (Te) is driven above the Curie temperature (Tc), inducing high-energy spin excitations within 20 fs, which store the magnetic energy (see text). The Fermi-Dirac distributions of electrons are also plotted. Demagnetization occurs later, in ~176 fs, driven by relaxation of nonequilibrium spins and the likely excitation of low-energy magnons. Full recovery of the spin system occurs within ~500 fs to ~76 ps, depending on the laser fluence. (B and C) Experimental setups for time-resolved ARPES and TMOKE, respectively, using ultrafast high-harmonic sources. IR, infrared.

  • Fig. 2 Magnetization dynamics in Ni.

    (A) Change of the TMOKE asymmetry and exchange splitting reduction ΔEex as a function of time delay for different laser fluences. The solid lines represent fitting results, from which we extract the three characteristic times for demagnetization (τdemag), fast recovery (τrecover1), and slow recovery (τrecover2) (see Materials and Methods). The fit to TMOKE (upper panel) and ARPES (lower panel and lower fluence) yields the same fluence-independent time constants. a.u., arbitrary units. (B) Typical TMOKE asymmetry before (td = −360 fs) and after (td = 500 fs) excitation with a pump fluence F ≈ 6 mJ/cm2. (C) Photoelectron spectra of Ni(111) along the Embedded Image direction before (td = −500 fs) and after (td = 500 fs) laser excitation, showing the collapse in the exchange splitting Eex after excitation (blue dashed lines). The dashed-dotted lines represent the momentum at which photoemission intensities are extracted. The photoemission intensities are plotted in the right panel with Eex extracted from a Voigt function fit to the data (dashed lines; see the Supplementary Materials). (D) Constant, fluence-independent demagnetization time observed for different laser fluences for both ARPES and TMOKE.

  • Fig. 3 Ultrafast charge dynamics in Ni.

    (A) Log plots of the photoemission intensity above EF for F ≈ 6 mJ/cm2 and at different td, integrated from k// ≈ 0.85 Å−1 to k// ≈ 1.3 Å−1 in the momentum space. The dashed lines represent the fitting of the photoemission intensities with the Fermi-Dirac distribution convolved with experimental energy resolution (see the Supplementary Materials). Inset: Integrated photoemission intensity as a function of pump-probe time delay. The yellow dashed box illustrates the integration region of electron population in (B). (B) Dynamics of the electron temperature and the relative electron population (n/n0) within ~0.2 eV above EF as a function of td. The electron population is normalized to the band electron population (n0) ~0.2 eV below EF (see the Supplementary Materials). (C) Comparison of the electron temperature [red dashed line, same as (B)] and the change of EUV transient reflectivity at a similar pump fluence. Inset: EUV transient reflectivity measurement. The resonant EUV light (65 eV) directly probes the charge dynamics around EF induced by the laser pump pulse. This measurement is averaged over k-space.

  • Fig. 4 Observation of multiple critical behaviors during ultrafast demagnetization in Ni.

    (A) Peak electron temperature extracted ~24 fs after excitation as a function of pump fluence. The open symbols represent the electron temperature extracted at different k// using Tr-ARPES. The solid red line is the fit using Eq. 1 considering the transient electron and magnetic heat capacity [inset of (B)], whereas the green dashed line considers only the contribution from transient electron heat capacity (see the Supplementary Materials). The yellow-colored region (ΔFS) is the energy transferred to the spin system within ~20 fs. (B) Change in the exchange splitting at 2 ps as a function of pump fluence. The red line represents a fit with an error function. The same critical fluence of Fc ≈ 2.8 mJ/cm2 is observed for the exchange splitting collapse and the peak electron temperature in (A). The transient electron heat capacity is plotted in the inset. (C) Peak electron temperature calculated using Eq. 1 and (Ce + Cm) Transient [inset of (B)] for the sample temperatures of 300 and 100 K. The red solid line is the same as in (A). (D) Change of exchange splitting at 2 ps as a function of laser fluence at different sample temperatures. The solid lines represent the error function fit of the experimental results. The dashed lines align the critical fluences observed in (C) and (D) for different sample temperatures.

  • Table 1 Fitting parameters for the electron and magnetic heat capacity under thermal equilibrium (25) and in the transient state.
    A
    (J/mol per K)
    A
    (J/mol per K)
    β
    (J/mol per K)
    B
    (J/mol per K)
    B
    (J/mol per K)
    Tc
    (K)
    γ
    (J/mol per K)
    Equilibrium0.775 ± 0.0452.46 ± 0.05−0.0718 ± 0.01213.5 ± 1.837.0 ± 5.5634 ± 13.03 ± 0.06
    Transient0.7752.46−0.071812.6 ± 3.442.0 ± 3.7646 ± 1287.69 ± 3.72

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/3/eaap9744/DC1

    section S1. Details of experimental setups.

    section S2. Dynamics of electron temperature.

    section S3. Dynamics of the electron population at 1.6 eV.

    section S4. Dynamics of exchange splitting.

    section S5. Temperature dependence of exchange splitting in static ARPES.

    section S6. Method for extracting TMOKE asymmetry dynamics from HHG spectra.

    section S7. Momentum dependence of TMOKE measurements.

    section S8. Transient electron and magnetic heat capacity.

    section S9. Effects of electron-phonon coupling and heat diffusion on Eq. 1.

    fig. S1. Experimental setup.

    fig. S2. Electron temperature fitting.

    fig. S3. Electron population dynamics.

    fig. S4. Analysis of exchange splitting.

    fig. S5. Global fitting of the exchange splitting dynamics.

    fig. S6. Collapse of exchange splitting at the Curie temperature.

    fig. S7. Momentum dependence of TMOKE measurements.

    fig. S8. Electron and spin heat capacities.

    fig. S9. Two-temperature model.

    table S1. Material parameters used in TTM simulation.

    References (4350)

  • Supplementary Materials

    This PDF file includes:

    • section S1. Details of experimental setups.
    • section S2. Dynamics of electron temperature.
    • section S3. Dynamics of the electron population at 1.6 eV.
    • section S4. Dynamics of exchange splitting.
    • section S5. Temperature dependence of exchange splitting in static ARPES.
    • section S6. Method for extracting TMOKE asymmetry dynamics from HHG spectra.
    • section S7. Momentum dependence of TMOKE measurements.
    • section S8. Transient electron and magnetic heat capacity.
    • section S9. Effects of electron-phonon coupling and heat diffusion on Eq. 1.
    • fig. S1. Experimental setup.
    • fig. S2. Electron temperature fitting.
    • fig. S3. Electron population dynamics.
    • fig. S4. Analysis of exchange splitting.
    • fig. S5. Global fitting of the exchange splitting dynamics.
    • fig. S6. Collapse of exchange splitting at the Curie temperature.
    • fig. S7. Momentum dependence of TMOKE measurements.
    • fig. S8. Electron and spin heat capacities.
    • fig. S9. Two-temperature model.
    • table S1. Material parameters used in TTM simulation.
    • References (43–50)

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