Ultrafast Demagnetization of Iron Induced by Optical versus Terahertz Pulses

Open Access

Ultrafast Demagnetization of Iron Induced by Optical versus Terahertz Pulses

A. L. Chekhov, Y. Behovits, J. J. F. Heitz, C. Denker, D. A. Reiss, M. Wolf, M. Weinelt, P. W. Brouwer, M. Münzenberg, and T. Kampfrath

Phys. Rev. X 11, 041055 – Published 20 December 2021

Abstract

We study ultrafast magnetization quenching of ferromagnetic iron following excitation by an optical versus a terahertz pump pulse. While the optical pump (photon energy of 3.1 eV) induces a strongly nonthermal electron distribution, terahertz excitation (4.1 meV) results in a quasithermal perturbation of the electron population. The pump-induced spin and electron dynamics are interrogated by the magneto-optic Kerr effect (MOKE). A deconvolution procedure allows us to push the time resolution down to 130 fs, even though the driving terahertz pulse is about 500 fs long. Remarkably, the MOKE signals exhibit an almost identical time evolution for both optical and terahertz pump pulses, despite the 3 orders of magnitude different number of excited electrons. We are able to quantitatively explain our results using a nonthermal model based on quasielastic spin-flip scattering. It shows that, in the small-perturbation limit, the rate of demagnetization of a metallic ferromagnet is proportional to the excess energy of the electrons, independent of the precise shape of their distribution. Our results reveal that, for simple metallic ferromagnets, the dynamics of ultrafast demagnetization and of the closely related terahertz spin transport do not depend on the pump photon energy.

Received 29 April 2021
Revised 15 September 2021
Accepted 4 October 2021

DOI:https://doi.org/10.1103/PhysRevX.11.041055

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Demagnetization Electron relaxation Spin dynamics

Magneto-optical Kerr effect Terahertz techniques

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

A. L. Chekhov ^1,2, Y. Behovits ^1,2, J. J. F. Heitz^1,2, C. Denker³, D. A. Reiss¹, M. Wolf², M. Weinelt ¹, P. W. Brouwer ¹, M. Münzenberg³, and T. Kampfrath ^1,2

¹Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
²Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany
³Institut für Physik, Universität Greifswald, Felix-Hausdorff-Straße 6, 17489 Greifswald, Germany

Popular Summary

When a ferromagnet such as iron is heated, its magnetization decreases because the ordered electron spins are forced to fluctuate more strongly. Heating of the magnet can be done extremely quickly by a femtosecond laser pulse, which in iron and nickel can lead to a loss of magnetization in as little as 100 fs. This ultrafast demagnetization provides important insights into the coupling of electrons with their ordered spins. Here, we explore how the state of the electrons just after the laser pulse—a nonthermal state, which cannot be described by an increased temperature—affects the subsequent spin dynamics.

To this end, we excite ferromagnetic iron with visible and terahertz laser pulses. While the visible photons induce a highly nonthermal state, the much less energetic terahertz photons just increase the electron temperature. Remarkably, for both types of pulses, we find that the magnetization of the iron sample undergoes an identical evolution down to our time resolution of 130 fs. Therefore, ultrafast magnetization dynamics is predominantly determined by the amount of heat dumped into the electrons at a given moment, independent of the precise distribution of electron energies that follows.

Besides its fundamental relevance, our result is good news for applications such as all-optical magnetic information writing and spintronic generation of terahertz electromagnetic pulses: They can be driven with any laser wavelength.

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Vol. 11, Iss. 4 — October - December 2021

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Figure 1
(a) Schematic of the experiment. A pump pulse at optical (photon energy of 3.1 eV) or THz (4.1 meV) frequency with transient electric field $E_{p} (t)$ excites a ferromagnetic Fe thin film with in-plane magnetization $M_{0}$ along the $y$ axis. The subsequent sample evolution is monitored by a time-delayed probe pulse (1.6 eV), whose polarization state is detected after reflection from the sample. (b) Calculated variations $Δ n (ε)$ of the electron occupation number versus electron energy $ε$ after deposition of $0.0 1 mJ / {cm}^{2}$ by photons with 4.1 meV (black curve) and 3.1 eV energy (blue curve). We assume constant electronic density of states and transition matrix elements [see Eq. (c29) in Appendix pp3]. For the THz pump, $Δ n (ε)$ can be well fit by the difference of two Fermi-Dirac distributions with temperatures $T_{0} + 140 K$ and $T_{0} = 300 K$ and the same chemical potential $μ_{0}$ (red curve). The shaded area shows the unperturbed Fermi-Dirac distribution $n_{0} (ε)$ with temperature $T_{e} = T_{0} = 300 K$ and chemical potential $μ_{0}$ .
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Figure 2
Typical traces of pump-induced MOKE rotation and ellipticity $Δ S (t)$ odd in $M_{0}$ . (a) Rotation (blue curve, scaled) and ellipticity (red) signals linear in the field $E_{p}$ of the driving THz pump pulse. Assuming this contribution arises from Zeeman torque, its derivative is proportional to the THz magnetic and electric field (black shaded curve). The inset shows the amplitude spectrum of the THz pump field $E_{p}$ . (b) THz-pump-induced MOKE rotation (blue) and ellipticity (red) quadratic in $E_{p}$ . (c) The same as (b), but for the optical pump pulse. Shaded areas (gray) indicate the corresponding pump intensity profiles $E_{p}^{2} (t)$ .
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Figure 3
Pump-induced variations of MOKE rotation and ellipticity $Δ S^{M_{0}, E_{p}^{2}} (t)$ odd in the sample magnetization $M_{0}$ and quadratic in the pump field $E_{p}$ . All signals are deconvoluted with respect to the intensity profile $E_{p}^{2} (t)$ of optical (3.1 eV) and THz (4.1 meV) pump pulses. They refer to the same fictitious pump profile $E_{fic}^{2} (t)$ as shown by the shaded black curve. Signals for the THz-pump data are scaled to match the optical one. The scaling factor of 2.7 corresponds to the ratio of the absorbed optical and THz pump fluences (see Appendix pp1).
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Figure 4
Two model scenarios of optically induced magnetization quenching. (a) The electronic densities of states $D^{↑} (ε)$ and $D^{↓} (ε)$ (black lines) and transition-matrix elements are independent of electron energy $ε$ . The total number $n^{σ} (ε) D^{σ} (ε)$ of electrons with spin $σ = ↑$ or $↓$ and energy $ε$ is indicated by the red area. The pump pulse (photon energy $ℏ ω_{p}$ , blue arrow) generates electrons and holes above and below the Fermi level $μ_{0}$ , thereby modifying the number of spin-up electrons $D^{↑} n^{↑}$ at a given energy $ε$ . Because $D^{↑}$ and $D^{↓}$ do not depend on $ε$ , the net number of spin-flip scattering events is zero, leaving the magnetization unchanged. (b) The spin-down density of states $D^{↓}$ increases linearly with $ε$ . Consequently, more scattering events for the spin-up electrons (①) than for the spin-up holes (②) are possible, resulting in magnetization quenching. When the photon energy is reduced to, for instance, $ℏ ω_{p} / 2$ , the difference in the number of final spin-down states for a spin-up electron (③) minus the analogous number for a spin-up hole (④) decreases by a factor of 2. This effect is, however, compensated by the number of pump-excited spin-up electrons, which has increased by a factor of 2. The resulting demagnetization rate is the same as for photon energy $ℏ ω_{p}$ , provided the deposited pump energy is the same.
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Figure 5
Extracted magnetization dynamics $Δ M (t) / M_{0}$ for optical (3.1 eV, blue squares) and THz (4.1 meV, red circles) excitation with a temporal profile indicated by the gray area. The data are inferred from the transients shown in Fig. 3. The black solid curve is a fit according to Eq. (5). The dotted curve is a result of a fit for THz excitation and subsequent convolution with a steplike exponential (decay time 100 fs) mimicking a situation where electron-electron thermalization after optical excitation is relevant (see Sec. 4).
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