Laser-induced terahertz spin transport in magnetic nanostructures arises from the same force as ultrafast demagnetization

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Laser-induced terahertz spin transport in magnetic nanostructures arises from the same force as ultrafast demagnetization

Reza Rouzegar, Liane Brandt, Lukáš Nádvorník, David A. Reiss, Alexander L. Chekhov, Oliver Gueckstock, Chihun In, Martin Wolf, Tom S. Seifert, Piet W. Brouwer, Georg Woltersdorf, and Tobias Kampfrath

Phys. Rev. B 106, 144427 – Published 24 October 2022

Abstract

Laser-induced terahertz spin transport (TST) and ultrafast demagnetization (UDM) are central but so far disconnected phenomena in femtomagnetism and terahertz spintronics. Here, we use broadband terahertz emission spectroscopy to reliably measure both processes in one setup. We find that the rate of UDM in a single simple ferromagnetic metal film $F$ such as ${Co}_{70} {Fe}_{30}$ or ${Ni}_{80} {Fe}_{20}$ has the same time evolution as TST from $F$ into an adjacent normal-metal layer $N$ such as $Pt$ or $W$ . As this remarkable agreement refers to two very different samples, an $F$ layer vs an $F | N$ stack, it does not result from the trivial fact that TST out of $F$ reduces the $F$ magnetization at the same rate. Instead, our observation strongly suggests that UDM in $F$ and TST in $F | N$ are driven by the same force, which is fully determined by the state of the ferromagnet. An analytical model quantitatively explains our measurements and reveals that both UDM in the $F$ sample and TST in the associated $F | N$ stack arise from a generalized spin voltage, i.e., an excess of magnetization, which is defined for arbitrary, nonthermal electron distributions. We also conclude that contributions due to a possible temperature difference between $F$ and $N$ , i.e., the spin-dependent Seebeck effect, and optical intersite spin transfer are minor in our experiment. Based on these findings, one can apply the vast knowledge of UDM to TST to significantly increase spin-current amplitudes and, thus, open promising pathways toward energy-efficient ultrafast spintronic devices.

Received 26 May 2021
Accepted 19 September 2022

DOI:https://doi.org/10.1103/PhysRevB.106.144427

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.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Light-induced magnetic effects Spin dynamics Ultrafast magnetic effects

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Reza Rouzegar ^1,2,*, Liane Brandt ³, Lukáš Nádvorník ^1,2,4, David A. Reiss ¹, Alexander L. Chekhov ^1,2, Oliver Gueckstock ^1,2, Chihun In^1,2, Martin Wolf², Tom S. Seifert¹, Piet W. Brouwer¹, Georg Woltersdorf³, and Tobias Kampfrath ^1,2,†

¹Department of Physics, Freie Universität Berlin, 14195 Berlin, Germany
²Department of Physical Chemistry, Fritz Haber Institute of the Max Planck Society, 14195 Berlin, Germany
³Institut für Physik, Martin-Luther-Universität Halle, 06120 Halle, Germany
⁴Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, 121 16 Prague, Czech Republic

^*m.rouzegar@fu-berlin.de
^†tobias.kampfrath@fu-berlin.de

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Issue

Vol. 106, Iss. 14 — 1 October 2022

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Images

Figure 1
Ultrafast demagnetization (UDM) vs terahertz spin transport (TST). (a) Side view of a single ferromagnetic metal layer ( $F$ ) with magnetization $M = M u_{y}$ parallel to the $y$ axis with unit vector $u_{y}$ . Excitation by a femtosecond laser pulse triggers UDM. The transient magnetic dipole gives rise to the emission of a terahertz pulse with field $E_{M} (t) \propto \partial_{t} M (t)$ . (b) $F | N$ stack consisting of $F$ and an adjacent normal paramagnetic metal layer ( $N$ ). Femtosecond laser excitation drives a spin current with density $j_{s} = j_{s} u_{z}$ from $F$ to $N$ . In $N$ , $j_{s}$ is converted into a charge current with density $j_{c} = j_{c} u_{x}$ , leading to the emission of a terahertz electromagnetic pulse with electric field $E_{j_{s}} (t) \propto j_{s} (t)$ directly behind the sample. Both $E_{M} (t)$ and $E_{j_{s}} (t)$ are linearly polarized perpendicular to $M$ and measured by electro-optic sampling.
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Figure 2
Typical terahertz electro-optic signals, odd with respect to magnetization $M$ , from $F$ and $F | N$ samples consisting of $F = CoFe (3 nm)$ and $N = Pt (3 nm)$ . (a) Terahertz emission signal $S_{F | N} (t, 0^{\circ})$ from an $F | N$ stack. When the sample is turned by 180° about $M$ , the signal $S_{F | N} (t, 180^{\circ})$ is obtained. Note that the sample is optically symmetrized by a cap window that is identical to the diamond substrate (see insets). (b) Same as (a) but for the $F$ sample. Note the substantial asymmetry between $S_{F} (t, 0^{\circ})$ and $S_{F} (t, 180^{\circ})$ . (c) Resulting signals $S_{F}^{+} (t)$ and $S_{F}^{-} (t)$ symmetric and antisymmetric with respect to sample turning. (d) Extracted magnetization dynamics from $S_{F}^{+} (t)$ of (c) (red curve), along with magnetization dynamics as measured by the magneto-optic Kerr effect (MOKE, black curve). The magnetization evolution derived from the terahertz signal was convoluted with a Gaussian (123 fs full width at half maximum) to match the time resolution of the MOKE measurement.
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Figure 3
Terahertz emission due to terahertz spin transport (TST) in $F | N$ stacks vs ultrafast demagnetization (UDM) in $F$ samples. (a) Terahertz signal $S_{F | N}^{-} (t)$ from an $F | N$ stack with $F = CoFe (3 nm)$ and $N = Pt (3 nm)$ , antisymmetric with respect to sample turning about $M$ (blue solid line), vs terahertz signal $S_{F}^{+} (t)$ from a single $F$ layer, symmetric with respect to sample turning (red solid line). The curves below show analogous signals for $F$ and $F | N$ samples with $F = CoFeB (5 nm)$ and $F = NiFe (9 nm)$ . Curves are scaled by the indicated factors and offset vertically for clarity. (b) Temporal evolution of the spin current $j_{s} (t)$ flowing in the $F | N$ sample and of the rate of change $\partial_{t} M (t)$ of the magnetization of the $F$ sample times the $F$ thickness $d_{F}$ , as extracted from the data of (a). Curves are vertically offset and normalized to their minima to allow for a better comparison of the relaxation dynamics. (c) Direct comparison of the signals $S_{F | N}^{-} (t)$ from the stacks $F | Pt (3 nm)$ and $F | W (3 nm)$ with $F = CoFeB (3 nm)$ and (d) the resulting spin current dynamics. (e) Direct comparison of the signals $S_{F}^{+} (t)$ from single $F = CoFeB (3 nm)$ (red) and $NiFe (3 nm)$ (blue) films and (f) the resulting rate of magnetization change.
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Figure 4
Simple model of ultrafast demagnetization (UDM) and terahertz spin transport (TST). (a) UDM. Schematic of the density of states of spin-up ( $↑$ ) and spin-down ( $↓$ ) Bloch electrons of a metallic ferromagnet such as Fe in the framework of the Stoner model. Quasi-elastic spin-flip scattering events (white curved arrow) lead to transfer of spin angular momentum to the crystal lattice. (b) TST. $N$ acts as an additional sink of spin angular momentum through spin-conserving electron transfer across the $F | N$ interface (blue curved arrows). In (a) and (b), the spin transfer rate scales with the generalized spin voltage $Δ {\tilde{μ}}_{s}$ [Eq. (7)], which equals $μ^{F ↑} - μ^{F ↓}$ in the case of Fermi-Dirac electron distributions. (c) Illustration of the interplay of spin voltage, electron temperature, and magnetization according to Eq. (9). At time $t = 0$ , the pump pulse excites the sample with temperature $T_{0}$ , causing a time-dependent uniform increase of the generalized electronic temperature to ${\tilde{T}}_{e} (t) = T_{0} + Δ {\tilde{T}}_{e} (t)$ (dashed line). At any subsequent time $t > 0$ , the system aims to change its magnetization from the instantaneous value $M (t)$ to $M_{eq} [{\tilde{T}}_{e} (t)]$ , where $M_{eq} (T)$ is the equilibrium magnetization vs temperature $T$ (black solid line). The spin voltage $Δ {\tilde{μ}}_{s} (t)$ is proportional to the excess magnetization $M (t) - M_{eq} [{\tilde{T}}_{e} (t)]$ [blue dashed arrow, see Eq. (9)]. Note that this consideration is strictly valid only in the small-perturbation regime where $M (t) \approx M_{0}$ (see Appendix pp2).
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Figure 5
Measured and modeled dynamics of the rate of magnetization change $\partial_{t} M (t)$ in $F$ samples and the spin-current density $j_{s} (t)$ from $F$ to $N$ in $F | N$ stacks. (a) Evolution of $\partial_{t} M (t)$ of an $F = CoFeB$ sample (red solid line) and $j_{s} (t)$ in $F | Pt$ and $F | W$ stacks (blue solid lines). Gray solid lines are fits based on Eq. (12) with $Γ_{es}$ and the overall amplitude scaling as the only fit parameters. (b) Analogous to (a) but for $\partial_{t} M (t)$ in $CoFeB$ and $j_{s} (t)$ in NiFe and NiFe|Pt.
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