# APL Special Topic Collection on "Ultrafast and terahertz spintronics": Guest editorial

Tobias Kampfrath, Andrei Kirilyuk, Stéphane Mangin, Sangeeta Sharma, Martin Weinelt

► To cite this version:

Tobias Kampfrath, Andrei Kirilyuk, Stéphane Mangin, Sangeeta Sharma, Martin Weinelt. APL Special Topic Collection on "Ultrafast and terahertz spintronics": Guest editorial. Applied Physics Letters, 2023, 123 (5), 10.1063/5.0167151. [hal-05006480](https://hal-univ-lorraine.fr/hal-05006480v1)

HAL Id: hal-05006480

https://hal.univ-lorraine.fr/hal-05006480v1

Submitted on 26 Mar 2025

APL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
## APL Special Topic Collection on "Ultrafast and terahertz spintronics": Guest editorial

Tobias Kampfrath¹,², Andrei Kirilyuk³, Stéphane Mangin⁴, Sangeeta Sharma⁵, Martin Weinelt¹

1. Department of Physics, Freie Universität Berlin, Germany

2. Department of Physical Chemistry, Fritz Haber Institute of the Max Planck Society, Berlin, Germany

3. Radboud University Nijmegen, Netherlands

4. Université de Lorraine, CNRS, IJL, F-54000 Nancy, France

5. Max Born Institute Berlin, Germany

## Scope statement

Spin-based electronics (spintronics) aims at extending electronic functionalities, which rely on the electron charge as information carrier, by the spin of the electron. Spintronics has large application potential in information storage and processing, but also in areas such as sensing and photonics. To make spintronic operations competitive and compatible with other information carriers like photons and electrons, their speed needs to be pushed to femtosecond time scales and, thus, terahertz frequencies.

In ultrafast spintronics, femtosecond optical laser pulses and, more recently, terahertz electromagnetic pulses are used to induce spin torque and spin transport and to monitor the subsequent time evolution. The two approaches, sometimes referred to as femto-magnetism and terahertz magnetism, have provided new, surprising and relevant insights as well as applications for spintronics. Examples include the ultrafast optical switching of magnetic order and the generation of broadband terahertz electromagnetic fields.

This APL Special Topic Collection is dedicated to provide a platform for the newest developments and future trends in the very active, dynamic and exciting research field of ultrafast spintronics.
FIGURES

<figure><img src="image_2.png" /><figcaption>FIG 1. Elementary spintronic operations. (a) Turning spins requires torque, (b) transport of spin angular momentum implies spin currents, (c) all of which need to be observed. In ultrafast and THz spintronics, the operations (a)-(c) are implemented using femtosecond laser pulses (visible to infrared) and terahertz (THz) electromagnetic pulses (1-30 THz).</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>FIG 2. Ultrafast demagnetization and ultrafast spin transport. (a) Excitation of a ferromagnetic thin film F with a femtosecond laser pulse (pump) leads to a transient quenching of the magnetization $M$. (b) Femtosecond laser-pulse excitation of a F|N stack consisting of a ferromagnetic layer F and normal-metal layer N triggers a transient ultrafast spin current with density $j_s$ from F to N. Spin-to-charge-current conversion converts the longitudinal spin current into a transient charge current that acts as a source of a terahertz electromagnetic pulse.</figcaption></figure>
**Spintronics.** Spin-based electronics (spintronics) is a highly active subfield of magnetism and, more generally, solid-state research. It aims at extending electronic functionalities, which rely on the electron charge as information carrier, by the spin of the electron¹.

Spintronics has large application potential in information storage and processing. Elementary spintronic operations (Fig. 1) include (a) control over magnetic order and, thus, over magnetically stored information by spin torque (Zeeman torque, spin-transfer torque, spin-orbit torque) (Fig. 1a), (b) the transport of spin angular momentum in the form of spin-polarized currents (Fig. 1b) or spin waves (magnons) and (c) the detection of spin dynamics (Fig. 1c)²,³. These operations have already been implemented in a commercial device, a magnetic random-access memory, with writing rates potentially reaching 1 GHz⁴.

**Why ultrafast spintronics?** To make spintronic operations competitive and compatible with other information carriers like photons⁵ and electrons⁶, their speed needs to be pushed to femtosecond time scales and, thus, terahertz frequencies. Working toward this goal comes with a number of exciting benefits.

First, one obtains a better understanding of fundamental magnetic and spintronic effects. Examples include spin-electron and spin-lattice coupling, magnon generation and relaxation and the initial stage of transport phenomena such as giant magnetoresistance (GMR)⁷, tunneling magnetoresistance (TMR)⁸, anisotropic magnetoresistance (AMR)⁹, the spin Seebeck effect (SSE)¹⁰,¹¹ and spin pumping¹²,¹³. Second, the occurrence of new physical effects can be expected because the THz range overlaps with important excitations of magnetic solids¹⁴. Examples are the frequencies of phonons and magnons and the relaxation rates of electronic intraband transport. Third and finally, applications beyond spintronics in fields such as ultrafast and THz photonics¹⁵ arise.

**Implementation.** To implement ultrafast spintronics, one needs to realize established spintronic operations, in particular those of Fig. 1, at femtosecond time scales. This goal requires the development of suitable experimental stimuli and probes of ultrafast spin dynamics and of theoretical methods modeling them.

Experimentally, femtosecond optical laser pulses and, more recently, terahertz electromagnetic pulses have been shown to be powerful tools to induce spin torque¹⁶,¹⁷,¹⁸,¹⁹,²⁰,²¹ (Fig. 1a) and spin transport²²,²³,²⁴,²⁵,²⁶,²⁷,²⁸,²⁹,³⁰,³¹,³² (Fig. 1b) and to monitor the subsequent time evolution (Fig. 1c). The two approaches, sometimes referred to as femto-magnetism and terahertz magnetism, have provided new, surprising and relevant insights as well as applications for spintronics. Examples include the ultrafast optical switching of magnetic order³³,³⁴ and the generation of broadband terahertz electromagnetic fields³⁵,³⁶,³⁷,³⁸,³⁹,⁴⁰,⁴¹,⁴²,⁴³.

Theory work is confronted with severe challenges because spontaneous magnetic ordering is a genuine many-electron phenomenon. Its description is largely based on model approaches such as the Stoner and Heisenberg model⁴⁴. In combination with ultrafast and highly nonequilibrium dynamics, the situation becomes even more complex. As a consequence, dedicated tools have been developed to address various phenomena such as ultrafast demagnetization³³ and spin transport²².

**This special topic.** Ultrafast and terahertz spintronics is a highly active research field, which not only becomes clear from the numerous research works being published, but also by concerted efforts such as the collaborative research centers SFB-TRR 227 and SFB-TRR 173 of the German Research Foundation, the s-Nebula consortium of the European Union and ....
As detailed below, the articles of this Special Topic address latest trends in ultrafast spintronics with regard to (1) understanding of fundamental effects of ultrafast magnetic-order quenching and (2) spin transport and in terms of (3) applications in magnetic switching and generation of THz electromagnetic pulses.

**Fundamental effects: ultrafast demagnetization**

**Relevance.** Ultrafast demagnetization, i.e., quenching of ferromagnetic order following excitation by an ultrashort laser pulse$^{45,46,47,48,49,50,51}$ (Fig. 2a), is a key phenomenon of ultrafast and THz spintronics. For example, it reveals the time scale of the equilibration of the ordered electron spins with electron-orbital and crystal-lattice degrees of freedom. Further, ultrafast demagnetization is a central component in all-optical ultrafast magnetization switching$^{34}$ (see below).

**Current status.** From a phenomenological viewpoint, excitation by the pump pulse induces (i) a spin accumulation, also known as spin voltage, i.e., a pump-induced excess of magnetization, or (ii) a pump-induced temperature difference between spin-up and spin-down electrons$^{52,53,54,55,56,57}$. Both (i) and (ii) act as driving forces of the temporal rate of change of the magnetization.

One can refine this model by splitting the electronic system in subsystems, e.g., localized d- or f-type electrons, which carry the ferromagnetic order and magnons, and highly mobile sp-type conduction electrons, which interact with the crystal lattice$^{58,59,60,61}$.

Microscopically, elementary processes such as electronic spin-flip scattering or electron-magnon and phonon-magnon scattering$^{62,63,64,65}$ need to be considered which relate to distinct models, for instance Stoner-$^{63}$ or sd-type$^{58,60}$.

**Challenges and this Special Topic.** Even though ultrafast demagnetization is a relatively mature research subject, there are still numerous open questions, the number of which naturally increases with the complexity of the material under study. Already in simple 3d-type model ferromagnets such as Ni, the role of the shape of the pump-induced nonequilibrium electron distribution$^{51,50}$, of spin excitations$^{66,67,68}$ and the static crystalline and spin order$^{69}$ on the magnetization dynamics has been addressed only recently.

The magnetization of rare-earth metals such as Gd and Tb is dominated by highly localized 4f electrons several electronvolts below the Fermi energy, resulting in potentially more complex ultrafast spin dynamics. Accordingly, Decker et al.$^{70}$ address ultrafast energy equilibration of Gd 4f and 5d electrons with the crystal lattice, while Andres et al.$^{71}$ report on an order of magnitude faster characteristic time of ultrafast demagnetization in Tb than in Gd, which is in part ascribed to the very different coupling of 4f spins and crystal lattice in the two materials.

In alloys and multilayers, (anti)ferromagnetically coupled spin sublattices enable additional interactions, in particular energy and spin transfer between the sublattices. Here, element-and/or state selective probing is highly desirable and enabled by extreme ultraviolet and soft X-ray pulses. Remarkable time-delayed dynamics on the 10-50 fs scale between spin subsystems are observed, for instance between Ni and Fe in the Fe$_{50}$Ni$_{50}$ alloy$^{72}$, between Pt and Co in [Co|Pt]$_{n}$ multilayers$^{73}$ and between electrons above and below the Fermi energy in [Co|Pd]$_{n}$ multilayers$^{74}$. A delayed response of a laser-excited ferrimagnetic iron garnet is also reported when weak vs strong external magnetic fields are applied$^{75}$. Theoretical models allow one to elucidate the role of spin transfer by exchange scattering$^{76}$.

Understanding of the probing mechanism is of central importance in ultrafast spintronics. Time-dependent density-functional theory (TD-DFT) is a powerful approach here. For example, it allows one to study to which extent the sum rules of X-ray magnetic circular
dichroism (XMCD), which are used to determine instantaneous magnetic moments, are still valid during and following ultrafast laser excitation<sup>77</sup>. To probe electron-magnon coupling in ferromagnetic Fe, the renormalization of electronic surfaces appears to be a promising new approach<sup>78</sup>.

**Outlook.** The microscopic understanding of excitations and couplings in solids demands very specific, high resolution and spin-sensitive probes. There is an ongoing development of free-electron lasers and high-repetition-rate higher-harmonic generation light sources in combination with dedicated multichannel spectrometers. These efforts will push experimental techniques, such as depth-sensitive resonant magnetic scattering, resonant inelastic X-ray scattering and spin-resolved photoemission to a higher level of performance and, thus, foster new microscopic insights into ultrafast spin dynamics. For example, first experiments<sup>79</sup> have combined terahertz pump pulses with photoemission probes and give unprecedented views of electron dynamics, which may open the field of light-wave controlled spintronics. Future work is expected to further proceed from elemental materials<sup>51,69</sup> to complex compounds or multilayers<sup>73,74</sup>, including recent material developments such as magnetic Weyl semimetals<sup>80</sup>.

**Fundamental effects: ultrafast spin transport**

**Relevance.** Studying the generation and manipulation of ultrafast charge and spin currents using femtosecond laser pulses is of prime importance. Fundamental questions revolve around the interaction of light with spintronic heterostructures, the mechanisms leading to ultrafast spin transport<sup>81,82,83,31,54,55,56,57,61</sup>, the dominant carrier<sup>84</sup> (conduction electrons or magnons), the subsequent transport dynamics (ballistic, superdiffusive and diffusive)<sup>81</sup> and its relaxation<sup>56</sup>. From an applied perspective, ultrafast spin currents are highly relevant for applying spin torque, the acceleration or slowing down of ultrafast demagnetization (see above) and magnetization switching. Another interesting application is the generation of THz electromagnetic pulses (see below).

**Current status.** It is well established that optical excitation of thin film structures such as two-layer stacks F|N, where F is a ferro- or ferrimagnetically ordered material and N is normal metal, leads to the generation of ultrafast spin currents from F to N<sup>22</sup> (Fig. 2b). Following the optical pump pulse, ultrafast spin transport is typically probed by a time-delayed optical probe pulse taking advantage of magneto-optic effects<sup>22</sup> (Fig. 1b) or the probe-emitted photoelectrons<sup>32</sup>. Alternatively, one can take advantage of spin-to-charge-current conversion, resulting in an in-plane charge current that emits a measurable THz electromagnetic pulse<sup>29,80,85,86</sup> (Fig. 2b).

Phenomenologically, and similar to ultrafast demagnetization (see above), two possible driving forces are discussed: a pump-induced difference of electron temperature between F and N (spin Seebeck effect<sup>10,11</sup>) and/or spin voltage<sup>53,54,55,56,57,31</sup>, both of which also apply to nonthermal electron distributions in certain models<sup>10,56</sup>. The resulting spin-polarized electron current injected into N starts out ballistically and, once scattering sets in, becomes superdiffusive<sup>81</sup> and eventually diffusive.

Remarkably, in stacks F|N made of simple metals such as F=Ni<sub>80</sub>F<sub>20</sub> and N=Pt, the ultrafast spin current from F to N has identical time evolution as the rate of change of the magnetization in ultrafast demagnetization of a single F layer<sup>56</sup>. This behavior indicates that ultrafast spin transport in F|N and ultrafast demagnetization in F are predominantly driven by the same force: the transient spin voltage of F<sup>56</sup>.

In addition to such band-like transport, a shift-type mechanism, optical intersite spin transfer (OISTR), was suggested recently<sup>87</sup> and experimentally confirmed subsequently<sup>88,89,90,91</sup>. In OISTR, optical excitation transfers electronic occupation into states with shifted center of mass of spin density, resulting in spin transfer from F to N.
A further spin-current mechanism can arise when circularly polarized pump pulses are applied⁹². Microscopically, the pump-helicity-dependent spin transport was explained by inverse spin-orbit torque.

Theoretical approaches to ultrafast spin transport are based on the Boltzmann transport equation⁹³ or time-dependent density-functional theory⁸⁷,⁹⁴,⁹⁵.

**Challenges and this Special Topic.** A central goal of ultrafast spintronics is to maximize the spin current amplitude for a given incident laser fluence, i.e., pulse energy per area (Fig. 2b). To obtain maximum driving spin voltage, materials such as magnetic Weyl semimetals⁸⁰, half-metals⁹⁶ and $Co_xFe_{1-x}$ alloys ($0 < x < 1$)⁸⁵ are studied. Maximum interface spin transmission is another crucial parameter and addressed by interface engineering⁹⁶ and introducing intermediate layers between F and N⁸⁶. The spatiotemporal structure of the spin current can be controlled by spin-sink layers⁹⁶ and depends on the time scales of electron-phonon coupling⁹⁷ and the transition from ballistic to diffusive transport⁹⁸. Finally, new spin-current sources need to be explored, for example, chiral antiferromagnets⁹⁹.

Future modeling needs to take all interactions between electron spins, electron orbital motion and phonons as well as spin, charge and heat transport on multiple time and length scales into account.

**Outlook.** Even though central aspects of ultrafast spin transport are not well understood, in particular those related to interfaces, promising applications have emerged and will motivate further works; While previous works have so far mostly considered for ultrafast spin transport by conduction electrons, ultrafast magnon transport¹⁰⁰ is expected to yield new and exciting insights and applications such as frequency comb generation¹⁰¹.

## Applications: magnetic-order switching

**Relevance.** Ultrafast all-optical switching of magnetic order can be of crucial importance for the development of future generations information-technology elements with low power consumption and fast operation. Ultimately, we aim at operation at THz rates. To reach this goal, a solid material base is required, that is, magnetic materials whose properties permit operation at such frequencies. Consequently, studies of magnetic materials in the THz range has been expanding strongly in the last decade. In particular, the goal is set to achieve full switching of magnetic order at the time scale of a few picoseconds, or even below that.

**Current status.** Several mechanisms of all-optical switching of magnetic order have been discovered by now. Amongst them, the most investigated is the ultrafast heating-only-induced switching of the magnetization of ferrimagnetic alloys, witnessed by several contributions in this issue¹⁰²,¹⁰³,¹⁰⁴,¹⁰⁵,¹⁰⁶. The switching occurs at the sub-picosecond time scale and is toggle by nature. The mechanism has been known for about 15 years and is relatively well understood by now¹⁰²,¹⁰³,¹⁰⁴,¹⁰⁵. Therefore, ferrimagnetic alloys are considered to be the most reliable possible material system for applications, for example, as recording medium in an ultrafast concept of opto-magnetic memory.

There are several compositions of the ferrimagnet alloys that exhibit single-shot toggle switching. The important ingredient is the presence of two coupled spin sublattices with different intra-sublattice exchange interaction. This feature could easily be realized in rare-earth/transition-metal alloys and multilayers, but also in rare-earth-free ferrimagnets such as Mn-based Heusler alloys.

**Challenges and this Special Topic.** The most important question related to application is how reliably the magnetization switching can be repeated. During the switching process, the magnetization first crosses zero on a sub-picosecond time scale, provided the pump pulse was short enough. However, the subsequent complete recovery of the magnetization along
its new (reversed) direction is slower and ultimately limits the repetition rate of the possible re-recording process. Various schemes can be applied to improve this situation<sup>102</sup>. Materials with strong magnetic anisotropy can both accelerate the recovery and assure the stability of small bits. This idea motivated a search among alloys containing various rare-earth materials<sup>103</sup>.

Another important aspect is the energy required for the magnetization reversal process, which is the issue dominating the data-storage industry as a whole. One could reduce this energy considerably by applying smart multilayer schemes<sup>105</sup>. Last but not least, the theoretical description of the switching process is not yet fully complete<sup>104</sup>, and novel schemes can be proposed for fast and less energy-hungry switching<sup>106</sup>.

**Outlook.** In view of energy consumption as well as residual heating effects, nonthermal mechanisms of ultrafast magnetization reversal attract more and more attention. To avoid heating, magnetic insulators will become materials of choice. The enabling mechanisms will of course be completely different from those in metals. The most interesting possibility may be to use the crystal lattice as the driving parameter. Thus, one can envisage magnetic switching by lattice strain on the femtosecond scale. Alternatively, an optically driven electron charge-transfer transition similarly affects the crystal fields and should, therefore, be able to induce a sufficiently strong transient magnetic anisotropy to achieve the switching.

## Applications: spintronic sources of THz electromagnetic pulses

**Relevance.** Upon excitation by a femtosecond laser pulse, a spintronic THz emitter (STE) emits an ultrashort THz electromagnetic pulse. Such pulses can be used as sensitive and ultrafast probes of all infrared-active resonances of all phases of matter, for example, molecular rotations and vibrations in gases and liquids as well as phonons, intraband electron transport, Cooper pairs excitons and magnons in solids. Due to this specificity, THz radiation has also found application in imaging and quality control.

**Current status.** As reviewed in detail in an Editorial of this Special Topic<sup>43</sup>, a typical STE consists of a ferromagnetic metal layer F, which acts as a spin-current source, in contact with one or two metal layers N for spin-to-charge-current conversion (Fig. 2b). In the current understanding of STEs, the incident femtosecond laser pulse deposits energy in FM (Fig. 2b) and, thus, induces a spin voltage that drives a spin current into the adjacent N (see above). Due to spin-to-charge-current conversion, the out-of-plane spin current is converted into an ultrafast in-plane charge current that acts as a source of a THz electromagnetic pulse.

Amongst other attractive features<sup>43</sup>, STEs are broadband without gaps in the emission spectrum at 0.3-30 THz<sup>35</sup>, more efficient than state-of-the-art emitters such as ZnTe and GaP<sup>35</sup>, independent of the pump wavelength from the infrared<sup>107</sup> to the visible<sup>108</sup> to the extreme ultraviolet<sup>109</sup>, scalable<sup>110,111</sup>, and their linear polarization can be set by an external magnetic field in a contact-less manner<sup>112</sup>.

**Open questions and this Special Topic.** An important goal regarding STEs is to extend the amplitude and bandwidth of the emitted THz pulses. It can be achieved by larger and faster spin currents (see above) and more efficient spin-to-charge-current conversion through material optimization and photonic measures<sup>43</sup>. For example, antiferromagnets are found to be interesting candidates for spin-to-charge-current conversion<sup>86</sup>. At the same time, the peculiar features of STEs need to be studied in detail to develop and demonstrate new functionalities.

Exciting functionalities and applications are reported also. Modulation of the THz polarization direction by an electric voltage rather than an external magnetic field is demonstrated. The
voltage is applied to the piezo-electric substrate on which the STE is grown, and the resulting
strain-induced magnetic anisotropy rotates the STE magnetization¹¹³.

The STE area can be upscaled straightforwardly. By simultaneously increasing the driving laser power, peak THz fields can be generated that are sufficiently strong (here 60 kV/cm) to modulate a second, air-plasma-based THz source¹¹⁴. By further upscaling, THz peak fields exceeding 1.5 MV/cm and fluences of about 1 mJ/cm² can be obtained¹¹¹, which are highly interesting for nonlinear THz spectroscopy in the elusive 1-10 THz window.

Finally, the lateral extent of the THz near-field directly behind the STE layer equals that of the intensity of the driving femtosecond laser beam. By placing the sample in the THz near-field, imaging beyond the diffraction limit can be realized¹¹⁵. At 1 THz, a spatial resolution that is a factor of 60 smaller than the wavelength of 300 µm is achieved. A similar approach is used to gain spatially resolved insights into a laterally nanostructured STE¹¹⁶.

**Outlook.** To further improve STEs, future research is expected to include novel materials as ultrafast spin-current sources and spin-to-charge-current converters and to explore the so far under-researched role of the F/N interface.

**Conclusion.**

Ultrafast and terahertz spintronics have significantly extended the scope and application range of spintronics and magnetism research. Future directions may take advantage of coherent spin dynamics¹¹⁷ for, e.g., neuromorphic computing¹¹⁸. State of the art theory, in particular, time-dependent density-functional theory⁹⁴,⁹⁵, will strongly support and possibly guide these developments.
References

<footnote n="1">¹ S. Maekawa, T. Kikkawa, H. Chudo, J. Ieda, E. Saitoh, Spin and spin current—From fundamentals to recent progress, J. Appl. Phys. 133, 020902 (2023)</footnote>

<footnote n="2">² E.Y. Vedmedenko, R.K. Kawakami, D. Sheka, P. Gambardella, A. Kirilyuk, A. Hirohata, C. Binek, O.A. Chubykalo-Fesenko, S. Sanvito, B. Kirby, J. Grollier, K. Everschor-Sitte, T. Kampfrath, C.-Y. You, A. Berger, The 2020 Magnetism Roadmap, J. Phys. D: Appl. Phys. 53, 453001 (2020)</footnote>

<footnote n="3">³ A. Leitenstorfer et al., The 2023 Terahertz Science and Technology Roadmap, Journal of Physics D: Applied Physics (2023)</footnote>

<footnote n="4">⁴ S. Bhatti, R. Sbiaa, A. Hirohata, H. Ohno, S. Fukami, S.N. Piramanayagam, Spintronics based random access memory: a review, Materials Today 20, 530 (2017)</footnote>

<footnote n="5">⁵ D. Hillerkuss et al., 26 Tbit s⁻¹ line-rate super-channel transmission utilizing all-optical fast Fourier transform processing, Nature Photon. 5, 364 (2011)</footnote>

<footnote n="6">⁶ J.A. del Alamo, Nanometre-scale electronics with III-V compound semiconductors, Nature 479, 317 (2011)</footnote>

<footnote n="7">⁷ L.Z. Jin, A. Tkach, F. Casper, V. Spetter, H. Grimm, A. Thomas, T. Kampfrath, M. Bonn, M. Kläui, D. Turchinovich, Accessing the fundamentals of magnetotransport in metals with terahertz probes, Nature Physics 11, 761 (2015)</footnote>

<footnote n="8">⁸ Z. Jin, J. Li, W. Zhang, C. Guo, C. Wan, X. Han, Z. Cheng, C. Zhang, A. V. Balakin, A. P. Shkurinov, Y. Peng, G. Ma, Y. Zhu, J. Yao, and S. Zhuang, Magnetic Modulation of Terahertz Waves via Spin-Polarized Electron Tunneling Based on Magnetic Tunnel Junctions, Phys. Rev. Applied 14, 014032 (2020)</footnote>

<footnote n="9">⁹ L. Nadvorník, M. Borchert, L. Brandt, R. Schlitz, K.A. de Mare, K. Výborný, I. Mertig, G. Jakob, M. Kläui, S.T.B. Goennenwein, M. Wolf, G. Woltersdorf, T. Kampfrath, Broadband terahertz probes of anisotropic magnetoresistance disentangle extrinsic and intrinsic contributions, Physical Review X 11, 021030 (2021)</footnote>

<footnote n="10">¹⁰ T. Seifert, S. Jaiswal, J. Barker, S.T. Weber, I. Razdolski, J. Cramer, O. Gueckstock, S. Maehrlein, L. Nadvornik, S. Watanabe, C. Ciccarelli, A. Melnikov, G. Jakob, M. Münzenberg, S.T.B. Goennenwein, G. Woltersdorf, B. Rethfeld, P.W. Brouwer, M. Wolf, M. Kläui, T. Kampfrath, Femtosecond formation dynamics of the spin Seebeck effect revealed by terahertz spectroscopy, Nature Communications 9, Article number: 2899 (2018)</footnote>

<footnote n="11">¹¹ F.N. Kholid, D. Hamara, M. Terschanski, F. Mertens, D. Bossini, M. Cinchetti, L. McKenzie-Sell, J. Patchett, D. Petit, R. Cowburn, J. Robinson, J. Barker, C. Ciccarelli,1, Temperature dependence of the picosecond spin Seebeck effect, Appl. Phys. Lett. 119, 032401 (2021)</footnote>

<footnote n="12">¹² J. Li et al., Spin current from sub-terahertz-generated antiferromagnetic magnons, Nature 578, 70-74 (2020)</footnote>

<footnote n="13">¹³ P. Vaidya et al., Subterahertz spin pumping from an insulating antiferromagnet, Science 368, 160-165 (2020)</footnote>

<footnote n="14">¹⁴ T. Kampfrath, K. Tanaka, K.A. Nelson, Resonant and nonresonant control over matter and light by intense terahertz transients, Nature Photonics 7, 680-690 (2013)</footnote>

<footnote n="15">¹⁵ Tom S. Seifert, Liang Chen, Zhengxing Wei, Tobias Kampfrath, Jingbo Qi, Spintronic Sources of Ultrashort Terahertz Pulses, Appl. Phys. Lett. 120, 180401 (2022)</footnote>

<footnote n="16">¹⁶ S. Bonetti, M.C. Hoffmann, M.J. Sher, Z. Chen, S.H. Yang, M.G. Samant, S.S.P. Parkin, and H.A. Dürr, THz-Driven Ultrafast Spin-Lattice Scattering in Amorphous Metallic Ferromagnets, Phys. Rev. Lett. 117, 087205 (2016)</footnote>

<footnote n="17">¹⁷ R. Salikhov, I. Ilyakov, L. Körber, A. Kákay, R.A. Gallardo, A. Ponomaryov, J.-C. Deinert, T.V.A.G. de Oliveira, K. Lenz, J. Fassbender, S. Bonetti, O. Hellwig, J. Lindner, S. Kovalev, Coupling of terahertz light with nanometre wavelength magnon modes via spin-orbit torque, Nat. Phys. (2023). https://doi.org/10.1038/s41567-022-01908-1</footnote>

<footnote n="18">¹⁸ G.-M. Choi, C.-H. Moon, B.-C. Min, K.-J. Lee, and D. G. Cahill, Thermal spin-transfer torque driven by the spindependent Seebeck effect in metallic spin-valves, Nat. Phys. 11, 576 (2015)</footnote>

<footnote n="19">¹⁹ A. Alekhin, I. Razdolski, N. Ilin, J. P. Meyburg, D. Diesing, V. Roddatis, I. Rungger, M. Stamenova, S. Sanvito, U. Bovensiepen et al., Femtosecond Spin Current Pulses Generated by the Nonthermal Spin-Dependent Seebeck Effect and Interacting with Ferromagnets in Spin Valves, Phys. Rev. Lett. 119, 017202 (2017)</footnote>

<footnote n="20">²⁰ I. Razdolski, A. Alekhin, N. Ilin, J. P. Meyburg, V. Roddatis, D. Diesing, U. Bovensiepen, and A. Melnikov, Nanoscale interface confinement of ultrafast spin transfer torque driving non-uniform spin dynamics, Nat. Commun. 8, 15007 (2017)</footnote>

<footnote n="21">²¹ M. L. M. Lalieu, R. Lavrijsen, R. A. Duine, and B. Koopmans, Investigating optically excited terahertz standing spin waves using noncollinear magnetic bilayers, Phys. Rev. B 99, 184439 (2019)</footnote>

<footnote n="22">²² G. Malinowski, N. Bergeard, M. Hehn, S. Mangin, Hot-electron transport and ultrafast magnetization dynamics in magnetic multilayers and nanostructures following femtosecond laser pulse excitation, Eur. Phys. J. B 91, 98 (2018)</footnote>
23 A. Eschenlohr, Spin dynamics at interfaces on femtosecond timescales, J. Phys. Condens. Matter 33, 13001 (2020)

24 A. El-Ghazaly, J. Gorchon, R. B. Wilson, A. Pattabi, J. Bokor, Progress towards ultrafast spintronics applications, J. Magn. Magn. Mater. 502, 166478 (2020)

25 G. Malinowski, F. Dalla Longa, J. H. H. Rietjens, P. V. Paluskar, R. Huijink, H. J. M. Swagten, B. Koopmans, Control of speed and efficiency of ultrafast demagnetization by direct transfer of spin angular momentum, Nat. Phys. 4, 855 (2008)

26 A. Melnikov, I. Razdolski, T.O. Wehling, E.Th. Papaioannou, V. Roddatis, P. Fumagalli, O. Aktsipetrov, A.I. Lichtenstein, U. Bovensiepen, Ultrafast Transport of Laser-Excited Spin-Polarized Carriers in Au/Fe/MgO(001), Phys. Rev. Lett. 107, 076601 (2012)

27 D. Rudolf, C. La-o-vorakiat, M. Battiato, R. Adam, J. M. Shaw, E. Turgut, P. Maldonado, S. Mathias, P. Grychtol, H. T. Nembach et al., Ultrafast magnetization enhancement in metallic multilayers driven by superdiffusive spin current, Nat. Commun. 3, 1037 (2012)

28 A. Eschenlohr, M. Battiato, P. Maldonado, N. Pontius, T. Kachel, K. Holldack, R. Mitzner, A. Föhlisch, P. M. Oppeneer, and C. Stamm, Ultrafast spin transport as key to femtosecond demagnetization, Nat. Mater. 12, 332 (2013)

29 T. Kampfrath, M. Battiato, P. Maldonado, G. Eilers, J. Nötzold, S. Mährlein, V. Zbarsky, F. Freimuth, Y. Mokrousov, S. Blügel et al., Terahertz spin current pulses controlled by magnetic heterostructures, Nat. Nanotechnol. 8, 256 (2013)

30 E. Turgut, C. La-o-vorakiat, J. M. Shaw, P. Grychtol, H. T. Nembach, D. Rudolf, R. Adam, M. Aeschlimann, C. M. Schneider, T. J. Silva et al., Controlling the Competition between Optically Induced Ultrafast Spin-Flip Scattering and Spin Transport in Magnetic Multilayers, Phys. Rev. Lett. 110, 197201 (2013)

31 G.-M. Choi, B.-C. Min, K.-J. Lee, and D. G. Cahill, Spin current generated by thermally driven ultrafast demagnetization, Nat. Commun. 5, 4334 (2014)

32 J. Chen, U. Bovensiepen, A. Eschenlohr, T. Müller, P. Elliott, E. K. U. Gross, J. K. Dewhurst, and S. Sharma, Competing Spin Transfer and Dissipation at Co/Cu(001) Interfaces on Femtosecond Timescales, Phys. Rev. Lett. 122, 067202 (2019)

33 A. Kirilyuk, A. V. Kimel, and T. Rasing, Ultrafast optical manipulation of magnetic order, Rev. Mod. Phys. 82, 2731 (2010)

34 A. Kirilyuk, A. V. Kimel, and T. Rasing, Laser-induced magnetization dynamics and reversal in ferrimagnetic alloys, Reports Prog. Phys. 76, 26501 (2013)

35 T. Seifert, S. Jaiswal, U. Martens, J. Hannegan, L. Braun, P. Maldonado, F. Freimuth, A. Kronenberg, J. Henrizi, I. Radu et al., Efficient metallic spintronic emitters of ultrabroadband terahertz radiation, Nat. Photonics 10, 483 (2016)

36 D. Yang, J. Liang, C. Zhou, L. Sun, R. Zheng, S. Luo, Y. Wu, and J. Qi, Powerful and tunable THz emitters based on the Fe/Pt magnetic heterostructure, Adv. Opt. Mater. 4, 1944 (2016)

37 Y. Wu, M. Elyasi, X. Qiu, M. Chen, Y. Liu, L. Ke, and H. Yang, High-performance THz emitters based on ferromagnetic/nonmagnetic heterostructures, Adv. Mater. 29, 1603031 (2017)

38 G. Torosyan, S. Keller, L. Scheuer, R. Beigang, and E. T. Papaioannou, Optimized spintronic terahertz emitters based on epitaxial grown Fe/Pt layer structures, Sci. Rep. 8, 1311 (2018)

39 E. T. Papaioannou and R. Beigang, THz spintronic emitters: a review on achievements and future challenges, Nanophotonics 10, 1243 (2021)

40 Z. Feng, H. Qiu, D. Wang, C. Zhang, S. Sun, B. Jin, and W. Tan, Spintronic terahertz emitter, J. Appl. Phys. 129, 10901 (2021)

41 C. Bull, S. M. Hewett, R. Ji, C.-H. Lin, T. Thomson, D. M. Graham, and P.W. Nutter, Spintronic terahertz emitters: status and prospects from a materials perspective, APL Mater. 9, 90701 (2021)

42 W. Wu, C. Yaw Ameyaw, M. F. Doty, and M. B. Jungfleisch, Principles of spintronic THz emitters, J. Appl. Phys. 130, 91101 (2021)

43 [23] T. S. Seifert, L. Cheng, Z. Wei, T. Kampfrath, and J. Qi, Spintronic sources of ultrashort terahertz electromagnetic pulses, Appl. Phys. Lett. 120, 180401 (2022)

44 W. Nolting and A. Ramakanth, Quantum Theory of Magnetism (Springer-Verlag, Berlin, Heidelberg, 2009).

45 E. Beaurepaire, J.-C. Merle, A. Daunois, and J.-Y. Bigot, Ultrafast Spin Dynamics in Ferromagnetic Nickel, Phys. Rev. Lett. 76, 4250 (1996)

46 J. Hohlfeld, E. Matthias, R. Knorren, and K. H. Bennemann, Nonequilibrium Magnetization Dynamics of Nickel, Phys. Rev. Lett. 78, 4861 (1997)
47 B. Koopmans, G. Malinowski, F. Dalla Longa, D. Steiauf, M. Fähnle, T. Roth, M. Cinchetti, and M. Aeschlimann, Explaining the paradoxical diversity of ultrafast laser-induced demagnetization, Nat. Mater. 9, 259 (2010)

48 R. B. Wilson, Y. Yang, J. Gorchon, C.-H. Lambert, S. Salahuddin, and J. Bokor, Electric current induced ultrafast demagnetization, Phys. Rev. B 96, 045105 (2017)

49 T. Roth, A. J. Schellekens, S. Alebrand, O. Schmitt, D. Steil, B. Koopmans, M. Cinchetti, and M. Aeschlimann, Temperature Dependence of Laser-Induced Demagnetization in Ni: A Key for Identifying the Underlying Mechanism, Phys. Rev. X 2, 021006 (2012)

50 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, Ultrafast Demagnetization of Iron Induced by Optical Versus Terahertz Pulses, Phys. Rev. X 11, 041055 (2021)

51 [1] M. Stiehl, M. Weber, C. Seibel, J. Hoefer, S. T. Weber, D. M. Nenno, H. C. Schneider, B. Rethfeld, B. Stadtmüller, and M. Aeschlimann, Role of primary and secondary processes in the ultrafast spin dynamics of nickel, Appl. Phys. Lett. 120, 62410 (2022)

52 B. Y. Mueller, T. Roth, M. Cinchetti, M. Aeschlimann, and B. Rethfeld, Driving force of ultrafast magnetization dynamics, New J. Phys. 13, 123010 (2011)

53 B. Y. Mueller and B. Rethfeld, Thermodynamic µT model of ultrafast magnetization dynamics, Phys. Rev. B 90, 144420 (2014)

54 A. Fognini, T. U. Michlmayr, A. Vaterlaus, and Y. Acremann, Laser-induced ultrafast spin current pulses: A thermodynamic approach, J. Phys. Condens. Matter 29, 214002 (2017)

55 K. Bühlmann, G. Saerens, A. Vaterlaus, and Y. Acremann, Detection of femtosecond spin voltage pulses in a thin iron film, Struct. Dyn. 7, 65101 (2020)

56 S.M. Rouzegar, L. Brandt, L. Nádvorník, D.A. Reiss, A.L. Chekhov, O. Gueckstock, C. In, M. Wolf, T.S. Seifert, P.W. Brouwer, G. Woltersdorf, T. Kampfrath, Laser-induced terahertz spin transport in magnetic nanostructures arises from the same force as ultrafast demagnetization, Physical Review B 106, 144427 (2022)

57 T. Lichtenberg, M. Beens, M. H. Jansen, B. Koopmans, R. A. Duine, Probing optically induced spin currents using terahertz spin waves in noncollinear magnetic bilayers, Phys. Rev. B 105, 144416 (2022)

58 A. Manchon, Q. Li, L. Xu, and S. Zhang, Theory of laser-induced demagnetization at high temperatures, Phys. Rev. B 85, 064408 (2012)

59 E. G. Tveten, A. Brataas, and Y. Tserkovnyak, Electron-magnon scattering in magnetic heterostructures far out of equilibrium, Phys. Rev. B 92, 180412(R) (2015)

60 M. Beens, R. A. Duine, and B. Koopmans, s-d model for local and nonlocal spin dynamics in laser-excited magnetic heterostructures, Phys. Rev. B 102, 054442 (2020)

61 M. Beens, R. A. Duine, and B. Koopmans, Modeling ultrafast demagnetization and spin transport: the interplay of spin-polarized electrons and thermal magnons, Phys. Rev. B 105, 144420 (2022)

62 K. Carva, M. Battiato, and P. M. Oppeneer, Ab Initio Investigation of the Elliott-Yafet Electron-Phonon Mechanism in Laser-Induced Ultrafast Demagnetization, Phys. Rev. Lett. 107, 207201 (2011)

63 B. Y. Mueller, A. Baral, S. Vollmar, M. Cinchetti, M. Aeschlimann, H. C. Schneider, and B. Rethfeld, Feedback Effect During Ultrafast Demagnetization Dynamics in Ferromagnets, Phys. Rev. Lett. 111, 167204 (2013)

64 W. Töws and G. M. Pastor, Many-Body Theory of Ultrafast Demagnetization and Angular Momentum Transfer in Ferromagnetic Transition Metals, Phys. Rev. Lett. 115, 217204 (2015)

65 K. Krieger, J. K. Dewhurst, P. Elliott, S. Sharma, and E. K. U. Gross, Laser-induced demagnetization at ultrashort time scales: predictions of TDDFT, J. Chem. Theory Comput. 11, 4870 (2015)

66 S. Eich, M. Plötzing, M. Rollinger, S. Emmerich, R. Adam, C. Chen, H. C. Kapteyn, M. Murnane, L. Plucinski, D. Steil, B. Stadtmüller, M. Cinchetti, M. Aeschlimann, C.M. Schneider, and S. Mathias, Sci. Adv. 3, e1602094 (2017)

67 P. Tengdin, W. You, C. Chen, X. Shi, D. Zusin, Y. Zhang, C. Gentry, A. Blonsky, M. Keller, P. M. Oppeneer, H. C. Kapteyn, Z. Tao, and M. M. Murnane, Sci. Adv. 4, eaap9744 (2018)

68 R. Gort, K. Bühlmann, S. Däster, G. Salvatella, N. Hartmann, Y. Zemp, S. Holenstein, C. Stieger, A. Fognini, T. U. Michlmayr, T. Bähler, A. Vaterlaus, and Y. Acremann, Phys. Rev. Lett. 121, 087206 (2018)

69 [6] Kumar Neeraj, Apoorva Sharma, Maria Almeida, Patrick Matthes, Fabian Samad, Georgeta Salvan, Olav Hellwig, Stefano Bonetti, Terahertz charge and spin transport in metallic ferromagnets: The role of crystalline and magnetic order, Appl. Phys. Lett. 120, 102406 (2022)

70 [2] Régis Decker, Artur Born, Kari Ruotsalainen, Karl Bauer, Robert Haverkamp, Robby Büchner, Annette Pietzsch and Alexander Föhlisch, Spin-lattice angular momentum transfer of localized and valence electrons in the demagnetization transient state of gadolinium, Appl. Phys. Lett. 119, 152403 (2021)
<footnote n="71">71 [3] Beatrice Andres, Sang Eun Lee and Martin Weinelt, The role of spin-lattice coupling for ultrafast changes of the magnetic order in rare earth metals, Appl. Phys. Lett. 119, 182404 (2021)</footnote>

<footnote n="72">72 [5] S. Jana, R. Knut, S. Muralidhar, R. S. Malik, R. Stefanuik, J. Åkerman, O. Karis, C. Schüßler-Langeheine and N. Pontius, Experimental confirmation of the delayed Ni demagnetization in FeNi alloy, Appl. Phys. Lett. 120, 102404 (2022)</footnote>

<footnote n="73">73 [7] M. Hennes, G. Lambert, V. Chardonnet, R. Delaunay, G. S. Chiuzbäian, E. Jal and B. Vodungbo, Element-selective analysis of ultrafast demagnetization in Co/Pt multilayers exhibiting large perpendicular magnetic anisotropy, Appl. Phys. Lett. 120, 072408 (2022)</footnote>

<footnote n="74">74 [8] Loïc Le Guyader, Daniel J. Higley, Matteo Pancaldi, Tianmin Liu, Zhao Chen, Tyler Chase, Patrick W. Granitzka, Giacomo Coslovich, Alberto A. Lutman, Georgi L. Dakovski, William F. Schlotter, Padraic Shafer, Elke Arenholz, Olav Hellwig, Mark L. M. Lalieu, Bert Koopmans, Alexander H. Reid, Stefano Bonetti, Joachim Stöhr and Hermann A. Dürr, State-resolved ultrafast charge and spin dynamics in [Co/Pd] multilayers, Appl. Phys. Lett. 120, 032401 (2022)</footnote>

<footnote n="75">75 [9] I. A. Dolgikh, F. Formisano, K. H. Prabhakara, M. V. Logunov, A. K. Zvezdin, P. C. M. Christianen and A. V. Kimel, Spin dynamics driven by ultrafast laser-induced heating of iron garnet in high magnetic fields, Appl. Phys. Lett. 120, 012401 (2022)</footnote>

<footnote n="76">76 [10] Kai Leckron, Alexander Baral and Hans Christian Schneider, Exchange scattering on ultrafast timescales in a ferromagnetic two-sublattice system, Appl. Phys. Lett. 120, 102407 (2022)</footnote>

<footnote n="77">77 [11] S. Sharma, S. Shallcross, P. Elliott, S. Eisebitt, C. von Korff Schmising and J. K. Dewhurst, Computational analysis of transient XMCD sum rules for laser pumped systems: When do they fail?, Appl. Phys. Lett. 120, 062409 (2022)</footnote>

<footnote n="78">78 [4] Beatrice Andres, Martin Weinelt, Hubert Ebert, Jürgen Braun, Alex Aperis and Peter M. Oppeneer, Strong momentum-dependent electron-magnon renormalization of a surface resonance on iron, Appl. Phys. Lett. 120, 202404 (2022)</footnote>

<footnote n="79">79 J. Reimann, S. Schlauderer, C. P. Schmid, F. Langer, S. Baierl, K. A. Kokh, O. E. Tereshchenko, A. Kimura, C. Lange, J. Güdde, U. Höfer, R. Huber, Subcycle observation of lightwave-driven Dirac currents in a topological surface band, Nature 562, 396-400 (2018)</footnote>

<footnote n="80">80 [14] Genaro Bierhance, Anastasios Markou, Oliver Gueckstock, Reza Rouzegar, Yannic Behovits, Alexander L. Chekhov, Martin Wolf, Tom S. Seifert, Claudia Felser and Tobias Kampfrath, Spin-voltage-driven efficient terahertz spin currents from the magnetic Weyl semimetals Co2MnGa and Co2MnAl, Appl. Phys. Lett. 120, 082401 (2022)</footnote>

<footnote n="81">81 M. Battiato, K. Carva, and P. M. Oppeneer, Superdiffusive Spin Transport As a Mechanism of Ultrafast Demagnetization, Phys. Rev. Lett. 105, 027203 (2010)</footnote>

<footnote n="82">82 D. M. Nenno, S. Kaltenborn, and H. C. Schneider, Boltzmann transport calculation of collinear spin transport on short timescales, Phys. Rev. B 94, 115102 (2016)</footnote>

<footnote n="83">83 J. Hurst, P.-A. Hervieux, and G. Manfredi, Spin current generation by ultrafast laser pulses in ferromagnetic nickel films, Phys. Rev. B 97, 014424 (2018)</footnote>

<footnote n="84">84 Pilar Jiménez-Cavero, Oliver Gueckstock, Lukáš Nádvorník, Irene Lucas, Tom S. Seifert, Martin Wolf, Reza Rouzegar, Piet W. Brouwer, Sven Becker, Gerhard Jakob, Mathias Kläui, Chenyang Guo, Caihua Wan, Xiufeng Han, Zuanming Jin, Hui Zhao, Di Wu, Luis Morellón, Tobias Kampfrath, Transition of laser-induced terahertz spin currents from torque- to conduction-electron-mediated transport, Physical Review B 105, 184408 (2022)</footnote>

<footnote n="85">85 [12] Robert Schneider, Mario Fix, Jannis Bensmann, Steffen Michaelis de Vasconcellos, Manfred Albrecht and Rudolf Bratschitsch, Composition-dependent ultrafast THz emission of spintronic CoFe/Pt thin films, Appl. Phys. Lett. 120, 042404 (2022)</footnote>

<footnote n="86">86 [13] O. Gueckstock, R. L. Seeger, T. S. Seifert, S. Auffret, S. Gambarelli, J. N. Kirchhof, K. I. Bolotin, V. Baltz, T. Kampfrath and L. Nádvorník, Impact of gigahertz and terahertz transport regimes on spin propagation and conversion in the antiferromagnet IrMn, Appl. Phys. Lett. 120, 062408 (2022)</footnote>

<footnote n="87">87 J. K. Dewhurst, P. Elliott, S. Shallcross, E. K. U. Gross, and S. Sharma, Laser-Induced intersite spin transfer, Nano Lett. 18, 1842 (2018)</footnote>

<footnote n="88">88 F. Siegrist, J. A. Gessner, M. Ossiander, C. Denker, Y.-P. Chang, M. C. Schröder, A. Guggenmos, Y. Cui, J. Walowski, U. Martens et al., Light-wave dynamic control of magnetism, Nature (London) 571, 240 (2019)</footnote>

<footnote n="89">89 M. Hofherr, S. Häuser, J. K. Dewhurst, P. Tengdin, S. Sakshath, H. T. Nembach, S. T. Weber, J. M. Shaw, T. J. Silva, H. C. Kapteyn et al., Ultrafast optically induced spin transfer in ferromagnetic alloys, Sci. Adv. 6, eaay8717 (2020)</footnote>
<footnote n="90">⁹⁰ F. Willems, C. T. L. Smeenk, N. Zhavoronkov, O. Kornilov, I. Radu, M. Schmidbauer, M. Hanke, C. von Korff Schmising, M. J. J. Vrakking et al., Probing ultrafast spin dynamics with high-harmonic magnetic circular dichroism spectroscopy, Phys. Rev. B 92, 220405(R) (2015)</footnote>

<footnote n="91">⁹¹ D. Steil, J. Walowski, F. Gerhard, T. Kiessling, D. Ebke, A. Thomas, T. Kubota, M. Oogane, Y. Ando, J. Otto et al., Efficiency of ultrafast optically induced spin transfer in Heusler compounds, Phys. Rev. Res. 2, 023199 (2020)</footnote>

<footnote n="92">⁹² T. J. Huisman, R. V. Mikhaylovskiy, J. D. Costa, F. Freimuth, E. Paz, J. Ventura, P. P. Freitas, S. Blügel, Y. Mokrousov, T. Rasing et al., Femtosecond control of electric currents in metallic ferromagnetic heterostructures, Nat. Nanotechnol. 11, 455 (2016)</footnote>

<footnote n="93">⁹³ W.-T. Lu, Y. Zhao, M. Battiato, Y. Wu, and Z. Yuan, Interface reflectivity of a superdiffusive spin current in ultrafast demagnetization and terahertz emission, Phys. Rev. B 101, 014435 (2020)</footnote>

<footnote n="94">⁹⁴ [33] Arqum Hashmi, Shunsuke Yamada, Atsushi Yamada, Kazuhiro Yabana and Tomohito Otobe, Nonlinear dynamics of electromagnetic field and valley polarization in WSe₂ monolayer, Appl. Phys. Lett. 120, 051108 (2022)</footnote>

<footnote n="95">⁹⁵ [34] S. Shallcross, Q. Z. Li, J. K. Dewhurst, S. Sharma and P. Elliott, Ultrafast optical control over spin and momentum in solids, Appl. Phys. Lett. 120, 032403 (2022)</footnote>

<footnote n="96">⁹⁶ [26] J. Hawecker, E. Rongione, A. Markou, S. Krishnia, F. Godel, S. Collin, R. Lebrun, J. Tignon, J. Mangeney, T. Boulier, J.-M. George, C. Felser, H. Jaffrès and S. Dhillon, Spintronic THz emitters based on transition metals and semi-metals/Pt multilayers, Appl. Phys. Lett. 120, 122406 (2022)</footnote>

<footnote n="97">⁹⁷ [15] M. Mattern, A. von Reppert, S. P. Zeuschner, J.-E. Pudell, F. Kühne, D. Diesing, M. Herzog and M. Bargheer, Electronic energy transport in nanoscale Au/Fe hetero-structures in the perspective of ultrafast lattice dynamics, Appl. Phys. Lett. 120, 092401 (2022)</footnote>

<footnote n="98">⁹⁸ [16] Sanjay Ashok, Christopher Seibel, Sebastian T. Weber, Johan Briones and Baerbel Rethfeld, Influence of diffusive transport on ultrafast magnetization dynamics, Appl. Phys. Lett. 120, 142402 (2022)</footnote>

<footnote n="99">⁹⁹ [17] Chen Ouyang, Xuan Wang and Yutong Li, Chirality-selective easily adjustable spin current from uniaxial antiferromagnets, Appl. Phys. Lett. 119, 142404 (2021)</footnote>

<footnote n="100">¹⁰⁰ [30] Ia. A. Filatov, P. I. Gerevenkov, M. Wang, A. W. Rushforth, A. M. Kalashnikova and N. E. Khokhlov, Spectrum evolution and chirping of laser-induced spin wave packets in thin iron films, Appl. Phys. Lett. 120, 112404 (2022)</footnote>

<footnote n="101">¹⁰¹ [29] A. A. Awad, S. Muralidhar, A. Alemán, R. Khymyn, D. Hanstorp and J. Åkerman, Femtosecond laser comb driven perpendicular standing spin waves, Appl. Phys. Lett. 120, 012405 (2022)</footnote>

<footnote n="102">¹⁰² [18] Felix Steinbach, Nele Stetzuhn, Dieter Engel, Unai Atxitia, Clemens von Korff Schmising and Stefan Eisebitt, Accelerating double pulse all-optical write/erase cycles in metallic ferrimagnets, Appl. Phys. Lett. 120, 112406 (2022)</footnote>

<footnote n="103">¹⁰³ [19] Zexiang Hu, Jean Besbas, Ross Smith, Niclas Teichert, Gwenael Atcheson, Karsten Rode, Plamen Stamenov and J. M. D. Coey, Single-pulse all-optical partial switching in amorphous DyxCo₁-x and TbxCo₁-x with random anisotropy, Appl. Phys. Lett. 120, 112401 (2022)</footnote>

<footnote n="104">¹⁰⁴ [20] J. K. Dewhurst, S. Shallcross, I. Radu, P. Elliott, C. v. Korff Schmising and S. Sharma, Ab initio study of ultrafast spin dynamics in Gdₓ(FeCo)₁-x, Appl. Phys. Lett. 120, 042401 (2022)</footnote>

<footnote n="105">¹⁰⁵ [21] C. S. Davies, I. Razdolski, T. Janssen, K. Mishra, A. Tsukamoto and A. Kirilyuk, Silicon-substrate-induced enhancement of infrared light absorption for all-optical magnetic switching, Appl. Phys. Lett. 120, 042406 (2022)</footnote>

<footnote n="106">¹⁰⁶ [22] G. Fabiani and J. H. Mentink, Parametrically driven THz magnon-pairs: Predictions toward ultimately fast and minimally dissipative switching, Appl. Phys. Lett. 120, 152402 (2022)</footnote>

<footnote n="107">¹⁰⁷ R. I. Herapath, S. M. Hornett, T. S. Seifert, G. Jakob, M. Kläui, J. Bertolotti, T. Kampfrath, and E. Hendry, Impact of pump wavelength on terahertz emission of a cavity-enhanced spintronic trilayer, Appl. Phys. Lett. 114, 041107 (2019)</footnote>

<footnote n="108">¹⁰⁸ E. T. Papaioannou, G. Torosyan, S. Keller, L. Scheuer, M. Battiato, V. K. Mag-Usara, J. L'huillier, M. Tani, and R. Beigang, Efficient terahertz generation using Fe/Pt spintronic emitters pumped at different wavelengths, IEEE Trans. Magn. 54, 9100205 (2018)</footnote>

<footnote n="109">¹⁰⁹ I. Ilyakov, N. Agarwal, J.-C. Deinert, J. Liu, A. Yaroslavtsev, L. Foglia, G. Kurdi, R. Mincigrucci, E. Principi, G. Jakob, M. Kläui, T.S. Seifert, T. Kampfrath, S. Kovalev, R.E. Carley, A.O. Scherz, M. Gensch, Terahertz-wave decoding of femtosecond extreme-ultraviolet light pulses, Optica 9, 545 (2022)</footnote>

<footnote n="110">¹¹⁰ T. Seifert, S. Jaiswal, M. Sajadi, G. Jakob, S. Winnerl, M. Wolf, M. Kläui, T. Kampfrath, Ultrabroadband single-cycle terahertz pulses with peak fields of 300 kV cm⁻¹ from a metallic spintronic emitter, Applied Physics Letters 110, 252402 (2017)</footnote>
<footnote n="111">111 R. Rouzegar, A.L. Chekhov, Y. Behovits, B.R. Serrano, M.A. Syskaki, C.H. Lambert, D. Engel, U. Martens, M. Münzenberg, M. Wolf, G. Jakob, M. Kläui, T.S. Seifert, T. Kampfrath, Broadband spintronic terahertz source with peak electric fields exceeding 1.5 MV/cm, Physical Review Applied 19, 034018 (2023)</footnote>

<footnote n="112">112 Oliver Gueckstock, Lukáš Nádvorník, Tom S. Seifert, Martin Borchert, Gerhard Jakob, Georg Schmidt, Georg Woltersdorf, Mathias Kläui, Martin Wolf, Tobias Kampfrath, Modulating the polarization of broadband terahertz pulses from a spintronic emitter at rates up to 10 kHz, Optica 8, 1013-1019 (2021)</footnote>

<footnote n="113">113 [25] G. Lezier, P. Koleják, J.-F. Lampin, K. Postava, M. Vanwolleghem and N. Tiercelin, Fully reversible magnetoelectric voltage controlled THz polarization rotation in magnetostrictive spintronic emitters on PMN-PT, Appl. Phys. Lett. 120, 152404 (2022)</footnote>

<footnote n="114">114 [28] Shaojie Liu, Chenhui Lu, Zhengquan Fan, Shixiang Wang, Peiyan Li, Xinhou Chen, Jun Pan, Yong Xu, Yi Liu and Xiaojun Wu, Modulated terahertz generation in femtosecond laser plasma filaments by high-field spintronic terahertz pulses, Appl. Phys. Lett. 120, 172404 (2022)</footnote>

<footnote n="115">115 [24] Finn-Frederik Stiewe, Tristan Winkel, Yuta Sasaki, Tobias Tubandt, Tobias Kleinke, Christian Denker, Ulrike Martens, Nina Meyer, Tahereh Sadat Parvini, Shigemi Mizukami, Jakob Walowski and Markus Münzenberg, Spintronic emitters for super-resolution in THz-spectral imaging, Appl. Phys. Lett. 120, 032406 (2022)</footnote>

<footnote n="116">116 [27] Peiyan Li, Shaojie Liu, Zheng Liu, Min Li, Hao Xu, Yong Xu, Heping Zeng and Xiaojun Wu, Laser terahertz emission microscopy of nanostructured spintronic emitters, Appl. Phys. Lett. 120, 201102 (2022)</footnote>

<footnote n="117">117 [32] Jingwen Li, Chia-Jung Yang, Ritwik Mondal, Christian Tzschaschel and Shovon Pal, A perspective on nonlinearities in coherent magnetization dynamics, Appl. Phys. Lett. 120, 050501 (2022)</footnote>

<footnote n="118">118 [31] A. Mitrofanova, A. Safin, O. Kravchenko, S. Nikitov and A. Kirilyuk, Optically initialized and current-controlled logical element based on antiferromagnetic-heavy metal heterostructures for neuromorphic computing, Appl. Phys. Lett. 120, 072402 (2022)</footnote>