# Element-Specific Magnetization Dynamics of Complex Magnetic Systems Probed by Ultrafast Magneto-Optical Spectroscopy

^{1}

^{2}

^{3}

^{4}

^{*}

^{†}

^{‡}

^{§}

^{‖}

## Abstract

**:**

## 1. Introduction

## 2. Results and Discussions

#### 2.1. Static Magneto-Optical Functions

#### 2.2. Time Resolved Faraday Rotation

#### 2.3. Time Resolved Magnetic Circular Dichroism and Helicity-Dependent Absorption

## 3. Conclusions

## 4. Materials and Methods

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CCD | charged coupled device |

FEL | free electron laser |

HHG | high harmonic generation |

MCD | magnetic circular dichroism |

OISTR | optical inter-site spin transfer |

XUV | extreme ultraviolet |

## References

- Beaurepaire, E.; Merle, J.C.; Daunois, A.; Bigot, J.Y. Ultrafast Spin Dynamics in Ferromagnetic Nickel. Phys. Rev. Lett.
**1996**, 76, 4250–4253. [Google Scholar] [CrossRef] [PubMed] - Kirilyuk, A.; Kimel, A.V.; Rasing, T. Ultrafast optical manipulation of magnetic order. Rev. Mod. Phys.
**2010**, 82, 2731–2784. [Google Scholar] [CrossRef] - Koopmans, B.; Malinowski, G.; Dalla Longa, F.; Steiauf, D.; Fähnle, M.; Roth, T.; Cinchetti, M.; Aeschlimann, M. Explaining the paradoxical diversity of ultrafast laser-induced demagnetization. Nat. Mater.
**2010**, 9, 259–265. [Google Scholar] [CrossRef] - Schmidt, A.B.; Pickel, M.; Donath, M.; Buczek, P.; Ernst, A.; Zhukov, V.P.; Echenique, P.M.; Sandratskii, L.M.; Chulkov, E.V.; Weinelt, M. Ultrafast Magnon Generation in an Fe Film on Cu(100). Phys. Rev. Lett.
**2010**, 105, 197401. [Google Scholar] [CrossRef] [Green Version] - Carpene, E.; Hedayat, H.; Boschini, F.; Dallera, C. Ultrafast demagnetization of metals: Collapsed exchange versus collective excitations. Phys. Rev. B
**2015**, 91, 174414. [Google Scholar] [CrossRef] - Eich, S.; Plötzing, M.; Rollinger, M.; Emmerich, S.; Adam, R.; Chen, C.; Kapteyn, H.C.; Murnane, M.M.; Plucinski, L.; Steil, D.; et al. Band structure evolution during the ultrafast ferromagnetic-paramagnetic phase transition in cobalt. Sci. Adv.
**2017**, 3, e1602094. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Malinowski, G.; Dalla Longa, F.; Rietjens, J.H.H.; Paluskar, P.V.; Huijink, R.; Swagten, H.J.M.; Koopmans, B. Control of speed and efficiency of ultrafast demagnetization by direct transfer of spin angular momentum. Nat. Phys.
**2008**, 4, 855–858. [Google Scholar] [CrossRef] - Battiato, M.; Carva, K.; Oppeneer, P.M. Superdiffusive Spin Transport as a Mechanism of Ultrafast Demagnetization. Phys. Rev. Lett.
**2010**, 105, 027203. [Google Scholar] [CrossRef] [Green Version] - Stanciu, C.D.; Tsukamoto, A.; Kimel, A.V.; Hansteen, F.; Kirilyuk, A.; Itoh, A.; Rasing, T. Subpicosecond Magnetization Reversal across Ferrimagnetic Compensation Points. Phys. Rev. Lett.
**2007**, 99, 217204. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Radu, I.; Vahaplar, K.; Stamm, C.; Kachel, T.; Pontius, N.; Dürr, H.A.; Ostler, T.A.; Barker, J.; Evans, R.F.L.; Chantrell, R.W.; et al. Transient ferromagnetic-like state mediating ultrafast reversal of antiferromagnetically coupled spins. Nature
**2011**, 472, 205–208. [Google Scholar] [CrossRef] [PubMed] - Ostler, T.; Barker, J.; Evans, R.; Chantrell, R.; Atxitia, U.; Chubykalo-Fesenko, O.; El Moussaoui, S.; Le Guyader, L.; Mengotti, E.; Heyderman, L.; et al. Ultrafast heating as a sufficient stimulus for magnetization reversal in a ferrimagnet. Nat. Commun.
**2012**, 3, 666. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Dewhurst, J.K.; Elliott, P.; Shallcross, S.; Gross, E.K.U.; Sharma, S. Laser-Induced intersite Spin Transfer. Nano Lett.
**2018**, 18, 1842–1848. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Chen, J.; Bovensiepen, U.; Eschenlohr, A.; Müller, T.; Elliott, P.; Gross, E.K.U.; Dewhurst, J.K.; Sharma, S. Competing Spin Transfer and Dissipation at Co/Cu(001) Interfaces on Femtosecond Timescales. Phys. Rev. Lett.
**2019**, 122, 067202. [Google Scholar] [CrossRef] [Green Version] - Steil, D.; Walowski, J.; Gerhard, F.; Kiessling, T.; Ebke, D.; Thomas, A.; Kubota, T.; Oogane, M.; Ando, Y.; Otto, J.; et al. Efficiency of ultrafast optically induced spin transfer in Heusler compounds. Phys. Rev. Res.
**2020**, 2, 023199. [Google Scholar] [CrossRef] - Siegrist, F.; Gessner, J.A.; Ossiander, M.; Denker, C.; Chang, Y.P.; Schröder, M.C.; Guggenmos, A.; Cui, Y.; Walowski, J.; Martens, U.; et al. Light-wave dynamic control of magnetism. Nature
**2019**, 571, 240–244. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Tengdin, P.; Gentry, C.; Blonsky, A.; Zusin, D.; Gerrity, M.; Hellbrück, L.; Hofherr, M.; Shaw, J.; Kvashnin, Y.; Delczeg-Czirjak, E.K.; et al. Direct light–induced spin transfer between different elements in a spintronic Heusler material via femtosecond laser excitation. Sci. Adv.
**2020**, 6, eaaz1100. [Google Scholar] [CrossRef] [Green Version] - Hofherr, M.; Häuser, S.; Dewhurst, J.K.; Tengdin, P.; Sakshath, S.; Nembach, H.T.; Weber, S.T.; Shaw, J.M.; Silva, T.J.; Kapteyn, H.C.; et al. Ultrafast optically induced spin transfer in ferromagnetic alloys. Sci. Adv.
**2020**, 6, eaay8717. [Google Scholar] [CrossRef] [Green Version] - Willems, F.; von Korff Schmising, C.; Strüber, C.; Schick, D.; Engel, D.W.; Dewhurst, J.K.; Elliott, P.; Sharma, S.; Eisebitt, S. Optical inter-site spin transfer probed by energy and spin-resolved transient absorption spectroscopy. Nat. Commun.
**2020**, 11, 871. [Google Scholar] [CrossRef] - Stöhr, J.; Siegmann, H.C. Magnetism: From Fundamentals to Nanoscale Dynamics; Springer: Berlin/Heidelberg, Germany, 2006; Volume 152, pp. 1–822. [Google Scholar] [CrossRef]
- Stamm, C.; Kachel, T.; Pontius, N.; Mitzner, R.; Quast, T.; Holldack, K.; Khan, S.; Lupulescu, C.; Aziz, E.F.; Wietstruk, M.; et al. Femtosecond modification of electron localization and transfer of angular momentum in nickel. Nat. Mater.
**2007**, 6, 740–743. [Google Scholar] [CrossRef] - Gutt, C.; Streit-Nierobisch, S.; Stadler, L.M.; Pfau, B.; Günther, C.M.; Könnecke, R.; Frömter, R.; Kobs, A.; Stickler, D.; Oepen, H.P.; et al. Single-pulse resonant magnetic scattering using a soft x-ray free-electron laser. Phys. Rev. B
**2010**, 81, 100401. [Google Scholar] [CrossRef] [Green Version] - La-O-Vorakiat, C.; Siemens, M.; Murnane, M.M.; Kapteyn, H.C.; Mathias, S.; Aeschlimann, M.; Grychtol, P.; Adam, R.; Schneider, C.M.; Shaw, J.M.; et al. Ultrafast Demagnetization Dynamics at the M Edges of Magnetic Elements Observed Using a Tabletop High-Harmonic Soft X-Ray Source. Phys. Rev. Lett.
**2009**, 103, 257402. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Mathias, S.; La-O-Vorakiat, C.; Grychtol, P.; Granitzka, P.; Turgut, E.; Shaw, J.M.; Adam, R.; Nembach, H.T.; Siemens, M.E.; Eich, S.; et al. Probing the timescale of the exchange interaction in a ferromagnetic alloy. Proc. Natl. Acad. Sci. USA
**2012**, 109, 4792–4797. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Willems, F.; Smeenk, C.T.L.; Zhavoronkov, N.; Kornilov, O.; Radu, I.; Schmidbauer, M.; Hanke, M.; von Korff Schmising, C.; Vrakking, M.J.J.; Eisebitt, S. Probing ultrafast spin dynamics with high-harmonic magnetic circular dichroism spectroscopy. Phys. Rev. B
**2015**, 92, 220405. [Google Scholar] [CrossRef] [Green Version] - Rudolf, D.; La-O-Vorakiat, C.; Battiato, M.; Adam, R.; Shaw, J.M.; Turgut, E.; Maldonado, P.; Mathias, S.; Grychtol, P.; Nembach, H.T.; et al. Ultrafast magnetization enhancement in metallic multilayers driven by superdiffusive spin current. Nat. Commun.
**2012**, 3, 1037. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Turgut, E.; La-o vorakiat, C.; Shaw, J.M.; Grychtol, P.; Nembach, H.T.; Rudolf, D.; Adam, R.; Aeschlimann, M.; Schneider, C.M.; Silva, T.J.; et al. Controlling the Competition between Optically Induced Ultrafast Spin-Flip Scattering and Spin Transport in Magnetic Multilayers. Phys. Rev. Lett.
**2013**, 110, 197201. [Google Scholar] [CrossRef] [Green Version] - Vodungbo, B.; Gautier, J.; Lambert, G.; Sardinha, A.B.; Lozano, M.; Sebban, S.; Ducousso, M.; Boutu, W.; Li, K.; Tudu, B.; et al. Laser-induced ultrafast demagnetization in the presence of a nanoscale magnetic domain network. Nat. Commun.
**2012**, 3, 999. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Pfau, B.; Schaffert, S.; Müller, L.; Gutt, C.; Al-Shemmary, A.; Büttner, F.; Delaunay, R.; Düsterer, S.; Flewett, S.; Frömter, R.; et al. Ultrafast optical demagnetization manipulates nanoscale spin structure in domain walls. Nat. Commun.
**2012**, 3, 1100. [Google Scholar] [CrossRef] [Green Version] - Weder, D.; von Korff Schmising, C.; Günther, C.M.; Schneider, M.; Engel, D.; Hessing, P.; Strüber, C.; Weigand, M.; Vodungbo, B.; Jal, E.; et al. Transient magnetic gratings on the nanometer scale. Struct. Dyn.
**2020**, 7, 054501. [Google Scholar] [CrossRef] [PubMed] - Schneider, M.; Pfau, B.; Günther, C.M.; von Korff Schmising, C.; Weder, D.; Geilhufe, J.; Perron, J.; Capotondi, F.; Pedersoli, E.; Manfredda, M.; et al. Ultrafast Demagnetization Dominates Fluence Dependence of Magnetic Scattering at Co M Edges. Phys. Rev. Lett.
**2020**, 125, 127201. [Google Scholar] [CrossRef] - von Korff Schmising, C.; Pfau, B.; Schneider, M.; Günther, C.M.; Giovannella, M.; Perron, J.; Vodungbo, B.; Müller, L.; Capotondi, F.; Pedersoli, E.; et al. Imaging Ultrafast Demagnetization Dynamics after a Spatially Localized Optical Excitation. Phys. Rev. Lett.
**2014**, 112, 217203. [Google Scholar] [CrossRef] [Green Version] - Turgut, E.; Zusin, D.; Legut, D.; Carva, K.; Knut, R.; Shaw, J.M.; Chen, C.; Tao, Z.; Nembach, H.T.; Silva, T.J.; et al. Stoner versus Heisenberg: Ultrafast exchange reduction and magnon generation during laser-induced demagnetization. Phys. Rev. B
**2016**, 94, 1–6. [Google Scholar] [CrossRef] [Green Version] - Zusin, D.; Tengdin, P.M.; Gopalakrishnan, M.; Gentry, C.; Blonsky, A.; Gerrity, M.; Legut, D.; Shaw, J.M.; Nembach, H.T.; Silva, T.J.; et al. Direct measurement of the static and transient magneto-optical permittivity of cobalt across the entire M-edge in reflection geometry by use of polarization scanning. Phys. Rev. B
**2018**, 97, 024433. [Google Scholar] [CrossRef] [Green Version] - Jana, S.; Malik, R.S.; Kvashnin, Y.O.; Locht, I.L.M.; Knut, R.; Stefanuik, R.; Di Marco, I.; Yaresko, A.N.; Ahlberg, M.; Åkerman, J.; et al. Analysis of the linear relationship between asymmetry and magnetic moment at the M edge of 3d transition metals. Phys. Rev. Res.
**2020**, 2, 013180. [Google Scholar] [CrossRef] [Green Version] - Kuneš, J.; Oppeneer, P.M.; Mertins, H.C.; Schäfers, F.; Gaupp, A.; Gudat, W.; Novák, P. X-ray Faraday effect at the L2,3 edges of Fe, Co, and Ni: Theory and experiment. Phys. Rev. B Condens. Matter Mater. Phys.
**2001**, 64, 1–10. [Google Scholar] [CrossRef] [Green Version] - Valencia, S.; Gaupp, A.; Gudat, W.; Mertins, H.C.; Oppeneer, P.M.; Abramsohn, D.; Schneider, C.M. Faraday rotation spectra at shallow core levels: 3p edges of Fe, Co, and Ni. New J. Phys.
**2006**, 8. [Google Scholar] [CrossRef] [Green Version] - Alves, C.; Lambert, G.; Malka, V.; Hehn, M.; Malinowski, G.; Hennes, M.; Chardonnet, V.; Jal, E.; Lüning, J.; Vodungbo, B. Resonant Faraday effect using high-order harmonics for the investigation of ultrafast demagnetization. Phys. Rev. B
**2019**, 100, 144421. [Google Scholar] [CrossRef] - Willems, F.; Sharma, S.; v. Korff Schmising, C.; Dewhurst, J.K.; Salemi, L.; Schick, D.; Hessing, P.; Strüber, C.; Engel, W.D.; Eisebitt, S. Magneto-Optical Functions at the 3 p Resonances of Fe, Co, and Ni: Ab initio Description and Experiment. Phys. Rev. Lett.
**2019**, 122, 217202. [Google Scholar] [CrossRef] [Green Version] - Willems, F.; von Korff Schmising, C.; Weder, D.; Günther, C.M.; Schneider, M.; Pfau, B.; Meise, S.; Guehrs, E.; Geilhufe, J.; Merhe, A.E.D.; et al. Multi-color imaging of magnetic Co/Pt heterostructures. Struct. Dyn.
**2017**, 4, 014301. [Google Scholar] [CrossRef] - Dewhurst, J.K.; Willems, F.; Elliott, P.; Li, Q.Z.; Schmising, C.V.K.; Strüber, C.; Engel, D.W.; Eisebitt, S.; Sharma, S. Element Specificity of Transient Extreme Ultraviolet Magnetic Dichroism. Phys. Rev. Lett.
**2020**, 124, 077203. [Google Scholar] [CrossRef] [Green Version] - Tiedtke, K.; Azima, A.; von Bargen, N.; Bittner, L.; Bonfigt, S.; Düsterer, S.; Faatz, B.; Frühling, U.; Gensch, M.; Gerth, C.; et al. The soft x-ray free-electron laser FLASH at DESY: Beamlines, diagnostics and end-stations. New J. Phys.
**2009**, 11, 023029. [Google Scholar] [CrossRef] - Rabinovitch, K.; Canfield, L.R.; Madden, R.P. A Method for Measuring Polarization in the Vacuum Ultraviolet. Appl. Opt.
**1965**, 4, 1005. [Google Scholar] [CrossRef] - Henke, B.; Gullikson, E.; Davis, J. X-Ray Interactions: Photoabsorption, Scattering, Transmission, and Reflection at E = 50–30,000 eV, Z = 1–92. At. Data Nucl. Data Tables
**1993**, 54, 181–342. [Google Scholar] [CrossRef] [Green Version] - Radu, I.; Stamm, C.; Eschenlohr, A.; Radu, F.; Abrudan, R.; Vahaplar, K.; Kachel, T.; Pontius, N.; Mitzner, R.; Holldack, K.; et al. Ultrafast and Distinct Spin Dynamics in Magnetic Alloys. Spin
**2015**, 5, 1–10. [Google Scholar] [CrossRef] - Davies, C.; Janssen, T.; Mentink, J.; Tsukamoto, A.; Kimel, A.; van der Meer, A.; Stupakiewicz, A.; Kirilyuk, A. Pathways for Single-Shot All-Optical Switching of Magnetization in Ferrimagnets. Phys. Rev. Appl.
**2020**, 13, 024064. [Google Scholar] [CrossRef] [Green Version] - Hennecke, M.; Radu, I.; Abrudan, R.; Kachel, T.; Holldack, K.; Mitzner, R.; Tsukamoto, A.; Eisebitt, S. Angular Momentum Flow during Ultrafast Demagnetization of a Ferrimagnet. Phys. Rev. Lett.
**2019**, 122, 1–10. [Google Scholar] [CrossRef] [PubMed] - La-O-Vorakiat, C.; Turgut, E.; Teale, C.A.; Kapteyn, H.C.; Murnane, M.M.; Mathias, S.; Aeschlimann, M.; Schneider, C.M.; Shaw, J.M.; Nembach, H.T.; et al. Ultrafast Demagnetization Measurements Using Extreme Ultraviolet Light: Comparison of Electronic and Magnetic Contributions. Phys. Rev. X
**2012**, 2, 011005. [Google Scholar] [CrossRef] [Green Version] - Vodungbo, B.; Gautier, J.; Lambert, G.; Zeitoun, P.; Lüning, J. Comment on “Ultrafast Demagnetization Measurements Using Extreme Ultraviolet Light: Comparison of Electronic and Magnetic Contributions”. Phys. Rev. X
**2013**, 3, 038001. [Google Scholar] [CrossRef] [Green Version] - Yao, K.; Willems, F.; von Korff Schmising, C.; Radu, I.; Strüber, C.; Schick, D.; Engel, D.; Tsukamoto, A.; Dewhurst, J.K.; Sharma, S.; et al. Distinct spectral response in M-edge magnetic circular dichroism. Phys. Rev. B
**2020**, 102, 100405. [Google Scholar] [CrossRef] - Tengdin, P.; You, W.; Chen, C.; Shi, X.; Zusin, D.; Zhang, Y.; Gentry, C.; Blonsky, A.; Keller, M.; Oppeneer, P.M.; et al. Critical behavior within 20 fs drives the out-of-equilibrium laser-induced magnetic phase transition in nickel. Sci. Adv.
**2018**, 4, 1–9. [Google Scholar] [CrossRef] [Green Version] - Vodungbo, B.; Barszczak Sardinha, A.; Gautier, J.; Lambert, G.; Valentin, C.; Lozano, M.; Iaquaniello, G.; Delmotte, F.; Sebban, S.; Lüning, J.; et al. Polarization control of high order harmonics in the EUV photon energy range. Opt. Express
**2011**, 19, 4346. [Google Scholar] [CrossRef] - von Korff Schmising, C.; Weder, D.; Noll, T.; Pfau, B.; Hennecke, M.; Strüber, C.; Radu, I.; Schneider, M.; Staeck, S.; Günther, C.M.; et al. Generating circularly polarized radiation in the extreme ultraviolet spectral range at the free-electron laser FLASH. Rev. Sci. Instrum.
**2017**, 88, 053903. [Google Scholar] [CrossRef] [Green Version] - Yao, K.; Willems, F.; Schmising, C.V.K.; Engel, D.; Strüber, C.; Hessing, P.; Pfau, B.; Schick, D.; Eisebitt, S.; Schneider, M. A tabletop setup for ultrafast helicity- dependent and element-specific absorption spectroscopy and scattering in the extreme ultraviolet spectral range A tabletop setup for ultrafast helicity-dependent and element-specific absorption spectroscopy and scattering in the extreme ultraviolet spectral range. Rev. Sci. Instrum.
**2020**, 91, 093001. [Google Scholar] [CrossRef] - Dewhurst, J.K. The Elk Code 2018. Available online: http://elk.sourceforge.net/ (accessed on 26 October 2020).
- Borchert, M.; Schmising, C.v.K.; Schick, D.; Engel, D.; Sharma, S.; Eisebitt, S. Manipulation of Ultrafast Demagnetization Dynamics by Optically Induced intersite Spin Transfer in Magnetic Compounds with Distinct Density of States. 2020, pp. 1–10. Available online: https://arxiv.org/abs/2008.12612 (accessed on 26 October 2020).
- Feng, T.; Heilmann, A.; Bock, M.; Ehrentraut, L.; Witting, T.; Yu, H.; Stiel, H.; Eisebitt, S.; Schnürer, M. 27 W 21 μm OPCPA system for coherent soft X-ray generation operating at 10 kHz. Opt. Express
**2020**, 28, 8724. [Google Scholar] [CrossRef] [PubMed]

**Figure 1.**Magneto-optical functions, $\Delta \beta $ and $\Delta \delta $, of an Fe${}_{26}$Gd${}_{74}$ alloy (

**a**) at the Gd ${N}_{4,5}$ resonance around a photon energy of $E=150$ eV as well as (

**b**) at the Fe ${M}_{2,3}$ resonance around a photon energy of $E=55$ eV. The dispersive part, $\Delta \delta $, is retrieved by the Kramers–Kronig relation and ${\theta}_{F}$ is calculated according to Equation (3).

**Figure 2.**(

**a**) Scheme of a Faraday setup using single color FEL radiation. A linearly polarized XUV pulse is transmitted through the sample and the Faraday rotation is detected by a Rabniovitch polarimeter. (

**b**) Scheme of an MCD setup using HHG radiation. The multiple emission peaks of the radiation are circularly polarized by a reflective phase-shifter, transmitted through the magnetic sample and detected by a spectrometer. In both setups, we realized a pump-probe geometry to measure optical driven ultrafast magnetization dynamics. Schematic depiction of (

**c**) an out-of-plane magnetized FeGd alloy and of an in-plane magnetized (

**d**) Co and (

**e**) CoPt film.

**Figure 3.**(

**a**) Detected intensity after reflection off the analyzer mirror as a function of rotation angle, $\alpha $, for $E\approx 149$ eV, resonant at the ${N}_{4,5}$ edge of Gd. The two measurements before optical excitation at $t=-10$ ps for two opposite directions of the sample magnetization, ${M}_{\pm}$, are shifted by the Faraday angle $2{\theta}_{F}={4}^{\circ}$. After optical excitation at $t=3$ ps, the Faraday angle is zero, ${\theta}_{F}=0$, and the measurements are centered around $\alpha ={0}^{\circ}$, independent of the applied magnetic field. The lines are non-linear least square fits according to Equation (4). (

**b**) Magnetic asymmetry before and after optical excitation is shown as a function of the analyzer angle. The maximum value reaches very large values of approximately $\pm 40$% for $\pm \alpha =\pm 2{\theta}_{F}=\pm {4}^{\circ}$.

**Figure 4.**(

**a**) Measurements of ${I}_{\pm}$ for opposite magnetization directions, ${M}_{\pm}$, as a function of the time delay at the Gd ${N}_{4,5}$ resonance at $E\approx 149$ eV. Corresponding values of $M\left(t\right)/{M}_{0}$ (

**b**) for the Gd and (

**c**) Fe sublattice determined according to Equation (5). Solid lines are non-linear least-square fit with a monoexponential function with a time constant $\tau =(233\pm 16)$ fs and $\tau =(94\pm 15)$ fs for Gd and Fe, respectively.

**Figure 5.**The magnetic asymmetry, A (MCD), of the Co film and the CoPt alloy as a function of the time delay for three different photon energies corresponding to the Co ${M}_{2,3}$ edge at 60.3 eV and to the Pt ${O}_{3}$ and ${N}_{7}$ edge at 54.1 eV and 72.6 eV, respectively. The lines are non-linear least square fits. The rms value for values before $t=0$ fs corresponds to <$3\times {10}^{-4}$ yielding an excellent signal to noise ratio in spite of small asymmetry values.

**Figure 6.**We show a calculation of the laser induced changes in the spin-dependent electron occupations in the $3d$ band, $\Delta {n}_{\mathrm{min}}/\mathrm{maj}$ around the Fermi energy for Co in the CoPt alloy (red lines) and for elemental Co (blue lines). Laser excitation promotes electrons from occupied states below the Fermi energy to available states above the Fermi energy. Minority states (spin down) of Co in the CoPt alloy are filled much more efficiently than in the elemental Co, indicating a transfer of minority states from Pt $5d$ to Co $3d$ states, significantly increasing the efficiency of the demagnetization dynamics. This is schematically indicated in the left panel with minority electrons transferred from Pt to Co.

**Figure 7.**Normalized helicity-dependent absorption, $\mu /{\mu}_{0}$ as a function of time delay for Co (blue squares) and CoPt (red circles). In the left panels, we show data measured at the Co ${M}_{2,3}$ resonance at 60 eV; in the right panel are the corresponding calculations. A positive magnetic field, ${M}_{+}$, predominantly probes changes in majority occupations (spin up) and a negative magnetic field, ${M}_{-}$, predominantly probes changes of the minority occupations (spin down). In CoPt we can clearly see that the absorption into minority states very rapidly decreases, which we interpret as the efficient filling of minority states by OISTR—i.e., transitions of Pt $5d$ to Co $3d$ minority states.

**Table 1.**Reflectances, ${R}_{s,p}$, and polarizing power, $P=({R}_{s}-{R}_{p})/({R}_{s}+{R}_{p})$, of the analyzer mirrors. The values for the ML mirror were determined at the Metrology Light source of PTB, Berlin, and the values for the Au mirror were calculated with a tabulated index of refraction at 56 eV [43]. The Brewster angles are measured in a grazing incidence geometry.

Analyzer | Brewster Angle | ${\mathit{R}}_{\mathit{s}}(\%)$ | ${\mathit{R}}_{\mathit{p}}(\%)$ | P |
---|---|---|---|---|

ML for 150 eV | ${45}^{\circ}$ | 7.0 | 0.021 | 0.994 |

Au miror for 56 eV | ${49}^{\circ}$ | 5.5 | 0.28 | 0.903 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

von Korff Schmising, C.; Willems, F.; Sharma, S.; Yao, K.; Borchert, M.; Hennecke, M.; Schick, D.; Radu, I.; Strüber, C.; Engel, D.W.;
et al. Element-Specific Magnetization Dynamics of Complex Magnetic Systems Probed by Ultrafast Magneto-Optical Spectroscopy. *Appl. Sci.* **2020**, *10*, 7580.
https://doi.org/10.3390/app10217580

**AMA Style**

von Korff Schmising C, Willems F, Sharma S, Yao K, Borchert M, Hennecke M, Schick D, Radu I, Strüber C, Engel DW,
et al. Element-Specific Magnetization Dynamics of Complex Magnetic Systems Probed by Ultrafast Magneto-Optical Spectroscopy. *Applied Sciences*. 2020; 10(21):7580.
https://doi.org/10.3390/app10217580

**Chicago/Turabian Style**

von Korff Schmising, Clemens, Felix Willems, Sangeeta Sharma, Kelvin Yao, Martin Borchert, Martin Hennecke, Daniel Schick, Ilie Radu, Christian Strüber, Dieter W. Engel,
and et al. 2020. "Element-Specific Magnetization Dynamics of Complex Magnetic Systems Probed by Ultrafast Magneto-Optical Spectroscopy" *Applied Sciences* 10, no. 21: 7580.
https://doi.org/10.3390/app10217580