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

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## Abstract

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## 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

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**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 |

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**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.; Shokeen, V.; Buck, J.; Bagschik, K.; Viefhaus, J.; Hartmann, G.; Manschwetus, B.; Grunewald, S.; Düsterer, S.; Jal, E.; Vodungbo, B.; Lüning, J.; Eisebitt, S. 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, Shokeen V, Buck J, Bagschik K, Viefhaus J, Hartmann G, Manschwetus B, Grunewald S, Düsterer S, Jal E, Vodungbo B, Lüning J, Eisebitt S. 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, Vishal Shokeen, Jens Buck, Kai Bagschik, Jens Viefhaus, Gregor Hartmann, Bastian Manschwetus, Soeren Grunewald, Stefan Düsterer, Emmanuelle Jal, Boris Vodungbo, Jan Lüning, and Stefan Eisebitt. 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