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

Round 1

Reviewer 1 Report

The authors have performed two experiments on ultrafast magnetization dynamics. One is a Free-Electron laser based study of FeGd, and the other is a laboratory HHG based study of CoPt. Both are time-resolved, but the techniques are different, the first being Faraday rotation and the second MCD. Compatibility between these diverse situations is established by the finding that for FeGd the Fe and Gd sub-lattices have very different time constants, while for CoPt, the time constants are equal, implying that the OISTR mechanism is active. The latter phenomenon has been described in reference 18, with the same experiment on CoPt, and so is not new here.

I am puzzled as to why the pdf sent to me is labelled in the footer “Submitted to Autom. Syst. Control, pages 1 – 16”.

The authors may wish to correct a few typos.

3. 3. Line 61. “referred to MCD”. “referred to as MCD”.
4. 4. Line 107 “of a FeGd”. “of an FeGd”
5. 4. Line 118 and caption of Fig. 2. “Rabniovitch”. “Rabinovitch”.
6. 6. Line 148. “We normalize our observable proportional to M(t) to the average” reads badly. Better

“We normalize our observable, proportional to M(t), to the average”

7. 7. Line 171. “hence on a similar magnitude as the”. “hence of a similar magnitude to the”
8. 7. Line 180. “exhibiting distinct number”. Either “exhibiting a distinct number” or “exhibiting distinct numbers”
9. 8. Line 207. “identical demagnetization times local on”. “identical local demagnetization times for”
10. 9. Line 218. “as implement”. “as implemented”.
11. 9. Line 223. “much more prominently, is”. “much more prominent is”
12. 10. Lines 240 and 242. “Fig.6”. Insert space.
13. 10. Line 245. “mark”. “remark”.
14. 12. Line 276. “on were”. “were”.

Author Response

We thank the referee for his/her careful reading of our manuscript and pointing out typos as well for his/her suggestions how to improve certain expression.  We have corrected all mentioned issues as suggested.

The authors may wish to correct a few typos.

1. 3. Line 61. “referred to MCD”. “referred to as MCD”.

We have corrected this (line 86)

1. 4. Line 107 “of a FeGd”. “of an FeGd”

We have corrected this at multiple instances (line 7, 64, 93, 113, caption Fig. 1,

1. 4. Line 118 and caption of Fig. 2. “Rabniovitch”. “Rabinovitch”.

We have corrected this (line 124)

1. 6. Line 148. “We normalize our observable proportional to M(t) to the average” reads badly. Better

“We normalize our observable, proportional to M(t), to the average”

We have corrected this (line 154)

1. 7. Line 171. “hence on a similar magnitude as the”. “hence of a similar magnitude to the”

We have corrected this (line 176)

1. 7. Line 180. “exhibiting distinct number”. Either “exhibiting a distinct number” or “exhibiting distinct numbers”

We have corrected this (line 180)

1. 8. Line 207. “identical demagnetization times local on”. “identical local demagnetization times for”

We have corrected this (line 213)

1. 9. Line 218. “as implement”. “as implemented”.

We have corrected this (line 218)

1. 9. Line 223. “much more prominently, is”. “much more prominent is”

We have corrected this (line 224)

1. 10. Lines 240 and 242. “Fig.6”. Insert space.

We have corrected this (line 246, 248)

1. 10. Line 245. “mark”. “remark”.

We have corrected this (line 251)

1. 12. Line 276. “on were”. “were”.

We have corrected this (line 289)

Reviewer 2 Report

The authors have presented the manuscript with the title: "Energy and spin-resolved ultrafast absorption spectroscopy of magnetic systems".

This article describes two topics:

1. A decoupled dynamics of the two sublattices of a FeGd alloy using a Free Electron Laser.
2. An optical intersite spin transfer in a CoPt alloy using circularly polarized radiation generated in a laboratory-based high harmonic generation setup.

I recognized attempts to connect these two topics in the abstract, however, this connection has to be improved.

Moreover, it has to be connected to the title, introduction, results, discussion, and conclusion.

Why a specific experimental setups were been chosen? What was the expectation of the results? What is the novelty of the experiments?

All these things have to be seriously improved before it will be considered for publication. 

Author Response

Comments and Suggestions for Authors

The authors have presented the manuscript with the title: "Energy and spin-resolved ultrafast absorption spectroscopy of magnetic systems".

This article describes two topics:

A decoupled dynamics of the two sublattices of a FeGd alloy using a Free Electron Laser.

An optical intersite spin transfer in a CoPt alloy using circularly polarized radiation generated in a laboratory-based high harmonic generation setup.

I recognized attempts to connect these two topics in the abstract, however, this connection has to be improved.

Moreover, it has to be connected to the title, introduction, results, discussion, and conclusion.

Why a specific experimental setups were been chosen? What was the expectation of the results? What is the novelty of the experiments?

All these things have to be seriously improved before it will be considered for publication. 

Response:

We appreciate the effort of the referee and have made changes to our manuscript to overcome his concerns. In particular, we now make the connections of the two experiments easier to appreciate by emphasizing the aspect of element-specificity and the complementary nature of the experiments probing the dispersive and absorptive part of the magneto-optical functions.

It is important to realize that ultrafast magneto-optical spectroscopy of magnetic systems with element specificity can either be performed via magnetic circular dichroism or via Faraday rotation measurements. In a transmission geometry, these are indeed the only two options available, if one seeks an observable that scales linearly with the magnetization. This and the importance of element-specificity to understand and ultimately control magnetic functionality is the motivation to directly compare the two methods in a single manuscript.

As a side note, we remark that measurements in reflection, as often employed in XUV experiments of magnetic samples (T-MOKE), offer an alternative approach, however, have some drawbacks compared to experiments performed in transmission. They are mostly surface sensitive, and therefore require a dedicated analysis to understand how (a) a depth-dependent excitation profile changes on ultrafast time scales (b) how a strongly varying absorption coefficient around an absorption edge influences the probing depth of the sample (c.f. Fig. 1) and (c) how changes of the electro-optical functions influence the non-magnetic part of the reflectance. Also thicker samples with buried layers are more challenging or even impossible to study in reflection.

To emphasize the common point of “element specificity”, and that we are probing the magneto-optical functions, we have made the following changes:

We have changed the title to:

“Element-specific magnetization dynamics of complex magnetic systems probed by ultrafast magneto-optical spectroscopy”

In the abstract, we have changed the following sentence to emphasize the aspect of element specificity and the complementary nature of the two experiments:

“Here, we present two complementary experimental geometries to access the element-specific magnetization dynamics of complex magnetic systems via ultrafast magneto-optical spectroscopy in the extreme ultraviolet spectral range.”

In line 46 we have added the following sentence to emphasize the role of the complex magneto-optical functions which are discussed in detail in 2.1:

“More generally, the optical response around such resonant transitions in magnetic materials can be parameterized by a complex magneto-optical function.”

In line 60ff we have made changes to emphasize that both presented experiments are complementary in a sense that they probe the real (dispersive) and imaginary (absorptive) part of the magneto-optical functions:

“In this contribution, we present two complementary experiments dedicated to an element-specific view of femtomagnetism based on ultrafast XUV spectroscopy of multi-component magnetic systems performed at the FEL facility, FLASH, DESY, Hamburg and at a HHG beamline at the Max Born Insitute, Berlin. At the FEL facility, we exploit the \textit{dispersive} (real) part of the magneto-optical functions in a resonant Faraday rotation geometry to study the ultrafast response of an FeGd alloy and reveal decoupled dynamics of the two sublattices Gd and Fe. In the experiment using HHG radiation, we compare the ultrafast response of a Co film and a CoPt alloy by measuring the \textit{absorptive} (imaginary) part of the magneto-optical functions in an MCD experiment. We were able to demonstrate that OISTR between Pt and Co atoms in the two-component CoPt alloy dominates the early time dynamics and leads to a faster and more efficient demagnetization.”

We now explicitly state in line 82 that after inspection of Eq. 1 it should be clear that only two experiments in a transmission geometry are possible, MCD and Faraday rotation:

“Equation \ref{eq:mo} directly implies that the element specific magnetization can be accessed either via the dispersive or absorptive part of the magneto-optical function leading to two possible experimental configurations in a transmission geometry, MCD and Faraday rotation.”

We feel that the first paragraph of our conclusion already stresses very prominently the aspect of “element-specificity”, however we have rewritten the second part of the conclusion and now focus on the two experimental realization and their disadvantages and advantages.

“We demonstrated this by two complementary experimental realizations probing either the \textit{dispersive} or the \textit{absorptive} part of the magneto-optical functions in a Faraday rotation and an MCD experiment, respectively.

In the first experiment, the polarization plane of transmitted photons tuned to the respective core-to-valence band transition in an GdFe alloy yielded large Faraday rotation angles and allowed us to reveal decoupled ultrafast magnetization dynamics of the Gd and Fe sublattices.  Three advantages of Faraday rotation measurements are noteworthy: first, it yields large magnetic asymmetries, second, it does not require polarization control of the XUV radiation, which has remained challenging in HHG and is not (yet) always available at free-electron laser facilities. And finally, the intrinsic contrast of Faraday measurements is only based on a phase difference and is therefore not detrimentally affected by strong absorption losses at the resonance of the probed element.

In the second experiment, we employed MCD contrast to reveal an efficient intersite spin transfer in the two-component CoPt alloy.  As the strength and direction of such spin-selective charge flow is determined by the available states above the Fermi energy of the involved elements \cite{Borchert2020}, we envision to tailor the ultrafast magnetic response and work towards realizing a metamagnetic phase transition on the fastest time scale. While MCD experiments in the XUV spectral range require circularly polarized radiation and are technically very demanding because of very small magnetic asymmetries, they offer the great potential to analyze the energy and helicity-dependent transient absorption in order to differentiate the ultrafast occupation changes of minority and majority electrons after optical excitation.

Finally, we remark that with our recent successful efforts to extend the photon range of HHG sources beyond the water window \cite{Feng2020}, we expect in the very near future first experiments with photon energies around the giant $N$ resonances of rare earth elements as well as around $L$ resonances of transition metals in laboratory based experiments.”

Finally, the referee asks about the novelty of our results, which we would like to address in the following. First, we are convinced that our careful and systematic comparison of the two complementary measurement techniques probing the element-specific response via magneto-optical spectroscopy in the extreme ultraviolet spectral range is very useful for the community of ultrafast spectroscopy and can serve as a valuable reference for future experiments. The pros and cons of the two possible measurement geometries are clearly described and will help scientists to choose the optimal configuration.  Also, note that exploiting polarization sensitivity in ultrafast spectroscopy is very rarely discussed in literature, its scope however is impressively demonstrated in our manuscript. The static magneto-optical functions of FeGd in the XUV spectral range have not been reported in literature previously, in spite of FeGd being a widely and intensively studied material system. We are also not aware of any experiment, that shows time resolved data measured at the rare-earth N edges. Experts in ultrafast spectroscopy are well aware of the difficulties to interpret observables extracted from a system in non-equilibrium; hence, the demonstrated verification of decoupled dynamics of Fe and Gd in FeGd is a priori not self-evident. Furthermore, we are only aware of one experiment in literature that addresses time resolved Faraday rotation (Alves et al.), however, on a different material system and using a different experimental approach. Using a Rabinovitch polarimeter in combination with dedicated (and well characterized) polarizing optics provides a very intuitive access to Faraday rotation, allows to choose the optimal angle alpha of the polarimeter for an optimized signal to noise-ratio of the element specific magnetization dynamics. While the main results of the MCD experiments have been indeed published previously, we present them here in a different context, show additional asymmetry data and extend the analysis of the time resolved, theoretically calculated occupations (Fig. 6). We are convinced that this warrants sufficient novelty for publication in Applied Sciences.

Round 2

Reviewer 2 Report

After authors did recommended corrections, I agree to the publication of this manuscript