Review on theoretical X-ray spectroscopy

A review of the theoretical developments to predict various kinds of soft X-ray spectra has been published by us recently. It describes how different observables can be extracted from the theoretical calculations: absorption (XAS), photoionization (PES or XPS), resonant inelastic scattering (RIXS), and Auger. The main focus is on L-edge spectra of transition metals and in particular on multi-reference methods as they appear to be essential for this type of systems. However, the review also contains a brief overview of other methods and applications. Enjoy!

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Huihui Wang is now a doctor

Last Friday Huihui Wang has defended her Ph.D. thesis “Laser-driven electron and spin-state quantum dynamics in transition metal complexes” which has been partially done within the joint project with the King Abdulaziz University in Jeddah and also supported by the DFG grant. I have already briefly written about the details of her work on dynamics triggered by isolated as well as trains of pulses.

Congratulations and we wish her further success in her scientific career!

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Repeat until successful

I have already told you about out activity in the field of electron dynamics and namely spin-flip dynamics. To wrap it briefly, we have looked what will happen to a system with the strong coupling of spin and orbital motion of electrons if we prepare a pure spin-state. One can imagine, e.g., a Fe2+ ion with four spin-up electrons forming a so-called quintet state. Now if such a system has a hole in the electronic core, which immediately causes strong spin-orbit coupling, an ultrafast spin-flip of an electron will occur leading to triplet final state with effectively only two spin-up electrons.

Well, sounds easy. However, such a situation is so far pure speculation, and we should ask ourselves, how to practically prepare this particular initial state? It is very special because it corresponds not to an eigenstate of a system but rather to a quantum superposition of such “natural” states. One can, of course, absorb light, but this light should also possess somewhat unusual characteristics. First of all, the light pulse should be very short. According to the uncertainty principle, the shorter is the pulse, the broader is it in energy range which it excites. And we exactly need excitation of lots of eigenstates to resemble the situation with an initially prepared core-excited pure-spin state.

Pulse trains

Out of possible light sources, two candidates would potentially fit: free electron lasers and high harmonic generation (HHG) setups. They are able to produce light with energy that is high enough to excite core states and emerged pulses have temporal durations below 1 femtosecond (10-15 seconds). Free electron lasers provide single isolated pulses, whereas HHG usually gives periodic sequences of pulses. We have already discussed in previous publications, how the transition metal complex reacts on the isolated pulse. I have briefly described it in this blog.

In a recent publication:

Huihui Wang, Tobias Möhle, Oliver Kühn, and Sergey I. Bokarev Ultrafast dissipative spin-state dynamics triggered by x-ray pulse trains, PHYSICAL REVIEW A, 98, 013408 (2018).

we have looked how spin of the system will behave if we subject it to repeated sub-femtosecond pulses as resulting from the HHG source. The key difference to isolated pulses is that the yield of spin-fliped states rises in a stepwise manner after every subpulse in a train as can be seen from a figure. This makes this process to occur faster and more complete. Even more important is that due to stimulated emission the population is dumped from core-excited to spin-flipped valence states. Thus, via a core excitation and stimulated emission, and thus mediated by the strong spin-orbit coupling in the core state, an spin-flip which is faster than few fs can be triggered in the manifold of valence electronic state. Usually such a transition requires up to few hundreds of femtoseconds and might be immensely accelerated in this process. Such dumping also decreases the destructive influence of the Auger decay.

Finally, we have looked at the role of the decoherence caused by nuclear motions. Molecular vibrations have been treated at the level of a heat bath. Essentially, the electron dynamics studied in this work is that fast, that relatively slow vibrational motions do not much influence the result.

We envisage that this effect could be used for clocking ultrafast events. In this respect, it is of core-hole clock type but has a different nature. In case of spin flips, the characteristic timescale may be varied by changing the carrier frequency and bandwidth of the incoming radiation, thus adjusting the strength of the coupling and thereby determining essentially the measured time window.

DFG project accepted!

I would like to invite you for the piece of virtual cake!

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What’s the reason for that? Two days ago I have got an approval of my DFG project entitled “Soft X-ray spectroscopy and correlated many-electron dynamics of molecular systems from first principles theory”. (For those who don’t work in science in Germany, DFG (Deutsche Forschungsgemeinschaft) stands for German Research Foundation.) This project goes along the lines of our recent publications in Physical Review Letters and Molecular Physics which served as a preliminary work basis for the project.  It includes my own research position and a Ph.D. student for 3 years as well as money for the midterm workshop.

Remarkably, I was pleased to get excellent reviews, and what is surprising, referees even give me encouraging pieces of advice how to promote my scientific career and use the financial support from DFG in the most efficient way.

The chocolate cake was made by my wife Olga and decorated with the basic working expression for this project. It was successfully annihilated by my colleagues, that is why I can suggest you only its virtual counterpart. Nice offer, zero calories!

More on spin state dynamics

Recently, I wrote about our ultrafast spin dynamics project. The first publication in Phys. Rev. Lett. was a proof of concept article where we have shown the possibility of soft X-ray light to trigger an unprecedentedly fast change of a spin state. A follow-up article presenting the theoretical method used in this investigation in detail also appeared recently in the issue of Molecular Physics devoted to the anniversary of Andre D. Bandrauk:

Huihui Wang, Sergey I. Bokarev, Saadullah G. Aziz, Oliver Kühn Density matrix-based time-dependent configuration interaction approach to ultrafast spin-flip dynamics Mol. Phys. (2017) 1-10.

In this article, we reformulate the problem in the form of a density matrix which allows one to treat general open quantum systems with energy dissipation. In addition to the more thorough study of the influence of different parameters of an excitation pulse on the dynamics, we also discuss a regime where the strong electron correlation plays a decisive role. It was shown that core-excited electronic states may demonstrate entangled dynamics both due to the strong spin-orbit coupling and electron correlation. This makes them interesting objects for the future studies of the ultimate limits of the ultrafast electron motion in atoms, molecules, and extended systems.

Ultrafast spin-flip dynamics in focus

Nowadays physics and chemistry are intensively developing within the ‘ultrafast paradigm’ addressing processes occurring on the femto- (10-15 s) and attosecond timescales (10-18 s). An outstanding progress has been achieved in understanding molecules in motion with femtosecond resolution including movies of chemical reactions. Going further down to hundreds and even tens of attoseconds, one can explore the fundamental limits of electronic motion in atoms and molecules.

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Apart from being of fundamental interest, the peculiarities of intricate electron dynamics in molecules have their practical implications, for instance, for molecular electronics limiting the speed of the signal transmission. That is why it has been extensively studied, although mostly theoretically since experimental observations represent a very non-trivial task and stay scarce.

During last decades, the devices where the spin of the electrons plays a decisive role has been suggested that gave birth to the new field of physics called spintronics. With this respect, the materials which undergo ultrafast spin-flip upon absorption of light attracted much attention. Systems, where such an effect was observed, are mostly transition metal complexes which can exist in low- and high-spin forms.

Recently, an article from the subgroup headed by me appeared on the pages of Physics Reviews Letters suggesting a new mechanism for the ultrafast spin-flip in transition metal complexes. It was demonstrated on the example of the Fe(II) aqua complex where the excitation with the soft X-ray light created a hole in the 2p level of iron. Due to the strong spin-orbit coupling in the core-excited electronic state the spin transition takes only about 2 fs what is about 100 times faster than rates reported for valence excitations before. Moreover, with a modest variation of the excitation pulse length and its carrier frequency one can potentially govern the efficiency of such spin transition. This makes a basis for future manipulations of the spin states using short wavelength light.

The effect in focus, of course, needs experimental verification. However, such an experiment requires intense isolated attosecond X-ray pulses and is very difficult to realize. Nevertheless, we expect the experimental evidence to appear due to the upcoming X-ray free electron lasers and future developments of high-harmonic generation setups.