A coupling between subsystems in matter, e.g., lattice, spin, charge, and orbital, is one of the foundations for functionalities, such as superconductivity, multiferroicity, and colossal magnetoresistance. Such a coupling mediated by an elementary excitation, e.g., phonon and magnon, having been investigated mainly in the frequency domain by spectroscopic techniques, can emerge or modulate the functionalities in ultrafast timescales even down to femtoseconds. One of the powerful techniques to investigate correlated subsystems is to utilize a tunable X-ray source, i.e., synchrotron radiation, allowing us to obtain sensitivity to different degrees of freedom due to atomic resonance. Hence, using X-ray free electron lasers (XFEL) provides a unique opportunity to investigate the coupling between subsystems in the time domain.
In my talk, I will show three synchrotron- or XFEL-based works about elementary excitations that fundamentally couple to another degree of freedom. (1) First, I will talk about chiral phonons [1]. Resonant inelastic X-ray scattering with circular polarization revealed the existence of chiral phonons in a prototypical chiral crystal, quartz, through angular momentum transfer between circularly polarized photons and chiral phonons. This observation settled the debate about whether phonons can be chiral or not. In addition, the angular momentum in chiral phonons makes them intrinsically magnetic and has created a recent hot topic in condensed matter physics: phonons with angular momentum. I will also show our future work on the direct demonstration of their magnetic character. (2) Second, I will discuss a characteristic excitation in magnetoelectric multiferroics -electromagnons- a hybrid mode between magnons and polar phonons, selectively investigated by time-resolved X-ray diffraction [2]. Tuning the photon energy into atomic resonance brings the sensitivity to magnetism, and, thus, we can measure the magnon part of electromagnon dynamics. On the other hand, time-resolved non-resonant X-ray diffraction picks up the phonon part of electromagnon dynamics. Combining the two independent results together revealed how the hybrid mode is excited following an intense THz pulse in a multiferroic material and how efficient the energy transfer process via the ultrafast spin-lattice coupling can be. (3) Finally, I will focus on the new technique demonstrated at the Furka endstation in the SwissFEL, time-resolved resonant diffuse scattering. Diffuse scattering arises due to the deviation from a static order, such as short-range correlation or elementary excitations. For example, photoexcitation can significantly increase the population of low-energy phonons. Thus, time-resolved diffuse scattering has revealed phonon correlations in the time domain with momentum resolution. Analogous to resonant X-ray diffraction, applying this technique at an atomic resonance, i.e., time-resolved resonant diffuse scattering, potentially allows us to measure elementary excitations given by electronic degrees of freedom. I will show the first preliminary results on magnons. The distribution of magnons follows a temperature in equilibrium but a time-dependent spin temperature in non-equilibrium because subsystems can have different temperatures at ultrafast timescale, known as the three temperatures model: an electronic temperature, a spin temperature, and a lattice temperature. There has been no established technique to determine a time-dependent spin temperature because magnetism is often measured in the ordered state, whereas the temperature following photoexcitation can easily go into the paramagnetic phase. Hence, time-resolved resonant diffuse scattering will fill the missing last parameter in the phenomenological model. Besides the results that have already been obtained, I will present a plan to extend this new method to different types of elementary excitations.

[1] H. Ueda et al., Nature 618, 946-950 (2023).
[2] H. Ueda et al., Nat. Commun. 14, 7778 (2023).