Materials and heterostructures that exhibit coupling between elastic and magnetic degrees of freedom are of both fundamental and technological interest. In particular, they have great potential for novel energy-efficient spintronic devices because acoustic waves can generate coherent and long-living spin waves through inverse magnetostriction, which consists in variations in the magnetization due to lattice deformations. As optical methods are versatile, non-invasive and contactless, an all-optical approach has been implemented and applied to study magnetoelastic coupling in a ferromagnetic film on a glass substrate.
The present thesis work was performed at the NFFA-SPRINT facility of IOM-CNR in the Fermi@Elettra hall at Trieste, where I actively contributed to the realization and characterization of an all new experimental setup which is able to combine transient grating spectroscopy with a time-resolved Faraday polarimetry.

This thesis contains a selection of the results on the shallow electron states of quantum materials that I obtained as doctoral student of the Scuola di Dottorato in Fisica, Astrofisica e Fisica Applicata at the Università degli Studi di Milano. I carried out my doctoral research activity mostly at the TASC-IOM CNR laboratory, in the framework of the NFFA and APE-beamline facilities (Elettra Sincrotrone Trieste), as well in dedicated sessions at the I2; beamline of the Diamond light source, Harwell Campus, UK. To access the electronic properties of materials I specialised myself in photoemission spectroscopy techniques. High quality samples are a prerequisite for any attempt to study quantum materials so that a major effort in my PhD project has been to master the growth of novel quantum materials by means of Pulsed Laser Deposition (PLD). Given that the PLD is integrated in the suite of UHV facilities attached in-situ to the APE beamline, I directly characterised the electronic properties of the PLD grown samples exploiting both the spectroscopic techniques available at the beamline (ARPES, X-ray photoemission and absorption spectroscopies: XPS and XAS), either ex-situ structural characterisation tools (X-ray diffraction –XRD– and X-ray reflectivity, XRR).

I explored the properties of systems that were fabricated aiming to exploit enhanced multiferroic behavior and potentially useful functionalities at room temperature. The systems of choice for this thesis were two prototypical multiferroic heterostructures composed by a ferromagnetic thin film deposited on a ferroelectric substrate: LSMO/BTO(001) and Fe,FeMn/PMN-PT(001). I focused on the magnetic response of the thin films to applied electric fields oriented perpendicular to the interface, and influencing the substrate. In both the chosen heterostructures the magnetic layers and ferroelectric substrates are all materials with high ordering temperature.