Probing electronic, magnetic, and structural degrees of freedom of new materials using diffraction and spectroscopic techniques

The competing or cooperative character between different degrees of freedom drives complex ground states in quantum materials. Besides their importance on a fundamental level, most of those phenomena also have technological applications. Thus, to fully comprehend the emergent macroscopic properties of these systems, a deep understanding of them on a microscopic level is needed. Therefore, in this thesis, we study some quantum materials with open questions about their magnetic, electronic, and thermal properties using X-ray diffraction and absorption techniques and Raman spectroscopy. For HoNiSi$_{3}$, where each component of the magnetic moment orders at a specific temperature, resonant X-ray magnetic diffraction measurements revealed that, in both transitions, the magnetic structure is commensurate with the crystalline structure, characterized by ferromagnetic planes stacked in a $\uparrow\downarrow\uparrow\downarrow$ sequence along the $\vec{b}$ axis, differing only in the direction of the magnetic moment. The compounds $AD_{2}$O$_{6}$ ($A$ = Ni, Co, Zn; $D$ = Sb, Ta) and CaMn$_{2}$Bi$_{2}$ were studied using Raman spectroscopy. In the first case, we identified an optical mode and the presence of a high phonon density of states in the low-frequency region, indicating a coupling between the optical and the acoustic phonons. The interaction results in a suppression of the thermal conductivity of these materials compared to the Sb-based samples. Additionally, the lowest energy optical mode behaves as a soft mode, suggesting that the Ta-based materials are close to structural phase transition. For CaMn$_{2}$Bi$_{2}$, with a possible hybridization gap, the width of one of its vibrational modes exhibits an abrupt change in its behavior consistent with an energy gap in the electronic structure, in good agreement with gap values obtained through electrical transport measurements. We also observed the presence of an excitation that disappears in the antiferromagnetic transition of the compound, consistent with a two-magnon excitation. Finally, we performed X-ray absorption, X-ray Magnetic Circular Dichroism, and X-ray diffraction measurements on Na$_{2}$IrO$_{3}$ powder samples, where Kitaev type interactions are potentially present, up to 100 GPa. For pressures lower than 30 GPa, the total magnetic moment of the Ir ion remains constant, but above this pressure, there is a drastic decrease in its value and in the antiferromagnetic interactions, which seem to saturate above 60 GPa. Also, this drastic reduction in both the Ir magnetic moment and the exchange interactions between them occurs precisely in the pressure range where we observe a structural phase transition, suggesting that this reduction is associated with the formation of Ir dimers (AU)