Long-range Ordering in Pr(2)NiO(4+δ) Single Crystals studied by Resonant Soft X-Ray Scattering

1 THE MATERIAL: STRUCTURE AND PROPERTIES OF PRASEODYMIUM NICKELATE 1.1 introduction The instability of a metal’s Fermi surface at low temperatures gives arise to the formation of spin or charge density waves, superconductivity, or other collective electronic ordering phenomena [1][2][3][4][5] . In such materials, known as strongly correlated materials, the mobility of the valence-state electrons is suppressed due to the interactions be- tween their mutual repulsion. The 3d-transition metal oxides (TMOs) represent an important category of the strongly correlated materials. In this thesis, the focus will be addressed to praseodymium nickelate, a transition metal oxide where the reduction of the valence shell leads to the switch of its behaviour from metallic to insulating and localization of spins [6][7][8] . The Fermi surface is modified depending on the repulsive interactions between valence-state electrons, leading to the formation of ordered states, which can be studied by using scattering techniques. The complexity of these structures requires high-quality and pure sam- ples and only single crystals can satisfy these conditions. The prepara- tion can be challenging but thanks to the development of techniques as the floating zone method (FZM), nowadays the growth of large single crystals is achievable in a reasonable time. 1.2 the crystal structure 1.2.1 The Perovskites and its derivatives The basic building block of many TMOs is the perovskite unit cell, named after the mineral CaTiO 3 , with general formula ABO [9] 3 (Fig- ure 1.1). It can be described by a three-dimensional (3D) cubic network ofcorner-sharingoctahedrawiththelargerAalkaline-earthorrare-earth metal cations occupying every site created by 8 BO 6 octahedra, where B is a transition metal, and the symmetry space group is Pm ¯ 3m [10] . The perovskite phases are very reactive and flexible in terms of oxygen stoichiometry and substitution of cations A and B with other cations of different sizes. In order to accommodate the electrostatic potential of doping ions, the octahedra rotate or distort their shape by tilting or elongate/shrink along favourable crystalline directions. These displace- ments within the unit cell lead to a lower symmetry and the size and the nature of A and B cations play a key role. Indeed, an important parameter to take into account the variation of the equilibrium positions of ions in the octahedra is the Goldschmidt tolerance factor t (Equation 1.1), which measures the degree of distor- tion as a function of the interatomic distances between cations and oxygen ions (d A−O and d B−O ) [11] . t = d A−O √ 2d B−O (1.1) 17