## Interplay of spin-orbital correlations and structural distortions in Ru- and Cr- based perovskite systems

##### Abstract

The transition metal oxides are emerging as the natural playground where the intriguing effects
induced by electron correlations can be addressed. Since the s electron of the transition metals
are transferred to the oxygen ions, the remaining electrons near the Fermi level have strongly
correlated d character and are responsible for the physical properties of the transition metal oxides.
These electron correlations, together with dimensionality and relativistic effect, play a crucial role
in the formation and the competition of different electronic, magnetic and structural phases, giving
rise to a rich phase diagram: Mott insulators, charge, spin and orbital orderings, metal-insulator
transitions, multiferroics and superconductivity. The investigation of correlated electron physics
usually refers to 3d transition metal oxides, mainly because of high-temperature superconductivity
in the cuprates and in the iron-pnictides, and colossal magneto-resistance in manganites, but also
because the highly extended 4d-shells would a priori suggest a weaker ratio between the intra-atomic
Coulomb interaction and the electron bandwidth. Nevertheless, the extension of the 4d-shells also
points towards a strong coupling between the 4d-orbitals and the neighbouring oxygen orbitals,
implying that these transition metal oxides have the tendency to form distorted structure with
respect to the ideal one. As a consequence, the change in the Metal-Oxygen-Metal bond angle often
leads to a narrowing of the d-bandwidth, bringing the system on the verge of a metal-insulator
transition or into an insulating state. Hence, 4d materials share common features with 3d systems
having additionally a significant sensitivity of the electronic states to the lattice structure, effective
dimensionality and, most importantly, to relativistic effects due to stronger spin-orbit coupling.
The main purpose of this thesis is a study of the mechanisms and the fundamental interactions
that control the formation and the competition of different magnetic and structural phase driven
by the electronic correlations, dimensionality and relativistic effects in Ru-, Cr- and Mn- based
perovskite systems, also considering what happens in hybrid or eutectic structures.
The mean field theory of itinerant uniform ferro/ metamagnetism and its consequences are
introduced. We present two analytically solvable models: the M6 Landau theory and the full
analytical solution of one-dimensional tight binding density of state. We compute the analytical
thermodynamic functional, the phase diagram, the quantum critical endpoint and the critical
magnetic field. Necessary and sufficient conditions to have itinerant metamagnetism are examined.
We analyse the interface Sr2RuO4-Sr3Ru2O7. We study the modification of the electronic structure
induced by nanometric inclusions of Sr2RuO4 embedded as c-axis stacking fault in Sr3Ru2O7 and
viceversa. The change of the density of states near the Fermi level is investigated as a function
of the electron density, the strength of the charge transfer at the interfaces between the inclusion
and the host, and of the distance from the inclusion. Then, we examine how the tendency towards
long range orders is affected by the presence of the nanometric inclusions. This is done by looking
at the basic criteria for broken symmetry states such as superconductivity, ferromagnetism and
metamagnetism. We show that, according to the strength of the charge transfer coupling, the
ordered phases may be enhanced or hindered, as a consequence of the interplay between the host
and the inclusion, and we clarify the role played by the orbital degree of freedom showing an
orbital selective behaviour within the t2g bands. A discussion on the connections between the
theoretical outcome and the experimental observations is also presented. We study the effect of
electronic correlation at interface Sr2RuO4-Sr3Ru2O7. We study in detail the role of the electronic
correlation in systems based on nanometric inclusions of Sr2RuO4 embedded as c-axis stacking
fault in Sr3Ru2O7 and viceversa. The metamagnetic properties in mean field theory approach using
the realistic density of state are analyzed. We study the analysis of the electronic reconstruction at
the interface Sr2RuO4-Sr3Ru2O7. We study the fermiology of Sr2RuO4 and Sr3Ru2O7 from first
principles: comparison, main features and calculation of effective hopping Ru-Ru are performed.
Effect of the octahedral rotation and dimensionality are analyzed studying ab-initio the interface
Sr2RuO4-Sr3Ru2O7. We show that the rotations strongly reduce the main hopping parameter
of the dxy band, making near the Van Hove singularity to the Fermi level. We study the
tetragonal-monoclinic transition in the compound KCrF3. We present the electronic structure and
the volume relaxation study for the KCrF3 in the two different crystalline phases. Following the
usual definition of the eg orbital | _ >= cos _
2 |3z2 −1⟩+sin _
2 |x2 −y2⟩, the calculation of the orbital
gives _ = 110:5◦ for the tetragonal structure, that is similar to LaMnO3. For the monoclinic phase,
we find _ = 120:9◦ and 102:2◦ for the two types of octahedron. We discuss similarities with KCuF3
and LaMnO3 in the orbital order. We deepen the study of KCrF3 studying the low-energy physics
and the non-collinear properties of its antiferromagnetic ground state. We present and compare the
hopping parameters for the cubic, tetragonal and monoclinic structures of KCrF3 using the eg basis
and the Maximally localised Wannier functions. Moreover, we analyse the strength of electronic
correlation using the Cococcioni method based on linear response approach. Although, the atomic
number of chromium is relatively small, it is observed experimentally that the spin-orbit effect can
play a non trivial role at low temperature. We go beyond the spin collinear approximation, the
spin-orbit coupling and the weak ferromagnetism are also examined. Finally, we study from first
principles the magnetic, electronic, orbital and structural properties of the LaMnO3 doped with
gallium atoms. The gallium atoms reduce the Jahn-Teller effect, and accordingly reduce the charge
gap. Surprisingly, the system does not go towards a metallic phase. The doping tends to reduce
the orbital order by weakening the antiferromagnetic phase and by favoring an unusual insulating
ferromagnetic phase due to the effect of the correlated disorder. It is also presented a general
discussion on the results obtained and some comments on prospective and open questions.
[edited by author]