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Concept# Spin–orbit interaction

Summary

In quantum physics, the spin–orbit interaction (also called spin–orbit effect or spin–orbit coupling) is a relativistic interaction of a particle's spin with its motion inside a potential. A key example of this phenomenon is the spin–orbit interaction leading to shifts in an electron's atomic energy levels, due to electromagnetic interaction between the electron's magnetic dipole, its orbital motion, and the electrostatic field of the positively charged nucleus. This phenomenon is detectable as a splitting of spectral lines, which can be thought of as a Zeeman effect product of two relativistic effects: the apparent magnetic field seen from the electron perspective and the magnetic moment of the electron associated with its intrinsic spin. A similar effect, due to the relationship between angular momentum and the strong nuclear force, occurs for protons and neutrons moving inside the nucleus, leading to a shift in their energy levels in the nucleus shell model. In the field of spin

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Compounds made of transition metal ions on a triangular lattice may have orbitally degenerate eg states. This is the case for LiNiO2 and NaNiO2 : the Ni3+ ions are in a low-spin state, leaving the last electron of the d-shell in the eg orbitals. In order to understand the magnetic behavior of such systems, we investigate a spin-orbital effective hamiltonian. Using exact diagonalization algorithms of finite clusters and variational approaches we have investigated the phase diagram as a function of the hopping integrals between eg orbitals and of the magnitude of the Hund's rule coupling. We show the existence of intermediate phases lying between a ferromagnetic state and the SU(4)-symmetric point. In particular we show that different types of spin arrangements can be realized ranging from dimer coverings to antiferromagnetic chains or 2D structures. In order to have a better characterization of the dimer-covering phase corresponding to LiNiO2, we derived an effective quantum dimer model adapted to the Kugel-Khomskii model we started with. The relevant terms for this quantum dimer hamiltonian are kinetic ones. A systematic investigation of this model has been carried out with exact diagonalizations and quantum Monte-Carlo. We show that a competition between two kinetic terms can lead to a resonating valence bond (RVB) state for a finite range of parameters. On the basis of the available experiments we argue that this RVB phase gives a correct description of LiNiO2. Another phase that lies nearby in parameter space, ferro-orbitally ordered, has been investigated by spin-wave calculations. The magnetization curves of NaNi02 showed the caracteristic feature of a spin-flop transition. We show that we can reproduce such a behavior in the frame of a spin-orbital model.

From recent advances in solid state physics, a novel material classification scheme has evolved
which is based on the concept of topology and provides an understanding of different phenomena
ranging from quantum transport to unusual flavors of superconductivity. Spin-orbit
coupling is a major term in defining the topology of materials, and its interplay with electron electron
correlations yields novel, intriguing phenomena. In the weak to intermediate correlation
regime, spin-orbital entanglement leads to the emergence of topological insulators,
which constitute Dirac materials with 2D spin-polarized helical edge or surface
states and an insulating bulk. In the specific case of topological insulators,
theory predicts that their unique band structure leads to a high thermoelectric performance,
which is of practical relevance for energy conversion applications.In the strong correlation regime, the spin-orbit coupling removes the orbital degeneracy,
thereby enhancing quantum fluctuations of the spin-orbit entangled states. This in turn can
lead to the emergence of novel phases such as quantum spin liquids and unconventional
superconductivity. The Kitaev quantum spin liquid (QSL) is a topological state of matter that
exhibits fractionalized excitations in the form of Majorana fermions.
The main aim of this thesis was to study these novel states of matter in the form of two different
materials that fall in the weak and strong correlation regime, respectively. On this basis, it
should furthermore be explored whether benefit can be taken of their properties by combining
them with other quantum materials into heterostructures.In the first part of this thesis, nanoplatelets of bismuth chalcogenide-based 3D topological
insulators were grown by chemical vapor deposition, and characterized by magnetotransport
experiments. Having established charge transport characteristics of the single components, in
the aim to exploit their high thermoelectric efficiency, the lateral heteroctructures of them
are fabricated. Their investigation by scanning photocurrent microscopy revealed strong
photocurrent generation at the p-n junction. The obtained results demonstrate that such type of hybrid
heterostructure is a promising route to enhance the thermoelectric performance in nanostructured
devices.
In the second part of this thesis, the Kitaev spin liquid candidate, RuCl3 was studied. Raman spectroscopy on exfoliated
RuCl3 revealed a broad magnetic continuumat low energies which according to its particular
deviation from bosonic character is assigned to the fractionalized excitations. Furthermore,
in complementary charge transport experiments, it was found that themagnetic fluctuations
and structural changes in thismaterial are highly entangled, and influence the emergence of
the fractionalized excitations.
Finally, it was investigated whether the magnetic insulator character of ®-RuCl3 can be exploited
to alter the graphene band structure through a proximity effect in vertical graphene/
RuCl3 heterostructures. Measurements of their low-temperature, nonlocal resistance confirmed
the possibility to induce pure spin currents in this manner. At the same time, the
charge transport through the graphene served as a probe of the magnetic ordering in RuCl3,
although the complex magnetic behavior in this material necessitates more studies.

2012