Spin-orbital entanglement and dynamic properties of spin-orbital systems
Final Report Abstract
The free electron has of course a charge and additionally a spin, a magnetic moment. When atoms for a solid, several of their orbitals may be involved in forming the most important electronic states, the ones easily reached using small amounts of energy. In that case, an additional quantum number becomes important, namely the orbital degree of freedom, which may offer two, three of even more states to the electron. Finally, spin and orbital are quantum degrees of freedom and the electron can not only be on one of the two (or more) basis states, but in any superposition. In many cases, rules of thumb help, like the Goodenough-Kanamori rules stating that if electrons on neighbouring sites are in the same orbital state, their spins will typically be opposite and vice versa. The topic of this project was to go beyond these rules and investigate ’entangled’ spins and orbitals. This can happen in the ground state, but even more in the dynamics as e.g. captured in excitations that can be measured in neutron scattering or resonant inelastic X-ray scattering (RIXS). The original plan was to investigate excitations for a ground state that is already highly entangled, i.e., where the neat rules do not work. However, it soon turned out to be better to start from a simpler situation, where the same orbital is occupied everywhere while spins alternate, and the investigate an excitation created by changing one of the orbitals. Such an orbital excitation turned out to strongly mix with the spin background, and also to be mathematically equivalent to a charge excitation rather than orbital. This approach proved to be very helpful in analysing and understanding RIXS data for cuprates and iridates. For example, we used this to quantify material properties (like crystal-field splittings) in iridates. Using the orbital/charge equivalence we were moreover able to infer that a single hole in a two-dimensional Mott insulator behaves fairly conventionally as a ’quasi-particle’, which was an open question in the research on cuprate high-temperature superconductors. While these excitations focused on compounds where electron-electron repulsion is strong enough to inhibit electron motion and make them insulating, we also studied iron-based superconductors, where charge motion is relevant in addition to spin and orbital. We were particularly interested in how the orbitals react to the magnetic state. In particular, we showed that nematic order, where it is already established whether the magnetic order with prefer horizontal or vertical stripes, but where the spins have not yet formed the long-range stripe pattern, leads to signals that mimic orbital order. While the research was in progress, spin-orbit coupling started to be considered more and more relevant to strongly correlated systems with strong Coulomb repulsion between electrons. We joined this effort, e.g., with our contributions to iridates. These compounds are hoped to provide an exotic state, a spin liquid, where spins interact but never order. We found that in different regimes, they can instead form very special type of order, an intricate lattice of vortices. The second new development was the heightened attention paid to ’topological’ aspects of condensed-matter systems. Topology refers here the a branch of mathematics that is concerned with the global features, e.g. with how many holes a surface has. In a spin system, topological order does not strongly depend on local details - and is hence quite robust - but nevertheless has pronounced quantum effects. One aspect of such states are edge modes that often support channels at the surface of the system, where electricity can flow, and moreover protect the current against scattering. We contributed here by showing that the interplay of spin and orbital degrees of freedom can lead to such states even in compounds without spin-orbit coupling, which is usually considered essential. Moreover, we established a scenario where magnetic excitations easily acquire nontrivial topology, just as charge excitations do in topological insulators.
Publications
- Intrinsic coupling of orbital excitations to spin fluctuations in Mott insulators, Phys. Rev. Lett. 107, 147201 (2011)
K. Wohlfeld, M. Daghofer, S. Nishimoto, G. Khaliullin, J. van den Brink
(See online at https://doi.org/10.1103/PhysRevLett.107.147201) - Fractional quantum-Hall liquid spontaneously generated by strongly correlated t2g electrons, Phys. Rev. Lett. 108, 126405 (2012)
J. W. F. Venderbos, S. Kourtis, J. van den Brink, M. Daghofer
(See online at https://doi.org/10.1103/PhysRevLett.108.126405) - Magnetic Excitation Spectra of Sr2 IrO4 Probed by Resonant Inelastic X-Ray Scattering: Establishing Links to Cuprate Superconductors, Phys. Rev. Lett. 108, 177003 (2012)
Jungho Kim, D. Casa, M. H. Upton, T. Gog, Young-June Kim, J. F. Mitchell, M. van Veenendaal, M. Daghofer, J. van den Brink, G. Khaliullin, B. J. Kim
(See online at https://doi.org/10.1103/PhysRevLett.108.177003) - Spectral density in a nematic state of iron pnictides, Phys. Rev. B 85, 184515 (2012)
M. Daghofer, A. Nicholson, A. Moreo
(See online at https://doi.org/10.1103/PhysRevB.85.184515) - Combined topological and Landau order from strong correlations in Chern bands, Phys. Rev. Lett. 113, 216404 (2014)
S. Kourtis and M. Daghofer
(See online at https://doi.org/10.1103/PhysRevLett.113.216404) - Excitonic Quasiparticles in a Spin-Orbit Mott Insulator, Nat. Commun. 5, 4453 (2014)
J. H. Kim, M. Daghofer, A. Said, T. Gog, J. van den Brink, G. Khaliullin, B. J. Kim
(See online at https://doi.org/10.1038/ncomms5453) - Femtosecond dynamics of magnetic excitations from resonant inelastic x-ray scattering in CaCu2O3, Phys. Rev. Lett. 112, 147401 (2014)
V. Bisogni, S. Kourtis, C. Monney, K. Zhou, R. Kraus, C. Sekar, V. Strocov, B. Büchner, J. van den Brink, L. Braicovich, T. Schmitt, M. Daghofer and J. Geck
(See online at https://doi.org/10.1103/PhysRevLett.112.147401) - Z2-vortex lattice in the ground state of the triangular Kitaev-Heisenberg model, Phys. Rev. B 93, 104417 (2016)
I. Rousochatzakis, U. K. Rössler, J. van den Brink, M. Daghofer,
(See online at https://doi.org/10.1103/PhysRevB.93.104417) - Spinon-orbiton repulsion and attraction mediated by Hund’s rule, Phys. Rev. B 98, 085120 (2018)
J. Heverhagen, M. Daghofer
(See online at https://doi.org/10.1103/PhysRevB.98.085120) - Nontrivial Triplon Topology and Triplon Liquid in Kitaev-Heisenberg-type Excitonic Magnets, Phys. Rev. Lett. 122, 177201 (2019)
P. S. Anisimov, F. Aust, G. Khaliullin, M. Daghofer
(See online at https://doi.org/10.1103/PhysRevLett.122.177201)
