The Low-Energy Models of Mott Insulators with a Finite Spin-Orbit Coupling

Erick Garcia, Paola Caterina Forino, Rong Cong +7 more

M. Iskin, Ahmet Tuna Bolukbasi

George Jackeli, Giniyat Khaliullin

We study the magnetic interactions in Mott-Hubbard systems with partially filled t_{2g} levels and with strong spin-orbit coupling. The latter entangles the spin and orbital spaces, and leads to a rich variety of the low energy Hamiltonians that extrapolate from the Heisenberg to a quantum compass model depending on the lattice geometry. This gives way to "engineer" in such Mott insulators an exactly solvable spin model by Kitaev relevant for quantum computation. We, finally, explain "weak" ferromagnetism, with an anomalously large ferromagnetic moment, in Sr2IrO4.

H. Takagi

Jize Zhao, Shijie Hu, Jun Chang +3 more

We study the evolution of magnetic structures driven by a synthetic spin-orbit coupling in a one-dimensional two-component Bose-Hubbard model. In addition to the Mott insulator-superfluid transition, in the Mott insulator phases we found a transition from a gapped ferromagnetic phase to a gapless chiral phase by increasing the strength of the spin-orbit coupling. Further increasing the spin-orbit coupling drives a transition from the gapless chiral phase to a gapped antiferromagnetic phase. These magnetic structures persist in superfluid phases. In particular, in the chiral Mott insulator and chiral superfluid phases, incommensurability is observed in characteristic correlation functions. These unconventional Mott insulator phase and superfluid phase demonstrate the different effects arising from the competition between the kinetic energy and the spin-orbit coupling.

W. M. H. Natori, Roderich Moessner, Johannes Knolle

We study the effect of a magnetic field on the low-energy description of Mott insulators with strong spin-orbit (SO) coupling. In contrast to the standard case of the Hubbard model without SO coupling, we show that Peierls phases can modulate the magnetic exchange at leading order in the interaction. Our mechanism crucially depends on the existence of distinct exchange paths between neighboring magnetic ions enclosing a well-defined area. Thus it will generically be present in any solid state realization of the Kitaev model and its extensions. We explicitly calculate the variation of the exchange constants of the so-called $JK\mathrm{\ensuremath{\Gamma}}$ model as a function of the magnetic flux. We discuss experimental implications of our findings for various settings of candidate Kitaev spin liquids.