We report a high-field electron spin resonance study in the sub-THz frequency domain of a single crystal of Sr$_2$IrO$_4$ that has been recently proposed as a prototypical spin-orbital Mott insulator. In the antiferromagnetically (AFM) ordered state
with noncollinear spin structure that occurs in this material at $T_{rm N} approx 240$ K we observe both the low frequency mode due to the precession of weak ferromagnetic moments arising from a spin canting, and the high frequency modes due to the precession of the AFM sublattices. Surprisingly, the energy gap for the AFM excitations appears to be very small, amounting to 0.83 meV only. This suggests a rather isotropic Heisenberg dynamics of interacting Ir$^{4+}$ effective spins despite the spin-orbital entanglement in the ground state.
Ultra-cold dipolar spinor fermions in zig-zag type optical lattices can mimic spin-orbital models relevant in solid-state systems, as transition-metal oxides with partially filled d-levels, with the interesting advantage of reviving the quantum natur
e of orbital fluctuations. We discuss two different physical systems in which these models may be simulated, showing that the interplay between lattice geometry and spin-orbital quantum dynamics produces a wealth of novel quantum phases.
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 ex
trapolate 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 Sr$_2$IrO$_4$.
The collective behavior of correlated electrons in the VO$_2-$interface layer of LaVO$_3$/SrTiO$_3$ heterostructure is studied within a quarter-filled $t_{2g}$-orbital Hubbard model on a square lattice. We argue that the ground state is ferromagnetic
driven by the double exchange mechanism, and is orbitally and charge ordered due to a confined geometry and electron correlations. The orbital and charge density waves open gaps on the entire Fermi surfaces of all orbitals. The theory explains the observed insulating behavior of the $p$-type interface between LaVO$_3$ and SrTiO$_3$.
We discuss the ground state of the spin-orbital model for spin-one ions with partially filled $t_{2g}$ levels on a honeycomb lattice. We find that the orbital degrees of freedom induce a spontaneous dimerization of spins and drive them into nonmagnet
ic manifold spanned by hard-core dimer (spin-singlet) coverings of the lattice. The cooperative ``dimer Jahn-Teller effect is introduced through a magnetoelastic coupling and is shown to lift the orientational degeneracy of dimers leading to a peculiar valence bond crystal pattern. The present theory provides a theoretical explanation of nonmagnetic dimerized superstructure experimentally seen in Li$_2$RuO$_3$ compound at low temperatures.
I review the microscopic spin-orbital Hamiltonian and ground state properties of spin one-half spinel oxides with threefold $t_{2g}$ orbital degeneracy. It is shown that for any orbital configuration a ground state of corresponding spin only Hamilton
ian is infinitely degenerate in the classical limit. The extensive classical degeneracy is lifted by the quantum nature of the spins, an effect similar to order-out-of-disorder phenomenon by quantum fluctuations. This drives the system to a non-magnetic spin-singlet dimer manifold with a residual degeneracy due to relative orientation of dimers. The magneto-elastic mechanism of lifting the ``orientational degeneracy is also briefly reviewed.
We study and solve the ground-state problem of a microscopic model for a family of orbitally degenerate quantum magnets. The orbital degrees of freedom are assumed to have directional character and are represented by static Potts-like variables. In t
he limit of vanishing Hunds coupling, the ground-state manifold of such a model is spanned by the hard-core dimer (spin singlet) coverings of the lattice. The extensive degeneracy of dimer coverings is lifted at a finite Hunds coupling through an order-out-of-disorder mechanism by virtual triplet excitations. The relevance of our results to several experimentally studied systems is discussed.
