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Register a new userEvolution of Spin-Orbital Entanglement with Increasing Ising Spin-Orbit Coupling
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Several realistic spin-orbital models for transition metal oxides go beyond the classical expectations and could be understood only by employing the quantum entanglement. Experiments on these materials confirm that spin-orbital entanglement has measurable consequences. Here, we capture the essential features of spin-orbital entanglement in complex quantum matter utilizing 1D spin-orbital model which accommodates SU(2)xSU(2) symmetric Kugel-Khomskii superexchange as well as the Ising on-site spin-orbit coupling. Building on the results obtained for full and effective models in the regime of strong spin-orbit coupling, we address the question whether the entanglement found on superexchange bonds always increases when the Ising spin-orbit coupling is added. We show that (i) quantum entanglement is amplified by strong spin-orbit coupling and, surprisingly, (ii) almost classical disentangled states are possible. We complete the latter case by analyzing how the entanglement existing for intermediate values of spin-orbit coupling can disappear for higher values of this coupling.
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The concept of the entanglement between spin and orbital degrees of freedom plays a crucial role in understanding various phases and exotic ground states in a broad class of materials, including orbitally ordered materials and spin liquids. We investigate how the spin-orbital entanglement in a Mott insulator depends on the value of the spin-orbit coupling of the relativistic origin. To this end, we numerically diagonalize a 1D spin-orbital model with the Kugel-Khomskii exchange interactions between spins and orbitals on different sites supplemented by the on-site spin-orbit coupling. In the regime of small spin-orbit coupling w.r.t. the spin-orbital exchange, the ground state to a large extent resembles the one obtained in the limit of vanishing spin-orbit coupling. On the other hand, for large spin-orbit coupling the ground state can, depending on the model parameters, either still show negligible spin-orbital entanglement, or can evolve to a highly spin-orbitally entangled phase with completely distinct properties that are described by an effective XXZ model. The presented results suggest that: (i) the spin-orbital entanglement may be induced by large on-site spin-orbit coupling, as found in the 5d transition metal oxides, such as the iridates; (ii) for Mott insulators with weak spin-orbit coupling of Ising-type, such as e.g. the alkali hyperoxides, the effects of the spin-orbit coupling on the ground state can, in the first order of perturbation theory, be neglected.
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 realisation of the Kitaev model and its extensions. We explicitly calculate the variation of the exchange constants of the so-called $JKGamma$ model as a function of the magnetic flux. We discuss experimental implications of our findings for various settings of candidate Kitaev spin liquids.
A hole injected into a Mott insulator will gain an internal structure as recently identified by exact numerics, which is characterized by a nontrivial quantum number whose nature is of central importance in understanding the Mott physics. In this work, we show that a spin texture associated with such an internal degree of freedom can explicitly manifest after the spin degeneracy is lifted by a emph{weak} Rashba spin-orbit coupling (SOC). It is described by an emergent angular momentum $J_{z}=pm3/2$ as shown by both exact diagonalization (ED) and variational Monte Carlo (VMC) calculations, which are in good agreement with each other at a finite size. In particular, as the internal structure such a spin texture is generally present in the hole composite even at high excited energies, such that a corresponding texture in momentum space, extending deep inside the Brillouin zone, can be directly probed by the spin-polarized angle-resolved photoemission spectroscopy (ARPES). This is in contrast to a Landau quasiparticle under the SOC, in which the spin texture induced by SOC will not be protected once the excited energy is larger than the weak SOC coupling strength, away from the Fermi energy. We point out that the spin texture due to the SOC should be monotonically enhanced with reducing spin-spin correlation length in the superconducting/pseudogap phase at finite doping. A brief discussion of a recent experiment of the spin-polarized ARPES will be made.
Using ab initio calculations, we have investigated an insulating tetragonally distorted perovskite BaCrO$_3$ with a formal $3d^2$ configuration, the volume of which is apparently substantially enhanced by a strain due to SrTiO$_3$ substrate. Inclusion of both correlation and spin-orbit coupling (SOC) effects leads to a metal-insulator transition and in-plane zigzag orbital-ordering (OO) of alternating singly filled $d_{xz}+id_{yz}$ and $d_{xz}-id_{yz}$ orbitals, which results in a large orbital moment $M_L$ ~ -0.78 $mu_B$ antialigned to the spin moment $M_S$ ~ $2|M_L|$ in Cr ions. Remarkably, this ordering also induces a considerable $M_L$ for apical oxygens. Our findings show metal-insulator and OO transitions, driven by an interplay among strain, correlation, and SOC, which is uncommon in 3d systems.
In atomic physics, the Hund rule says that the largest spin and orbital state is realized due to the interplay of the spin-orbit coupling (SOC) and the Coulomb interactions. Here, we show that in ferromagnetic solids the effective SOC and the orbital magnetic moment can be dramatically enhanced by a factor of $1/[1-(2U^prime-U-J_H)rho_0]$, where $U$ and $U^prime$ are the on-site Coulomb interaction within the same oribtals and between different orbitals, respectively, $J_H$ is the Hund coupling, and $rho_0$ is the average density of states. This factor is obtained by using the two-orbital as well as five-orbital Hubbard models with SOC. We also find that the spin polarization is more favorable than the orbital polarization, being consistent with experimental observations. This present work provides a fundamental basis for understanding the enhancements of SOC and orbital moment by Coulomb interactions in ferromagnets, which would have wide applications in spintronics.
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