Mott-insulating transition metal oxides containing ${t}_{2g}^{4}$ ions with strong spin-orbit coupling were recently demonstrated to display unusual magnetism due to a dynamical mixing of the low-energy multiplet states via exchange processes. Here we derive exchange interactions in the situation where a tetragonal or trigonal crystal field selects a single relevant excited state on top of the singlet ionic ground state, producing an effective spin- $\frac{1}{2}$ . We show that these moments universally obey antiferromagnetic transverse-field Ising model (TFIM) with an intrinsic transverse field generated by the splitting of the two ionic singlets. Using ${\mathrm{Ru}}^{4+}$ as a example ion, we provide quantitative estimates of the exchange and illustrate the emergent TFIM physics based on phase diagrams and excitation spectra obtained for several 2D lattices---square, honeycomb, as well as for the frustrated triangular lattice.Mott-insulating transition metal oxides containing ${t}_{2g}^{4}$ ions with strong spin-orbit coupling were recently demonstrated to display unusual magnetism due to a dynamical mixing of the low-energy multiplet states via exchange processes. Here we derive exchange interactions in the situation where a tetragonal or trigonal crystal field selects a single relevant excited state on top of the singlet ionic ground state, producing an effective spin-$\frac{1}{2}$. We show that these moments universally obey antiferromagnetic transverse-field Ising model (TFIM) with an intrinsic transverse field generated by the splitting of the two ionic singlets. Using ${\mathrm{Ru}}^{4+}$ as a example ion, we provide quantitative estimates of the exchange and illustrate the emergent TFIM physics based on phase diagrams and excitation spectra obtained for several 2D lattices---square, honeycomb, as well as for the frustrated triangular lattice.

arXiv:2401.02532Physical review. B./Physical review. BJan 16, 20243 citations

Artificial SU(3) spin-orbit coupling and exotic Mott insulators

Mohsen Hafez-Torbati, Walter Hofstetter

Motivated by recent progress in the realization of artificial gauge fields and SU( $N$ ) Mott insulators using alkaline-earth-like atoms in optical lattices, we develop an unbiased SU( $N$ ) real-space dynamical mean-field theory approach to study the effect of spin-orbit coupling and on-site Hubbard interaction $U$ on SU(3) fermionic systems. We investigate the behavior of the local magnetization, double occupancies, and the triple occupancy versus the Hubbard interaction across the metal to Mott insulator transition. We map out the magnetic phase diagram in the large- $U$ limit and show that the spin-orbit coupling can stabilize long-range orders such as ferromagnets, spirals, and stripes with different orientations in SU(3) Mott insulators.Motivated by recent progress in the realization of artificial gauge fields and SU($N$) Mott insulators using alkaline-earth-like atoms in optical lattices, we develop an unbiased SU($N$) real-space dynamical mean-field theory approach to study the effect of spin-orbit coupling and on-site Hubbard interaction $U$ on SU(3) fermionic systems. We investigate the behavior of the local magnetization, double occupancies, and the triple occupancy versus the Hubbard interaction across the metal to Mott insulator transition. We map out the magnetic phase diagram in the large-$U$ limit and show that the spin-orbit coupling can stabilize long-range orders such as ferromagnets, spirals, and stripes with different orientations in SU(3) Mott insulators.

arXiv:1809.05704Physical review. B./Physical review. BDec 20, 201825 citations

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

Dorota Gotfryd

Mar 24, 20210 citations

Mott-insulating transition metal oxides containing

{t}_{2g}^{4}

ions with strong spin-orbit coupling were recently demonstrated to display unusual magnetism due to a dynamical mixing of the low-energy multiplet states via exchange processes. Here we derive exchange interactions in the situation where a tetragonal or trigonal crystal field selects a single relevant excited state on top of the singlet ionic ground state, producing an effective spin-

\frac{1}{2}

. We show that these moments universally obey antiferromagnetic transverse-field Ising model (TFIM) with an intrinsic transverse field generated by the splitting of the two ionic singlets. Using

{\mathrm{Ru}}^{4+}

as a example ion, we provide quantitative estimates of the exchange and illustrate the emergent TFIM physics based on phase diagrams and excitation spectra obtained for several 2D lattices---square, honeycomb, as well as for the frustrated triangular lattice.

Motivated by recent progress in the realization of artificial gauge fields and SU(

N

) Mott insulators using alkaline-earth-like atoms in optical lattices, we develop an unbiased SU(

N

) real-space dynamical mean-field theory approach to study the effect of spin-orbit coupling and on-site Hubbard interaction

U

on SU(3) fermionic systems. We investigate the behavior of the local magnetization, double occupancies, and the triple occupancy versus the Hubbard interaction across the metal to Mott insulator transition. We map out the magnetic phase diagram in the large-

U

limit and show that the spin-orbit coupling can stabilize long-range orders such as ferromagnets, spirals, and stripes with different orientations in SU(3) Mott insulators.