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In late transition metal ions with one electron in a d-shall, the spin-orbit coupling (SOC) stabilizes j=3/2 quartet of an effective total angular momentum and allows for the emergence of the multi-orbital physics and related spin-orbital frustration.

The aim of this talk is to present our works performed along this line. More specifically, I will show that in a thin film of double perovskite Sr2FeMoO6, strong SOC could give rise to a robust ferrimagnetic state with an emergent spin-polarized electronic structure consisting of flat bands and four massive or massless Dirac dispersions, with an interesting response to the applied magnetic field [1].

Next, considering Mott insulators, molybdenum and osmium double perovskites, as examples, I discuss how resulting spin-orbital frustration can lead to a host of quantum phases that includes unusual ordered patterns and nonmagnetic disordered valence bond states [2]. Finally, I present an example of a honeycomb lattice j=3/2 system, such as zirconium trichloride, in which, paradoxically, the strong SOC enhances the symmetry of spin-orbital space to emergent SU(4) symmetric couplings [3].

References
[1] M. G. Yamada, & G. Jackeli, Phys. Rev. Materials 4, 074007 (2020).

[2] J. Romhányi, L. Balents, & G. Jackeli, Phys. Rev. Lett. 118, 217202 (2017).

[3] M. G. Yamada, M. Oshikawa, & G. Jackeli, Phys. Rev. Lett. 121, 217202 (2018).