Dynamic Jahn-Teller effect and emergent magnetism in cubic 5d¹ double perovskites

Electron-phonon (vibronic) coupling changes the nature of the magnetism of spin-orbit Mott insulators:

From this viewpoint, a family of 5d¹ double perovskites is of great interest because they have strong spin-orbit and vibronic couplings [1].

The nature of the ordered multipolar phases in the 5d¹ compounds is still puzzling.

In a Re compound, two types of quadrupolar orders develop simultaneously above the magnetic transition temperature, which disagrees with the previous predictions based on a spin-orbit model [2].

In Ta compounds, antiferromagnetic and ferro z² quadrupole orders simultaneously develop at low temperature, while the mechanism is unknown [3].

In this work, we propose an effective model that includes the effects of the interplay of the spin-orbit and vibronic couplings, and on this basis explain the two unsolved questions.

Due to the dynamic Jahn-Teller effect on $d^1$ sites, the local quantum states respond not only spin-orbital superexchange interaction but also elastic interaction.

Varying the elastic interaction parameters, we reproduce the phases observed in the Re and Ta compounds.

[1] N. Iwahara, V. Vieru, and L. F. Chibotaru, Phys. Rev. B 98, 075138 (2018).

[2] D. Hirai et al., Phys. Rev. Research 2, 022063 (2020).

[3] H. Ishikawa et al., Phys. Rev. B 100, 045142 (2019).