In a classic paper about 50 years ago Kugel and Khomskii demonstrated that in strongly-correlated systems orbital ordering can arise from a purely electronic super-exchange mechanism and not just the conventional co-operative Jahn-Teller effect. Since then, finding materials in which the Kugel-Khomskii (KK) super-exchange mechanism dominates has proven to be a challenge, however. For the two textbook cases for orbital ordering, KCuF3 and LaMnO3, it was in fact shown that, although strong, KK super-exchange alone can not explain the presence of orbital ordering at very high temperature; other mechanisms, such as the (Coulomb-enhanced) Jahn-Teller effect and/or the Born-Mayer repulsion, are at work [1,2,3]. Recently, however, we have identified representative systems in which KK super-exchange is key [4,5]. In this talk I will discuss such paradigmatic examples and the unusual interplay between spin and orbital degrees of freedom that can occur in these materials.
[1] E. Pavarini, E. Koch, A.I. Lichtenstein, Phys. Rev. Lett. 101, 266405 (2008)
[2] E.Pavarini and E. Koch, Phys. Rev. Lett. 104, 086402 (2010)
[3] H. Sims, E. Pavarini, and E. Koch, Phys. Rev. B 96, 054107 (2017)
[4] X-J. Zhang, E. Koch and E. Pavarini, Phys. Rev. B 106, 115110 (2022)
[5] X-J. Zhang, E. Koch and E. Pavarini, to be published