Significance of Single-ion Anisotropy in d³ Mott Insulator

Magnetic anisotropy is essential in the development of 2D spintronic devices as the Mermin-Wagner theorem forbids long-range magnetic order in 2D magnetic isotropic systems. For spin moment S bigger than 1/2, the single-ion anisotropy is possible via spin-orbit coupling. However, d³ Mott insulators with octahedra environment map to the half-filled t_2g-orbitals and the single-ion anisotropy is absent despite the S=3/2 local moment, as spin-orbit coupling is inactive due to zero total angular momentum according to the Hund’s rule. On the other hand, preferred magnetic moment directions have been reported in d³ materials. Here we derive the single-ion anisotropy interaction using the strong-coupling expansion. The cubic crystal field splitting, trigonal distortions, and Hund’s coupling in addition to spin-orbit coupling from both transition metal and anion sites are taken into account. Intriguing Interplay among them determines the easy-plane vs. easy-axis single ion anisotropy. We apply our theory to CrX₃ and present the origin of single-ion anisotropy difference in CrCl₃ and CrI₃. Our theory can be generalized to 4d³ and 5d³ systems.