Magnetic Anisotropy in Spin-3/2 with Heavy Ligand in Honeycomb Mott Insulators: Application to CrI${}_3$

Abstract

Ferromagnetism in the two-dimensional CrI${}_3$ has generated a lot of excitement, and it was recently proposed that the spin-orbit coupling (SOC) in Iodine may generate bond-dependent spin interactions leading to magnetic anisotropy. Here we derive a microscopic spin model of S=3/2 on transition metals surrounded by heavy ligands in honeycomb Mott insulators using a strong-coupling perturbation theory. For ideal octahedra we find Heisenberg and Kitaev interactions, which favor the magnetic moment along the cubic axis via quantum fluctuations. When a slight trigonal distortion of the octahedra is present together with the SOC, three additional interactions arise, comprised of the off-diagonal symmetric $\Gamma$ and ${\Gamma }^{\prime }$, and single-ion anisotropy. The resulting magnetic anisotropy pins the moment perpendicular to the honeycomb plane as observed in a single-layer of CrI${}_3$, suggesting the significance of SOC and trigonal distortion in understanding magnetism of two dimensional Mott insulators. Comparison to the spin-orbit coupled $J_{\mathrm{eff}}$= 1/2 and S=1 models is also presented.

14 pages, 7 figures. Reorganized sections and added new author and new section

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Cited by in corpus (52)

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• Magnetic field effect on topological spin excitations in CrI${}_3$
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• Beyond Kitaev physics in strong spin-orbit coupled magnets
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• Non-Kitaev vs. Kitaev Honeycomb Cobaltates
• Unveiling the S=3/2 Kitaev Honeycomb Spin Liquids
• Electronic and magnetic properties of the RuX${}_3$ (X=Cl, Br, I) family: Two siblings -- and a cousin?
• Theory of magnetism in the van der Waals magnet CrI3
• Ground-state phase diagram of spin-$S$ Kitaev-Heisenberg models
• Gaps in Topological Magnon Spectra: Intrinsic vs. Extrinsic Effects
• Strain tunability of perpendicular magnetic anisotropy in van der Waals ferromagnets VI3
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