Fundamental Spin Interactions Underlying the Magnetic Anisotropy in the Kitaev Ferromagnet CrI${}_3$

Abstract

We lay the foundation for determining the microscopic spin interactions in two-dimensional (2D) ferromagnets by combining angle-dependent ferromagnetic resonance (FMR) experiments on high quality CrI${}_3$ single crystals with theoretical modeling based on symmetries. We discover that the Kitaev interaction is the strongest in this material with $K\sim -5.2$ meV, 25 times larger than the Heisenberg exchange $J\sim -0.2$ meV, and responsible for opening the $\sim$5 meV gap at the Dirac points in the spin-wave dispersion. Furthermore, we find that the symmetric off-diagonal anisotropy $\Gamma \sim -67.5$ $\mu$eV, though small, is crucial for opening a $\sim$0.3 meV gap in the magnon spectrum at the zone center and stabilizing ferromagnetism in the 2D limit. The high resolution of the FMR data further reveals a $\mu$eV-scale quadrupolar contribution to the $S=3/2$ magnetism. Our identification of the underlying exchange anisotropies opens paths toward 2D ferromagnets with higher $T_{\text{C}}$ as well as magnetically frustrated quantum spin liquids based on Kitaev physics.

5 pages, 4 figures

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• Magnetism and Spin Dynamics in Room-Temperature van der Waals Magnet Fe${}_5$GeTe${}_2$
• Topological magnonics in the two-dimensional van der Waals magnet CrI3
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• Magnetic Anisotropy in Spin-3/2 with Heavy Ligand in Honeycomb Mott Insulators: Application to CrI${}_3$
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• Accessing new magnetic regimes by tuning the ligand spin-orbit coupling in van der Waals magnets
• Electron correlation effects on exchange interactions and spin excitations in 2D van der Waals materials
• Microscopic origin of magnetism in monolayer $3d$ transition metal dihalides
• Spin Dynamics in van der Waals Magnetic Systems
• Imaging and control of critical spin fluctuations in two-dimensional magnets
• Quantum rescaling, domain metastability and hybrid domain-walls in two-dimensional CrI3 magnets
• Heisenberg-Kitaev model in a magnetic field: $1/S$ expansion
• Coherent Helicity-Dependent Spin-Phonon Oscillations in the Ferromagnetic van der Waals Crystal CrI3
• Bosonic Bott Index and Disorder-Induced Topological Transitions of Magnons
• A Combined First Principles Study of the Structural, Magnetic, and Phonon Properties of Monolayer CrI${}_3$
• Magnon valley Hall effect in CrI3-based vdW heterostructures
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• A Perspective on Magnon Spin Nernst Effect in Antiferromagnets
• Topological magnons driven by the Dzyaloshinskii-Moriya interaction in the centrosymmetric ferromagnet Mn${}_5$Ge${}_3$
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• Antiferromagnetism in two-dimensional materials: progress and computational challenges
• Magnetic Anisotropy in Two-dimensional van der Waals Magnetic Materials and Their Heterostructures: Importance, Mechanisms, and Opportunities
• Light-induced topological magnons in two-dimensional van der Waals magnets
• Whirling interlayer fields as a source of stable topological order in moiré CrI3
• Control of magnetic states and spin interactions in bilayer CrCl${}_3$ with strain and electric fields: an ab initio study
• Triple-meron crystal in high-spin Kitaev magnets
• Magnon-magnon interaction and magnon relaxation time in ferromagnetic Cr2Ge2Te6 monolayer
• Kitaev spin-orbital bilayers and their moiré superlattices
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• A Kitaev-type spin liquid on a quasicrystal
• Quantum liquids of the S=3/2 Kitaev honeycomb and related Kugel-Khomskii models
• Higher-order Topological Phases of Magnons in van der Waals Honeycomb Ferromagnets
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• Thermal Hall effect in a van der Waals ferromagnet CrI3
• Magnetic fragmentation and fractionalized Goldstone modes in a bilayer quantum spin liquid
• Large photogalvanic spin current by magnetic resonance in bilayer Cr trihalides
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• Insights on magnon topology and valley-polarization in 2D bilayer quantum magnets
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