Fundamental Spin Interactions Underlying the Magnetic Anisotropy in the Kitaev Ferromagnet <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>CrI</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>
Inhee Lee, Franz Utermohlen, Daniel Weber, Kyusung Hwang, Chi Zhang, Johan van Tol, Joshua E. Goldberger, Nandini Trivedi, P. C. Hammel
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 ${\mathrm{CrI}}_{3}$ single crystals with theoretical modeling based on symmetries. We discover that the Kitaev interaction is the strongest in this material with $K\ensuremath{\sim}\ensuremath{-}5.2\text{ }\text{ }\mathrm{meV}$, 25 times larger than the Heisenberg exchange $J\ensuremath{\sim}\ensuremath{-}0.2\text{ }\text{ }\mathrm{meV}$, and responsible for opening the $\ensuremath{\sim}5\text{ }\text{ }\mathrm{meV}$ gap at the Dirac points in the spin-wave dispersion. Furthermore, we find that the symmetric off-diagonal anisotropy $\mathrm{\ensuremath{\Gamma}}\ensuremath{\sim}\ensuremath{-}67.5\text{ }\text{ }\ensuremath{\mu}\mathrm{eV}$, though small, is crucial for opening a $\ensuremath{\sim}0.3\text{ }\text{ }\mathrm{meV}$ 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 $\ensuremath{\mu}\mathrm{eV}$-scale quadrupolar contribution to the $S=3/2$ magnetism. Our identification of the underlying exchange anisotropies opens paths toward 2D ferromagnets with higher ${T}_{C}$ as well as magnetically frustrated quantum spin liquids based on Kitaev physics.