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Register a new userFundamental Spin Interactions Underlying the Magnetic Anisotropy in the Kitaev Ferromagnet CrI$_3$
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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.
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Magnetic anisotropy is crucially important for the stabilization of two-dimensional (2D) magnetism, which is rare in nature but highly desirable in spintronics and for advancing fundamental knowledge. Recent works on CrI$_3$ and CrGeTe$_3$ monolayers not only led to observations of the long-time-sought 2D ferromagnetism, but also revealed distinct magnetic anisotropy in the two systems, namely Ising behavior for CrI$_3$ versus Heisenberg behavior for CrGeTe$_3$. Such magnetic difference strongly contrasts with structural and electronic similarities of these two materials, and understanding it at a microscopic scale should be of large benefits. Here, first-principles calculations are performed and analyzed to develop a simple Hamiltonian, to investigate magnetic anisotropy of CrI$_3$ and CrGeTe$_3$ monolayers. The anisotropic exchange coupling in both systems is surprisingly determined to be of Kitaev-type. Moreover, the interplay between this Kitaev interaction and single ion anisotropy (SIA) is found to naturally explain the different magnetic behaviors of CrI$_3$ and CrGeTe$_3$. Finally, both the Kitaev interaction and SIA are further found to be induced by spin-orbit coupling of the heavy ligands (I of CrI$_3$ or Te of CrGeTe$_3$) rather than the commonly believed 3d magnetic Cr ions.
The family of atomically thin magnets holds great promise for a number of prospective applications in magneto-optoelectronics, with CrI$_3$ arguably being its most prototypical member. However, the formation of defects in this system remains unexplored to date. Here, we investigate native point defects in monolayer CrI$_3$ by means of first-principles calculations. We consider a large set of intrinsic impurities and address their atomic structure, thermodynamic stability, diffusion and aggregation tendencies as well as local magnetic moments. Under thermodynamic equilibrium, the most stable defects are found to be either Cr or I atomic vacancies along with their complexes, depending on the chemical potential conditions. These defects are predicted to be quite mobile at room temperature and to exhibit a strong tendency to agglomerate. In addition, our calculations indicate that the defect-induced deviation from the nominal stoichiometry largely impacts the local magnetic moments, thereby suggesting a marked interplay between magnetism and disorder in CrI$_3$. Overall, this work portrays a comprehensive picture of intrinsic point defects in monolayer CrI$_3$ from a theoretical perspective.
The spin transfer effect in ferromagnet-quantum dot (insulator)-ferromagnet Aharonov-Bohm (AB) ring system with Rashba spin-orbit (SO) interactions is investigated by means of Keldysh nonequilibrium Green function method. It is found that both the magnitude and direction of the spin transfer torque (STT) acting on the right ferromagnet electrode can be effectively controlled by changing the magnetic flux threading the AB ring or the gate voltage on the quantum dot. The STT can be greatly augmented by matching a proper magnetic flux and an SO interaction at a cost of low electrical current. The STT, electrical current, and spin current are uncovered to oscillate with the magnetic flux. The present results are expected to be useful for information storage in nanospintronics.
We investigate the impact of mechanical strains and a perpendicular electric field on the electronic and magnetic ground-state properties of two-dimensional monolayer CrI$_3$ using density functional theory. We propose a minimal spin model Hamiltonian, consisting of symmetric isotropic exchange interactions, magnetic anisotropy energy, and Dzyaloshinskii-Moriya (DM) interactions, to capture most pertinent magnetic properties of the system. We compute the mechanical strain and electric field dependence of various spin-spin interactions. Our results show that both the amplitudes and signs of the exchange interactions can be engineered by means of strain, while the electric field affects only their amplitudes. However, strain and electric fields affect both the directions and amplitudes of the DM vectors. The amplitude of the magnetic anisotropy energy can also be substantially modified by an applied strain. We show that in comparison with an electric field, strain can be more efficiently used to manipulate the magnetic and electronic properties of the system. Notably, such systematic tuning of the spin interactions is essential for the engineering of room-temperature spintronic nanodevices.
The magnetic properties in two-dimensional van der Waals materials depend sensitively on structure. CrI3, as an example, has been recently demonstrated to exhibit distinct magnetic properties depending on the layer thickness and stacking order. Bulk CrI3 is ferromagnetic (FM) with a Curie temperature of 61 K and a rhombohedral layer stacking, while few-layer CrI3 has a layered antiferromagnetic (AFM) phase with a lower ordering temperature of 45 K and a monoclinic stacking. In this work, we use cryogenic magnetic force microscopy to investigate CrI3 flakes in the intermediate thickness range (25 - 200 nm) and find that the two types of magnetic orders hence the stacking orders can coexist in the same flake, with a layer of ~13 nm at each surface being in the layered AFM phase similar to few-layer CrI3 and the rest in the bulk FM phase. The switching of the bulk moment proceeds through a remnant state with nearly compensated magnetic moment along the c-axis, indicating formation of c-axis domains allowed by a weak interlayer coupling strength in the rhombohedral phase. Our results provide a comprehensive picture on the magnetism in CrI3 and point to the possibility of engineering magnetic heterostructures within the same material.
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