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Register a new userOrbitally-resolved ferromagnetism of monolayer CrI$_3$
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Added by
Vladimir Mazurenko Dr.
Publication date
2019
fields
Physics
and research's language is
English
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Few-layer CrI$_3$ is the most known example among two-dimensional (2D) ferromagnets, which have attracted growing interest in recent years. Despite considerable efforts and progress in understanding the properties of 2D magnets both from theory and experiment, the mechanism behind the formation of in-plane magnetic ordering in chromium halides is still under debate. Here, we propose a microscopic orbitally-resolved description of ferromagnetism in monolayer CrI$_3$. Starting from first-principles calculations, we construct a low-energy model for the isotropic Heisenberg exchange interactions. We find that there are two competing contributions to the long-range magnetic ordering in CrI$_3$: (i) Antiferromagnetic Andersons superexchange between half-filled $t_{2g}$ orbitals of Cr atoms; and (ii) Ferromagnetic exchange governed by the Kugel-Khomskii mechanism, involving the transitions between half-filled $t_{2g}$ and empty $e_g$ orbitals. Using numerical calculations, we estimate the exchange interactions in momentum-space, which allows us to restore the spin-wave spectrum, as well as estimate the Curie temperature. Contrary to the nearest-neighbor effective models, our calculations suggest the presence of sharp resonances in the spin-wave spectrum at 5--7 meV, depending on the vertical bias voltage. Our estimation of the Curie temperature in monolayer CrI$_3$ yields 55--65 K, which is in good agreement with experimental data.
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Atomically thin films of layered chromium triiodide (CrI$_3$) have recently been regarded as suitable candidates to a wide spectrum of technologically relevant applications, mainly owing to the opportunity they offer to achieve a reversible transition between coexisting in-plane ferro- and out-of-plane antiferro-magnetic orders. However, no routes for inducing such a transition have been designed down to the single-layer limit. Here, we address the magnetic response of monolayer CrI$_3$ to in-plane lattice deformations through a combination of isotropic Heisenberg spin Hamiltonians and first-principles calculations. Depending on the magnitude and orientation of the lattice strain exerted, we unveil a series of direction-dependent parallel-to-antiparallel spins crossovers, which yield the emergence of ferromagnetic, Neel antiferromagnetic, zigzag and stripy antiferromagnetic ground states. Additionally, we identify a critical point in the magnetic phase diagram whereby the exchange couplings vanish and the magnetism is quenched. Our work establishes guidelines for extensively tailoring the spin interactions in monolayer CrI$_3$ via strain engineering, and further expands the magnetically ordered phases which can be hosted in a two-dimensional crystal.
The marked interplay between the crystalline, electronic, and magnetic structure of atomically thin magnets has been regarded as the key feature for designing next-generation magneto-optoelectronic devices. In this respect, a detailed understanding of the microscopic interactions underlying the magnetic responses of these crystals is of primary importance. Here, we combine model Hamiltonians with multi-reference configuration interaction wavefunctions to accurately determine the strength of the spin couplings in the prototypical single-layer magnet CrI$_3$. Our calculations identify the (ferromagnetic) Heisenberg exchange interaction $J = -1.44$ meV as the dominant term, being the inter-site magnetic anisotropies substantially {weaker}. We also find that single-layer CrI$_3$ features an out-of-plane easy axis ensuing from a single-ion anisotropy $A = -0.10$ meV, and predict $g$-tensor in-plane components $g_{xx} = g_{yy} = 1.90$ and out-of-plane component $g_{zz} = 1.92$. In addition, we assess the performance of a dozen widely used density functionals against our accurate correlated wavefunctions {calculations} and available experimental data, thereby establishing reference results for future first-principles investigations. Overall, our findings offer a firm theoretical ground to experimental observations.
Microscopic origin of the ferromagnetic (FM) exchange coupling in CrCl$_3$ and CrI$_3$, their common aspects and differences, are investigated on the basis of density functional theory combined with realistic modeling approach for the analysis of interatomic exchange interactions. We perform a comparative study based on the pseudopotential and linear muffin-tin orbital methods by treating the effects of electron exchange and correlation in GGA and LSDA, respectively. The results of ordinary band structure calculations are used in order to construct the minimal tight-binding type models describing the behavior of the magnetic Cr $3d$ and ligand $p$ bands in the basis of localized Wannier functions, and evaluate the effective exchange coupling ($J_{rm eff}$) between two Cr sublattices employing four different technique: (i) Second-order Greens function perturbation theory for infinitesimal spin rotations of the LSDA (GGA) potential at the Cr sites; (ii) Enforcement of the magnetic force theorem in order to treat both Cr and ligand spins on a localized footing; (iii) Constrained total-energy calculations with an external field, treated in the framework of self-consistent linear response theory. We argue that the ligand states play crucial role in the ferromagnetism of Cr trihalides, though their contribution to $J_{rm eff}$ strongly depends on additional assumptions, which are traced back to fundamentals of adiabatic spin dynamics. Particularly, by neglecting ligand spins in the Greens function method, $J_{rm eff}$ can easily become antiferromagnetic, while by treating them as localized, one can severely overestimate the FM coupling. The best considered approach is based on the constraint method, where the ligand states are allowed to relax in response to each instantaneous reorientation of the Cr spins, controlled by the external field.
We have investigated the magnetic properties of highly anisotropic layered ferromagnetic semiconductor CrI$_3$ in presence of hydrostatic pressure ($P$). At ambient pressure, magnetization exhibits a clear anomaly below 212 K along with a thermal hysteresis over a wide temperature range (212-180 K), where a first-order structural transition is observed. CrI$_3$ undergoes a second-order ferromagnetic-paramagnetic phase transition with Curie temperature $T_C$=60.4 K. With application of pressure, the transition becomes sharper and $T_C$ is found to increase from 60.4 to 64.9 K as $P$ increases from 0 to 1.0 GPa. $T_C$ increases with $P$ in a sublinear fashion. The thermal hysteresis in magnetization and the increase of $T_C$ with pressure suggest that the spin and lattice degrees of freedom are coupled. The observed increase in $T_C$ has been explained on the basis of change in inter-layer coupling and Cr-I-Cr bond angle with pressure.
We study ferromagnetic ordering and microscopic inhomogeneity in tensile strained LaCoO$_3$ using numerical simulations. We argue that both phenomena originate from effective superexchange interactions between atoms in the high-spin (HS) state mediated by the intermediate-spin excitations. We derive a model of the HS excitation as a bare atomic state dressed by electron and electron-hole fluctuations on the neighbor atoms. We construct a series of approximations to account for electron correlation effects responsible for HS fluctuations and magnetic exchange. The obtained amplitudes and directional dependence of magnetic couplings between the dressed HS states show a qualitative agreement with experimental observations and provide a new physical picture of LaCoO$_3$ films.
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