Atomically thin ferromagnetic (FM) films were recently prepared by mechanical exfoliation of bulk FM semiconductor Cr2Ge2Te6. They provide a platform to explore novel two-dimensional (2D) magnetic phenomena, and offer exciting prospects for new technologies. By performing systematic ab initio density functional calculations, here we study two relativity-induced properties of these 2D materials [monolayer (ML), bilayer (BL) and trilayer (TL) as well as bulk], namely, magnetic anisotropy energy (MAE) and magneto-optical (MO) effects. Competing contributions of both magneto-crystalline anisotropy energy (C-MAE) and magnetic dipolar anisotropy energy (D-MAE) to the MAE, are computed. Calculated MAEs of these materials are large, being in the order of ∼0.1 meV/Cr. Interestingly, we find that the out-of-plane magnetic anisotropy is preferred in all the systems except the ML where an in-plane magnetization is favored because here the D-MAE is larger than the C-MAE. Crucially, this explains why long-range FM order was observed in all the few-layer Cr2Ge2Te6 except the ML because the out-of-plane magnetic anisotropy would open a spin-wave gap and thus suppress magnetic fluctuations so that long-range FM order could be stabilized at finite temperature. In the visible frequency range, large Kerr rotations up to ∼1.0 • in these materials are predicted and they are comparable to that observed in famous MO materials such as PtMnSb and Y3Fe5O12. Moreover, they are ∼100 times larger than that of 3d transition metal MLs deposited on Au surfaces. Faraday rotation angles in these 2D materials are also large, being up to ∼120 deg/µm, and are thus comparable to the best-known MO semiconductor Bi3Fe5O12. These findings thus suggest that with large MAE and MO effects, atomically thin Cr2Ge2Te6 films would have potential applications in novel magnetic, MO and spintronic nanodevices. *
For topological insulators to be implemented in practical applications, it is a prerequisite to select suitable substrates that are required to leave insulators’ nontrivial properties and sizable opened band gaps (due to spin-orbital couplings) unaltered. Using ab initio calculations, we predict that Ge(111) surface qualified as a candidate to support stanene sheets, because the band structure of √3 × √3 stanene/Ge(111) (2 × 2) surface displays a typical Dirac cone at Γ point in the vicinity of the Fermi level. Aided with the result of Z2 invariant calculations, a √3 × √3 stanene/Ge(111) (2 × 2) system has been proved to sustain the nontrivial topological phase, with the prove being confirmed by the edge state calculations of stanene ribbons. This finding can serve as guidance for epitaxial growth of stanene on substrate and render stanene feasible for practical use as a topological insulator.
Using first-principles computations, we discuss topological properties of germanene in buckled as well as planar honeycombs with asymmetric passivation via hydrogen and nitrogen (GeHN) atoms. GeHN in the planar structure is found to harbor a quantum anomalous Hall (QAH) insulator phase. Our analysis indicates that the buckled GeHN also possesses a QAH phase under tensile strain. We computed the associated Chern numbers and edge states to confirm the presence of the QAH state. In particular, chiral edge bands connecting conduction and valence bands were found at the edges of a planar zigzag GeHN nanoribbon. By considering a range of buckling distances, we demonstrate how the system undergoes the transition from the trivial to the QAH phase between the buckled and planar structures. Finally, we show CdTe(111) to be a suitable substrate for supporting buckled germanene in the QAH phase. Our results suggest that functionalized germanene could provide a robust QAH-based platform for spintronics applications.
We review our recent work on the Gutzwiller conjugate gradient minimization method, an ab initio approach developed for correlated electron systems. The complete formalism has been outlined that allows for a systematic understanding of the method, followed by a discussion of benchmark studies of dimers, one- and two-dimensional single-band Hubbard models. In the end, we present some preliminary results of multi-band Hubbard models and large-basis calculations of F2 to illustrate our efforts to further reduce the computational complexity.
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