Large magneto-optical effects and magnetic anisotropy energy in two-dimensional Cr2Ge2Te6

Abstract

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. *

Magnetism and magneto-optical effects in bulk and few-layer CrI3: a theoretical GGA + U study

“…This is in strong contrast to the case of the Cr 2 Ge 2 Te 6 multilayers where the MAE is much smaller and depends significantly on the film thickness [26]. In particular, for ML Cr 2 Ge 2 Te 6 , the magnitude of MCE becomes smaller than that of MDE such that the MAE is negative, favoring an in-plane magnetization [26]. Importantly, since the significant out-of-plane MAE is needed to stabilize long-range magnetic orders in a 2D material by suppressing the thermal spin fluctuations, this explains why the FM state is observed in ML CrI 3 [2] but not in ML Cr 2 Ge 2 Te 6 [1].…”

“…Using the calculated magnetic moments, the ΔE d is obtained as the difference in E d between the in-plane and out-of-plane magnetizations. In a 2D material, since all the R and q are in-plane, the second term in equation (2) would be zero for the out-of-plane magnetization, thereby resulting in the positive M qq¢ while for an in-plane magnetization the M qq¢ is negative [26]. Therefore, the MDE always prefers an in-plane magnetization in a 2D material.…”

“…To better describe onsite Coulomb repulsion between Cr 3d electrons, we adopt the GGA+U scheme [36] in the present calculations. Feng et al [26] recently carried out systematic GGA+U calculations for bulk and multilayer Cr 2 Ge 2 Te 6 with different effective Coulomb energy U values and concluded that the appropriate U value for Cr 3d electrons is 1.0 eV. Given the similarity between the Cr 2 Ge 2 Te 6 and CrI 3 , here we also use U=1.0 eV.…”

Electronic structure and magnetic properties of few-layer Cr 2 Ge 2 Te 6 : the key role of nonlocal electron–electron interaction effects

“…By carrying out spin-polarized non-relativistic calculations, we have checked that HSE06 hybrid functional endows the VBM and CBM with spin-up character, differently from what happens in the spGGA. We conclude that the application of a scissor operator to open the gap leads to wrong electronic and optical properties 59 . The calculated scalar-relativistic electronic gap for bulk Cr 2 Ge 2 Te 6 is E g ∼ 0.73 eV, which is, as expected, larger than the one calculated with the inclusion of SOC.…”

Strain-Induced Room-Temperature Ferromagnetic Semiconductors with Large Anomalous Hall Conductivity in Two-Dimensional Cr2Ge2Se6

“…The magnetic structure in monolayer CrI 3 and Cr 2 Ge 2 Te 6 was recently discussed in terms of Kitaev interaction [9]. Photoluminescence and magneto-optical effects have also been discussed [10,11]. The ferromagnetism with high T c was also reported in experiment in the monolayer VSe 2 [12] and MnSe 2 [13].…”