Significantly enhanced interlayer ferromagnetic coupling in van der Waals Fe 3 GeTe 2 bilayer
by Be-ion intercalation
Cite as: Appl. Phys. Lett.120, 073106 (2022);doi: 10.1063/5.0081270 Submitted: 8 December 2021
.
Accepted: 11 February 2022.
Published Online: 18 February 2022
XiaokunHuang,1,2,a) JinlinXu,1XinNie,1ChaoChen,1,2WeiWang,3GuangSong,4 XiangpingJiang,1,2,a) and Jun-MingLiu1,5
AFFILIATIONS
1School of Materials Science and Engineering, Jingdezhen Ceramic Institute, Jingdezhen 333001, China
2National Engineering Research Center for Domestic & Building Ceramics, Jingdezhen 333001, China
3Key Laboratory of Flexible Electronics & Institute of Advanced Materials, Jiangsu National Synergetic Innovation Center for Advanced Materials, Nanjing Tech University, Nanjing 211816, China
4Department of Physics, Huaiyin Institute of Technology, Huaian 223003, China
5Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China
a)Authors to whom correspondence should be addressed:[email protected]and[email protected]
ABSTRACT
Two-dimensional (2D) van der Waals (vdW) ferromagnetic (FM) materials have recently received attention due to their potential applications in next-generation spintronic devices. However, the reduced dimensionality and weak interlayer vdW interaction seriously sup- press the magnetic Curie temperatureTc, raising the concern with enhancing the interlayer FM coupling. It is argued that proper ion interca- lation may enhance the interlayer coupling by establishing strong chemical bonding. In this work, this issue in a 2D vdW FM Fe3GeTe2
(FGT) bilayer as an example is addressed, and our first-principles calculations predict that beryllium (Be) can be a promising intercalant for such enhancement. It is revealed that the Be-ion migration in-between the vdW gap has only moderate energy barriers owing to its small ionic radius, suggesting the feasibility of reversible intercalation. Particularly, Be-ion intercalation can significantly enhance the interlayer FM coupling by reducing the interlayer distance. The strong bonding that pulls two FGT monolayers closer is ascribed to orbital hybridization between Be-ions and interfacial Te-FeI sites. Be-ion intercalation also contributes to electron doping via charge transfer, favoring the enhanced intralayer FM coupling. This work suggests an alternative scheme for reversibly controlled ferromagnetism enhancement in 2D vdW ferromagnets using ion intercalation.
Published under an exclusive license by AIP Publishing.https://doi.org/10.1063/5.0081270
Since the discovery of intrinsic ferromagnetism in two-dimensional (2D) van der Waals (vdW) ferromagnetic (FM) materials such as CrI3 and Fe3GeTe2 (FGT),1,2 2D vdW ferromagnets have been on the frontiers due to their potential for usage in next-generation spintronic devices.3–16The interlayer vdW interaction allows easy exfoliation and nano-fabrication but unfortunately leads to weak interlayer coupling.17 As a result, the magnetic Curie point (Tc) for most known 2D vdW ferromagnets is far below room temperature. Such a drawback hinders their practical applications on the one hand and raises the issue on how to enhance the interlayer coupling on the other hand.
Recently, ion intercalation has emerged as a powerful scheme to modulate spin exchanges in 2D vdW ferromagnets.18–23Owing to the layered structure, ion intercalation in-between neighboring
monolayers can provide extremely high-level carrier doping and modulate the electronic structure of the host, thus effectively tun- ing both the interlayer and intralayer exchanges. Particularly, ion intercalation in some 2D materials can be reversibly controlled by electrochemical methods, thus offering opportunities for electri- cally controlled spintronic applications. For example, a notable experiment by Denget al.shows that Li-ion intercalation induced by ionic gating for trilayer FGT can reversibly tuneTcfrom 100 K to 300 K.18 Our calculations also reveal that Li-ion intercalation can induce electron doping that leads to the exchange enhance- ment.23The enhancement can be ascribed to a simple geometric reason that Li-ion intercalation acts like a bridge to link the adja- cent two monolayers, offering additional exchange channels.
Nevertheless, such added interlayer exchange paths are yet too long for pursuing strong magnetism comparable with 3D magnets.
Taking a Li-ion intercalated FGT bilayer as an example, we see that the shortest interlayer Fe–Fe separation is5.7 A˚ ,23much larger than that (4 A˚ ) in typical 3D oxide magnets such as LaxSr1xMnO3.24–26 Considering the electron-hopping mediated exchanges, the interlayer distance is a critical parameter.27,28It would be highly appreciated if the intercalant ions not only reduce the interlayer separation so that the stronger interlayer coupling can be established but also preserve high migration mobility, enabling reversible electrochemical control of the intercalation.
In the following, one strategy is to access the intercalation of even smaller ions than Li-ions, while Li-ions may slightly expand the inter- layer separation.23,29In this regard, alkaline-earth metal beryllium (Be) can be a promising intercalant. On the one hand, it has much smaller ionic radius than the Li-ion (Be0.45 A˚ vs Li0.76 A˚ ),30beneficial for the migration mobility. On the other hand, it has relatively large electronegativity (1.57, Pauling scale),31 benefitting to the covalent interaction with the host for strong interlayer coupling. Immediate to our attention is the impact of Be-ion intercalation on the interlayer exchange for a 2D vdW ferromagnet such as a FGT bilayer here. In this work, we investigate the effects of Be-ion intercalation in the FGT bilayer using the first-principles calculations as implemented in the VASP32–36with the computational details given in thesupplementary material.
FGT is a vdW ferromagnet37–41with the well-confirmed bilayer configuration shown inFig. 1(a)if the Be-ion is ignored. Each FGT monolayer consists of five sublayers (in the sequence of 1–5 or 7–11) with a stacking sequence of Te-FeI-(FeIIGe)-FeI-Te (FeIand FeIIrepre- sent two inequivalent Wyckoff sites), and each atom position is marked by one of the out-of-plane or in-plane dashed lines (in the
sequence of A, B, C, A, …). Now, one Be-ion is assumed to be inserted into the vdW gap, and determination of its position is of the first pri- ority. For simplification, we consider a 33 supercell model of the FGT bilayer with one Be-ion, denoted as Be1/9-FGT2, and discuss the optimized Be-ion occupancy marked by one of the (A, B, C) lines. We calculate the intercalation energies of the Be1/9-FGT2bilayer model with different Be-ion sites (denoted as A-site, B-site, and C-site), defined as Eint¼E(Be1/9-FGT2) E(FGT2) E(Be), noting that E(Be1/9-FGT2), E(FGT2), and E(Be) are the energies for the Be1/9- FGT2bilayer, pristine FGT bilayer, and single Be atom, respectively.
The intercalation energies for the A-site and B-site (equivalent to the C-site) are3.495 and3.200 eV, respectively, indicating that Be-ion intercalation is energetically favored and the A-site occupancy is pre- ferred. To check whether the energy of the Be1/9-FGT2bilayer model could be further lowered, we preset various displacements of the Be- ion from the A-site and allow the supercell model to fully relax. All the displacements vanish after the structural relaxation, suggesting that the A-site [Fig. 1(a)] is the most favorable intercalation site.
Then we consider the A-site occupancy of more than one Be-ion, noting that interactions if any between the Be-ions affect their distri- bution. Two types of Be-ion distributions at the same intercalation level are studied. As shown in Fig. S1, the two 33 in-plane supercells of FGT bilayers with Be-ions at the three nearest-neighbor and three next-nearest-neighbor A-sites represent the gathered and dispersed distributions, respectively. The calculated energy for the dispersed dis- tribution is5 meV/Be lower than the gathered type, indicating the preference of the dispersed distribution, a reasonable output. As the energy difference is small, the effect of thermal fluctuations may be sig- nificant. Thus,ab initiomolecular dynamic (AIMD) simulation on the 33 supercell bilayer with dispersed Be-ion distribution is performed under a canonical ensemble with temperatures controlled atT¼300 K
FIG. 1.(a) Side and top views of the Be1/9-FGT2bilayer model. (b) AIMD evolu- tion of the total energy (E0) and tempera- ture (T) of the supercell with dispersed Be-ion distribution. The snapshot is the top view of the supercell after 10 ps. (c) Calculated interlayer distances (d) for the Bex-FGT2bilayers. The inset shows the average in-plane lattice constants per unit-cell (aUC) and monolayer thicknesses for the Bex-FGT2bilayers. (d) Calculated energy profiles of two designed Be-ion migration paths.
by the Nose–Hoover thermostat [Fig. 1(b)]. The thermally induced variations ofTand total energy during simulation are within a narrow range, and the lattice is well maintained without reconstruction after 10 ps, indicating the good thermal stability of the Be-ion distribution.
To stimulate Be-ion intercalation levels higher than 1/9, we design additional four Bex-FGT2bilayer models (x¼1, 2/3, 1/3, and 1/4) with dispersed Be-ion distributions. Their fully relaxed structures and lattice parameters are shown in Fig. S2 andFig. 1(c), respectively.
It is seen that these Be-ion intercalations cause no remarkable changes in the monolayer lattice structure including the distortion, in-plane lattice constant, and thickness. However, the interlayer distance (d), defined as the interfacial Te-Te distance [Fig. 1(a)], shows serious decreasing with increasingxand converges to 2.59 A˚ atx1, which is 11.4% and 18.7% smaller than the calculated values for the pristine FGT bilayer and the Li1-FGT2bilayer model,23respectively.
The reduced interlayer distance suggests that the bonding between the Be-ion and neighboring FGT monolayers is strong enough to pull the two monolayers closer. A potential side effect would be the possibly higher barrier for Be-ion migration in the interlayer gap. We study the energy profiles of the Be-ion migration paths con- necting two nearest-neighbor A-sites at a relatively highx¼2/3 as a representative case. As shown in Fig. 1(d), two possible paths are designed and calculated. The migration barrier against the direct shift- ing (path 1) of the Be-ion is higher than 1.0 eV, while the two-step concerted motion (path 2) that involves an intermediate position near the C-site has the significantly reduced barrier (0.57 eV), even lower than the result (0.73 eV) for the Li2/3-FGT2bilayer (Fig. S3), indicating the higher mobility of the Be-ion. Thus, reversible Be-ion intercalation may be experimentally feasible. Despite the smaller interlayer distance of the Be2/3-FGT2than the Li2/3-FGT2bilayer, the much smaller ionic radius allows the migrating Be-ion to pass through the interfacial Te- octahedrons more easily, i.e., a lower migration barrier.
Clearly, Be-ion intercalation can significantly enhance the inter- layer exchange. To quantitatively investigate this effect, we calculate the interlayer magnetic coupling, commonly defined asEM¼(EAFM
EFM)/u, whereEAFMandEFMare the energies for the Bex-FGT2
bilayer assuming the interlayer anti-ferromagnetic (AFM) and FM configurations, respectively, anduis the number of in-plane unit-cells in the supercell model. Certainly, the positive and negativeEMindicate the interlayer FM and AFM ground states, respectively. The calculated EM as a function of x is shown in Fig. 2. The pristine FGT bilayer (x¼0.0) favors the FM state withEM¼19.5 meV. Asxis low (x1/3),EMsignificantly increases withx, reaching the maximum at x1/3, indicating that Be-ion intercalation does promote the inter- layer FM coupling. The maximal value (52.5 meV) of EMhere is larger than that of the Li-ion intercalated FGT bilayer (31.6 meV),23 hinting the potential to access room temperature ferromagnetism for FGT by only low-level Be-ion intercalation.18Asxis high (x>1/3), EMreversely decreases withx, suggesting that excessive Be-ion interca- lation is detrimental to the interlayer FM coupling and even leads to the AFM state. Indeed, we re-checkEMby setting different HubbardU values in a reasonable range (see Fig. S4) and confirm that such qualita- tive dependence ofEMonxis credible. It should be mentioned that we focus on the ferromagnetism enhancement in this work. The FM-AFM transition would be discussed in the future considering its complexity.
It is expected that Be-ion intercalation would promote the inter- layer bonding, leading to the enhanced interlayer coupling. It is noted
that bond formation is always linked to electron transfer, which is an important issue for understanding the underlying mechanism of the interlayer coupling. We start by checking the distribution of doping electrons from the inserted Be-ion. To obtain a simple visual of the dis- tribution, we calculate the difference of the electron density between the FGT bilayers with and without Be-ion intercalation. The result for the Be1/3-FGT2bilayer is shown inFig. 3(a)as a representative case. It is seen that the doping electrons are concentrated in the gap region.
For the other four bilayers (Bex-FGT2,x¼1, 2/3, 1/4, and 1/9), the similar distributions are obtained (Fig. S5), indicating the negligible influence of the intercalation level.
In order to quantitatively determine the allocations of the Be-ion induced doping electrons, we perform the Bader charge analysis for the bilayer models. It is found that each Be-ion itself retains0.8e, leaving 1.2e onto the FGT bilayer, i.e., charge transfer of 1.2e between Be and FGT bilayers. This effect generates twofold conse- quence. On the one hand, the transfer charge amount (1.2e) is larger than that for the case of Li-ion intercalation where only0.8e is trans- ferred onto the FGT bilayer,23suggesting that one intercalated Be-ion is more effective than one intercalated Li-ion in providing additional hopping carriers for interlayer exchange. On the other hand, one inter- calated Be-ion retains0.8e, which is also much more than that for one intercalated Li-ion (0.2e), implying that the larger electronega- tivity of Be leads to the stronger covalent bonding. Due to these differ- ences, it is now understandable why Be-ion intercalation shortens the interlayer distance while the Li-ion intercalation enlarges the vdW sep- aration, noting that the bonding of the Li-ion exhibits more typical ionic nature.
To gain more insights into the covalent bonding, we investigate the electronic structures. The calculated density of states (DOS) and the electronic band structure for the Be1/3-FGT2bilayer as a represen- tative case are shown inFig. 3(b)and Fig. S6, respectively. The total DOS and band structure of the two spin channels are asymmetric, demonstrating the favored FM order. The orbital-resolved projected DOS of the Be-ion are also asymmetric, indicating the large influence from the two FGT monolayers. Most of the Be-2s occupied states locate at the bottom of the energy window and exhibit a peak in each spin channel, which suggests the localization feature, while the Be-2p orbitals show relatively extended energy dispersions and have49%
FIG. 2.CalculatedEMfor the Bex-FGT2bilayers.
more occupied states than the Be-2sorbital. Thus, the Be-2porbitals play the dominant role in forming orbital hybridization with the FGT bilayer for covalent bonding.
To identify the sublayers of the FGT bilayer involved in the bonding with the Be-ion, we check the allocations of the transfer elec- trons. The average changes of electron numbers (Dn) for different parts of one Fe3GeTe2formula cell in various Bex-FGT2bilayers are calculated [Fig. 3(c)]. It is seen thatDnalmost increases linearly with x, a reasonable result consistent with that the doping electrons show the same distributions as x increases [Fig. 3(a) and Fig. S5].
Particularly, the interfacial Te and FeIsublayers [sublayers 4, 5, 7, and 8 inFig. 1(a)] gain almost all the electrons, indicating that the doping effect penetrates the interfacial Te sublayers and affects the FeIsites.
Noting that the transfer electrons are completely obtained by the inter- facial Te sublayers in the Li-ion intercalated FGT bilayer,23the charge modulation by the Be-ion is relatively deep. To inspect the modulation depth, we study the electron redistributions between the Be-ion and FGT bilayer by checking the contour plot of the differential electron density. The result for the Be1/3-FGT2bilayer is shown inFig. 3(d)as a representative case. The yellow covalence regions indicate the bonding between the Be-ion and interfacial Te-FeIsites. In comparison, the interaction between the Li-ion and FeIsite is negligible (Fig. S7). Thus, the larger charge modulation depth by the Be-ion is another evidence linked to its stronger bonding. For now, the bonding nature of the Be- ion has been systematically addressed, presenting the physical basis for unveiling the enhanced interlayer coupling.
As a complementary, we discuss the intralayer FM coupling. It is revealed that the intralayer FM coupling of the metallic FGT can be characterized by the exchange splitting of the Fe-3dbands40according to the Stoner theory. We believe that the electron doping by the Be-ion
triggers spin redistribution of the Fe-3d orbitals, leading to the enhanced exchange splitting.23This is because the interfacial Te sub- layers gain most of the transfer electrons [Fig. 3(c)], so that the Fe sub- layers have to promote electrons from the minority spin channel (spin down) to the majority one (spin up) in order to catch up with the raised Fermi level. Such spin redistribution pushes the energy bands of the spin up channel to move downward, relative to the spin down channel, in order to keep the highest occupied states of the two chan- nels on the same level, thus enhancing the exchange splitting.
To confirm this physical scenario, we calculate the difference between the spin-projected electron density of the FM Bex-FGT2 bilayers with and without the Be-ions for the four cases (x¼2/3, 1/3, 1/4, and 1/9). The result for the Be1/3-FGT2bilayer as a representative case is shown inFig. 4(a), and the others are shown in Fig. S8. The four bilayers exhibit the same distribution patterns that Be-ion interca- lations induce electron gain and loss in the spin up and spin down channels of the Fe sites, respectively, confirming the spin redistribu- tion. Consequently, the average occupation numbers of the spin up and spin down channels of the Fe-3dorbitals increases and decreases withx, respectively [Fig. 4(b)], leading to the enhanced magnetization [Fig. 4(c)]. Then we check the exchange splitting of the Fe-3dbands by calculating the energy difference between the centers of the PDOS of the two spin channels. The energy difference increases withx[Fig.
4(d)], confirming the enhanced exchange splitting. Noting that the spin redistribution occurs inside each FGT monolayer, the enhanced exchange splitting corresponds to the stronger intralayer FM coupling.
Therefore, our results reveal that Be-ion intercalation can enhance both the interlayer and intralayer FM couplings of the FGT bilayer. Meanwhile, the larger charge transfer effect and stronger cova- lent bonding by Be-ion intercalation suggest that it is a more powerful FIG. 3.(a) Integrals of the electron density difference in the ab plane (Dq) atx¼1/3, Dq¼q(Be1/3-FGT2)q(FGT2). (b) Total DOS of the Be1/3-FGT2bilayer and PDOS of the Be-2sand -2pstates. The Fermi level is set as 0 eV. (c) Average changes of electron numbers (Dn) in different parts of one Fe3GeTe2formula cell (defined as one in-plane unit cell of one monolayer) according tox. (d) Top and side views of the contour plot of the differential electron density (qdiff) for the Be1/3-FGT2bilayer, qdiff¼q(Be1/3-FGT2)q(FGT2)q(Be).
The yellow and blue isosurface regions indi- cate the electron gain and loss, respectively.
The isosurface value is 0.003e/Bohr3.
scheme than Li-ion intercalation. In addition, noting that the high- level Be-ion intercalation seriously reduces the interlayer FM coupling, an optimal intercalation level is expected in terms of maximal Tc. However, this work lacks quantitative estimation for the enhancedTc, because the traditional method to extract the exchange parameters from the energy differences between different magnetic configurations is not suitable for this system due to the seriously reduced magnetic moments of the Fe sites by the forced reorientation of their spins (see Fig. S9 and Table S1). We leave this problem to future investigation.
In summary, we theoretically studied the impact of Be-ion inter- calation on the FGT bilayer. The moderate migration barrier suggests that reversible Be-ion intercalation may be experimentally feasible. Be- ion intercalation remarkably reduces the interlayer distance by estab- lishing the strong covalent bonding, leading to the significantly enhanced interlayer FM coupling. Moreover, the Be-ion induced elec- tron doping enlarges the exchange splitting, favoring the stronger intralayer FM coupling. This work suggests that Be-ion intercalation can be a powerful scheme for reversibly controlled 2D ferromagnetism enhancement.
See thesupplementary materialfor computational details, struc- tures of the dispersed and gathered Be-ion distribution models, struc- tures of the Bex-FGT2(x¼1, 2/3, 1/3, and 1/4) bilayer models, Li-ion migration paths of the Li2/3-FGT2bilayer model, the dependence of EMonxat different HubbardU, electron density differences for the cases ofx¼1, 2/3, 1/4, and 1/9, the band structure for the Be1/3-FGT2
bilayer model, the differential electron density for the Li1/3-FGT2
bilayer model, spin-projected electron density differences for the cases ofx¼2/3, 1/4, and 1/9, and magnetic moments for two typical mag- netic configurations.
This work was financially supported by grants from the National Natural Science Foundation of China (Nos. 11947092, 52062018, 51762024, and 52162003), the Natural Science Foundation of Jiangxi Province (Nos. 20212BAB201019, 20192BAB212002, and 20192BAB206008), and the Foundation of Jingdezhen Science and Technology Bureau (No. 2021ZDGG002).
Part of the numerical calculations was carried out in the High Performance Computing Center (HPCC) of Nanjing University.
AUTHOR DECLARATIONS Conflict of Interest
The authors have no conflicts to disclose.
DATA AVAILABILITY
The data that support the findings of this study are available within the article and itssupplementary material.
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