Unconventional ferrimagnetism and enhanced magnetic ordering temperature in monolayer CrCl3 by introducing O impurities and Cl vacancies

Among chromium trihalides, a specific group of layered van der Waals magnetic materials, chromium trichloride (CrCl3) is the only system relatively stable under ambient conditions. This is also observed in reduced dimensionality where the emergence of extrinsic long-range ordered oxidized and Cl-vacancy-defective CrCl3 phases is experimentally reported. In this work, the magnetic properties of such two-dimensional (2D) systems are studied using density functional theory (DFT) calculations, including the electron-electron (U) repulsion interactions, and Monte Carlo (MC) simulations. Once the Cl vacancies are introduced, the results indicate that the monolayer CrCl3 has a magnetic moment that is enhanced linearly (up to 3.14 µ B /Cr) in the (1%–10%) vacancy concentration range. This determines a strengthening of the ferromagnetic state and a two-fold increase of the Curie temperature (up to 146 K) as valuated from MC simulations. More interestingly, once oxygen extrinsic impurities are considered, the monolayer CrCl3 structure is hybridized forming a stable ordered phase (O–CrCl3) with oxygen atoms allocated on the Cr atomic layer in the center of the honeycomb ring formed by Cr atoms. The magnetic moments of the O–CrCl3 system are localized on both Cr and O atoms, with oxygen antiferromagnetically coupled to chromium, resulting in a 2D ferrimagnetic hexagonal lattice system with an average magnetic moment of 2.14 µ B /Cr and a high magnetic ordering temperature (110 K) predicted with DFT in the mean field approach.


Introduction
Since the first experimental reports of intrinsic magnetism down to the monolayer limit in layered van der Waals (vdW) crystals CrI 3 [1] and Cr 2 Ge 2 Te 6 [2], growing research attention has been driven to characterize and manipulate the magnetic properties of the emerging class of two-dimensional (2D) magnets.In particular, the entire group of chromium trihalides (CrX 3 , X = I, Br, Cl) was found to have intrinsic 2D magnetism with the magnetic ordering temperature decreasing when going from I, to Br, to Cl [3,4].For this reason, the very first research efforts have been focused primarily on few-layers of CrI 3 [1] and CrBr 3 [5].However, these crystals result particularly sensitive to ambient conditions, undergoing rapid structural and property degradation through a reaction catalyzed by light [6,7].On the contrary, few-layer CrCl 3 , which has an higher structural binding energy with respect to CrI 3 and CrBr 3 [8], was proved to be more stable under ambient conditions remaining relatively unaltered at the microscopic level for several hours even once exfoliated at low dimensionality [9].Obviously, contamination is inevitable in ambient conditions and causes effects not present in the pristine CrCl 3 .Indeed, as reported in a previous study [10], CrCl 3 few-layers result prone to oxidation manifesting an extrinsic O-CrCl 3 reconstructed structure on the surface flakes, protected by Cr 2 O 3 on the edges.This phase is particularly stable as the oxygen atoms intercalate in the hybridized CrCl 3 monolayer altering the electronic structure and inducing doping [10].
Moreover, it must be considered that the whole class of 2D vdW materials manifests vacancy defects [11][12][13], especially once exfoliated.In the case of mechanically exfoliated CrCl 3 , the flakes have intrinsically Cl vacancies with a concentration of about 2% that can be increased up to a 5% via thermal annealing [10], similarly to what is found experimentally in transition metal dichalcogenides [11,14].
These peculiar occurrences are relevant in determining the magnetic properties of this class of 2D materials.Indeed, different studies have highlighted the pivotal role of halogen vacancies in strengthening the ferromagnetic (FM) interaction [12,15] and enhancing the magnetic ordering temperature [16], which is worth to be considered for CrCl 3 , since manifests a FM transition at relatively low temperature (13 K) in the monolayer [17].Besides, the Curie temperatures (T C ) of Cr trihalides are generally predicted to be raised upon doping [18][19][20] and including oxygen impurities [21].
In this work, the effect of Cl vacancies and O impurities on the magnetic properties of monolayer CrCl 3 are studied, by means of first-principle calculations based on density functional theory (DFT).It is shown that the Cl vacancies enhance the average magnetization linearly in the (1%-10%) concentration range, nearly doubling the T C of the FM transition.Oxygen impurities, resulting in an ordered oxidized monolayer O-CrCl 3 structure, induce an unconventional ferrimagnetic (FIM) phase transition with oxygen antiferromagnetically coupled to chromium and relatively high critical temperature.

Computational details
DFT calculations were carried out using the Vienna ab initio simulation package code [22], based on the projector augmented wave method [23].The Perdew-Burke-Ernzerhof exchange-correlation functional was considered within the generalized gradient approximation (GGA), and the GGA + U eff Dudarev's method [24] is applied to describe the correlated Cr 3d electrons, using a U eff set to 5 eV.This energy was chosen considering the previous results in reference [25], where different U eff were tested for the monolayer CrCl 3 .The cutoff of the kinetic energy is 500 eV.The k-mesh in the Brillouin zone is 5 × 5 × 1 via Monkhorst-Pack method [26].The energy convergence tolerance is 1.0 × 10 −5 eV atom −1 , and the force certification is 0.01 eV Å −1 .A vacuum space of 15 Å is employed to avoid the influence of interlayer interaction and the vdW interaction correlation is considered by using the semi-empirical dispersion-corrected (DFT-D2) force-field approach.The supercell approach was used to simulate different concentrations of Cl vacancies using 3 × 3, 2 × 2, and 2 × 1 supercells, accounting for 1.85%, 4.16%, and 8.33% concentrations, respectively.Magnetic ordering temperatures were calculated by means of MC simulations using the method described in reference [27].

Results and discussion
The CrCl 3 crystallizes in the monocline AlCl 3 structure (space group C/2m) room temperature and rhombohedral BiI 3 structure (space group: R-3) below 240 K [3,25].The crystal is formed by stacked layers of CrCl 3 held together by weak vdW interaction that allows exfoliation down to the monolayer limit [9,25].In the monolayer configuration, the pristine CrCl 3 belong to the P-31m space group [25], and, in this paper, two modified configurations of monolayer CrCl 3 structure (Cl-defective CrCl 3 and ordered oxidized O-CrCl 3 ), which emerge in low-dimensional CrCl 3 [10], are investigated.Firstly, the crystal structures are discussed and then the magnetic properties of such monolayer systems.
The optimized structural parameters of the different phases, calculated by total energy minimization in the FM configuration, which is the ground state for the monolayer CrCl 3 [25,28], are reported in detail in table S1 of the supporting information (SI)(available online at stacks.iop.org/JPMater/5/014004/mmedia), while the main relevant parameters are also reported in table 1.The crystal structure of the pristine CrCl 3 monolayer is shown in figure 1(a), having an in-plane lattice parameter (5.89 Å) close to the value reported for the bulk phase [3].The distance between the two Cl planes results in 2.68 Å and the Cr-Cl bond length is 2.35 Å, with a symmetric Cl-Cr-Cl bond angle of 90.0 • .Different Cl vacancy concentrations are simulated with Cl-defective CrCl 3 supercells (panels (b)-(d) of figure 1).Three different model structures are considered containing one Cl vacancy: 3 × 3 supercell (CrCl 2.94 ), 2 × 2 supercell (CrCl 2.88 ), and 2 × 1 supercell (CrCl 2.75 ) corresponding to 1.85%, 4.16%, and 8.33% of Cl vacancy concentrations, respectively.Considering figure 1, Cr 2 atoms are Cr atoms with the nearest neighbor Cl vacancy, while Cr 1 stands for a Cr atom, which results as unperturbed considering the magnetic properties with respect to pristine case (see table S2 in the SI).Correspondingly, introducing Cl vacancies, two Cl sublattices are formed (Cl 1 and Cl 2 ).For all the concentrations, the in-plane lattice parameters undergo a 1.0% expansion and the Cl-Cl distance is shrunk by 5%.The vacancies also induce a local distortion of the CrCl 6 octahedron, with a  shrinking of the Cr 2 -Cl bond length, and the Cl-Cr-Cl bond angles (labeled α and β in table 1) are slightly modified, breaking the symmetry.Even in the case of the ordered oxidized O-CrCl 3 monolayer, the structure is modified with respect to pristine one (figure 2).Indeed, oxygen atoms intercalats into the CrCl 3 layered structure, and allocates on the Cr atomic layer exactly in the center of the honeycomb lattice formed by Cr atoms, similar to the model of Li adsorption in [29].This process is energetically favored by the peculiar large hole in the surface Cl layer, which acts as a pore.The O adsorption increases the in-plane lattice parameter (6.13 Å).In the O-CrCl 3 phase, both the Cl-Cl distance and the Cr-Cl bond lengths are slightly relaxed, resulting in 2.75 and 2. The impact of Cl vacancies on the magnetic properties of monolayer CrCl 3 is investigated via DFT calculation in both GGA and GGA + U methods, as both methods provide qualitatively analogous results in terms of magnetic properties.However, the insertion of the Hubbard's term (U) is recommended for the description of strongly correlated systems like CrCl 3 , and in a previous study by Gao et al [25], the effects of different U values from 3.0 to 6.0 eV were tested in terms of magnetic and electronic properties, proving that the results are consistent as U varies in this energy range.For this reason, in this article, a value of U eff = 5.0 eV on the Cr site is selected, which is typical for Cr 3d electrons and has proved to grasp effectively the electronic properties of both Cl-defective and oxidized CrCl 3 monolayers, as reported in previous work [10].
The magnetic moments, calculated with both the GGA and GGA + U methods are reported in table 1.The magnetization is mainly localized on the Cr site with little contribution stemming from Cl atoms (Cl magnetic moment is less than 0.10 µ B ).The Cr magnetic moment (3.15 µ B ) is close to the value of metallic Cr [3,4] and the average total magnetic moment results large (2.94 µ B /Cr) for the pristine phase, which is close to previous theoretical [25,30] and experimental [17] results.The magnetism is almost linearly enhanced with the introduction of Cl vacancies.In the case of Cl-defective CrCl 3 , the shrinking of the Cr 2 -Cl bond length induces a strengthening of the magnetic interaction with an enhancement of more than 10% of the Cr magnetic moment, reaching 3.53 µ B in presence of nearest neighbor Cl vacancy (Cl 2 ).This results in an enhanced total magnetic moment (up to 3.14 µ B /Cr) for CrCl 2.75 .
Focusing on the magnetic order, it should be stressed out that the CrCl 3 monolayer has a proven long-range FM order due to its magnetic anisotropy [30][31][32][33][34].In particular, there are indications that magnetic shape anisotropy rather than magneto-crystalline effects, which are weak in CrCl 3 , is the driving force to enable magnetic anisotropy of CrCl 3 monolayer [31,33].Indeed, CrCl 3 has little spin-orbit coupling [31] and the anisotropic interaction for Cr-Cl-Cr is expected to be weak at variance to the heavier Cr-I-Cr, which is instead relevant for the magnetic anisotropy of CrI 3 [35].However, both FM and AFM configurations are considered on the same monolayer structures and the energy difference (△E = E FM − E AFM ) of pristine and Cl-defective phases are reported in table 1.The FM ground state is significantly lowered by the inclusion of Cl vacancies.A semi-quantitative estimation of T C can be performed through MC simulations on both the pristine and Cl-defective CrCl 3 systems.For the T C calculations, the Heisenberg model is considered for CrCl 3 , which was demonstrated to effectively describe its magnetic proprieties [30,31,36] at variance with Ising-like CrI 3 and CrBr 3 [1,[37][38][39].The T C of each Cl-defective CrCl 3 systems are reported in table 1 calculated with MC simulations within both GGA and GGA + U methods for comparison.Moreover, figure 3 shows the temperature dependence of the average magnetization and heat capacity for the pristine and Cl-defective CrCl 3 monolayers, which were calculated with MC simulations in the GGA + U approximation.
In any case, the magnetization grows sharply below the critical temperature and the heat capacity shows a broad peak at the transition.The GGA + U (GGA) calculations predict T C = 61 K (46 K) for monolayer CrCl 3 in accordance with previously reported results on similar MC calculations within the same approximations [30].Including Cl vacancies, the T C grows up to 146 K (105 K), and the effect of a significant increase of T C is already found in the CrCl 2.94 configuration, which simulates a realistic case.Indeed, the 1.85% Cl vacancy concentration is the most representative of real conditions since it is the closest one to what estimated intrinsically in exfoliated CrCl 3 at room temperature and up to 200 • C, as demonstrated in a previous study by thermal stability check via core levels analysis [10].It is worth stressing that critical temperatures calculated with MC simulations can overestimate or underestimate the experimental data.This depends on the system, and on the exchange-correlation energy functionals used in DFT calculations [30,[40][41][42][43][44][45][46].However, the qualitative temperature trends with the introduction of vacancies point to a relevant increase in the T C (nearly doubling), highlighting the fundamental role that Cl vacancies have on the magnetic interactions of CrCl 3 even at low concentrations.
To better understand the role of vacancies on magnetic behavior, the spin-resolved projected density of states (PDOS) of pristine and Cl-defective systems are reported in figure 4. As clearly visible, Cl vacancies induce in-gap spin up-polarized states, mainly contributed by Cr 3d, which increase the electrons near the Fermi level (set to 0).Moreover, it must be considered that, already in the pristine case, the spin splitting  degree of Cr 3d and Cl 3p states in the valence band are asymmetric, promoting spin up states.This splitting is further enhanced by the introduction of Cl vacancies.
Hereafter, the magnetic properties of the O-CrCl 3 system are discussed.Interestingly, oxygen atoms result magnetic with a large magnetic moment (1.37 µ B ), while Cr magnetic moment (3.05 µ B ) remains comparable to the one calculated for the pristine phase (the Cl magnetic moment is negligible even in this case).The unit cell for the oxidized phase is Cr 2 Cl 6 O and the one O atom is AFM coupled to two FM Cr atoms, giving rise to a FIM ordering (see figure 5) with a net magnetization of 4.28 µ B per unit cell, resulting in an average magnetic moment of 2.14 µ B /Cr.The same conclusions are also valid for GGA calculations, which predict magnetic moments of 1.37 µ B and 2.86 µ B for O and Cr atoms, respectively, and a total magnetization of 4.38 µ B per unit cell.This configuration is particularly favored by the drastic energetic increase in △E reaching 1163.4 (1075.6)meV for GGA + U (GGA) methods.
The large magnetic moment of oxygen atoms is peculiar and deserves further investigation about its origin.Specifically, as found in spin-resolved PDOS of the monolayer O-CrCl 3 (figure 4(e)), the electrons close to the Fermi level are contributed by an emerging in-gap spin down-polarized O 2p state, and the occupied valence band states are strongly narrowed due to massive hybridization.Considering that the pristine system has holes residing on Cl 3p orbitals (figure 4(a)), the Bader charges of the oxidized monolayer were checked (see table S3 in SI).The extremely small value of Bader charge for O (6.23) indicates that sizable holes are present on the O 2p states.Indeed, due to the large electronegativity of Cl, the oxygen atoms tend to form covalent bonds with the neighboring Cr atoms, rather than ionic as in transition metal oxides.Consequently, there is enough space for the unpaired spins.Therefore, considering the narrowed valence bands width and the relative abundance of holes, the O-CrCl 3 system has magnetism stemming from p electrons, similar to the case of SrO 1−x N x [47], in which magnetism is achieved without conventional magnetic atoms.
The prediction of the magnetic ordering temperature for a FIM system via MC simulation is not straightforward, since the system does not obey the Curie-Weiss law.However, for qualitative comparison with the other phases, it can be proposed a simplified approach based on mean field approximation [25,48].The mean field GGA + U estimates of T C for the pristine CrCl 3 monolayer (60 K) is comparable with MC simulations of this paper (table 1), while the mean field critical temperature for the O-CrCl 3 monolayer is relatively high (110 K).
It is interesting to consider these predictions of the magnetic properties of Cl-defective and oxidized phases of CrCl 3 and correlate them with recent magnetic investigations performed on low-dimensional CrCl 3 crystals [49].In the study of Serri [49], via independent SQUID, x-ray magnetic circular dichroism, and magnetic force measurements on mechanically exfoliated CrCl 3 flakes, it was reported a significant increase of the FM transition field at low temperatures (compared to the one of CrCl 3 in the bulk crystal phase).These observations also agree with magnetotransport [50][51][52][53] and magneto-optical studies [51], which consistently highlighted that ultra-thin flakes of Cr trihalides exhibit different magnetic interactions compared to the pristine bulk crystals.Considering the predictions of the current, it is advisable not to rule out that other factors related to the exfoliation process, like a not negligible production of Cl vacancies and/or O impurities of the topmost layer, are determining the observed anomalies of the magnetic behavior.
According to the literature [9,54], single crystals of CrCl 3 can be synthesized from commercially available CrCl 3 powder and monolayers can be easily isolated by mechanical exfoliation [9].Based on these experimental results, we suggest that Cl-defective CrCl 3 monolayers with such vacancy concentrations can be prepared via thermal annealing processes, as evidenced in a previous study [10].On the other hand, the ordered oxidized O-CrCl 3 phase, which spontaneously emerges in ambient conditions [10], can be investigated starting from an isolated CrCl 3 monolayer and exposing it to a controlled flow of oxygen under vacuum conditions.

Conclusions
In summary, first-principles DFT calculations were performed on pristine, Cl-defective, and ordered oxidized monolayer CrCl 3 systems.The results show that the inclusion of Cl vacancies strengthens the FM state of monolayer CrCl 3 , which has magnetization mainly localized on Cr atoms and linearly enhanced (up to 3.14 µ B /Cr) in the (1%-10%) vacancy concentration range, determining a two-fold increase of the FM Curie temperature (up to 146 K).Furthermore, the calculations show that the ordered oxidized monolayer O-CrCl 3 structure is an unconventional 2D FIM system with two different kinds of magnetic atoms (Cr and O) per unit cell, with oxygen antiferromagnetically coupled to chromium, with an average magnetic moment of 2.14 µ B /Cr.The calculated mean field magnetic ordering temperature is, even in this case, higher than the pristine case (110 K).The realization of a FIM lattice represents an additional ingredient that makes the 2D magnetic transition metal trihalides systems even more interesting.Indeed, the inclusion of magnetic oxygen atom in the Cr honeycomb lattice opens to the realization of a 2D FIM hexagonal lattice further extending both the realization of new magnetic phases and their excitations.Besides, the O-CrCl 3 configuration can be considered an alternative platform to explore different magnetic excitations in the two dimensions, like magnons dispersion and their topological properties [55,56].Finally, the observed enhancement of the critical temperature by Cl vacancies introduction can represent a low-cost method to enhance the magnetic ordering temperature of this class of 2D materials.
37 Å.Due to symmetry reduction, there are two very different Cl-Cr-Cl bond angles of 98.81 • and 83.06 • .The O-Cl distance is 2.69 Å.

Figure 2 .
Figure 2. Top view and side view of monolayer O-CrCl3 structure.Cr, Cl, and O atoms are represented in violet, green, and red spheres, respectively.