Changing the spin disorder of two-dimensional magnetic Cr2TiC2Tx to long-range order through noble metal adhesion

Summary To enhance the use of Cr2TiC2Tx MXene in spin electronics, it is essential to transform its spin-disordered state into a long-range ordered spin state. In this study, first-principles calculations show that Rh layers adhered to the Cr2TiC2Tx surfaces can transform its spin disordered state into a long-range spin order by donating electrons to the O terminations, resulting in Cr2TiC2Tx becoming a single-layer A-type antiferromagnet. As the proportion of F termination increases from 0 to 100%, the exchange coupling constant J1 of the compound escalates from 0.5 to 15.9 meV. Concurrently, the Néel temperature experiences a significant rise from 8 K to 110 K. The analysis of the density of states reveals that the obtained Cr2TiC2Tx exhibits excellent conductivity with O termination and semiconductor characteristics with F termination. These unique features make Cr2TiC2Tx a promising magnetic material for application in spin electronics.


INTRODUCTION
2][3][4][5] Besides, the strong AFM coupling between magnetic moments in AFM materials can result in a resonance frequency in the terahertz (THz) range. 6,7heir high-speed intrinsic spin-wave modes at THz frequencies endow them with the ability to carry information with low loss and high-speed propagation.][10][11] Investigating the magnetic properties of AFM materials and their application to spin electronic devices has attracted increasing attention. 1,12,13In recent years, the technology for manipulating magnetic states of AFM has been improved thanks to the efforts of researchers around the world.For example, it has been found that the magnetic order can be tuned through external factors, such as electricity, light. 4,14The spin direction of AFM materials can be manipulated by heating, applying an external magnetic field, or applying an electric current or an electric field to the system.It can also be tuned through the electrode change induced by the piezoelectric effect. 15any studies have indicated that two-dimensional (2D) magnetic materials can be used to prepare ultrathin spin-electronic devices and realize ultra-compact spintronics. 16,17In contrast to traditional bulk materials, 2D materials are mechanically flexible, and their magnetic properties can be easily tuned through surface engineering.Many different 2D AFM materials have been synthetized, which can be broadly classified into the three following categories: zigzag, Ne ´el, and A-type AFM materials. 16Most 2D A-type AFM materials investigated so far, such as CrI 3 and VSe 2 , exhibit intralayer ferromagnetic (FM) and interlayer AFM couplings in their bilayer form. 18,191][22] This single-layer A-type AFM material can have high spin-wave frequencies due to its strong exchange coupling between two magnetic layers. 7,23][26] Recently, Gogotsi et al. synthesized the magnetic Cr-based MXene (Cr 2 TiC 2 T x ), in which the terminations (T x ) are a mixture of F and O in varying ratios. 27However, the results from field-cooled (FC) and zero field-cooled (ZFC) magnetization experiments suggest a spin-glass state with a magnetic phase transition temperature of 30 K. In this spin-glass state, ferromagnetic and AFM domains are randomly distributed, and the directions of the magnetic moments are randomly frozen, exhibiting long-range disorder.The dominant AFM interactions were confirmed by the negative Weiss temperature.Such a spin disorder can be attributed to the nonuniform mixture of the O and F terminations.Cr 2 TiC 2 O 2

CALCULATION MODELS
Cr 2 TiC 2 T x MXene is mainly terminated by F and O atoms. 29Thus, Cr 2 TiC 2 O n/4 F 2Àn/4 (n = 0, 1, 2, 3, 4, 5, 6, 7, and 8) models similar to previously reported models in the literature were used in the present study, 28 and the same adsorbing configuration for the F and O terminations was considered as shown in Figure 1.
Cr 2 TiC 2 T x MXene was sandwiched between noble metal layers to form an M/Cr 2 TiC 2 O n/4 F 2Àn/4 /M (M = Ph, Pd, and Ag) heterojunction.The three noble metal layers were made to adhere to both Cr 2 TiC 2 O n/4 F 2Àn/4 surfaces.Our previous works showed that the strain of MXene may cause an FM-AFM phase transition. 22,30Therefore, to avoid the influence of external strain on the spin arrangement, the optimized lattice of pure Cr 2 TiC 2 O n/4 F 2Àn/4 was used, and it was fixed in the heterojunctions.For the adsorption of the noble metal layers, three adsorption sites with high symmetry were considered, as shown in Figure 2A, where a 2 3 2 supercell Cr 2 TiC 2 O 2 is taken as an example.These three sites are the top O atom site (T O ), hollow A-site (H A ) with a C atom below it, and hollow B-site (H B ) with a Cr atom below it.The M/Cr 2 TiC 2 O n/4 F 2Àn/4 /M heterojunctions were modeled with three atomic layers both above and below the H A , T O , and H B sites, the side views of which are illustrated in Figures 2C-2E.The FM and three AFM arrangements (AFM1, AFM2, and AFM3) shown in Figures 2F-2I were considered.

RESULTS AND DISCUSSION
Magnetic arrangements of the M/Cr 2 TiC 2 O n/4 F 2Àn/4 /M heterojunctions Firstly, we need to determine the adsorption configurations of the M/Cr 2 TiC 2 O n/4 F 2Àn/4 /M heterojunctions.The calculation results show that the noble metals are preferentially adsorbed on the T O site.For models in which the noble metals are adsorbed on the H A and H B sites, the noble metals are then transferred to the T O site upon structural optimization.This result is similar to our previous finding, according to which Au atomic layers are also preferentially adsorbed on the O top sites of the Cr 2 NO 2 surface. 17 In order to investigate the spin order of the M/Cr 2 TiC 2 O n/4 F 2Àn/4 /M heterojunctions, the spin direction of the Cr atoms was determined by calculating the magnetic anisotropy energy (MAE) according to the following equation: where E 100 and E 001 are the total energies of the M/Cr 2 TiC 2 O n/4 F 2Àn/4 /M heterojunctions with the spin of the Cr atoms along the [001] and [100] directions, respectively.N Cr is the number of Cr atoms.A negative value of the MAE indicates that the magnetic easy axis of the Cr atoms is along the c-axis, while a positive value indicates that the magnetic easy axis is in the xy-plane.
To understand the effect of the metal layer adhesion on the spin direction of Cr 2 TiC 2 T x MXene, the MAE values of the M/Cr 2 TiC 2 O 2 /M and M/Cr 2 TiC 2 F 2 /M systems were calculated and analyzed.Pure Cr 2 TiC 2 F 2 favors the AFM1 arrangement with the spins lying in the xy-plane, as shown in Figure 4.Such a spin arrangement remains unchanged even when the noble metal layers adhere to the Cr 2 TiC 2 F 2 surfaces, while the MAE value decreases slightly from 61 meV (for pure Cr 2 TiC 2 F 2 ) to 29 (for M = Ag), 38 (for M = Pd), and 34 meV (for M = Rh).Different from the case of Cr 2 TiC 2 F 2 , the adhesion of noble metal layers causes a marked variation in the spin arrangement of Cr 2 TiC 2 O 2 .The ground state of Cr 2 TiC 2 O 2 is FM with the magnetic easy axis perpendicular to the noble metal layers.However, the adhesion of the Rh and Pd layers causes the ground state to exhibit the AFM1 arrangement with the magnetic easy axis in the xy-plane.Thus, M/Cr 2 TiC 2 O 2 /M ends up having the same spin arrangement as M/Cr 2 TiC 2 F 2 /M, finally leading to the long-range spin order for Cr 2 TiC 2 T x MXene.The adhesion of the Ag layers does not induce any change in the direction of the magnetic easy axis.However, it makes Cr 2 TiC 2 O 2 favor the AFM2 state, which is different from the preferred state of Cr 2 TiC 2 F 2 .

Magnetic properties of the Rh/Cr 2 TiC 2 T x /Rh heterojunction
As mentioned before, the Rh layers are the most effective in inducing a long-range spin order for the AFM1 arrangement.The magnetic properties of the Rh/Cr 2 TiC 2 O n/4 F 2Àn/4 /Rh heterojunction were analyzed in detail.The average magnetic moment of the Cr atoms (M Cr ) decreases as n increases, as shown in Figure 5A.Such a trend is also similar to that of pure Cr 2 TiC 2 O n/4 F 2Àn/4 .On the other hand, the adhesion of the Rh layers leads to an increase in M Cr .For the Cr 2 TiC 2 O 1.25 F 0.75 (n = 5) system, the O coverage is similar to that reported experimentally for the Cr 2 TiC 2 O 1.3 F 0.8 structure, 27,29 and the theoretical value of M Cr is 2.64 m B . 28As the Rh layers adhere to its surfaces, the M Cr value becomes 2.88 m B , which corresponds to an increase of about 9.1%.Monte Carlo (MC) simulations were used to estimate the Ne ´el temperature (T N ) of the Rh/Cr 2 TiC 2 O n/4 F 2Àn/4 /Rh heterojunctions; these simulations were implemented using the MCSOLVER package. 31The corresponding exchange coupling parameters (J 1 , J 2 , and J 3 ) were calculated through the Heisenberg model.Here, J 1 , J 2 , and J 3 represent the nearest, next-nearest, and next-next-nearest neighbor exchange coupling parameters, as shown in Figure 2B.The number of Cr ions with the same/opposite spin direction with respect to the nearest, nextnearest, and next-next-nearest neighbor Cr ions do not change in the presence of the Rh layers.Thus, the Heisenberg-Hamiltonian equations for the J 1 , J 2 , and J 3 parameters of the Rh/Cr 2 TiC 2 O n/4 F 2Àn/4 /Rh heterojunctions are the same as those of the pure Cr 2 TiC 2 O n/4 F 2Àn/4 systems, as it has been shown in a previous study. 28s shown in Figure 5C, the T N of the Rh/Cr 2 TiC 2 F 2 /Rh heterojunction (i.e., for n = 0) is up to 110 K.However, T N decreases as n increases: It is about 20-50 K for n = 4 and decreases to 8 K for n = 0. Nonetheless, recent studies have pointed out that there exist several methods for increasing the T N or Curie temperature (T C ) of 2D magnetic materials, such as electron doping. 32Thus, manipulating the magnetic properties of these single-layer A-type AFM materials may bring novel results and spintronic applications.
Similar to T N , the exchange coupling parameter J 1 also decreases as n increases, as shown in Figure 5D.It reaches the minimum value for the Rh/Cr 2 TiC 2 O 2 /Rh heterojunction with n = 8.Such a decrease of J 1 is the main factor behind the decrease of T N , as J 1 represents the exchange coupling between each pair of nearest-neighbor Cr ions.However, J 1 remains positive as n increases from 0 to 8.This leads to each pair of nearest-neighbor Cr ions of the Rh/Cr 2 TiC 2 O n/4 F 2Àn/4 /Rh heterojunctions having the same spin direction, and thus the material is a single-layer A-type antiferromagnet.In contrast to J 1 , the values of J 2 and J 3 can be both positive and negative as n increases from 0 to 8, as shown in Figures 5E and 5F.

Electronic mechanism behind the variation of the magnetic properties
The electron transfer (De) between noble metals and Cr 2 TiC 2 T x MXene was analyzed to investigate the interaction in the heterojunctions.Here, we use Cr 2 TiC 2 O 2 and Cr 2 TiC 2 F 2 as two typical representatives of Cr 2 TiC 2 T x MXene.The Bader charge analysis was performed to investigate the electron transfer in the heterojunctions.A positive value of De represents an electron gain, while a negative value represents an electron loss.Overall, the electrons are transferred from the noble metals to Cr 2 TiC 2 T x MXene as the heterojunctions are formed.According to Anderson's theoretical analysis, 33 when the number of electrons is less than that required to fill the shells to half, the FM arrangement is favored; however, when the number of electrons is higher, the AFM arrangement is preferred.It is these electrons that are transferred from the noble metals to MXene that cause the FM-to-AFM1 phase transition in Cr 2 TiC 2 O 2 and hence give rise to the long-range spin order of Cr 2 TiC 2 T x when the distribution of the O and F terminations on its surfaces is inhomogeneous.Among the three noble metals, Rh has the greatest ability to donate electrons, as shown in Figures 6B-6G.Hence, the long-range spin order is more easily induced in the Rh/ Cr 2 TiC 2 O n/4 F 2Àn/4 /Rh heterojunctions than in the other heterojunctions.The binding energy (E b ) and the layer distance (d L ) between Cr 2 TiC 2 T x and the noble metal layers were also calculated to analyze the interaction between the two material systems.Specifically, d L is the average distance between the F or O terminations and the nearest noble metals along the c-axis.E b was calculated as follows:

NÞ;
where E(Total) is the total energy of the M/Cr 2 TiC 2 O n/4 F 2Àn/4 /M heterojunction, E(M) and E(Cr 2 TiC 2 O n/4 F 2Àn/4 ) are the total energies of the individual layers in the same supercell of the corresponding structures, and N is the number of M atoms in one layer.The factor 2 in the denominator stems from the fact that each supercell has two identical interfaces.The E b of the M/Cr 2 TiC 2 F 2 /M heterojunctions is in the range of 0.02-0.09eV per M atom.Such a low E b and high d L indicate that the interaction between M and Cr 2 TiC 2 F 2 is a van der Waals interaction.This can be attributed to the inertness of the F atoms.The E b of the M/Cr 2 TiC 2 O 2 /M heterojunctions is in the range of 0.8-1.5 eV per M atom.This moderate interaction does not destroy the Cr 2 TiC 2 T x structure but has an influence on its magnetic properties.
The total density of states (DOS) of Cr 2 TiC 2 O 2 and Cr 2 TiC 2 F 2 in the M/Cr 2 TiC 2 T x /M heterojunctions was calculated for determining their electronic properties and promoting their development for spintronic applications.In general, as the interaction between noble metals and Cr 2 TiC 2 T x MXene is moderate (for Cr 2 TiC 2 O 2 ) or relatively weak (for Cr 2 TiC 2 F 2 ), the variation in the electronic structure is limited, as shown in Figure 7.For the M/Cr 2 TiC 2 O 2 /M heterojunctions, the DOS around the Fermi level is in the range of 2-6 states/eV, which means that these systems are excellent conductors.The M/Cr 2 TiC 2 F 2 /M heterojunctions retain clear semiconductor characteristics, especially for M = Pd or Ag.Thus, the electronic transport characteristics vary with the Cr 2 TiC 2 O n/4 F 2Àn/4 terminations in the heterojunctions.
Compared with the strong influence that the adhesion of the Rh layers has on the magnetic properties of Cr 2 TiC 2 T x , the effect of these layers on the electronic transport properties is considerably less pronounced.Regardless of the inhomogeneous O coverage, it can be a single-layer A-type AFM material under the adhesion of Rh layers, while the conductive ability can be tuned by the oxygen coverage.The structure of Cr 2 TiC 2 T x MXene is similar to that of bilayer CrI 3 , both of which have two Cr atomic layers.Differently, the Ne ´el temperature of Rh/ Cr 2 TiC 2 T x /Rh MXene ranges between 5$110K depending on the F contents, while for bilayer CrI 3 it is 31 K. 34 In Cr 2 TiC 2 T x MXene, there are strong metallic bonds between the two Cr atomic layers, making the structure relatively stable, whereas in bilayer CrI 3 , the layers are held together by van der Waals forces.Besides, the extra electrons can induce FM-AFM transition for Cr 2 TiC 2 T x MXene.If it will become experimentally possible to manipulate the terminations of Cr 2 TiC 2 T x , it is envisaged that this single-layer A-type AFM material will have promising application in spin electronics.

Conclusions
In summary, first-principles calculations were conducted to investigate the magnetic and electronic properties of M/Cr 2 TiC 2 T x /M heterojunctions.It was found that pure Cr 2 TiC 2 T x prefers an FM arrangement for a high O coverage (>75%), while it prefers an AFM arrangement for a low O coverage (<60%).Thus, the non-uniform distribution of the O terminations on the Cr 2 TiC 2 T x surfaces causes this material to be in a spin disordered state.However, the Rh layers adhered to the Cr 2 TiC 2 T x surfaces can change this spin disorder to long-range spin order by donating electrons to the O terminations, transforming Cr 2 TiC 2 T x into a single-layer A-type antiferromagnet.As the proportion of F termination increases from 0 to 100%, the exchange coupling constant J 1 of the compound escalates from 0.5 to 15.9 meV.Concurrently, the Ne ´el temperature experiences a significant rise from 8 K to 110 K.The DOS analysis shows that Cr 2 TiC 2 T x exhibits excellent conductivity with O termination and semiconductor characteristics with F termination.These unique features make Cr 2 TiC 2 T x a promising magnetic material for application in spin electronics.

Limitations of the study
This investigation utilized first-principles calculations to demonstrate that the adhesion of Rh layers onto Cr 2 TiC 2 T x surfaces can induce a transition from a spin-disordered state to long-range spin order through electron donation to the O terminations, thereby converting Cr 2 TiC 2 T x into a single-layer A-type antiferromagnet.Nonetheless, this study is not without its limitations that warrant further attention.First, the reliance on first-principles methods means that the complexity of the model may not be fully captured, underscoring the necessity for additional experimental corroboration.Second, the assessment of the Ne ´el temperature is relatively low, just 110 K.The challenge of enhancing this Ne ´el temperature, or alternatively, the strategic exploitation of this low-temperature attribute in the design of spintronic devices, presents a pivotal direction for future research endeavors.

STAR+METHODS
Detailed methods are provided in the online version of this paper and include the following:

Figure 1 .
Figure 1.Side views of different F and O adsorption configurations for Cr 2 TiC 2 O n/4 F 2Àn/4 with n = 0, 1, 2, 3, 4, 5, 6, 7, and 8 Thus, in the following, the model in which the noble metals are adsorbed on the T O site for the M/Cr 2 TiC 2 O n/4 F 2Àn/4 /M heterojunctions is used.The energies of the FM and three AFM arrangements of M/Cr 2 TiC 2 O n/4 F 2Àn/4 /M were compared to find the ground state.For convenience, the energy differences of the AFM1 (DE AFM1 ), AFM2 (DE AFM2 ), and AFM3 (DE AFM3 ) states with respect to the FM state for the different M/Cr 2 TiC 2 O n/4 F 2Àn/4 /M systems were calculated.If all the DE AFM are positive, M/Cr 2 TiC 2 O n/4 F 2Àn/4 /M prefers to be in the FM state.Previous research works have shown that DE AFM1 increases from À0.18 to 0.29 eV as n increases from 0 to 8 for pure Cr 2 TiC 2 O n/4 F 2Àn/4 , 28 which indicates that Cr 2 TiC 2 O n/4 F 2Àn/4 prefers to be in the AFM1 state in the case of a low O coverage, while it prefers to be in the FM state in the case of a high O coverage.Owing to the inhomogeneous O distribution and coverage, Cr 2 TiC 2 T x MXene presents a spin-glass state.Similar to pure Cr 2 TiC 2 O n/4 F 2Àn/4 , DE AFM1 increases as n increases for the M/Cr 2 TiC 2 O n/4 F 2Àn/4 /M heterojunctions, as shown in Figure 3.By contrast, DE AFM1 remains negative for the Rh/Cr 2 TiC 2 O n/4 F 2Àn/4 /Rh and Pd/Cr 2 TiC 2 O n/4 F 2Àn/4 /Pd heterojunctions as n increases from 0 to 8.This indicates that the M/Cr 2 TiC 2 O n/4 F 2Àn/4 /M (M = Pd or Rh) heterojunctions prefer the AFM1 arrangement regardless of the degree of coverage and distribution of the O terminations.This prevents the occurrence of the magnetic phase transition caused by the F and O terminations and can thus lead to a long-range spin order for these two heterojunctions.Specifically, the adhesion of the Rh and Pd layers causes a magnetic phase transition for Cr 2 TiC 2 O 2 (n = 8) from the FM to the AFM1 state.From the point of view of DE AFM1 , the adhesion of the Rh layers is better than that of the Pd layers, which benefits the formation of a stable, long-range spin order for the AFM1 arrangement.In contrast to the Rh and Pd layers, the adhesion of the Ag layers causes a magnetic phase transition for Cr 2 TiC 2 O 2 from the FM to the AFM2 state.Thus, Ag/Cr 2 TiC 2 O n/4 F 2Àn/4 /Ag prefers to be in the AFM1 (AFM2) state for a low (high) O coverage.This also results in the Ag/Cr 2 TiC 2 O n/4 F 2Àn/4 /Ag heterojunction exhibiting the spin-glass state.

Figure 2 .
Figure 2. Top and side views for simulated models (A) and (B) Top and side view of the 2 3 2 Cr 2 TiC 2 O 2 supercell, where the three possible adsorption sites for the noble metals are indicated.(C-E) Side views of the three different M/Cr 2 TiC 2 O n/4 F 2Àn/4 /M heterojunction models investigated.(F-I) Side views of the (F) FM, (G) AFM1, (H) AFM2, and (I) AFM3 arrangements of the M/Cr 2 TiC 2 O n/4 F 2Àn/4 /M heterojunctions.

For pure Cr 2
TiC 2 O n/4 F 2Àn/4 , the MAE value is positive for n < 3, and it becomes negative for n > 5, as shown in Figure 5B.This means that the magnetic easy axis is in the xy-plane for a low O coverage, while it is along the c-axis for a high O coverage.This inhomogeneous O coverage is what causes the spin disorder for Cr 2 TiC 2 O n/4 F 2Àn/4 .However, the MAE value remains positive when the Rh layers adhere to the Cr 2 TiC 2 O n/4 F 2Àn/4 surfaces regardless of the value of n (between 0 and 8).This indicates that the adhesion of the Rh layers to the Cr 2 TiC 2 O n/4 F 2Àn/4 surfaces can cause the spins to lie in the xy-plane and form a long-range spin arrangement even in the presence of an inhomogeneous O coverage.

Figure 3 .
Figure 3. Energy difference of the AFM1 (DE AFM1 ), AFM2 (DE AFM2 ), and AFM3 (DE AFM3 ) states with respect to the FM state for the different M/Cr 2 TiC 2 O n/4 F 2Àn/4 /M heterojunctions For the M/Cr 2 TiC 2 O 2 /M heterojunctions, De M ranges between À0.23 and À0.35.It indicates that the electrons move from the noble metal to MXene.The absolute values of De M of the M/Cr 2 TiC 2 O 2 /M heterojunctions are obviously higher than those of the M/Cr 2 TiC 2 F 2 /M heterojunctions, as shown in Figure 6A.Such difference in De M is mainly caused by the extra unoccupied orbital of the O atoms with respect to the F atoms.The majority of the transferred electrons occupy the orbitals of the O atoms, while the remaining electrons occupy the orbitals of the Cr atoms.