Two dimensional CrGa2Se4: a spin-gapless ferromagnetic semiconductor with inclined uniaxial anisotropy

Qian Chen a, Ruqian Wang a, Zhaocong Huang a, Shijun Yuan a, Haowei Wang b, Liang Ma *a and Jinlan Wang a
aSchool of Physics, Southeast University, Nanjing, 211189, China. E-mail:
bMechanical Engineering Department, California State University Fullerton, Fullerton, California 92831, USA

Received 20th November 2020 , Accepted 15th February 2021

First published on 17th February 2021


Magnetic semiconductors with high critical temperature have long been the focus in materials science and are also known as one of the fundamental questions in two-dimensional (2D) materials. Based on density functional theory calculations, we predict a 2D spin-gapless ferromagnetic semiconductor of CrGa2Se4 monolayer, in which the type of spin-polarized current can be tuned by tailoring the Fermi energy. Moreover, the magnetic anisotropy energy calculations indicate that the CrGa2Se4 monolayer possesses spin anisotropy both in the basal plane and the vertical plane. This originates from the distortion-induced rearrangement of the 3d electrons in the CrSe6 octahedron and results in an inclined easy axis out of the film. The Curie temperature (Tc) of ferromagnetic phase transition for 2D CrGa2Se4 is more than 200 K. This 2D material shows promising transport properties for spintronics applications and is also important for fundamental research in 2D magnetism.

1. Introduction

Magnetic ordering in two-dimensional (2D) materials, being one of the key factors for 2D spintronic devices, has received considerable attention from both experimental and theoretical perspectives.1–3 A significant amount of theoretical efforts were made to pave the way for realizing 2D magnetism.4–7 However, after the discovery of graphene in 2004,8 magnetic ordering has remained absent in the family of 2D materials for more than ten years. It is only since 2017 that several notable 2D magnetic atomic crystals have gradually been realized experimentally, including CrI3,9 CrGeTe3,10,11 Fe3GeTe2,12,13 VSe2,14 and CrTe2.15 However, the practical use of these 2D magnets faces huge challenges. Apart from their instability in air and difficulty in mass production,16–19 one of the most critical needs concerns the realization of room-temperature 2D ferromagnets.20–22 Therefore, it will be instructive to find more true 2D systems with higher transition temperatures.

The exchange interaction and uniaxial magnetic anisotropy have been demonstrated to play important roles in designing high-temperature 2D ferromagnets. Promising candidates are those compounds containing 3d transition metals (TM), in which the spin–orbit coupling (SOC) interaction mediates the super-exchange between TM ions. On the other hand, the 2D multi-sublayer structure is supposed to maximize the preservation of the magneto-crystalline anisotropy from the bulk phase and therefore enhances the magnetic anisotropy. In addition, acceptable structural distortion resulting from the intralayer stress may bring uniaxial anisotropy even in the basal plane, creating a more favorable condition for long-range ferromagnetic ordering. Based on the above-mentioned clues, in this communication, we carry out a case study on the magnetic properties of the CrGa2Se4 monolayer. Such a 2D compound composed with standard Cr–Se octahedral cages shows monoclinic symmetry [see Fig. 1], which gives us a rather clear path to investigate the magneto-crystalline induced uniaxial anisotropy. Moreover, based on density functional theory (DFT) simulations, the predicted spin-gapless ferromagnetic semiconductor with high Curie temperature (Tc) makes 2D CrGa2Se4 a promising candidate for spintronics.

image file: d0nr08296a-f1.tif
Fig. 1 (a) Side views of three T-type configurations for the CrGa2Se4 monolayer. (b) Top view of the T-I configuration with arrows represents the basic vectors a and b in the basal plane. (c) The optimized crystal structure with the T-I configuration is shown in the polyhedral view.

2. Method

The calculations are performed based on the spin-polarized DFT using the projector augmented wave (PAW) method23 as implemented in the Vienna ab initio Simulation Package (VASP).24 The exchange and correlation potential are described using general gradient approximation (GGA) in the scheme of Perdew–Burke–Ernzerhof (PBE).25 In addition, the on-site coulombic corrections are addressed with Hubbard-type term (GGA + U)26 and the value of U = 3.5 eV is set for Cr-3d orbitals following that reported in ref. 27 and 28. The hybrid density functional theory based on Heyd–Scuseria–Ernzerhof (HSE06)29,30 is employed to obtain band structure in high accuracy. The kinetic energy cutoff for plane-wave basis functions is set to 500 eV. A vacuum space of more than 20 Å is inserted to avoid artificial interactions due to the periodic condition. The Brillouin zone is sampled by a Γ-centered Monkhorst-Park k-mesh31 with a separation less than 0.02 Å−1. Both the lattice constant and ions are relaxed until the remaining force on each atom falls below 0.01 eV Å−1 and the convergence threshold for energy is set as 10−6 eV. The SOC effects are considered to calculate the magneto-crystalline anisotropy energy (MAE) and obtain the easy axis of the magnetic system.32 The Curie temperature was estimated with Monte Carlo simulation based on the Heisenberg model.33

3. Results and discussion

The previous study had reported the FeGa2S4-type-layered ternary chalcogenides TMGa2X4 (X = S, Se, and Te), which can be viewed as a 1T TMX2 layer sandwiched in the middle of two GaX layers.3,34 In our calculation, three different T-type configurations (T-I, T-II, and T-III) depending on the stacking patterns of GaSe and CrSe2 sublayers are considered, as shown in Fig. 1a. Here, the H-type configurations are found with much higher energy than T-types (see Fig. S1 and Table S1) and thus are not included in this study. Through a series of self-consistent calculations on the structural geometry with different magnetic coupling, the lowest energy state of CrGa2Se4 is found in the T-I configuration, whose top view is illustrated in Fig. 1b. The slightly distorted tetrahedral voids are occupied by Ga ions, while the octahedral cages are occupied by Cr ions, (see Fig. 1c). Such distortion reduces the crystal symmetry from D3d to C2h space group, corresponding to small different lattice constants of a = 3.92 Å and b = 3.86 Å. It is worth noting that the CrSe6 octahedral is stretched in the direction of the z-axis, as indicated in Fig. 1c, so that the Cr–Se distance in the z-direction (2.75 Å) is larger than those in the xy plane (2.59 Å). The ab initio molecule dynamic (AIMD) simulations were performed to evaluate the structural stability at room temperature. The simulation lasted for 6 ps under a constant-temperature and volume (NVT) ensemble by the Nosé–Hoover method. Fig. S2 shows that both the temperature and energy of the T-I CrGa2Se4 fluctuate around a certain value as time elapses, and the snapshot at 6 ps retains the 2D crystal, which indicates its stability at room temperature.

The magnetism of the CrGa2Se4 monolayer originates from the ferromagnetic (FM) coupling of local spin moments on Cr ions. As presented in Fig. 2a, three different magnetic ordering states, including FM, zigzag antiferromagnetic (zAFM), and stripe antiferromagnetic (sAFM), are considered in this study. Fig. 2b shows that the calculated total energies of all AFM states are higher than those of the FM state for all three T-type structural configurations, and the T-I configuration has the lowest energy in all three FM states. Therefore, we will focus on the FM state of the T-I configuration in the following discussions. As shown in Fig. 1, the neighboring magnetic Cr ions in the CrGa2Se4 monolayer are mediated via Se ions with the average Cr–Se–Cr bond angle of about 95°. Following the Goodenough–Kanamori–Anderson (GKA) rules,35–37 such super-exchange interaction often brings FM coupling as the cation–anion–cation bond angle close to 90°, which explains the FM ordering in the CrGa2Se4 monolayer.

image file: d0nr08296a-f2.tif
Fig. 2 (a) Schematics for the FM and AFM states of the CrGa2Se4 monolayer. (b) Energy difference with respect to the ground state for type I, II, and III configurations. (c) The simulated magnetic moment and susceptibility with respect to temperature.

In order to evaluate the stability of FM ordering at elevated temperatures, the Tc of this CrGa2Se4 monolayer is predicted using the Monte Carlo (MC) simulation based on the anisotropic Heisenberg model, in which the Hamiltonian is described as

image file: d0nr08296a-t1.tif(1)
where Jn is the exchange coupling parameter, A is the anisotropy energy parameter and Si is the spin vector of the local moments. Based on the energy difference (ΔE) between the FM and AFM states shown in Fig. 2b, we extract the nearest neighbor and second-nearest neighbor coupling parameters with J1 = 12 meV and J2 = 1.9 meV. By employing the SOC correction, we obtained the magnetic anisotropy energy (MAE) for each Cr atom in the CrGa2Se4 monolayer, which will be discussed in more detail later. A supercell containing 50 × 50 cells is used to simulate the random spin-flipping in the monolayer at different temperatures. As shown in Fig. 2c, the estimated Tc of the CrGa2Se4 monolayer is about 220 K, much higher than the ∼60 K of CrGeTe3.10 The high Tc of CrGa2Se4 corresponds to its larger coupling parameters than those of CrGeTe3.38

The band structures with HSE06 functional indicate that the CrGa2Se4 monolayer is a ferromagnetic semiconductor. As displayed in Fig. 3a, in both majority- and minority-spin channels, the band structures possess bang gaps with values of 0.36 eV and 1.35 eV. The valence band maximum (VBM) and conduction band minimum (CBM) are dominated by the Se-p and Ga-s orbitals, respectively (see Fig. S3). More interestingly, VBM and CBM show the opposite spin characters and are touched indirectly at the Fermi level. This is called the spin-gapless semiconductor (SGS), which has been discovered in some bulk Heusler compounds,39,40 but is rarely reported in 2D materials. In this case, the 100% spin-polarized current in the CrGa2Se4 monolayer can be tuned by tailoring the Fermi energy. In this sense, it is a likely promising candidate for engineering 2D spintronic field-effect transistors.

image file: d0nr08296a-f3.tif
Fig. 3 (a) Spin-polarized HSE band structure of the CrGa2Se4 monolayer with the projection on Cr-3d orbitals. The schematic of the paths and high symmetrical points in the first Brillouin zone is on the right side. (b) Schematic representation of the orbital splitting in the octahedral field.

Each Cr atom in the CrGa2Se4 monolayer carries the local moment of 4μB, which is associated with the electronic configuration of its 3d orbitals. It is known that when the TM atoms are subjected to an octahedral crystal field, and their 3d orbitals split into two sets: two-fold degenerate eg states of dx2y2 and dz2 in high level, and three-fold degenerate t2g states of dxy, dyz, and dxz in low level. Fig. 3b presents the schematic of the Cr-3d electrons arranged on the t2g and eg states. As each Cr atom donates two electrons (one in the 4s-orbitals and the other in the 3d-orbitals) to neighboring Se atoms, the remaining three electrons fill the t2g states and the other one occupies the eg states, which give rise to a high-spin configuration with a magnetic moment of 4μB according to the Hund's rule. Nevertheless, the degenerate eg states further split in the CrGa2Se4 monolayer. As mentioned above, the CrSe6 octahedron is stretched in the direction of the z-axis to lower the energy of the dz2 orbital according to the Jahn–Teller effect. The band structure projection on Cr-3d orbitals in the majority-spin channel indicates that the energy of the dz2 orbital goes down to the t2g level. The schematic representation of the orbital configuration for this distorted octahedron is also shown in Fig. 3b, from which we can see the high-spin state of 4μB is retained but the electrons in orbitals with a z-component is increased. This asymmetry of the electronic distribution in spatial orientation results in significant magnetic anisotropy.

MAE is calculated to verify the easy axis in this 2D system. In the basal plane of the CrGa2Se4 monolayer, the angular dependence of the total energy (shown in Fig. 4a) indicates a large magnetic anisotropy. The dipolar energy is as high as 380 μeV and the magnetization direction is much more favorable in the line with an angle of 30° with respect to the basic vector a. This easy line in the basal plane is the projection of the z-axis of CrSe6 octahedron (see Fig. 1c). Therefore, we further calculate the anisotropy energy in the plane consists of basic vector c and z-axis. As shown in Fig. 4b, a strong uniaxial anisotropy is also present in the vertical plane with the dipolar energy of 240 μeV and we found the easy axis in the z-direction with an angle of 60° with respect to the basic vector c. Such spin anisotropy both in the basal and vertical planes makes the magnetism Hamiltonian of this system close to the Ising model. Based on the above analysis of the orbital configuration, the Cr-3d electrons in the octahedral field are dominated by the orbitals with z-component, which indicates clearly that the distortion induced rearrangement of the 3d electrons is responsible for such slant easy axis.

image file: d0nr08296a-f4.tif
Fig. 4 (a) The energy variation depends on the polar angle of magnetization in the basal plane and (b) in the plane perpendicular to the vector b of the CrGa2Se4 monolayer. The corresponding vertical perspectives of the crystal lattice are in the right panel.

4. Conclusion

In summary, we predict an inclined uniaxial magnetic anisotropy in 2D ferromagnetic materials with the help of first-principles calculations. Using a CrGa2Se4 monolayer as an example, we found that the easy axis orients neither perpendicular nor parallel to the basal plane, but on an oblique line out of the film. Both in-plane and out-plane magnetic anisotropy with large MAE sustains the long-range ferromagnetic order at high temperatures. Moreover, it is also demonstrated that the CrGa2Se4 monolayer is a 2D spin-gapless ferromagnetic semiconductor, in which the type of spin conductivity with 100% polarization is sensitive to the gate voltage. This is promising for a wider range of applications on 2D spintronic devices. Therefore, we suspect this theoretical study on the 2D CrGa2Se4 monolayer is noteworthy for both fundamental physics and technological advances.

Conflicts of interest

There are no conflicts to declare.


This work is supported by the National Key R&D Program of China 2017YFA0403600 (Q. C.), National Natural Science Funds of China 21903014 (L. M.), 21973011 (Q. C.), Basic Research Program of Jiangsu Province BK20190328 (L. M.). Q. C. and L. M. acknowledge the computational resources at the Big Data Computing Center of Southeast University and National Supercomputing Center in Tianjin.


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Electronic supplementary information (ESI) available: Total energy in different structural configurations; the structures of H-type CrGa2Se4 monolayer; AIMD simulations; band structures of CrGa2Se4 monolayer with the projection on Se-p and Ga-s orbitals. See DOI: 10.1039/d0nr08296a
These authors contributed equally to this work.

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