⇦Chinese Physics Letters, 2023, Vol. 40, No. 5, Article code 057701 Magnetic Phase Transition in Strained Two-Dimensional CrSeTe Monolayer Zhiqiang Ji (纪智强)†, Tian Huang (黄田)†, Ying Li (黎迎), Xiaoyu Liu (刘宵宇), Lujun Wei (魏陆军), Hong Wu (武红), Jimeng Jin (金吉萌)*, Yong Pu (普勇)*, and Feng Li (李峰)* Affiliations New Energy Technology Engineering Laboratory of Jiangsu Provence & School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China Received 18 February 2023; accepted manuscript online 6 April 2023; published online 20 April 2023 †These authors contributed equally to this work.
*Corresponding authors. Email: 190276843@qq.com; puyong@njupt.edu.cn; lifeng@njupt.edu.cn Citation Text: Ji Z Q, Huang T, Li Y et al. 2023 Chin. Phys. Lett. 40 057701    Abstract Tunable magnetic phase transition in two-dimensional materials is a fascinating subject of research. We perform first-principle calculations based on density functional theory to clarify the magnetic property of CrSeTe monolayer modulated by the biaxial compressive strain. Based on the stable structure confirmed by the phonon calculation, CrSeTe is determined to be a ferromagnetic metal that undergoes a phase transition from a ferromagnetic state to an antiferromagnetic state with nearly 2.75% compressive strain. We identify the stress-magnetism behavior originating from the changes in interactions between the nearest-neighboring Cr atoms ($J_{1}$) and the next-nearest-neighboring Cr atoms ($J_{2}$). Through Monte Carlo simulation, we find that the Curie temperature of the CrSeTe monolayer is 160 K. The CrSeTe monolayer could be an intriguing platform for the two-dimensional systems and potential spintronic material.
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 DOI:10.1088/0256-307X/40/5/057701 © 2023 Chinese Physics Society Article Text Since the discovery of graphene, many two-dimensional (2D) materials have also been extensively researched. These materials have highly elastic physical properties and huge application potential.[1-3] The research of two-dimensional magnetic materials is very popular. Intrinsic magnetism was first observed in 2D materials Cr$_{2}$Ge$_{2}$Te$_{6}$ and CrI$_{3}$,[4,5] and their magnetism came from local magnetic moment. Subsequently, 2D magnetic metals, such as Fe$_{3}$GeTe$_{2}$ and Fe$_{3}$GaTe$_{2}$, were successfully prepared,[6,7] and their magnetic properties were derived from itinerant electron. Also, 2D CrSiTe$_{3}$ and Cr$X_{3}$ ($X$ = Br, Cl) can be successfully prepared experimentally.[8-10] Transition metal chalcogenide Janus TM$XY$, such as MoSSe, has been successfully prepared experimentally.[11,12] Environmentally stable CrSe$_{2}$ nanosheets can grow on WSe$_{2}$ substrates with the thickness that can be adjusted to a single layer.[13] The bulk CrTe$_{2}$ is layered and has a high Curie temperature of approximately 310 K.[14] The few-layer 1T-CrTe$_{2}$ can be exfoliated from the bulk phase.[15] Also, single- and few-layer CrTe$_{2}$ can be successfully grown by the molecular beam epitaxy method, with the Curie temperature up to 300 K,[16] making the Janus CrSeTe monolayer fabricated possibly. Controlling the spin of two-dimensional materials can be used to process information, which can replace current hard drives and develop quantum computing.[17] Tuning the magnetic order is essential in applying spintronic devices, such as magnetic memories and sensors.[18-20] Large magnetoresistance and large room-temperature magnetoresistance have been observed in full 2D spin valve devices.[21-25] Strain engineering has been widely used to adjust the properties of nanomaterials through substrate lattice mismatching.[26,27] MnPSe$_{3}$ can be adjusted by using biaxial tensile strain, causing a magnetic phase transition from an antiferromagnetic (AFM) state to a ferromagnetic (FM) state.[28] The magnetic phase of the MoN$_{2}$ monolayer can be changed from FM to AFM by tensile strain.[29] In this Letter, we systematically investigate the geometric, electronic, and magnetic properties of a CrSeTe monolayer. It is found that the 2D CrSeTe monolayer is stable and intrinsically a ferromagnetic metal, which can be changed to the AFM phase by applying a biaxial compressive strain. We identify the stress-magnetism behavior originating from the changes in interactions between the nearest-neighboring Cr atoms ($J_{1}$) and the next-nearest-neighboring Cr atoms ($J_{2}$). The Curie temperature of the CrSeTe monolayer is predicted to be 160 K. Our study shows that the CrSeTe monolayer is a suitable candidate for spintronic devices. Methods. Our calculations were performed within the framework of DFT implemented in the Vienna ab initio simulation package (VASP).[30-32] The generalized gradient approximation (GGA) of the Perdew–Burke–Ernzerhof functional[33] is used as the exchange-correlation potential. The plane-wave cutoff energy is set at 500 eV, and the energy convergence criterion is $10^{-5}$ eV. To fully relax the initial structure and to avoid the interaction between the layers in the nearest-neighboring unit cells, the vacuum length is set to 15 Å. Atomic positions are fully optimized until the Hellman–Feynman forces are less than 0.01 eV/Å. The Monkhorst–Pack scheme is chosen to sample the Brillouin zone integration, with $8 \times 8 \times 1$ $k$-points for the primitive cell and $2 \times 2 \times 1$ $k$-points for the ($4 \times 4$) supercell. Electronic correlations for the Cr-$d$ orbitals are taken into account by the GGA + $U$ method.[34] The effective onsite Coulomb interaction parameter $U$ and exchange interaction parameter $J$ are set to be 3.5 and 0.5 eV, respectively.[35-37] To verify its dynamical stability, we calculate phonon dispersion using the PHONOPY package[38] integrated with density functional perturbation theory.[39] Results and Discussion. Figure 1(a) shows that the CrSeTe monolayer has a hexagonal graphene-like honeycomb lattice. It consists of three sublayers with Te and Se atoms at the top and bottom surfaces, a Cr layer sandwiched between them. The lattice constant is 3.97 Å, and the Cr–Se and Cr–Te bond lengths are 2.50 and 2.85 Å, respectively. The angle of Te–Cr–Se is 95.36$^{\circ}$. Through DFT calculation, the magnetic moment of Cr is $3.297\mu_{\scriptscriptstyle{\rm B}}$, of Te is $-0.130 \mu_{\scriptscriptstyle{\rm B}}$, and of Se is $-0.287\mu_{\scriptscriptstyle{\rm B}}$. The magnetic moments are mainly localized on the magnetic centers of Cr atoms, 3.29$\mu_{\scriptscriptstyle{\rm B}}$ per atom, much more than those on Te or Se atoms which are negligibly small. To confirm the structural stability of the CrSeTe monolayer, we calculate phonon spectra as shown in Fig. 1(b). There is no imaginary frequency in the Brillouin zone, which indicates that the CrSeTe monolayer is dynamically stable.[40,41]
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Fig. 1. Geometric structure (a) and phonon band structure (b) of CrSeTe monolayer.
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Fig. 2. (a) FM, (b) AFM1, and (c) AFM2 order in a ($4 \times 4$) CrSeTe supercell. The spin-up is marked with red arrows, and the spin-down is marked with black arrows. (d) The total energy of FM, AFM1, and AFM2 states with the strained lattice parameter, and the energy difference ($\Delta E$) between AFM1 and FM states.
To determine the ground state of the 2D CrSeTe monolayer, we consider three different magnetic states: FM, AFM1, and AFM2 by a $4 \times 4 \times 1$ supercell [see Figs. 2(a), 2(b), and 2(c)]. Here we do not consider the non-magnetic state because its energy is much higher. The FM state has the lowest energy, suggesting that FM is the ground state. The results can be seen in Fig. 2(d) from the points at 0%. The calculations indicate that the intrinsic CrSeTe monolayer is ferromagnetic. Compressive strain can induce the magnetic phase transition of the CrSeTe monolayer, which can be seen in Fig. 2(d). A series of in-plane biaxial compressive strains are applied from $-7$% to 0%. The value of stress involved is described by using the change of the lattice parameter $\varepsilon = (a-a_{0})/a_{0}$, where $a$ is the updated lattice constant with biaxial strains and $a_{0}$ is the original lattice constant. The negative values indicate compressive stresses. The energy of AFM1 is always smaller than AFM2 under compressive strain, so $\Delta E$ is defined as $\Delta E=E_{\rm AFM1} -E_{\rm FM}$. When the compressive strain is increased from 0% to 7%, $\Delta E$ is drastically reduced from 447 meV to $-935$ meV. Near the compression strain of 2.75%, $\Delta E$ changes from a positive value to a negative value, indicating a magnetic phase transition from FM to AFM state. During the compressive strain, the bond length and angle of the CrSeTe monolayer will change, as shown in Figs. 3(a) and 3(b). When enhanced compressive strain is applied, the bond lengths of Cr–Te and Cr–Se slightly change. In contrast, the distance in Cr–Cr decreases significantly, and the angle of Cr–Se–Cr gradually decreases from 91$^{\circ}$. Since the bond angle of Cr–Se/Te–Cr is close to 90$^{\circ}$, according to the Goodenough–Kanamori–Anderson rules,[42-44] the indirect exchange coupling between two nearest-neighboring Cr cations through intervening Se/Te anion is FM. When the compressive strain increases, the indirect FM coupling weakens, and the direct coupling increases, effectively changing the exchange interaction between Cr atoms. To explore the mechanism of the magnetic phase transition, we use the Heisenberg model Hamiltonian to characterize the magnetic coupling in the CrSeTe monolayer: \begin{align} H=-\sum\limits_{i,j}{J_{ij} S_{i} S_{j}}, \tag {1} \end{align} where $J_{ij}$ is the exchange parameter between the $i$th and $j$th magnetic ion sites, $S = 3/2$ for Cr. We calculate the exchange strength of the nearest neighbor ($J_{1}$) and the next-nearest neighbor ($J_{2}$). Moreover, we calculate the energies of the three different spin orders (FM, AFM1, and AFM2) and apply Eq. (1), \begin{align} &E_{\rm FM} =E_{0} -16(3J_{1} S^{2}+3J_{2} S^{2}), \tag {2}\\ &E_{\rm AFM1} =E_{0} -16(-J_{1} S^{2}+J_{2} S^{2}), \tag {3}\\ &E_{\rm AFM2} =E_{0} -16(-J_{1} S^{2}-J_{2} S^{2}). \tag {4} \end{align} In our calculations, when no stress is applied, $J_{1}$ and $J_{2}$ are 7.95 meV and $-4.85$ meV, respectively. $J_{1}$ is ferromagnetic exchange, and $J_{2}$ is antiferromagnetic exchange. Both $J_{1}$ and $J_{2}$ will gradually decrease when biaxial compressive strain is applied. When a biaxial compression strain of $-7$% is used, $J_{1}$ is reduced from the original 7.95 meV to 3.34 meV, and $J_{2}$ is reduced from the original $-4.85$ meV to $-9.83$ meV. The ferromagnetic exchange is weakened, and the antiferromagnetic interaction is strengthened, resulting in a transition from the FM phase to the AFM phase.
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Fig. 3. (a) Bond length and (b) bonding angle of the CrSeTe monolayer versus strain. (c) The exchange coupling parameters $J_{1}$ and $J_{2}$ of the CrSeTe monolayer are represented with dashed lines. (d) The changes of $J_{1}$ and $J_{2}$ of the CrSeTe monolayer versus strain.
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Fig. 4. Density of states of the CrSeTe monolayer under the biaxial compressive strains of 0%, $-2$%, and $-4$%. We plot the detail of density of states.
Next, we study the electronic properties of the CrSeTe monolayer. As shown in Fig. 4, when no stress is applied, the spin-up and spin-down channels of the CrSeTe monolayer have no gap, and electrons around the Fermi level are contributed by Cr-$d$, Se-$p$, and Te-$p$ orbitals. The CrSeTe monolayer is a ferromagnetic metal. When biaxial compressive strain is applied, the electronic properties of the CrSeTe monolayer will change. When a biaxial compression strain of $-2$% is used, the CrSeTe monolayer still exhibits the properties of a ferromagnetic metal. However, when the stress is increased to $-4$%, the CrSeTe monolayer will become an antiferromagnetic metal. The change of electronic properties can prove that applying biaxial compressive stress can realize the transformation of FM and AFM phases of the CrSeTe monolayer. Curie temperature $T_{\scriptscriptstyle{\rm C}}$ is an essential parameter for practical applications of spintronic devices. Monte Carlo (MC) simulations with the Heisenberg model were performed to estimate the $T_{\scriptscriptstyle{\rm C}}$ of the CrSeTe monolayer. Here, we consider the nearest-neighboring exchange parameter $J$, and the estimated $J$ is 5.53 meV. $T_{\scriptscriptstyle{\rm C}}$ can be estimated from specific heat capacity peak positions or magnetic susceptibility. The calculated magnetic moment, specific heat capacity, and susceptibility as functions of temperature for CrSeTe monolayer are illustrated in Figs. 5(a), 5(b), and 5(c), respectively. It can be seen that $T_{\scriptscriptstyle{\rm C}}$ for the CrSeTe monolayer is 160 K, which can be a promising candidate for spintronic applications.
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Fig. 5. (a) The magnetic moment, (b) capacity, and (c) magnetic susceptibility versus temperature for the CrSeTe monolayer.
In summary, we have studied the geometrical structure, dynamic stability, and magnetic and electronic properties of a CrSeTe monolayer based on first-principle calculations. The CrSeTe monolayer is dynamically stable and intrinsically a ferromagnetic metal. The magnetic phase transition occurs when around 2.75% compressive strain is applied. When a biaxial compression strain is used, the ferromagnetic exchange is weakened, and the antiferromagnetic exchange is strengthened, resulting in a transition from the FM phase to the AFM phase. Calculating the electronic properties can also prove the occurrence of the magnetic phase transition. The Curie temperature of the CrSeTe monolayer is predicted to be 160 K. In addition, CrSeTe monolayers are metallic materials with high carrier mobility, which can reduce the energy consumption of devices. Moreover, the asymmetric geometry of CrSeTe leads to the presence of a built-in electric field, which makes the electrical properties of the materials more susceptible to the regulation of external factors. This property can be used to create magnetic-electric storage mediums and magnetically sensitive sensors, thereby further improving the functionality of devices. These findings are expected to stimulate further experimental studies on this material. Acknowledgment. This work was supported by the National Natural Science Foundation of China (Grant Nos. 61874060, U1932159, and 61911530220), the Natural Science Foundation of Jiangsu Province (Grant No. BK20181388), the Natural Science Research of Jiangsu Higher Education Institutions of China (Grant No. 21KJD140005), and the Foundation of Nanjing University of Posts and Telecommunications (NUPT) ‘1311 Talent Program’. The authors gratefully acknowledge the computing time granted by the Shanghai Supercomputer Centre. This work was also supported by the Natural Science Foundation of Jiangsu Province (Grant No. 20KJB430010), and NUPTSF (Grant No. NY219164). 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