Diverse magnetism in stable and metastable structures of CrTe

Abstract

In this paper, we systematically investigated the structural and magnetic properties of CrTe by combining particle swarm optimization algorithm and first-principles calculations. By considering the electronic correlation effect, we predicted the ground-state structure of CrTe to be NiAs-type (space group P 6₃/mmc) structure at ambient pressure, consistent with the experimental observation. Moreover, we found two extra meta-stable Cmca and R\overline{3}m structures which have negative formation enthalpy and stable phonon dispersion at ambient pressure. The Cmca structure is a layered antiferromagnetic metal. The cleaved energy of a single layer is 0.464 J/m², indicating the possible synthesis of CrTe monolayer. The R\overline{3}m structure is a ferromagnetic half-metal. When external pressure is applied, the ground-state structure of CrTe transitions from P 6₃/mmc structure to R\overline{3}m structure at a pressure of 34 GPa, then to Fm\overline{3}m structure at 42 GPa. We thought these results help to motivate experimental studies of the CrTe compounds in the application of spintronics.

Graphical abstract

Keywords

CrTe / meta-stable structure / antiferromagnetic metal / ferromagnetic half-metal

1 Introduction

The present spintronic devices mainly consist of ferromagnetic (FM) materials, which have shortcomings such as low integration and slow operating frequency [1]. In 2006, antiferromagnetic (AFM) metals are predicted to have giant magnetoresistance [2], which was then observed in the experiment [3]. Antiferromagnets have several advantages in spintronic application, such as high magnetic susceptibility, high switching frequency, the absence of stray fields, and strong spin transfer torque capability [4, 5]. Magnetic transition-metal chalcogenides (TMCs) with rich structural and magnetic properties are regarded as promising candidate materials in spintronics [6–8]. It is significant to explore the unknown FM and AFM structures of TMCs.

Here we focus on the CrTe compounds. On the experimental side, according to the phase diagram determined by Ipser et al. [9], the Cr_1−δ Te system has the hexagonal NiAs (NA) structure for δ≤0.1. NA CrTe is a FM material with a Curie temperature of 340 K [10]. Furthermore, Wang et al. [11] synthesized the film of NA CrTe with a thickness of 11–45 nm and found that it still had a hard magnetism. Apart from the NA structure, a metastable zinc-blende (ZB) CrTe [12] has been grown using molecular-beam epitaxy on GaAs (100) substrate. Eto et al. [13] founded that CrTe occurred a structural transition from the NA structure to the MnP (MP) one at pressures between 13 and 14 GPa. Moreover, a CrTe₃ compound with a layered structure was synthesized with a long-range AFM order [14], indicating that layered structure may also exist in the CrTe compounds.

On the theoretical side, using the full-potential linear augmented plane waves (FP-LAPWs) method, Charifi et al. [15] compared the energy of CrTe in NA, ZB, MP, and Rock-salt (RS) structure, and found that NA structure was the ground state. Dijkstra et al. [16] found that NA CrTe had strong Cr 3d-Te 5p hybridization and the Cr 3d_{z^2}-\text{Cr}3d_{z^2} overlap along the c axis. Kanchana et al. [17] predicted that NA CrTe had a magnetic transition from FM to non-magnetic (NM) state in around 45.3 GPa utilizing the tight-binding linear muffin-tin orbital method. It was predicted that ZB CrTe had a total energy 0.36 eV higher than the NA CrTe [18]. Block et al. [19] founded that ZB CrTe was a half-metal with a bandgap in the minority channel at the Fermi level, due to stronger CrTe covalent bonding than NA CrTe. Liu et al. [20] showed that CrTe in RS structure was only marginally unstable against the NA CrTe, and more stable than the ZB CrTe. However, Belkadi [21] recently predicted that the RS structure was the ground-state structure of CrTe by modified Becke-Johnson (MBJ) exchange potential method. Moulkhalwa et al. [22] found that the electronic correlation effect had a large influence on the structural and magnetic properties of Cr-based chalcogenides, which has not been well considered in previous calculations.

Considering contradictory results in previous works, in this paper, we investigated the crystal and magnetic structures of CrTe using structure searching technology combined with first-principles calculations. We predicted that the NA structure (space group P 6₃/mmc) was the ground-state structure by considering the electronic correlation effect. Two extra meta-stable phases including Cmca and R\overline{3}m structures were founded. The Cmca phase has a layered structure and is an AFM metal. The R\overline{3}m phase is a FM half-metal. Their electronic and magnetic properties were carefully analyzed. When the external pressure increases, the ground-state structure of CrTe changes from P 6₃/mmc to R\overline{3}m at 34 GPa , and then to Fm\overline{3}m structure at 42 GPa.

2 Methods of computational

The searching of crystal structure was performed by particle swarm optimization algorithm, as implemented in the CALYPSO code [23–25]. Given the chemical composition and external pressure, the atomic arrangement with the global lowest energy on the potential energy surface can be determined [23]. This algorithm has been applied to many systems with reliability [26, 27]. We searched for the low-energy structures of bulk (CrTe)_n with number of formula n from 1 to 4 in the process of the structure prediction. To judge the stability of the CrTe in various structures, we adopted the formation enthalpy (∆H) that is defined as

\begin{array}{}\text{(1)}& \text{Δ}H=[h(\text{CrTe})-h(\text{Cr})-h(\text{Te})]/\mathrm{2,}\end{array}

where 2 is the number of atoms per CrTe formula. The h(CrTe) is the enthalpies per formula corresponding to the most stable magnetic state of CrTe. h(Cr) and h(Te) are the enthalpy of Cr substance (space group Im\overline{3}m ) [28] and Te substance (space group P 3₁21) [29], respectively. The first-principles calculations were performed using the Vienna ab initio simulation package (VASP) [30, 31]. The projector augmented wave (PAW) [32] pseudopotentials and Perdew, Burke, and Ernzerhof (PBE) [33] exchange-correlation functionals were used. A plane-wave basis set with an energy cutoff of 500 eV and a monkhorst-Pack [34] k-points with a grid spacing of 2π × 0.08 Å⁻¹ were used. The crystal structures and atomic positions were fully optimized with a force convergence threshold of 0.01 eV/Å. To consider the correlation effects of Cr-d orbitals, we applied the PBE+U scheme [35]. The onsite effective U_f value of Cr-d electrons in CrTe system was determined to be 4 eV (see Fig. S1) by the linear response methods [36]. The phonon spectrum was calculated using density functional perturbation theory [37].

3 Results and discussion

3.1 Meta-stable structures

Calculated formation enthalpies of CrTe compounds, within the chemical compositions available in the experiment [9–14], show that Cr–Te compound with a Cr:Te ratio of 1:1 has the lowest formation enthalpy ∆H (see Fig. S9). Through the structural search at ambient pressure, several structures in CrTe system with a large negative ∆H including Cmca, P 6₃/mmc (NA), R\overline{3}m and Fm\overline{3}m (RS) structures are predicted (see Fig. 1), while the ZB and MnP structures have much smaller negative ∆H. The energy-volume curve of four low-energy structures are displayed in Fig. 2. Considering the layered structure of the Cmca phase, we adopted the van der Waals (vdw) functional [38] in the first-principles calculations. In PBE calculations, the Cmca structure is the ground-state structure and P 6₃/mmc structure is a meta-stable one [see Fig. 2(a)]. However, in PBE+U calculations, the P 6₃/mmc (NA) structure becomes the ground-state structure [see Fig. 2(b)] which is consistent with the available experiments [9, 10]. It was indicated that the electronic correlation effect has to be considered in the investigation of the structures of CrTe. Our results about the ground state of CrTe in PBE and PBE+U calculations are different from previous works [15, 17, 20–22] (see Table S1). Firstly, both the Cmca and R\overline{3}m phases have not been considered in previous works. Secondly, the FP-LAPWs method and MBJ method [15, 20–22] may not be suited for determining the ground state of CrTe. For example, the FP-LAPWs method can not calculate stress tensor, which makes the optimization tedious for low symmetry cases [39]. On the other side, the MBJ method is a potential-only functional and is not suited for computing Hellmann–Feynman forces [40]. In the following content, we will display the results of PBE+U calculations.

The optimized lattice parameters of low-energy CrTe structures are given in Table 1. The phonon spectrums of four low-energy structures show no imaginary phonon frequencies, confirming their dynamical stability [see Figs. 3(a) and (b), and Fig. S2]. Meanwhile, Table 2 lists the elastic constants of the four structures of CrTe, which satisfy the Born criterion [41, 42], indicating that they are mechanically stable. Detailed information about the Born criterion for each phase can be found in Table S2 of the supplementary material.

Two meta-stable structures including Cmca and R\overline{3}m structures were predicted, which were not reported in previous works. The Cmca structure has a layered crystal lattice with each layer be held together by the vdw interaction. Its single layer consists of Cr₄Te₄ cells with four edge-shared CrTe₄ quadrangular pyramids [see Fig. 3(d)]. We have compared the energy of Cmca structure in nonmagnetic (NM), FM and, different AFM states. It was founded that the FM state was unstable and would change to the NM state. The magnetic ground state of the Cmca phase is the AFM state [see Fig. 3(c)], in which the spin distribution in a single layer is opposite [see Fig. 3(d)]. The AFM state, which helps to decrease the Pauli repulsion between electrons, results in shorter Cr–Te bond lengths than that of other structures (see Table 1). Moreover, the calculated cleaved energy of a single layer is 0.464 J/m², similar to that of graphene (0.43 J/m²) [43], indicating the possible synthesis of monolayer CrTe.

On the other side, the ground state of the R\overline{3}m structure is the FM state. The AFM state energy is 195.58 meV/f.u. higher than the FM state, similar to Fm\overline{3}m and P 6₃/mmc structure (see Fig. S3). The basic unit of R\overline{3}m structure is the octahedron, similar to Fm\overline{3}m and P 6₃/mmc structure (see Fig. S4). As seen from Fig. 2, in both PBE and PBE+U calculations, the energy of R\overline{3}m structure is slightly higher than that of P 6₃/mmc (NA) structure, but lower than Fm\overline{3}m (RS) structures as well as ZB structures. Thus, it was possible to synthesize the R\overline{3}m structure in future experiments.

3.2 Electronic and magnetic properties

As shown in Fig. S5, the charge density difference of CrTe in various structures indicates that electrons are transferred from Cr atoms to the middle zone of Cr–Te bonds, which indicates a mixture of ionic and covalent bonding interactions between Cr and Te atoms [44]. The Cr–Te bond lengths (d_{Cr−T e}) of P 6₃/mmc, R\overline{3}m , and F m3m structures is longer than that of the Cmca phase (see Table 1). The extension of d_{Cr−T e} leads to a decrease in covalent bond interaction, contrary to the ionic bonding interaction [20]. Therefore, the unpaired electrons accumulated on the Cr and Te atoms in CrTe of these three structures slightly increase compared to Cmca structure, leading to a variation of magnetism.

Figure 4 shows spin-dependent band structure and partial density of states (DOS) of the Cmca and R\overline{3}m structure with U_f = 4.0 eV at its equilibrium volume. The Cmca structure is an AFM metal which indicates the possible existence of giant magnetoresistance [2]. On the other side, R\overline{3}m is a FM half-metal with 100% spin-polarized carrier at Fermi level. The DOS near the Fermi level is mainly from the Cr-3d orbitals in both phases (see Fig. 4). The analysis of crystal orbital hamilton populations (–COHP) shows that the DOS near the Fermi level consist of anti-bonding states between Cr-3d and Te-5p orbitals (see Fig. S6). Here, we founded that the electron correlation effect has a large influence on the electronic structure of CrTe. For example, the Cmca structure become an AFM semiconductor with a bandgap of 0.126 eV if U_f of Cr was ignored (see Fig. S7).

3.3 Magnetic and structural phase diagram under pressure

We next implored the evolution of the stable structure and phase transition of CrTe as a function of external pressure. Figure 5 plots the pressure-formation enthalpies curve of the CrTe in various structures. We set the formation enthalpies of P 6₃/mmc phase to zero for a comparison.

As seen from Fig. 5, the P 6₃/mmc structure was found to be the most stable phase at a range of 0∼34 GPa. However, the energy differences among P 6₃/mmc, R\overline{3}m , and Fm\overline{3}m structures are small. At a range of 30∼45 GPa, pressure-induced phase transitions occur. The P 6₃/mmc structure transforms to the R\overline{3}m structure at 34 GPa and then to Fm\overline{3}m structure at 42 GPa. Here the transition critical pressures were estimated by linear interpolation. During the phase transition, CrTe becomes a FM metal (see Fig. S8). We also checked the MnP-type CrTe (space group P nma) which was also observed in the experiment [13]. We predicted that P nma structure has higher formation enthalpy than R\overline{3}m and Fm\overline{3}m structures at high pressure (see Fig. 5). Thus, the high-pressure phase of CrTe should be R\overline{3}m and Fm\overline{3}m structures. Thus, the high-pressure phase of CrTe should be R\overline{3}m and Fm\overline{3}m structures. The pressure-induced phase transition path is given below [45]:

\begin{array}{}\text{(2)}& P{6}_3/mmc\stackrel{34\text{GPa}}{\to }R\overline{3}m\stackrel{42\text{GPa}}{\to }Fm\overline{3}m\mathrm{.}\end{array}

4 Conclusion

In conclusion, we investigated the crystal structures and magnetic properties of CrTe by using particle swarm optimization algorithm combined with the first-principles calculations. It is necessary to consider the electronic correlation effect in determining the ground state of CrTe. The ground state of CrTe was founded to be the NiAs-type (space group P 6₃/mmc) structure at ambient pressure, consistent with available experiments. Apart from that, we predicted two meta-stable phases including Cmca and R\overline{3}m structures. CrTe in Cmca structures is a layered AFM metal. CrTe in R\overline{3}m structures is a FM half-metal and may be synthesized in the future experiment, due to that its energy is slightly higher than ground-state P 6₃/mmc structure at ambient pressure. The CrTe in P 6₃/mmc structure is the most stable at low pressure. However, the ground-state structure of CrTe would transition to R\overline{3}m and Fm\overline{3}m structures at the pressure of about 34 and 42 GPa, respectively. Meanwhile, CrTe becomes a FM metal at high pressure.

References

[1] A. Brataas, A. D. Kent, and H. Ohno, Current-induced torques in magnetic materials, Nat. Mater. 11(5), 372 (2012)

[2] A. S. Núñez, R. A. Duine, P. Haney, and A. H. Mac-Donald, Theory of spin torques and giant magnetoresistance in antiferromagnetic metals, Phys. Rev. B 73(21), 214426 (2006)

[3] B. G. Park, J. Wunderlich, X. Martí, V. Holý, Y. Kurosaki, M. Yamada, H. Yamamoto, A. Nishide, J. Hayakawa, H. Takahashi, A. B. Shick, and T. Jungwirth, A spin-valve-like magnetoresistance of an antiferromagnet-based tunnel junction, Nat. Mater. 10(5), 347 (2011)

[4] E. V. Gomonay and V. M. Loktev, Spintronics of antiferromagnetic systems, Low Temp. Phys. 40(1), 17 (2014)

[5] Y. Wang, C. Song, J. Zhang, and F. Pan, Spintronic materials and devices based on antiferromagnetic metals, Prog. Nat. Sci. 27(2), 208 (2017)

[6] N. V. Baranov, N. V. Selezneva, and V. A. Kazantsev, Magnetism and superconductivity of transition metal chalcogenides, Phys. Met. Metallogr. 119(13), 1301 (2018)

[7] W. Zhang, P. K. J. Wong, R. Chua, and A. T. S. Wee, in: Spintronic 2D Materials, Materials Today, edited by W. Liu and Y. Xu, Elsevier, 2020, pp 227–251

[8] M. A. Mc Guire, Cleavable magnetic materials from van der Waals layered transition metal halides and chalcogenides, J. Appl. Phys. 128(11), 110901 (2020)

[9] H. Ipser, K. L. Komarek, and K. O. Klepp, Transition metal-chalcogen systems viii: The Cr–Te phase diagram, J. Less Common Met. 92(2), 265 (1983)

[10] T. Kanomata, Y. Sugawara, T. Kaneko, K. Kamishima, H. Aruga Katori, and T. Goto, Giant magnetovolume effect of CrTe, J. Alloys Compd. 297(1–2), 5 (2000)

[11] M. Wang, L. Kang, J. Su, L. Zhang, H. Dai, H. Cheng, X. Han, T. Zhai, Z. Liu, and J. Han, Two-dimensional ferromagnetism in CrTe flakes down to atomically thin layers, Nanoscale 12(31), 16427 (2020)

[12] M. G. Sreenivasan, J. F. Bi, K. L. Teo, and T. Liew, Systematic investigation of structural and magnetic properties in molecular beam epitaxial growth of metastable zincblende CrTe toward half-metallicity, J. Appl. Phys. 103(4), 043908 (2008)

[13] T. Eto, M. Ishizuka, S. Endo, T. Kanomata, and T. Kikegawa, Pressure-induced structural phase transition in a ferromagnet CrTe, J. Alloys Compd. 315(1–2), 16 (2001)

[14] M. A. Mc Guire, V. O. Garlea, S. Kc, V. R. Cooper, J. Yan, H. Cao, and B. C. Sales, Antiferromagnetism in the van der Waals layered spin-lozenge semiconductor CrTe₃, Phys. Rev. B 95(14), 144421 (2017)

[15] Z. Charifi, D. Guendouz, H. Baaziz, F. Soyalp, and B. Hamad, Ab-initio investigations of the structural, electronic, magnetic and mechanical properties of CrX (X = As, Sb, Se, and Te) transition metal pnictides and chalcogenides, Phys. Scr. 94(1), 015701 (2019)

[16] J. Dijkstra, H. H. Weitering, C. F. Bruggen, C. Haas, and R. A. Groot, Band-structure calculations, and magnetic and transport properties of ferromagnetic chromium tellurides (CrTe, Cr₃Te₄, Cr₂Te₃), J. Phys.: Condens. Matter 1(46), 9141 (1989)

[17] V. Kanchana, G. Vaitheeswaran, and M. Rajagopalan, Pressure-induced structural and magnetic phase transition in ferromagnetic CrTe, J. Magn. Magn. Mater. 250, 353 (2002)

[18] W. H. Xie, Y. Q. Xu, B. G. Liu, and D. G. Pettifor, Half-metallic ferromagnetism and structural stability of zincblende phases of the transition-metal chalcogenides, Phys. Rev. Lett. 91(3), 037204 (2003)

[19] T. Block and W. Tremel, Large magnetoresistance at room temperature in the off-stochiometric chalcogenide Cr_0.92Te, J. Alloys Compd. 422(1–2), 12 (2006)

[20] Y. Liu, S. K. Bose, and J. Kudrnovský, First-principles theoretical studies of half-metallic ferromagnetism in CrTe, Phys. Rev. B 82(9), 094435 (2010)

[21] A. Belkadi, K. O. Obodo, Y. Zaoui, H. Moulkhalwa, L. Beldi, and B. Bouhafs, First-principles studies of structural, electronic and magnetic properties of the CrS, CrSe and CrTe compounds, SPIN 08(04), 1850019 (2018)

[22] H. Moulkhalwa, Y. Zaoui, K. O. Obodo, A. Belkadi, L. Beldi, and B. Bouhafs, Half-metallic and half-semiconductor gaps in Cr-based chalcogenides: DFT+ U calculations, J. Supercond. Nov. Magn. 32(3), 635 (2019)

[23] Y. Wang, J. Lv, L. Zhu, and Y. Ma, CALYPSO: A method for crystal structure prediction, Comput. Phys. Commun. 183(10), 2063 (2012)

[24] Y. Wang, J. Lv, L. Zhu, and Y. Ma, Crystal structure prediction via particle-swarm optimization, Phys. Rev. B 82(9), 094116 (2010)

[25] B. Gao, P. Gao, S. Lu, J. Lv, Y. Wang, and Y. Ma, Interface structure prediction via CALYPSO method, Sci. Bull. (Beijing) 64(5), 301 (2019)

[26] A. P. Drozdov, M. I. Eremets, I. A. Troyan, V. Ksenofontov, and S. I. Shylin, Conventional superconductivity at 203 kelvin at high pressures in the sulfur hydride system, Nature 525(7567), 73 (2015)

[27] F. Peng, Y. Sun, C. J. Pickard, R. J. Needs, Q. Wu, and Y. Ma, Hydrogen clathrate structures in rare earth hydrides at high pressures: Possible route to room-temperature superconductivity, Phys. Rev. Lett. 119(10), 107001 (2017)

[28] Y. Nishihara, Y. Yamaguchi, M. Tokumoto, K. Takeda, and K. Fukamichi, Superconductivity and magnetism of bcc Cr–Ru alloys, Phys. Rev. B 34(5), 3446 (1986)

[29] A. J. Bradley, The crystal structures of the rhombohedral forms of selenium and tellurium, Lond. Edinb. Dublin Philos. Mag. J. Sci. 48(285), 477 (2009)

[30] G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54(16), 11169 (1996)

[31] G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59(3), 1758 (1999)

[32] P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50(24), 17953 (1994)

[33] J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77(18), 3865 (1996)

[34] H. J. Monkhorst and J. D. Pack, Special points for Brillouin-zone integrations, Phys. Rev. B 13(12), 5188 (1976)

[35] W. E. Pickett, S. C. Erwin, and E. C. Ethridge, Reformulation of the LDA+U method for a local-orbital basis, Phys. Rev. B 58(3), 1201 (1998)

[36] M. Cococcioni and S. de Gironcoli, Linear response approach to the calculation of the effective interaction parameters in the LDA+U method, Phys. Rev. B 71(3), 035105 (2005)

[37] A. Togo and I. Tanaka, First principles phonon calculations in materials science, Scr. Mater. 108, 1 (2015)

[38] S. Grimme, Semiempirical GGA-type density functional constructed with a long-range dispersion correction, J. Comput. Chem. 27(15), 1787 (2006)

[39] P. Blaha, K. Schwarz, F. Tran, R. Laskowski, G. K. H. Madsen, and L. D. Marks, WIEN2k: An APW+LO program for calculating the properties of solids, J. Chem. Phys. 152(7), 074101 (2020)

[40] K. Choudhary, Q. Zhang, A. C. Reid, S. Chowdhury, N. Van Nguyen, Z. Trautt, M. W. Newrock, F. Y. Congo, and F. Tavazza, Computational screening of high-performance optoelectronic materials using OptB88vdW and TB-mBJ formalisms, Sci. Data 5(1), 180082 (2018)

[41] F. Mouhat and F. X. Coudert, Necessary and sufficient elastic stability conditions in various crystal systems, Phys. Rev. B 90(22), 224104 (2014)

[42] Z. J. Wu, E. J. Zhao, H. P. Xiang, X. F. Hao, X. J. Liu, and J. Meng, Crystal structures and elastic properties of superhard IrN₂ and IrN₃ from first principles, Phys. Rev. B 76(5), 054115 (2007)

[43] T. Björkman, A. Gulans, A. V. Krasheninnikov, and R. M. Nieminen, van der Waals bonding in layered compounds from advanced density-functional first-principles calculations, Phys. Rev. Lett. 108(23), 235502 (2012)

[44] K. Nakada, H. Shimizu, and H. Yamada, Electronic structure and magnetism of CrTe with NiAs-type structure, J. Magn. Magn. Mater. 272–276, 464 (2004)

[45] I. Benabdelkader, H. Bendaoud, K. O. Obodo, L. Beldi, and B. Bouhafs, An ab initio study on the transition path of carbon dioxide at high pressure: Evidence for a new intermediate P4¯m2 phase, Comput. Condens. Matter 21, e00429 (2019)

Rights & permissions

Higher Education Press 2021