Intrinsic multiferroic semiconductors with magnetoelastic coupling: two-dimensional MoTe<i>X</i> (<i>X</i> = F, Cl, Br, I) monolayers

Gao Jin-Wei; Chen Lu; Li Xu-Hong; Shi Jun-Qin; Cao Teng-Fei; Fan Xiao-Li

doi:10.7498/aps.73.20240829

Abstract

Two-dimensional materials with both ferromagnetism and ferroelasticity present new possibilities for developing spintronics and multifunctional devices. These materials provide a novel method for controlling the direction of the magnetization axis by switching the ferroelastic state, achieving efficient and low-power operation of magnetic devices. Such properties make them a promising candidate for the next generation of non-volatile memory, sensors, and logic devices. By performing the first-principles calculations, the ferromagnetism, ferroelasticity, and magnetoelastic coupling in MoTeX (X = F, Cl, Br, I) monolayers are systematically investigated. The results indicate that the MoTeX monolayers are intrinsic semiconductors holding both ferromagnetism and ferroelasticity. The pronounced in-plane magnetic anisotropy suggests that the MoTeX monolayers can resist thermal disturbances and maintain long-range magnetic order. The Curie temperatures of MoTeX monolayers are 144.75 K, 194.55 K, 111.45 K, and 92.02 K, respectively. Our calculations show that the four MoTeX monolayers possess two stable ferroelastic states, with their easy magnetization axes perpendicular to each other. The ferroelastic transition barriers between the two ferroelastic states of MoTeF, MoTeCl, MoTeBr, MoTeI monolayers are 0.180 eV/atom, 0.200 eV/atom, 0.209 eV/atom, and 0.226 eV/atom, respectively, with their corresponding reversible strains of 54.58%, 46.32%, 43.06%, and 38.12%. These values indicate the potential for reversible magnetic control through reversible ferroelastic transition at room temperature. Owing to their unique magnetoelastic coupling properties, MoTeX monolayers exhibit the ability to control reversible magnetization axis at room temperature, laying the foundation for the development of highly controllable and stable spintronic devices.

Keywords:

Authors and contacts

Center of Advanced Lubrication and Seal Materials, School of Material Science and Engineering, Northwestern Polytechnic University, Xi’an 710072, China

Corresponding author: Fan Xiao-Li, xlfan@nwpu.edu.cn

Funds: Project supported by the Key Program of the Natural Science Fund of Shaanxi Province, China (Grant No. 2021JZ-07), the Leading Talents in Scientific and Technological Innovation Program of Shaanxi Province, China, and the Innovation Capability Support Program of Shaanxi Province, China (Grant No. 2024RS-CXTD-30).

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References

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Cited By

图 1 MoTeX (X = F, Cl, Br, I)单层膜的顶视图(a)和侧视图(b). J₁, J₂和J₃分别是最邻近的第一、第二和第三个Mo原子之间的层内磁交换参数; (c)铁磁(FM)俯视图; (d)— (f) MoTeX单层膜的三种反铁磁(AFM)构型. 橙色、蓝色和绿色的球分别代表Mn, O和X原子

Figure 1. (a) Top and (b) side views of the MoTeX (X = F, Cl, Br, I) monolayers. J₁, J₂ and J₃ are the intralayer magnetic exchange parameters between the first, second and third nearest neighboring Mo atoms, respectively; (c) top views of ferromagnetic (FM); (d)–(f) three antiferromagnetic (AFM) configurations of MoTeX monolayers. The orange, blue and green balls represent Mn, O and X atoms, respectively.

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图 2 单层MoTeX (X = F, Cl, Br, I)的声子谱　(a) MoTeF; (b) MoTeCl; (c) MoTeBr; (d) MoTeI. (e) 分子动力学模拟开始和结束时原子结构的俯视图和侧视图. (f) MoTeF, MoTeCl, MoTeBr和MoTeI单层膜在300 K, 5 ps下的AIMD模拟过程中总能量的波动

Figure 2. Phonon spectra of MoTeX (X = F, Cl, Br, I) monolayers: (a) MoTeF; (b) MoTeCl; (c) MoTeBr; (d) MoTeI. (e) Top and side views of atomic structures at the start and end of molecular dynamics (MD) simulation. (f) Evolution of total energies of MoTeF, MoTeCl, MoTeBr and MoTeI monolayers during AIMD simulation at 300 K for 5 ps.

DownLoad: Full-Size Img PowerPoint

图 3 (a) MoTeF, (b) MoTeCl, (c) MoTeBr, (d) MoTeI单层膜杨氏模量随面内角的变化; (e) MoTeF, (f) MoTeCl, (g) MoTeBr, (h) MoTeI单层膜泊松比随面内角的变化

Figure 3. Variations of Young’s modulus of (a) MoTeF, (b) MoTeCl, (c) MoTeBr, and (d) MoTeI monolayers with respect to the in-plane angle. Variations of Poisson’s ratio of (e) MoTeF, (f) MoTeCl, (g) MoTeBr and (h) MoTeI monolayers with respect to the in-plane angle.

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图 4 单层MoTeX (X = F, Cl, Br, I)的能带结构与态密度图　(a) MoTeF; (b) MoTeCl; (c) MoTeBr; (d) MoTeI. 费米能级用0 eV的虚线表示. 红色和蓝色曲线分别表示自旋向上和自旋向下通道. 单层MoTeX (X = F, Cl, Br, I)的总态密度(TDOS)和投影态密度　(e) MoTeF; (f) MoTeCl; (g) MoTeBr; (h) MoTeI

Figure 4. Electronic band structures of MoTeX (X = F, Cl, Br, I) monolayers: (a) MoTeF; (b) MoTeCl; (c) MoTeBr; (d) MoTeI. Fermi level is denoted by the dashed line at 0 eV. Red and blue curves represent the spin up and spin down channels, respectively. Total density of states (TDOS) and project density of states of MoTeX (X = F, Cl, Br, I) monolayers: (e) MoTeF; (f) MoTeCl; (g) MoTeBr; (h) MoTeI monolayers.

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图 5 MoTeX (X = F, Cl, Br, I)单层膜的投影态密度图　(a) MoTeF; (b) MoTeCl; (c) MoTeBr; (d) MoTeI

Figure 5. Projected electronic band structures of MoTeX (X = F, Cl, Br, I) monolayers: (a) MoTeF; (b) MoTeCl; (c) MoTeBr; (d) MoTeI.

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图 6 MoTeX (X = F, Cl, Br, I)单层的磁矩和比热随温度的变化　(a) MoTeF; (b) MoTeCl; (c) MoTeBr; (d) MoTeI

Figure 6. Magnetic moment and specific heat as a function of temperature for MoTeX (X = F, Cl, Br, I) monolayers: (a) MoTeF; (b) MoTeCl; (c) MoTeBr; (d) MoTeI.

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图 7 MoTeX (X = F, Cl, Br, I)单层磁各向异性能　(a) MoTeF; (b) MoTeCl; (c) MoTeBr; (d) MoTeI

Figure 7. Angular dependence of the magnetic anisotropy energy for the MoTeX (X = F, Cl, Br, I) monolayers along the xoy, yoz, and xoz planes: (a) MoTeF; (b) MoTeCl; (c) MoTeBr; (d) MoTeI.

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图 8 (a) MoTeX (X = F, Cl, Br, I)单层的铁弹性转换和磁弹性耦合示意图, 铁弹性开关将使易磁化轴旋转90º, 如红色箭头所示; (b) MoTeX单层膜沿铁弹性过渡路径的相对能量

Figure 8. (a) Schematic diagram showing the ferroelastic switching and coupling between magnetism and ferroelasticity for the MoTeX (X = F, Cl, Br, I) monolayers, the ferroelastic switching will rotate the easy magnetization axis by 90º, as illustrated by the red arrows; (b) relative energy of the MoTeX monolayers along the ferroelastic transition path.

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表 1 MoTeX (X = F, Cl, Br, I)的晶格常数、可逆应变、反铁磁构型相对铁磁构型的能量

Table 1. Lattice constant, reversible strain and the relative energies of FM and possible AFM configurations of MoTeX monolayers. The energy of FM configuration is a reference.

ML	a/Å	b/Å	(\|b\|/\|a\|–1)×100%	E_FM/(meV·Mo^–1)	E_AFM1/(meV·Mo^–1)	E_AFM2/(meV·Mo^–1)	E_AFM3/(meV·Mo^–1)
MoTeF	3.704	5.726	54.58	0	283	270	552
MoTeCl	3.906	5.715	46.31	0	306	301	509
MoTeBr	3.992	5.710	43.04	0	361	334	453
MoTeI	4.124	5.696	38.11	0	390	378	397

DownLoad: CSV

表 2 MoTeX (X = F, Cl, Br, I)单层膜的弹性模量和力学性能

Table 2. Elastic modulus and mechanical properties of MoTeX (X = F, Cl, Br, I) monolayers.

ML	C₁₁/(N·m^–1)	C₁₂/(N·m^–1)	C₂₂/(N·m^–1)	C₆₆/(N·m^–1)	Y_max/(N·m^–1)	Y_min/(N·m^–1)	μ_max	μ_min
MoTeF	63.412	8.814	89.320	13.750	88.095	41.059	0.504	0.099
MoTeCl	54.424	5.000	86.926	13.809	86.467	39.404	0.448	0.058
MoTeBr	50.724	5.294	84.128	13.564	83.576	38.237	0.436	0.063
MoTeI	49.090	5.157	81.298	13.273	80.756	37.283	0.432	0.063

DownLoad: CSV

表 3 MoTeX (X = F, Cl, Br, I)单层膜交换作用路径参数. d₁, d₂和d₃是第一, 第二和第三近邻Mo原子之间的距离, θ₁, θ₂和θ₃是第一, 第二和第三近邻Mo原子与Te原子之间的夹角

Table 3. Parameters along the exchange interaction path of MoTeX (X = F, Cl, Br, I) monolayers. d₁, d₂ and d₃ are the distances between the first, second and third nearest neighboring Mo atoms, and θ₁, θ₂ and θ₃ are the angles formed between the first, second and third nearest neighboring Mo atoms and Te atoms.

ML	d_1(Mo-Mo)/Å	d_2(Mo-Mo)/Å	d_3(Mo-Mo)/Å	θ_1(Mo-Te-Mo)	θ_2(Mo-Te-Mo)	θ_3(Mo-Te-Mo)
MoTeF	3.70	4.24	5.72	81.94	95.85	164.47
MoTeCl	3.90	4.29	5.71	87.06	96.79	161.32
MoTeBr	3.99	4.29	5.71	89.18	96.83	160.74
MoTeI	4.12	4.28	5.69	92.40	97.05	159.54

DownLoad: CSV

表 4 MoTeX (X = F, Cl, Br, I)单层的磁交换常数与磁晶各向异性能

Table 4. Magnetic exchange constant and magnetocrystalline anisotropy energy of MoTeX (X = F, Cl, Br, I) monolayer

ML	$ {J}_{1} $/eV	$ {J}_{2} $/eV	$ {J}_{3} $/eV	E[100]/(μeV·atom^–1)	E[010]/(μeV·atom^–1)	E[001]/(μeV·atom^–1)	T_c/K
MoTeF	0.14	7.72	–0.22	0	487	782	114
MoTeCl	1.85	6.65	–1.70	0	613	518	195
MoTeBr	3.79	6.25	–5.31	0	91	430	111
MoTeI	4.76	6.08	–3.93	0	–282	165	92

DownLoad: CSV

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[19]	Akgenc B, Vatansever E, Ersan F 2021 Phys. Rev. Mater. 5 83403 Google Scholar
[20]	Abdullahi Y Z, Ersan F, Vatansever Z D, Akturk E, Akturk O U 2020 J. Appl. Phys. 128 113903 Google Scholar
[21]	Vaclavkova D, Delhomme A, Faugeras C, Potemski M, Bogucki A, Suffczynski J, Kossacki P, Wildes A R, Gremaud B, Saul A 2020 2D Mater. 7 035030 Google Scholar
[22]	Xiao G, Xiao W Z, Feng Y X, Rong Q Y, Chen Q 2023 Nanoscale 15 17963 Google Scholar
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[26]	Xu S, Jia F, Zhao G, Wu W, Ren W 2021 J. Mater. Chem. C 9 9130 Google Scholar
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[33]	Blochl P 1994 Phys. Rev. B 50 17953 Google Scholar
[34]	Kresse G, Furthumller J 1996 Phys. Rev. B 54 11169 Google Scholar
[35]	Blochl P E, Forst C J, Schimpl J 2003 Bull. Mater. Sci. 26 33 Google Scholar
[36]	Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188 Google Scholar
[37]	Togo A, Oba F, Tanaka I 2008 Phys. Rev. B 8 134106 Google Scholar
[38]	Togo A, Tanaka I 2015 Scr. Mater. 108 1 Google Scholar
[39]	Cadelano E, Palla P L, Giordano S, Colombo L 2010 Phys. Rev. B 82 235414 Google Scholar
[40]	Kanamori J 1960 J. Appl. Phys. 31 S14 Google Scholar
[41]	Goodenough J B 1955 Phys. Rev. 100 564 Google Scholar
[42]	Dang N T, Kozlenko D P, Lis O N, Kichanov S E, Lulin Y V, Golosova N O, Savenko B N, Duong D L, Phan T L, Tran T A, Phan M H 2023 Adv. Sci. 10 2206842 Google Scholar
[43]	Miao N, Xu B, Zhu L, Zhou J, Sun Z 2018 J. Am. Chem. Soc. 140 2417 Google Scholar
[44]	Gao Z, Wang Y, Gao J, Cui Z, Zhang X, Shi J, Fan X 2022 Comput. Mater. Sci. 213 111611 Google Scholar
[45]	Henkelman G, Uberuaga B P, Jonsson H 2000 J. Chem. Phys. 113 9901 Google Scholar
[46]	Wang H, Li X, Sun J, Liu Z, Yang J 2017 2D Mater. 4 045020 Google Scholar
[47]	Pang Z, Ji W, Zhang C, Wang P, Li P 2021 Chem. Phys. Lett. 763 138163 Google Scholar
[48]	Zhang S, Liu B 2018 Nanoscale. 10 5990 Google Scholar
[49]	Li W, Li J 2016 Nat. Commun. 7 10843 Google Scholar

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Intrinsic multiferroic semiconductors with magnetoelastic coupling: two-dimensional MoTeX (X = F, Cl, Br, I) monolayers

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Corresponding author: Fan Xiao-Li, xlfan@nwpu.edu.cn

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Intrinsic multiferroic semiconductors with magnetoelastic coupling: two-dimensional MoTeX (X = F, Cl, Br, I) monolayers

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Corresponding author: Fan Xiao-Li, xlfan@nwpu.edu.cn

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