First-Principles Study on Two-Dimensional Monolayer TiCuX2 (X=S, Se, Te)

doi:10.16553/j.cnki.issn1000-985x.2025.0059

Abstract

Abstract: In order to explore the influence of the number of transition metal atoms on the magnetic properties of two-dimensional magnetic materials， and to find magnetic two-dimensional materials with excellent properties， based on density functional theory， with the aid of first-principles calculation software VASP， a systematic theoretical study of two-dimensional monolayer TiCuX₂ （X=S， Se， Te） was carried out. The electronic structure， stability， magnetism， atomic exchange interaction and Curie temperature of three materials of TiCuX₂ （X=S， Se， Te） were calculated. The stability of three materials are proved by the calculation results of formation energy and phonon spectrum. The electronic structure and magnetic calculation analysis show that the three materials exhibit semi metallic ferromagnetism except TiCuX₂ which is magnetic. In addition， based on PBE+U and hybrid functional theory， a deeper theoretical study of the three materials were carried out in this paper， and the results show that the magnetic moments of three structures are all integer magnetic moments of 1 μB， and three materials remain magnetic. Finally， based on the Heisenberg model and the exchange of mutual parameters， the Curie temperatures of three structures were calculated by Monte Carlo method.

Key words: first-principle; two-dimensional magnetic material; TiCuX₂; electronic structure; Curie temperature

CLC Number:

O469

LIANG Zhiqiang, CHANG Rong. First-Principles Study on Two-Dimensional Monolayer TiCuX₂ (X=S, Se, Te)[J]. Journal of Synthetic Crystals, 2026, 55(1): 142-150.

Figures/Tables 11

Fig.1 Top （a） and side （b） views of two-dimensional monolayer TiCuX2 （X=S， Se， Te）

Table 1 Lattice parameter a， atomic bond length， total energy Etot， and formation energy Ef of all structures

Structure	a/Å	Bond length/Å			$E t o t$ /eV	$E f$ /（eV·atom^-1）
Structure	a/Å	Ti—Cu	Ti—X （X=S， Se， Te）	Cu—X （X=S， Se， Te）	$E t o t$ /eV	$E f$ /（eV·atom^-1）
TiCuS₂	3.949	2.792	2.363	2.363	-23.159	-1.472
TiCuSe₂	4.044	2.859	2.493	2.493	-21.404	-1.107
TiCuTe₂	4.157	2.939	2.687	2.687	-19.483	-0.740

Table 1 Lattice parameter a， atomic bond length， total energy Etot， and formation energy Ef of all structures

Structure	a/Å	Bond length/Å			$E t o t$ /eV	$E f$ /（eV·atom^-1）
Structure	a/Å	Ti—Cu	Ti—X （X=S， Se， Te）	Cu—X （X=S， Se， Te）	$E t o t$ /eV	$E f$ /（eV·atom^-1）
TiCuS₂	3.949	2.792	2.363	2.363	-23.159	-1.472
TiCuSe₂	4.044	2.859	2.493	2.493	-21.404	-1.107
TiCuTe₂	4.157	2.939	2.687	2.687	-19.483	-0.740

Fig.2 Phonon spectra of two-dimensional monolayer TiCuX2 （X=S， Se， Te）

Table 2 Elastic constant Cij， isotropic shear modulus G， elastic modulus E and Poisson ratio ν of all structures

Structure	C₁₁/GPa	C₁₂/GPa	C₆₆/GPa	$G$ /GPa	$ν$	$E$ /GPa
TiCuS₂	47.908	12.798	26.786	43.305	0.342	56.917
TiCuSe₂	42.042	8.074	21.057	30.515	0.217	45.768
TiCuTe₂	31.035	4.755	14.538	17.521	0.396	30.307

Table 2 Elastic constant Cij， isotropic shear modulus G， elastic modulus E and Poisson ratio ν of all structures

Structure	C₁₁/GPa	C₁₂/GPa	C₆₆/GPa	$G$ /GPa	$ν$	$E$ /GPa
TiCuS₂	47.908	12.798	26.786	43.305	0.342	56.917
TiCuSe₂	42.042	8.074	21.057	30.515	0.217	45.768
TiCuTe₂	31.035	4.755	14.538	17.521	0.396	30.307

Fig.3 Elastic modulus， shear modulus and Poisson ratio of monolayer TiCuX2 （X=S， Se， Te）

Fig.4 Electronic band of PBE/PBE+U/HSE of monolayer TiCuX2 （X=S， Se， Te）

Fig.5 Density of state of monolayer TiCuX2 （X=S， Se， Te）

Table 3 Atomic magnetic moments， total magnetic moments Mt， magnetic anisotropy energy MAE， and Curie temperature Tc of all structures

Structure	Atomic magnetic moment/µB			$M t$ /µB	MAE/eV	T_c/K
Structure	Ti	Cu	X	$M t$ /µB	MAE/eV	T_c/K
TiCuS₂	0.916	-0.029	-0.030	1.000	9.071	140
TiCuSe₂	0.941	-0.030	-0.032	1.000	79.832	250
TiCuTe₂	0.834	-0.007	-0.033	1.000	109.25	180

Table 3 Atomic magnetic moments， total magnetic moments Mt， magnetic anisotropy energy MAE， and Curie temperature Tc of all structures

Structure	Atomic magnetic moment/µB			$M t$ /µB	MAE/eV	T_c/K
Structure	Ti	Cu	X	$M t$ /µB	MAE/eV	T_c/K
TiCuS₂	0.916	-0.029	-0.030	1.000	9.071	140
TiCuSe₂	0.941	-0.030	-0.032	1.000	79.832	250
TiCuTe₂	0.834	-0.007	-0.033	1.000	109.25	180

Fig.6 MAE of monolayer TiCuX2 （X=S， Se， Te）

Fig.7 Atomic exchange interactions between monolayer TiCuX2 （X=S， Se， Te）

Fig.8 Variation of magnetic susceptibility and magnetic moment of monolayer TiCuX2 （X=S， Se， Te）

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First-Principles Study on Two-Dimensional Monolayer TiCuX₂ (X=S, Se, Te)

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