Two-dimensional rare-earth Janus 2 H-GdXYXYCl Br I X6Y monolayers Bipolar ferro-magnetic semiconductors with high Curie temperature and large valley polarization Cunquan Li1and Yukai An1

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Two-dimensional rare-earth Janus 2H-GdXY (X,Y=Cl, Br, I, X6=Y) monolayers: Bipolar

ferro-magnetic semiconductors with high Curie temperature and large valley polarization

Cunquan Li1and Yukai An1, ∗

1Key Laboratory of Display Materials and Photoelectric Devices,

Ministry of Education, Tianjin Key Laboratory for Photoelectric Materials and Devices,

National Demonstration Center for Experimental Function Materials Education,

School of Material Science and Engineering, Tianjin University of Technology, Tianjin, 300384, China

Two-dimensional (2D) ferromagnetic semiconductors show great interest due to their potential applications

for the nanoscale electronic devices. In this work, the Janus 2H-GdXY (X,Y=Cl, Br, I, X6=Y) monolayers with

rare-earth element Gd (4 f7+5d1) are predicted by the ﬁrst-principles calculations. Small exfoliation energy

of less than 0.25 J/m2and excellent dynamical/thermal stabilities can be conﬁrmed for the Janus 2H-GdXY

monolayers, which exhibit the bipolar magnetic semiconductor character with high Curie temperatures above

260 K and large spin-orbit coupling effect, and can be further transformed into the half-semiconductor phase

under proper tensile strains (5-6%). In addition, the in-plane magnetic anisotropy can be observed in the 2H-

GdICl and 2H-GdIBr monolayers. On the contrary, the 2H-GdBrCl monolayer exhibits perpendicular magnetic

anisotropy character, which originates from the competition between Gd-p/dand halogen atom-porbitals. Cal-

culated valley optical actions of the Janus 2H-GdXY monolayers exhibit distinguished valley-selective circular

dichroisms, which is expected to realize the special valley excitation by polarized light. Spontaneously valley-

Zeeman effect in the valance band for the Janus 2H-GdXY monolayers induces a giant valley splitting of 60-120

meV, which is also robust against various external biaxial strains. Tunable valley degree of freedom in the Janus

2H-GdXY systems is very necessary for encoding and processing information.

I. INTRODUCTION

Two-dimensional (2D) materials show an increasing inter-

est owing to their broad application prospects in nanoscale

electronic devices. It has been proved by the Mermin-Wagner

theorem that 2D magnetic ordering can be prohibited due to

the thermal ﬂuctuations [1]. As a breakthrough development,

intrinsic ferromagnetic (FM) ordering was experimentally dis-

covered in the CrI3[2] and VI3[3] monolayers, which ex-

hibit the Curie temperatures (Tc) of 45 K and 49 K, respec-

tively. These studies attract much attention and further stim-

ulate in looking for 2D magnetic materials at the nanoscale.

Until now, signiﬁcant progress has been made with 2D ma-

terials with magnetic ordering, while the rare intrinsic semi-

conducting ferromagnetism and low Tclimit their potential

applications in spintronic devices [4–6]. The Tcof 2D materi-

als can be effectively enhanced by applying the charge carrier

doping [7], biaxial strain [8], and external electric ﬁelds [9],

etc. However, these methods are still not the ideal solutions

for the practical applications in spintronics.

Recently, transition metal dichalcogenides chlorides

(TMDs) monolayers with hexagonal structure own a pair of

non-equivalent energy valleys at the Dirac points of the Bril-

louin zone, which can be excited using left- or right-handed

light and attract a great deal of attention. The valley, which

indicates the maximum of valence band or minimum of con-

duction band, is a new degree of freedom of carriers besides

the charge and spin. The two inequivalent valleys constitute

a binary index for low energy carriers and this degree of free-

dom can be encoded and manipulated as an information car-

rier in valleytronics [10]. Inspired with the analysis above,

∗ykan@tjut.edu.cn

searching for intrinsic ferro-valley (ferromagnetic materials

with spontaneous valley polarization) [11] materials with high

Tcand large valley polarization are necessary for the candi-

dates of valleytronics. In order to realize this, it is vital to

choose a system with special electrons and orbitals. Recently,

rare-earth element-based systems, especially for the Gd ele-

ment, have become a hot topic of research. In fact, as early as

1965, Mee et al [12] ﬁrstly synthesized the block GdI2with

van der Waals structure. Very recently, GdI2monolayer with

high Tcof 241 K and sizable MAE was ﬁrstly predicted by

Wang et al [13], and its large valley polarization (149 meV)

and robustness to external biaxial strain were investigated by

Feng et al [14]. Immediately after, the GdX2(X=I, F, Cl, Br)

monolayers [15–17] were further predicted, especially that the

GdCl2monolayer shows high Tcof about 224 K and large

perpendicular magnetic anisotropy (PMA) character. Exper-

imentally, Janus (special types of materials which have two

faces at the nanoscale) TMDs monolayers has been synthe-

sized successfully in special conditions [18,19]. And, based

on DFT calculations, some magnetic Janus monolayers, such

as FeClBr [20], MnSSe [21], Cr2X3S3(X=Br, I) monolay-

ers [22], etc., have been predicted. Due to the super-/direct-

exchange interactions and spin-orbit coupling (SOC) in these

2D magnetic Janus systems, an intrinsic valley polarization

can be observed in both valance and conduction bands. Fur-

thermore, for the Janus 2H-GdClF monolayer with ferromag-

netic ordering, it is noted that the tunable valley polarization

can be observed and driven by external biaxial strains [23]. In

light of these key factors about the systems with Gd element

mentioned above, the Janus 2H-GdXY monolayers can be ex-

pected as a ferrovalley material with large valley polarization

and are very likely to be synthesized by the surface replace-

ment technology [18].

In this work, the stability, valley polarization and magnetic

anisotropy of Janus 2H-GdXY monolayers are systematically

arXiv:2210.05273v2 [cond-mat.mtrl-sci] 24 Mar 2023

studied by the DFT calculations. All Janus 2H-GdXY mono-

layers show FM semiconductor characters with high Tcbe-

yond 260 K. Interestingly, only the 2H-GdBrCl monolayer

possess the PMA behavior, while the 2H-GdICl and 2H-

GdIBr monolayers exhibit the in-plane magnetic anisotropy

(IMA) character. The competition between Gd atom-p/dor-

bitals and halogen atom-porbital can result in a transition of

easy axis direction from the [001] to [100] plane for the Janus

2H-GdXY monolayers. A spontaneous and robust valley po-

larization is observed, which can be effectively adjusted by

the external biaxial strains.

II. COMPUTATIONAL DETAILS

All density functional theory (DFT) calculations are per-

formed using the projected augmented wave (PAW) [24,25]

approach as implemented in the Vienna ab-initio package

(VASP) [26,27]. Considering the exchange and correlation

functional interactions, the Perdew-Burke-Ernzerhof (PBE)

within generalized gradient approximation (GGA) is applied

[28]. The van der Waals (vdW) correction is considered for

the bulk GdXY using the Grimme (DFT-D3) method [29]. The

plane wave cut-off energy is set to 500 eV and a vacuum space

of 18 Å is applied along the z-axis [001] direction to avoid the

interactions between adjacent layers. The crystal structure of

the Janus 2H-GdXY monolayers is completely relaxed until a

force of less than 0.01 eV/Å per atom and an energy differ-

ence of less than 10−6eV between two convergence steps is

observed. The Brillouin zone is sampled using converged Γ-

centered k-meshes with a density of 144 k-points (12×12×1)

for structural relaxation and 576 k-points (24×24×1) for the

electronic calculations [30]. The electron conﬁgurations in-

cluding 5s25p64f75d16s2for Gd [31], 4s24p5for Br, 3s23p5

for Cl, and 5s25p5for I atom are considered. The SOC ef-

fect is included in the calculations to investigate electronic,

magnetic and valley-related properties of the Janus 2H-GdXY

monolayers. The rotationally invariant local spin density ap-

proximation (LSDA)+Hubbard (U) method is employed to

treat the strongly correlated corrections to the Gd 4 felec-

trons [32] and the corresponding on-site U/exchange inter-

action Jparameters is set at 9.20 eV/1.20 eV [13,33]. The

Phonon dispersion spectrum of the Janus 2H-GdXY mono-

layers are obtained by the PHONOPY code [34,35] using a

2×2×1 supercell. Ab initio molecular dynamic (AIMD) sim-

ulations [36] adopt the NVT ensemble [37] based on the Nosé-

Hothermostat [38] controlled the temperature of systems at

300 K with a total of 8.0 ps at 2.0 f s per time step. The

VASPKIT code is used to process some of the VASP data [39].

The Tcof the Janus 2H-GdXY monolayers are estimated by

using the Monte Carlo simulation package MCSOLVER [40]

based on the Wolff algorithm. The Berry curvature and opti-

cal properties are calculated based on Fukui’s method [41] by

VASPBERRY code which is developed by Prof. Kim [42].

III. RESULTS AND DISCUSSION

Figure 1(a) displays the crystal structure of the Janus 2H-

GdXY monolayers. Clearly, the loss of reﬂection symme-

try of Gd atom reduces the symmetry of the systems. The

optimized lattice constants for the 2H-GdBrCl, 2H-GdICl,

and 2H-GdIBr monolayers are 3.835, 3.96, and 4.019 Å, re-

spectively. The FM and anti-ferromagnetic (AFM) ordering

of crystal structures for the Janus 2H-GdXY monolayers is

shown in Fig. 1(b) and 1(c). The ferromagnetic stability ener-

gies (∆E=EAFM−EFM) between the FM and AFM ordering

for the 2H-GdBrCl, 2H-GdICl, and 2H-GdIBr monolayers

are 165.2, 154.9, and 152.2 meV, respectively, strongly sug-

gesting the existence of FM coupling among three systems.

Figure S1 of the Supplemental Material (SM) [43] shows the

spin density images of the Janus 2H-GdXY monolayers. One

can see that the magnetic moments are mainly contributed by

the Gd and Cl (Br) atoms for the Janus 2H-GdICl (2H-GdIBr)

monolayers and by all Gd, Cl and Br atoms for the Janus 2H-

GdBrCl monolayer, suggesting that the valence electrons tend

to gather around the Cl (Br) atom with stronger electroneg-

ativity. In order to prove the stability of Janus 2H-GdXY

monolayers, the calculations of phonon dispersion and AIMD

simulation are carried out. As shown in Fig. 1(d)-1(f), the

phonon dispersions exhibit the positive value in the whole

Brillouin zone, strongly suggesting the dynamical stability for

the Janus 2H-GdXY monolayers. In addition, with time evo-

lution, the small ﬂuctuations (about ±1 eV) of free energy, the

total magnetic moment is kept at about 128.0 µBand the orig-

inal conﬁguration does not show large distortion have implied

a good thermal stability of the Janus 2H-GdXY monolayers

[Fig. S2(a)-S2(c) of the SM [43]]. To estimate the possibility

of mechanical exfoliation, the exfoliation energy of the Janus

2H-GdXY monolayers is calculated in four-layer slab models

with AB-stacking [44] [Fig. S3(a) of the SM [43]] from their

layered bulk crystals. Considering the small value of sepa-

ration distance, the exfoliation process is performed with the

ﬁxed atomic positions. As shown in Fig. S3(b)-S3(d) of the

SM [43], the increase of separation distance (d−d0) leads

to an obvious increase in the energy differences ∆E=Ed−Ed0,

which converge to 0.232, 0.243, and 0.239 J/m2, respectively,

for the Janus 2H-GdBrCl, 2H-GdICl, and 2H-GdIBr mono-

layers, respectively. These cleavage energies are remarkably

lower than the measured value (0.36 J/m2) for the graphite

[45], which can be further conﬁrmed by the variation of cleav-

age strength (the ﬁrst-order derivative of cleavage energy).

This means that the Janus 2H-GdXY monolayers are easily

to exfoliate experimentally.

The band structures of the Janus 2H-GdXY monolayers

without considering SOC are shown in in Fig. 2(a)-2(c). The

energies at the K and K0valleys are equal, suggesting that

the valley splitting does not appear without considering SOC.

The typical bipolar magnetic semiconductor character [BMS:

the valence and conduction bands possess opposite spin po-

larization when approaching the Fermi level (EF)] [46] with

an indirect band gap can be observed, where the valence band

maximum (VBM) located at the Γpoint and the conductor

band minimum (CBM) located at the M point have the oppo-

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Two-dimensionalrare-earthJanus2H-GdXY(X,Y=Cl,Br,I,X6=Y)monolayers:Bipolarferro-magneticsemiconductorswithhighCurietemperatureandlargevalleypolarizationCunquanLi1andYukaiAn1,1KeyLaboratoryofDisplayMaterialsandPhotoelectricDevices,MinistryofEducation,TianjinKeyLaboratoryforPhotoelectricMaterialsandDe...

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Two-dimensional rare-earth Janus 2 H-GdXYXYCl Br I X6Y monolayers Bipolar ferro-magnetic semiconductors with high Curie temperature and large valley polarization Cunquan Li1and Yukai An1

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