Structural distortion induced Dzyaloshinskii-Moriya interaction in monolayer CrI 3at van der Waals heterostructures Hongxing Liand Wei-Bing Zhangy

2025-05-02 0 0 970.29KB 7 页 10玖币

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Structural distortion induced Dzyaloshinskii-Moriya interaction in monolayer CrI3at

van der Waals heterostructures

Hongxing Li∗and Wei-Bing Zhang†

Hunan Provincial Key Laboratory of Flexible Electronic Materials Genome Engineering,

School of Physics and Electronic Sciences, Changsha University of

Science and Technology, Changsha 410114, People’s Republic of China

Guanghui Zhou

Department of Physics, Key Laboratory for Low-Dimensional

Quantum Structures and Quantum Control (Ministry of Education),

and Synergetic Innovation Center for Quantum Eﬀects and Applications,

Hunan Normal University, Changsha 410081, People’s Republic of China

The van der Waals (vdW) magnetic heterostructures provide ﬂexible ways to realize partic-

ular magnetic properties that possess both scientiﬁc and practical signiﬁcance. Here, by ﬁrst-

principles calculation, we predict strong Dzyaloshinskii-Moriya interactions (DMIs) by constructing

CrI3/Metal vdW heterostructures. The underlaying mechanisms are ascribed the large spin-orbital

coupling (SOC) of the I atom and the structural distortion in CrI3layer caused by interlayer in-

teraction. This is diﬀerent from the traditional way that deposit magnetic ﬁlms on substrate to

generate DMI, wherein DMI is dominated by interlayer hybridization and large SOC of substrates.

In addition, both Heisenberg exchange and magnetic anisotropy are modulated dramatically, such

as Heisenberg exchange is nearly doubled on Au(111), and the out-of-plane magnetism is enhanced

by 88% on Ir(111). Our work may provide a experimentally accessible strategy to induce DMI in

vdW magnetic materials, which will be helpful to the design of spintronics devices.

I. INTRODUCTION

Magnetism is the fundament of many modern tech-

nologies, such as magnetic storage. It is an interesting

research ﬁeld for a long history, and new magnetic phe-

nomena emerge continually [1]. Due to the Pauli exclu-

sion principle, and spin-orbital coupling (SOC) in solid,

several energy terms related to magnetism are developed,

including exchange interaction, magnetic anisotropy, and

so on, and the magnetic properties are determined by

synergetic eﬀects of these terms [2]. Since the magnetic

energy terms are related to both atomic and electronic

structures, by selecting elements and designing struc-

tures, particular magnetic properties can be achieved [3].

The magnetic interfaces are rather accessible artiﬁ-

cial structures. In 2000, Heinze et al. [4] deposited

Mn atomic monolayer on W(110) substrate, and a two-

dimensional (2D) antiferromagnetic structure is revealed.

In addition, because the inversion symmetry is broken in

interface, Dzyaloshinskii-Moriya interaction (DMI) may

arise. DMI is antisymmetric, and can result in nonlinear

magnetic structure, such as Skyrmions [3]. Skyrmion is a

kind of spin structure that is topologically protected and

behaves like particles, and can be applied in data storage

and logic technologies [5]. The Skyrmion lattice in 2D

system is ﬁrstly realized by depositing monolayer Fe ﬁlm

on Ir(111) surface [6].

At present, the major strategy to generate DMI is de-

positing 3dmagnetic atoms on heavy 5dnonmagnetic

∗lihx@csust.edu.cn

†zhangwb@csust.edu.cn

metal surface. Along with the experimental progress,

many theoretical works have been carried out to under-

standing the underlying mechanisms. Belabbes et al. [7]

systematically study a series of 3datoms on diﬀerent 5d

substrates. They found that the strength and chirality of

DMI are determined by occupations of 3dorbital and the

hybridization between 3dand 5dorbitals. Yang et al. [8]

elaborate that, in Co/Pt interface, despite magnetic mo-

ments are located at Cr site, the DMI is contributed by

heavy Pt atoms that adjacent to Co layer. These works

indicate that 3d-5dhybridization and the large SOC of

substrates play critical roles to generate DMI.

In 2017, intrinsic 2D ferromagnetic materials CrI3and

Cr2Ge2Te6are discovered successfully [9, 10], opening

a new chapter in the magnetic materials. CrI3layer is

ferromagnetic with out-of-plane magnetism. Both the

exchange interaction and magnetic anisotropy arise from

Cr-I-Cr superexchange path in which I atom has large

SOC strength [11, 12]. However, DMI is absent in CrI3

layer because the inversion symmetry. How to induce

DMI in CrI3and other 2D magnetic material is an in-

teresting topic now. Liu et al. [13] and Behera et al.

[14] theoretically induce DMI in CrI3layer by applying

perpendicular electric ﬁeld, but very large electric ﬁeld

is required. Xu et al. [15] substitute one I atom layer in

CrI3by Br(Cl) to fabricate Cr(I, X)3Janus monolayer,

strong DMI, as well as topological spin texture are pre-

dicted.

In this study, we overlay CrI3layer on the widely-

used substrates Ir(111), Pt(111) and Au(111). Note that

monolayer CrI3has been prepared on Au(111) success-

fully [16]. Surprisingly, strong DMI in CrI3/Metal is pre-

dicted by ﬁrst-principles calculations. The primary un-

arXiv:2210.10949v1 [cond-mat.mtrl-sci] 20 Oct 2022

FIG. 1. (a) The structural schematic diagram of CrI3/Metal. The red and green vectors indicate spin wave with opposite

chirality. The interlayer charge density diﬀerence for (b) CrI3/Ir(111), (c) CrI3/Pt(111), and (d) CrI3/Au(111). Pink and light

green represent charge accumulation and depletion, respectively. The isosurface is set to 0.002 e/˚

A3.

derlaying mechanisms are ascribed to the large SOC of I

atom and structural distortion in CrI3layer induced by

interlayer interactions. This is diﬀerent from the conven-

tional 3d/5dinterfaces, in which the DMI is dominated

by interlayer hybridization and large SOC of substrates.

Our results will provide a guideline for the design of spin-

tronics devices based on CrI3and other 2D magnetic ma-

terials.

II. CALCULATIONAL DETAILS

All our calculations are performed on Vienna ab initio

simulation package (VASP) based on the framework of

density functional theory [17, 18]. The interaction be-

tween electron and core is calculated by projected aug-

mented wave (PAW) method [19]. The generalized gradi-

ent approximation (GGA) with Perdew-Burke-Ernzerhof

(PBE) functional [20] is adapted to evaluate the en-

ergy exchange-correlation. An eﬀective Hubbard value

Ueff =2 eV is added to Cr 3dorbital within the scheme

proposed by Dudarev et al. [21]. The cutoﬀ energy of

the plane-wave basis is set to 400 eV. Brillouin zone sam-

pling is done by a 5×5×1 Γ-center k-point mesh [22]. The

convergence criteria for residual force and electronic step

are 0.01 eV/˚

A and 10−5eV, respectively. The DFT+D2

method is used to take the interlayer vdW force into ac-

count [23].

The heterostructures are constructed by overlaying

CrI32×2 supercell on Ir(111), Pt(111) and Au(111) 5×5

supercell with four atom layers, as shown in Fig. 1(a).

During structural relaxation, the bottom atom layer of

substrate is ﬁxed to simulate the bulk condition. A vac-

uum slab of 15 ˚

A is added to avoid the artiﬁcial in-

teraction between the periodic structures. The lattice

constant of CrI3is optimized to be 7.01 ˚

A. To match

the substrate, the CrI3monolayer should be compressed

(stretched) by -3.2%, -1.0% and 3.0% for Ir(111), Pt(111)

and Au(111), respectively.

III. RESULTS AND DISCUSSIONS

After structural relaxation, the I atoms that face to

substrates are pulled down, elongating the bottom Cr-

I bonds. The average Cr-I bond length is summarized

in Table I. We can ﬁnd there is considerable diﬀerence

between bottom and upper Cr-I bonds, and the largest

value is 0.13 ˚

A in CrI3/Ir(111), indicating remarkable

structural distortion in CrI3layer. This is diﬀerent from

the situation that putting CrI3onto 2D substrates, which

the crystal undergoes negligible deformation [24–26]. To

evaluate the interlayer interaction, adsorption energies

Ead are calculated by

Ead = (ECrI3+EM etal −ECrI3/Metal)/m (1)

where ECrI3,EM etal and ECrI3/Metal are the energy

of CrI3layer, substrate and CrI3/Metal heterostructure,

and mis number of unit cell of CrI3in CrI3/Metal with

a value of 4. The results are 967, 752, and 400 meV for

CrI3/Ir(111), CrI3/Pt(111), and CrI3/Au(111), respec-

tively.

TABLE I. The calculated structural parameters for

CrI3/Metal heterostructures.

CrI3/Ir(111) CrI3/Pt(111) CrI3/Au(111)

d(˚

A) 2.67 2.61 3.05

Bottom Cr-I (˚

A) 2.86 2.81 2.83

Upper Cr-I (˚

A) 2.73 2.74 2.77

∆l(˚

A) 0.13 0.07 0.06

Ead (meV) 967 752 400

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StructuraldistortioninducedDzyaloshinskii-MoriyainteractioninmonolayerCrI3atvanderWaalsheterostructuresHongxingLiandWei-BingZhangyHunanProvincialKeyLaboratoryofFlexibleElectronicMaterialsGenomeEngineering,SchoolofPhysicsandElectronicSciences,ChangshaUniversityofScienceandTechnology,Changsha410114,P...

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Structural distortion induced Dzyaloshinskii-Moriya interaction in monolayer CrI 3at van der Waals heterostructures Hongxing Liand Wei-Bing Zhangy

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