# Spin-Filter Magnetic Tunnel Junctions Based on A-Type Antiferromagnetic CrSBr with Giant Tunnel Magnetoresistance

^{1}

^{2}

^{*}

## Abstract

**:**

^{7}% and 10

^{5}% with two-, four- and six-layer CrSBr at zero bias, respectively. Subsequently, we systematically analyze the transmission spectra, transmission eigenstates, electrostatic potentials, band structures and local density of states to elaborate the underlying mechanism of the TMR effect in the sf-MTJs. Our results indicate the great prospect of CrSBr-based sf-MTJs in applications, and provide guidance for futural experiments.

## 1. Introduction

_{2}Ge

_{2}Te

_{6}[16], CrI

_{3}[17], Fe

_{3}GeTe

_{2}[18] etc. [19]—has opened a promising avenue to establish 2D MTJs. Two-dimensional vertical MTJs are a kind of 2D heterojunction which can be epitaxially grown on a substrate layer by vdW forces. They have better interface quality and a smaller size than traditional MTJs with MgO [20], AlO

_{x}barrier [21] and bulk FM layers.

_{3}multilayers were recently adopted to design and fabricate sf-MTJs in laboratory [28]. The two-dimensional CrI

_{3}multilayer has an A-type magnetic order [29], which means that its intralayer coupling is FM while its interlayer coupling is antiferromagnetic (AFM) [30]. Figure 2a presents an A-type AFM bilayer with an intralayer FM order but interlayer AFM coupling, where the two layers have opposite magnetic moments. A large enough external in-plane (out-of-plane) magnetic field can switch the interlayer coupling from an interlayer AFM to FM order [28], meaning that the magnetization changes from antiparallel to parallel, as shown in Figure 2b (the magnetization in a large in-plane magnetic field) and Figure 2c (the magnetization in a large out-of-plane magnetic field). As a result, we can employ the A-type AFM multilayer instead of FM layers with different coercivities to design sf-MTJ. Of course, the A-type layers must be insulators or semiconductors because they also work as tunnel barriers.

_{3}sf-MTJ [28], which is an order of magnitude larger than the TMR in MgO MTJs [25,31]. The results have strongly confirmed the advantage of sf-MTJs based on 2D A-type AFM materials.

_{3}, there exist many other 2D A-type AFM materials, such as CrCl

_{3}[32] and MnBi

_{2}Te

_{4}[33] in experimental observations and YTiO

_{3}[34], in first-principle calculations. Among them, CrSBr is a 2D A-type AFM semiconductor with a band gap of approximately 1.5 eV [35]. Bulk CrSBr single crystals can be grown from Cr and S

_{2}Br

_{2}by chemical vapor transport or other methods for obtaining metallic alloys [36,37] and the monolayer CrSBr flake can be easily exfoliated due to the interlayer vdW forces [35,38]. CrSBr has a high Néel temperature (${T}_{N}~140\mathrm{K}$), which allows the realization of 2D spintronic devices in experiments [38,39]. In addition, unlike metals and oxide compounds [40,41], most 2D magnetic materials tend to degrade in air through oxidation or hydration [16,17,42] but CrSBr is stable in air so that it may be stored under ambient conditions for one month without degradation [39]. In short, CrSBr is air-stable, has a relatively high Néel temperature and shows semiconductor characteristics with a band gap approximately 1.5 eV, allowing many methods to manipulate the magnetism [38]. It is thus a proper candidate to investigate and reveal the spin-resolved transmission at a low dimension. Therefore, we propose to employ multilayer CrSBr to design sf-MTJs in this work and investigate the transmission performances by DFT. These studies provide a promising direction for the future MTJ design.

## 2. Results

^{7}% and 10

^{5}%, respectively. Compared with two-layer sf-MTJ, the TMR of the four-layer sf-MTJ dramatically increases from 10

^{2}% to 10

^{7}% orders of magnitude. We notice that the increase comes from the change in ${G}_{AP}$, which is much smaller in the four-layer sf-MTJ than that in the two-layer. In the six-layer device, the value of ${G}_{AP}$ does not show a significant change while ${G}_{P}$ becomes much smaller on account of its increasing thickness, resulting in the decrease in TMR. In conclusion, the sf-MTJ with graphene electrodes and four-layer CrSBr has a giant TMR, making it a promising device model in future experiments and applications, adding to the other aforementioned advantages of CrSBr.

## 3. Discussion

_{3}sf-MTJ shows a good characteristic [28] because CrI

_{3}is insulating but CrSBr is a semiconductor.

^{7}% and 10

^{5}%). However, the spectra of APC carry little information for the lack of spots with high transmission probability. Therefore, we only provide the transmission spectra of spin-up electrons in PC that have distinct transmission characteristics to illustrate the giant TMRs in Figure 7a,b.

## 4. Materials and Methods

^{−5}eV, the cut-off energy was set to 400 eV and the thickness of the vacuum layer along the c direction was 10 Å. In all the calculations in our work, the vdW forces were considered by the DFT-D3 method [44].

^{+}is the transmission probability along the positive direction from the left to right electrode.

## 5. Conclusions

^{7}% and 10

^{5}% depending on the number of CrSBr layers. The transmission spectra of the sf-MTJs were calculated and the spin-up and spin-down states showed significant differences in transmission. We analyzed the underlying mechanism of the high TMR through the transmission spectra, eigenstates, electrostatic potentials and LDOS of the two-layer device. The results show that the device had a good filtering characteristic of ${\Delta}_{2}$ electrons which dominated the transmission. The HSE06 band structures confirmed the electron transfer from graphene to CrSBr in the device and demonstrated the details in transmission spectra. The LDOS presented the electron distribution in the device and supported the existence of the TMR effect.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**(

**a**) A-type AFM bilayer with intralayer FM order and interlayer AFM order; (

**b**) A-type AFM bilayer in an external in-plane magnetic field; (

**c**) A-type AFM bilayer in an external out-of-plane magnetic field. Different external field can change the interlayer coupling into in-plane FM in 2 (

**b**) or out-of-plane FM in 2 (

**c**).

**Figure 3.**(

**a**) Structure of monolayer CrSBr (3 × 3) viewed along the a axis, b axis and c axis. Cr, S and Br atoms are colored in blue, yellow and red, respectively; (

**b**) The perspective view diagram of a graphene/bilayer CrSBr/graphene sf-MTJ device. C atoms are colored in gray; (

**c**) The device model based on the 2/4/6-layer CrSBr. The red and black squares represent electrodes and central regions, respectively.

**Figure 4.**The transmission spectra (transmission probabilities of electrons with different transverse Bloch wave vectors) of (

**a**) Majority spin states in PC; (

**b**) Minority spin states in PC; (

**c**) Majority spin states in APC; and (

**d**) Minority spin states in APC. The colors represent different transmission probabilities with a logarithmic for presenting more information. (

**e**) The transmission eigenstates of the spots with the highest probability in (

**a**,

**b**) are from a c axis perspective. The figures are the calculated results of the modeling.

**Figure 5.**(

**a**) The electrostatic potential of the bilayer CrSBr in PC; and (

**b**) The electrostatic potential of bilayer CrSBr in APC. The location of the vacuum energy level is marked by a blue solid line, and the energy levels of CBM are marked by blue dashed lines. The horizontal axis represents the position in the direction of transmission. The thickness of the vacuum is 10 Å. The figures are the calculated results of the modeling.

**Figure 6.**The local density of the states of the sf-MTJ based on bilayer CrSBr. (

**a**) Up states in PC; (

**b**) Down states in PC; (

**c**) Up states in APC; and (

**d**) Down states in APC. The vertical axis is the electron energy levels in which the Fermi level is set as 0 eV. The horizontal axis is the position of the device along the transmission direction. Different layers of the device marked above the figure by ${\mathrm{Gr}}_{\mathrm{L}}$ (the graphene on the left); ${\mathrm{CSB}}_{\mathrm{L}}$ (the left layer of the bilayer CrSBr); ${\mathrm{CSB}}_{\mathrm{R}}$ (the right layer of the bilayer CrSBr); and ${\mathrm{Gr}}_{\mathrm{R}}$ (the graphene on the left). Red colors indicate a high density of states. The figures are the calculated results of modeling.

**Figure 7.**(

**a**) Transmission spectrum of up states in 4-layer sf-MTJ under PC; (

**b**) Transmission spectrum of up states in 6-layer sf-MTJ under PC. The spots with highest transmission probabilities are circled by red; (

**c**) Transmission spectrum of graphene electrodes. Transmission spectra in the figure represent the transmission probabilities of electrons with different transverse Bloch wave vectors; (

**d**,

**e**) The transmission eigenstates of the spots with highest probability in (

**a**,

**b**) from the c axis perspective. The figures are the calculated results of the modeling.

**Table 1.**The values of ${G}_{P}$ (the 2nd column), ${G}_{AP}$ (the 3rd column) and TMR (the 4th column) of MTJs with different numbers of CrSBr layers through calculations.

Number of CrSBr Layers | ${\mathit{G}}_{\mathit{P}}\left(\mathbf{Siemens}\right)$ | ${\mathit{G}}_{\mathit{A}\mathit{P}}\left(\mathbf{Siemens}\right)$ | TMR |
---|---|---|---|

2 | 4.35 × 10^{−10} | 1.01 × 10^{−10} | 3.3 × 10^{2}% |

4 | 1.87 × 10^{−12} | 9.19 × 10^{−18} | 2.0 × 10^{7}% |

6 | 7.52 × 10^{−14} | 6.86 × 10^{−17} | 1.1 × 10^{5}% |

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**MDPI and ACS Style**

Liu, H.; Liu, Y.-Y.; Wen, H.; Wu, H.; Zong, Y.; Xia, J.; Wei, Z.
Spin-Filter Magnetic Tunnel Junctions Based on A-Type Antiferromagnetic CrSBr with Giant Tunnel Magnetoresistance. *Magnetochemistry* **2022**, *8*, 89.
https://doi.org/10.3390/magnetochemistry8080089

**AMA Style**

Liu H, Liu Y-Y, Wen H, Wu H, Zong Y, Xia J, Wei Z.
Spin-Filter Magnetic Tunnel Junctions Based on A-Type Antiferromagnetic CrSBr with Giant Tunnel Magnetoresistance. *Magnetochemistry*. 2022; 8(8):89.
https://doi.org/10.3390/magnetochemistry8080089

**Chicago/Turabian Style**

Liu, Hao, Yue-Yang Liu, Hongyu Wen, Haibin Wu, Yixin Zong, Jianbai Xia, and Zhongming Wei.
2022. "Spin-Filter Magnetic Tunnel Junctions Based on A-Type Antiferromagnetic CrSBr with Giant Tunnel Magnetoresistance" *Magnetochemistry* 8, no. 8: 89.
https://doi.org/10.3390/magnetochemistry8080089