#
Comparative Study of Magnetic Properties of (Mn_{1−x}A${}_{x}^{\mathrm{IV}}$ )Bi_{2}Te_{4} A^{IV} = Ge, Pb, Sn

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

- The first approach involves the insertion of additional (m − 1) [Bi${}_{2}$Te${}_{3}$] QLs between one [MnBi${}_{2}$Te${}_{4}$] SL resulting in the series of compounds MnBi${}_{2m}$Te${}_{3m+1}$ with $m\ge 1$ [14,19,20,21]. This series includes the homologous phases MnBi${}_{2}$Te${}_{4}$ (m = 1:124), MnBi${}_{4}$Te${}_{7}$ (m = 2:147), and MnBi${}_{6}$Te${}_{10}$ (m = 3:16$\overline{10}$), all of which can be classified as ${\mathbb{Z}}_{2}$ AFM TIs. However, as the number of [Bi${}_{2}$Te${}_{3}$] QLs increases, significant changes occur in the magnetic properties. For the 147 phase, T${}_{\mathrm{N}}$ is already 13 K and H${}_{\mathrm{SF}}$ does not exceed 0.3 T. The phase 16$\overline{10}$ possesses an uncertain type of magnetic ordering which can be either AFM or FM, depending on growth conditions and the presence of defects [22,23]. For phases with higher m, the system resembles non-interacting 2D ferromagnets formed by the [MnBi${}_{2}$Te${}_{4}$] SL [21].
- The second approach is to substitute Bi atoms with Sb atoms, resulting in Mn(Bi${}_{1-y}$Sb${}_{y}$)${}_{2}$Te${}_{4}$ compounds [24]. This substitution generally leads to an increase in the number of anti-site defects, such as Mn${}_{\mathrm{Bi},\mathrm{Sb}}$ (Mn occupying the position of Bi or Sb atoms) [25,26]. Consequently, this substitution affects the magnetic order of the SL, transforming it from ferromagnetic to ferrimagnetic [18]. By adjusting the growth parameters, it is possible to further increase the number of anti-site defects and induce a transition from antiferromagnetic to ferromagnetic behavior in the ground state [26].
- Another way is to dilute Mn atoms in MnBi${}_{2}$Te${}_{4}$ with non-magnetic atoms. The A${}^{\mathrm{IV}}$ = Ge, Pb, Sn elements can be chosen as suitable substituents. There are ternary TI compounds, such as A${}^{\mathrm{IV}}$Bi${}_{2}$Te${}_{4}$, with the same $R\overline{3}m$ symmetry group as MnBi${}_{2}$Te${}_{4}$ [13,27], allowing for arbitrary ratios of Mn substitution in solid solutions (Mn${}_{1-x}$A${}_{x}^{\mathrm{IV}}$)Bi${}_{2}$Te${}_{4}$. Several studies [28,29,30,31,32] have demonstrated the synthesis of these crystals and confirmed the absence of additional substitution defects, as in the case of substitution of Sb for Bi atoms. Moreover, this substitution appears to be isovalent and does not introduce any additional charge according to ARPES studies [32].

## 2. Materials and Methods

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ARPES | Angle-resolved photoemission spectroscopy |

AFM, FM, PM | Antiferromagnetic, ferromagnetic, paramagnetic |

EDC | Energy distribution curves |

EDX | Energy-dispersive X-ray spectroscopy |

H${}_{\mathrm{SF}}$ | Spin-flop transition field |

QAHE | Quantum anomalous Hall effect |

QL/SL | Quintuple [Bi${}_{2}$Te${}_{3}$]/septuple [MnBi${}_{2}$Te${}_{4}$] layers block |

SQUID | Superconducting quantum interference device |

TI | Topological insulator |

T${}_{\mathrm{N}}$ | Néel temperature |

XPS | X-ray photoemission spectroscopy |

ZFC, FC | Zero field cooled, field cooled |

Phases 124, 147, 16$\overline{10}$ | (Mn${}_{1-x}$A${}_{x}^{\mathrm{IV}}$)Bi${}_{2m}$Te${}_{3m+1}$ with m = 1, 2, 3 (A${}^{\mathrm{IV}}$ = Ge, Pb, Sn) |

## References

- Chang, C.Z.; Li, M. Quantum anomalous Hall effect in time-reversal-symmetry breaking topological insulators. J. Phys. Condens. Matter
**2016**, 28, 123002. [Google Scholar] [CrossRef] - He, K.; Xue, Q.K. The Road to High-Temperature Quantum Anomalous Hall Effect in Magnetic Topological Insulators. SPIN
**2019**, 09, 1940016. [Google Scholar] [CrossRef] - Giustino, F.; Lee, J.H.; Trier, F.; Bibes, M.; Winter, S.M.; Valentí, R.; Son, Y.W.; Taillefer, L.; Heil, C.; Figueroa, A.I.; et al. The 2021 quantum materials roadmap. J. Phys. Mater.
**2021**, 3, 042006. [Google Scholar] [CrossRef] - Chang, C.Z.; Liu, C.X.; MacDonald, A.H. Colloquium: Quantum anomalous Hall effect. Rev. Mod. Phys.
**2023**, 95, 011002. [Google Scholar] [CrossRef] - Otrokov, M.M.; Rusinov, I.P.; Blanco-Rey, M.; Hoffmann, M.; Vyazovskaya, A.Y.; Eremeev, S.V.; Ernst, A.; Echenique, P.M.; Arnau, A.; Chulkov, E.V. Unique Thickness-Dependent Properties of the van der Waals Interlayer Antiferromagnet MnBi
_{2}Te_{4}Films. Phys. Rev. Lett.**2019**, 122, 107202. [Google Scholar] [CrossRef] [PubMed] - Otrokov, M.M.; Klimovskikh, I.I.; Bentmann, H.; Estyunin, D.; Zeugner, A.; Aliev, Z.S.; Gaß, S.; Wolter, A.U.B.; Koroleva, A.V.; Shikin, A.M.; et al. Prediction and observation of an antiferromagnetic topological insulator. Nature
**2019**, 576, 416–422. [Google Scholar] [CrossRef] - Zhang, D.; Shi, M.; Zhu, T.; Xing, D.; Zhang, H.; Wang, J. Topological Axion States in the Magnetic Insulator MnBi
_{2}Te_{4}with the Quantized Magnetoelectric Effect. Phys. Rev. Lett.**2019**, 122, 206401. [Google Scholar] [CrossRef] [PubMed] - Li, J.; Li, Y.; Du, S.; Wang, Z.; Gu, B.L.; Zhang, S.C.; He, K.; Duan, W.; Xu, Y. Intrinsic magnetic topological insulators in van der Waals layered MnBi
_{2}Te_{4}-family materials. Sci. Adv.**2019**, 5, eaaw5685. [Google Scholar] [CrossRef] - Gong, Y.; Guo, J.; Li, J.; Zhu, K.; Liao, M.; Liu, X.; Zhang, Q.; Gu, L.; Tang, L.; Feng, X.; et al. Experimental Realization of an Intrinsic Magnetic Topological Insulator. Chin. Phys. Lett.
**2019**, 36, 076801. [Google Scholar] [CrossRef] - Deng, Y.; Yu, Y.; Shi, M.Z.; Guo, Z.; Xu, Z.; Wang, J.; Chen, X.H.; Zhang, Y. Quantum anomalous Hall effect in intrinsic magnetic topological insulator MnBi
_{2}Te_{4}. Science**2020**, 367, 895. [Google Scholar] [CrossRef] - Liu, C.; Wang, Y.; Li, H.; Wu, Y.; Li, Y.; Li, J.; He, K.; Xu, Y.; Zhang, J.; Wang, Y. Robust axion insulator and Chern insulator phases in a two-dimensional antiferromagnetic topological insulator. Nat. Mater.
**2020**, 19, 522–527. [Google Scholar] [CrossRef] [PubMed] - Ge, J.; Liu, Y.; Li, J.; Li, H.; Luo, T.; Wu, Y.; Xu, Y.; Wang, J. High-Chern-number and high-temperature quantum Hall effect without Landau levels. Natl. Sci. Rev.
**2020**, 7, 1280–1287. [Google Scholar] [CrossRef] - Lee, D.S.; Kim, T.H.; Park, C.H.; Chung, C.Y.; Lim, Y.S.; Seo, W.S.; Park, H.H. Crystal structure, properties and nanostructuring of a new layered chalcogenide semiconductor, Bi2MnTe4. CrystEngComm
**2013**, 15, 5532–5538. [Google Scholar] [CrossRef] - Aliev, Z.S.; Amiraslanov, I.R.; Nasonova, D.I.; Shevelkov, A.V.; Abdullayev, N.A.; Jahangirli, Z.A.; Orujlu, E.N.; Otrokov, M.M.; Mamedov, N.T.; Babanly, M.B.; et al. Novel ternary layered manganese bismuth tellurides of the MnTe-Bi
_{2}Te_{3}system: Synthesis and crystal structure. J. Alloys Compd.**2019**, 789, 443–450. [Google Scholar] [CrossRef] - Yan, J.Q.; Zhang, Q.; Heitmann, T.; Huang, Z.; Chen, K.Y.; Cheng, J.G.; Wu, W.; Vaknin, D.; Sales, B.C.; McQueeney, R.J. Crystal growth and magnetic structure of MnBi
_{2}Te_{4}. Phys. Rev. Mater.**2019**, 3, 064202. [Google Scholar] [CrossRef] - Li, H.; Liu, S.; Liu, C.; Zhang, J.; Xu, Y.; Yu, R.; Wu, Y.; Zhang, Y.; Fan, S. Antiferromagnetic topological insulator MnBi
_{2}Te_{4}: Synthesis and magnetic properties. Phys. Chem. Chem. Phys.**2020**, 22, 556–563. [Google Scholar] [CrossRef] - Estyunin, D.A.; Klimovskikh, I.I.; Shikin, A.M.; Schwier, E.F.; Otrokov, M.M.; Kimura, A.; Kumar, S.; Filnov, S.O.; Aliev, Z.S.; Babanly, M.B.; et al. Signatures of temperature driven antiferromagnetic transition in the electronic structure of topological insulator MnBi
_{2}Te_{4}. APL Mater.**2020**, 8, 021105. [Google Scholar] [CrossRef] - Lai, Y.; Ke, L.; Yan, J.; McDonald, R.D.; McQueeney, R.J. Defect-driven ferrimagnetism and hidden magnetization in MnBi
_{2}Te_{4}. Phys. Rev. B**2021**, 103, 184429. [Google Scholar] [CrossRef] - Wu, J.; Liu, F.; Sasase, M.; Ienaga, K.; Obata, Y.; Yukawa, R.; Horiba, K.; Kumigashira, H.; Okuma, S.; Inoshita, T.; et al. Natural van der Waals heterostructural single crystals with both magnetic and topological properties. Sci. Adv.
**2019**, 5, eaax9989. [Google Scholar] [CrossRef] - Hu, C.; Gordon, K.N.; Liu, P.; Liu, J.; Zhou, X.; Hao, P.; Narayan, D.; Emmanouilidou, E.; Sun, H.; Liu, Y.; et al. A van der Waals antiferromagnetic topological insulator with weak interlayer magnetic coupling. Nat. Commun.
**2020**, 11, 97. [Google Scholar] [CrossRef] - Klimovskikh, I.I.; Otrokov, M.M.; Estyunin, D.; Eremeev, S.V.; Filnov, S.O.; Koroleva, A.; Shevchenko, E.; Voroshnin, V.; Rybkin, A.G.; Rusinov, I.P.; et al. Tunable 3D/2D magnetism in the (MnBi
_{2}Te_{4})(Bi_{2}Te_{3})_{m}topological insulators family. NPJ Quantum Mater.**2020**, 5, 54. [Google Scholar] [CrossRef] - Yan, C.; Zhu, Y.; Miao, L.; Fernandez-Mulligan, S.; Green, E.; Mei, R.; Tan, H.; Yan, B.; Liu, C.X.; Alem, N.; et al. Delicate Ferromagnetism in MnBi
_{6}Te_{10}. Nano Lett.**2022**, 22, 9815–9822. [Google Scholar] [CrossRef] [PubMed] - Tcakaev, A.V.; Rubrecht, B.; Facio, J.I.; Zabolotnyy, V.B.; Corredor, L.T.; Folkers, L.C.; Kochetkova, E.; Peixoto, T.R.F.; Kagerer, P.; Heinze, S.; et al. Intermixing-Driven Surface and Bulk Ferromagnetism in the Quantum Anomalous Hall Candidate MnBi
_{6}Te_{10}. Adv. Sci.**2023**, 10, 2203239. [Google Scholar] [CrossRef] - Chen, B.; Fei, F.; Zhang, D.; Zhang, B.; Liu, W.; Zhang, S.; Wang, P.; Wei, B.; Zhang, Y.; Zuo, Z.; et al. Intrinsic magnetic topological insulator phases in the Sb doped MnBi
_{2}Te_{4}bulks and thin flakes. Nat. Commun.**2019**, 10, 4469. [Google Scholar] [CrossRef] - Murakami, T.; Nambu, Y.; Koretsune, T.; Xiangyu, G.; Yamamoto, T.; Brown, C.M.; Kageyama, H. Realization of interlayer ferromagnetic interaction in MnSb
_{2}Te_{4}toward the magnetic Weyl semimetal state. Phys. Rev. B**2019**, 100, 195103. [Google Scholar] [CrossRef] [PubMed] - Liu, Y.; Wang, L.L.; Zheng, Q.; Huang, Z.; Wang, X.; Chi, M.; Wu, Y.; Chakoumakos, B.C.; McGuire, M.A.; Sales, B.C.; et al. Site Mixing for Engineering Magnetic Topological Insulators. Phys. Rev. X
**2021**, 11, 021033. [Google Scholar] [CrossRef] - Kuznetsova, L.A.; Kuznetsov, V.L.; Rowe, D.M. Thermoelectric properties and crystal structure of ternary compounds in the Ge(Sn,Pb)Te-Bi
_{2}Te_{3}systems. J. Phys. Chem. Solids**2000**, 61, 1269–1274. [Google Scholar] [CrossRef] - Zhu, J.; Naveed, M.; Chen, B.; Du, Y.; Guo, J.; Xie, H.; Fei, F. Magnetic and electrical transport study of the antiferromagnetic topological insulator Sn-doped MnBi
_{2}Te_{4}. Phys. Rev. B**2021**, 103, 144407. [Google Scholar] [CrossRef] - Qian, T.; Yao, Y.T.; Hu, C.; Feng, E.; Cao, H.; Mazin, I.I.; Chang, T.R.; Ni, N. Magnetic dilution effect and topological phase transitions in (Mn
_{1−x}Pb_{x})Bi_{2}Te_{4}. Phys. Rev. B**2022**, 106, 045121. [Google Scholar] [CrossRef] - Changdar, S.; Ghosh, S.; Vijay, K.; Kar, I.; Routh, S.; Maheshwari, P.K.; Ghorai, S.; Banik, S.; Thirupathaiah, S. Nonmagnetic Sn doping effect on the electronic and magnetic properties of antiferromagnetic topological insulator MnBi
_{2}Te_{4}. Phys. B Condens. Matter**2023**, 657, 414799. [Google Scholar] [CrossRef] - Frolov, A.S.; Usachov, D.Y.; Tarasov, A.V.; Fedorov, A.V.; Bokai, K.A.; Klimovskikh, I.; Stolyarov, V.S.; Sergeev, A.I.; Lavrov, A.N.; Golyashov, V.A.; et al. Magnetic Dirac semimetal state of (Mn,Ge)Bi
_{2}Te_{4}. arXiv**2023**, arXiv:2306.13024. [Google Scholar] - Estyunina, T.P.; Shikin, A.M.; Estyunin, D.A.; Eryzhenkov, A.V.; Klimovskikh, I.I.; Bokai, K.A.; Golyashov, V.A.; Kokh, K.A.; Tereshchenko, O.E.; Kumar, S.; et al. Evolution of Mn
_{1−x}Ge_{x}Bi_{2}Te_{4}Electronic Structure under Variation of Ge Content. Nanomaterials**2023**, 13, 2151. [Google Scholar] [CrossRef] [PubMed] - Chen, W.Q.; Teo, K.L.; Jalil, M.B.A.; Liew, T. Compositional dependencies of ferromagnetic Ge
_{1−x}Mn_{x}Te grown by solid-source molecular-beam epitaxy. J. Appl. Phys.**2006**, 99, 08D515. [Google Scholar] [CrossRef] - Hassan, M.; Springholz, G.; Lechner, R.T.; Groiss, H.; Kirchschlager, R.; Bauer, G. Molecular beam epitaxy of single phase GeMnTe with high ferromagnetic transition temperature. J. Cryst. Growth
**2011**, 323, 363–367. [Google Scholar] [CrossRef] [PubMed] - Ren, Z.; Taskin, A.A.; Sasaki, S.; Segawa, K.; Ando, Y. Optimizing Bi
_{2−x}Sb_{x}Te_{3−y}Se_{y}solid solutions to approach the intrinsic topological insulator regime. Phys. Rev. B**2011**, 84, 165311. [Google Scholar] [CrossRef] - Xu, Y.; Miotkowski, I.; Liu, C.; Tian, J.; Nam, H.; Alidoust, N.; Hu, J.; Shih, C.K.; Hasan, M.Z.; Chen, Y.P. Observation of topological surface state quantum Hall effect in an intrinsic three-dimensional topological insulator. Nat. Phys.
**2014**, 10, 956–963. [Google Scholar] [CrossRef] - Kokh, K.A.; Makarenko, S.V.; Golyashov, V.A.; Shegai, O.A.; Tereshchenko, O.E. Melt growth of bulk Bi2Te3 crystals with a natural p-n junction. CrystEngComm
**2014**, 16, 581–584. [Google Scholar] [CrossRef] - Iwasawa, H.; Schwier, E.F.; Arita, M.; Ino, A.; Namatame, H.; Taniguchi, M.; Aiura, Y.; Shimada, K. Development of laser-based scanning μ-ARPES system with ultimate energy and momentum resolutions. Ultramicroscopy
**2017**, 182, 85–91. [Google Scholar] [CrossRef] - Szuszkiewicz, W.; Hennion, B.; Witkowska, B.; Łusakowska, E.; Mycielski, A. Neutron scattering study of structural and magnetic properties of hexagonal MnTe. Phys. Status Solidi
**2005**, 2, 1141–1146. [Google Scholar] [CrossRef] - Mogi, M.; Yoshimi, R.; Tsukazaki, A.; Yasuda, K.; Kozuka, Y.; Takahashi, K.S.; Kawasaki, M.; Tokura, Y. Magnetic modulation doping in topological insulators toward higher-temperature quantum anomalous Hall effect. Appl. Phys. Lett.
**2015**, 107, 182401. [Google Scholar] [CrossRef] - Chen, K.Y.; Wang, B.S.; Yan, J.Q.; Parker, D.S.; Zhou, J.S.; Uwatoko, Y.; Cheng, J.G. Suppression of the antiferromagnetic metallic state in the pressurized MnBi
_{2}Te_{4}single crystal. Phys. Rev. Mater.**2019**, 3, 094201. [Google Scholar] [CrossRef] - Shikin, A.M.; Estyunin, D.A.; Zaitsev, N.L.; Glazkova, D.; Klimovskikh, I.I.; Filnov, S.O.; Rybkin, A.G.; Schwier, E.F.; Kumar, S.; Kimura, A.; et al. Sample-dependent Dirac-point gap in MnBi
_{2}Te_{4}and its response to applied surface charge: A combined photoemission and ab initio study. Phys. Rev. B**2021**, 104, 115168. [Google Scholar] [CrossRef]

**Figure 1.**The temperature dependencies of the magnetic susceptibility $\chi \left(T\right)$ (top line) and magnetization as a function of applied magnetic field M(H) (middle and bottom lines) were measured for (Mn${}_{1-x}$Pb${}_{x}$)Bi${}_{2}$Te${}_{4}$ samples using the SQUID method. The $\chi \left(T\right)$ measurement involved applying an external field of 5 mT (0.1 T) perpendicular to the sample surface plane along the crystallographic axis c. The red curve represents the ZFC condition, while the blue curve corresponds to the FC condition. The M(H) dependencies were measured at a temperature of 2 K are presented in the middle line; the M(H) curves at different temperatures are displayed in the bottom line. Critical temperature and external magnetic field values at which phase transitions occur are indicated on the panels, with the corresponding parameters for the 124 phase marked in red.

**Figure 2.**Dependencies of $\chi \left(T\right)$ (top line) and M(H) (middle and bottom lines) for (Mn${}_{1-x}$Sn${}_{x}$)Bi${}_{2}$Te${}_{4}$ samples. The notation is the same as in Figure 1. The orange dotted curve in the $\chi \left(T\right)$ panel for Sn = 52% is ${d}^{2}\chi \left(T\right)/d{T}^{2}$.

**Figure 3.**Dependencies of $\chi \left(T\right)$ (top line) and M(H) (middle and bottom lines) for (Mn${}_{1-x}$Ge${}_{x}$)Bi${}_{2}$Te${}_{4}$ samples. The notation is the same as in Figure 1.

**Figure 4.**The experimental values of T${}_{\mathrm{N}}$ and H${}_{\mathrm{SF}}$ as a function of the substituent concentration A${}^{\mathrm{IV}}$ = Ge, Pb, Sn are presented. Linear approximations of the experimental data points (green dashed and black solid lines) are shown (see details in the text).

**Figure 5.**ARPES dispersion relations for (Mn${}_{1-x}$Pb${}_{x}$)Bi${}_{2}$Te${}_{4}$ with a nominal Pb concentration of 10%. In panel (

**a**), the temperature dependence of the state distribution (EDC) at the $\Gamma $-point is shown within the range of 14 K to 30 K. The positions of Te p${}_{z}$ states are indicated by blue dashed lines, and the onset of the Te p${}_{z}$ state splitting is marked by a vertical cyan line. The temperature dependence of the Te p${}_{z}$ splitting value is presented at the bottom, as well as its approximation by the power law. Panels (

**b**,

**c**) display dispersion relations at 14 K and 24 K, presented as N(E) (top line) and ${d}^{2}N/d{E}^{2}$ (bottom line). In the bottom line, $\Delta E$ and ${E}_{g}$ show the splittings of the Te p${}_{z}$ states and the size of the bulk band gap, respectively. In panel (

**d**), the decomposition of EDCs at the $\Gamma $-point into spectral components are shown. At the top, we provide additional estimates of the Pb content obtained by the EDX method directly for the investigated surface. The TSS labels on the panels mark the topological surface states; BCB and BVB labels mark regions of bulk conduction and valence bands.

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Estyunin, D.A.; Rybkina, A.A.; Kokh, K.A.; Tereshchenko, O.E.; Likholetova, M.V.; Klimovskikh, I.I.; Shikin, A.M.
Comparative Study of Magnetic Properties of (Mn_{1−x}A_{2}Te_{4} A^{IV} = Ge, Pb, Sn. *Magnetochemistry* **2023**, *9*, 210.
https://doi.org/10.3390/magnetochemistry9090210

**AMA Style**

Estyunin DA, Rybkina AA, Kokh KA, Tereshchenko OE, Likholetova MV, Klimovskikh II, Shikin AM.
Comparative Study of Magnetic Properties of (Mn_{1−x}A_{2}Te_{4} A^{IV} = Ge, Pb, Sn. *Magnetochemistry*. 2023; 9(9):210.
https://doi.org/10.3390/magnetochemistry9090210

**Chicago/Turabian Style**

Estyunin, Dmitry A., Anna A. Rybkina, Konstantin A. Kokh, Oleg E. Tereshchenko, Marina V. Likholetova, Ilya I. Klimovskikh, and Alexander M. Shikin.
2023. "Comparative Study of Magnetic Properties of (Mn_{1−x}A_{2}Te_{4} A^{IV} = Ge, Pb, Sn" *Magnetochemistry* 9, no. 9: 210.
https://doi.org/10.3390/magnetochemistry9090210