Magnetic and electrical transport study of the intrinsic magnetic topological insulator MnBi₂Te₄ with Ge doping

Abstract

As an intrinsic magnetic topological insulator with magnetic order and non-trivial topological structure, MnBi₂Te₄ is an ideal material for studying exotic topological states such as quantum anomalous Hall effect and topological axion insulating states. Here, we carry out magnetic and electrical transport measurements on (Mn_1–xGe_x)Bi₂Te₄ (x = 0, 0.15, 0.30, 0.45, 0.60, and 0.75) single crystals. It is found that with increasing x, the dilution of magnetic moments gradually weakens the antiferromagnetic exchange interaction. Moreover, Ge doping reduces the critical field of ferromagnetic ordering, which may provide a possible way to implement the quantum anomalous Hall effect at lower magnetic field. Electrical transport measurements suggest that electrons are the dominant charge carriers, and the carrier density increases with the Ge doping ratio. Additionally, the Kondo effect is observed in the samples with x = 0.45, 0.60, and 0.75. Our results suggest that doping germanium is a viable way to tune the magnetic and electrical transport properties of MnBi₂Te₄, opening up the possibility of future applications in magnetic topological insulators.

Graphical abstract

Keywords

MnBi ₂Te ₄ / intrinsic magnetic topological insulator / transition points / Kondo effect

1 Introduction

Quantum anomalous Hall effect (QAHE) is a representative topological quantum phenomenon, demonstrating quantized Hall resistance and near-zero longitudinal resistance in the absence of an external magnetic field, suggesting broad application prospects in dissipationless electronic devices [1-3]. Among the various approaches proposed to achieve the QAHE, the magnetic topological insulator emerges as the most favorable system based on both experimental and theoretical investigations, primarily owing to its intrinsically robust spin−orbit coupling [4,5]. QAHE was first realized in thin films of (Bi, Sb)₂Te₃ doped with Cr in 2013 [6]. However, the observed QAHE is limited to temperatures as low as several tens of millikelvin due to the presence of inhomogeneity or disorder caused by random magnetic doping. Therefore, there is a strong motivation to find intrinsic magnetic topological insulators (TIs) that can exhibit high-temperature QAHE. In this regard, MnBi₂Te₄, a recently discovered intrinsic antiferromagnetic (AFM) TI, has attracted considerable attention [7-9].

MnBi₂Te₄ has a van der Waals (vdW) layered structure, which consists of Te−Bi−Te−Mn−Te−Bi−Te septuple layers (SLs) stacking along the c-axis [10]. Magnetic measurements reveal that the Mn ions exhibit a high-spin S = 5/2 configuration with a magnetic moment of approximately 5μ_B, and an antiferromagnetic transition at 24 K is observed. Consequently, MnBi₂Te₄ presents a unique natural heterostructure comprising antiferromagnetic planes intertwined with layers of TIs [11-16]. Furthermore, theoretical calculations suggest that the MnBi₂Te₄ may exhibit QAHE states, with a gap of approximately 50−80 meV, significantly exceeding that of a magnetically doped topological insulator, indicating the potential for achieving QAHE at higher temperatures [17-19]. However, achieving a ferromagnetic (FM) state in MnBi₂Te₄ necessitates an ultra-high magnetic field, making it challenging to realize a QAHE state under low magnetic fields [20]. One effective approach is to substitute the Mn element with nonmagnetic ions (such as Pb) to reduce the critical field required to align the magnetic moments to the ferromagnetic state [21,22]. However, studies on the nonmagnetic ionic substitution of Mn in MnBi₂Te₄ are still few and lack comprehensive analysis, hence further studies are needed.

In this study, we conducted a comprehensive analysis to investigate the impact of Ge doping on the magnetic and electrical transport properties of the antiferromagnetic topological insulator MnBi₂Te₄. To achieve this, we prepared single crystals of (Mn_1–xGe_x)Bi₂Te₄ with different Ge doping concentrations (x = 0, 0.15, 0.30, 0.45, 0.60, and 0.75). It was observed that Ge doping significantly influenced the antiferromagnetic ordering, as evidenced by the decrease in the Néel temperature (T_N) with increasing Ge concentration. This suggests that magnetic engineering is feasible in (Mn_1–xGe_x)Bi₂Te₄. Furthermore, the transition points were found to decrease compared to pure MnBi₂Te₄. Since a Chern insulator can be observed at the ferromagnetic regime, reducing the transition field in MnBi₂Te₄ can realize a QAHE state at a relatively low magnetic field, beneficial to its further applications in devices and spintronics [23-25]. Additionally, Hall resistivity measurements show an increase in the n-type carrier density as the increase of doping concentration, indicating the modulation of carrier density via Ge doping.

2 Experimental details

Single crystals of (Mn_1−xGe_x)Bi₂Te₄ of high quality were grown by the self-flux method. Mixtures of (Mn_1−x+Ge_x)Te and Bi₂Te₃ powder (nominal x = 0, 0.15, 0.30, 0.45, 0.60, and 0.75) with the 1:1 ratio were placed in an alumina crucible, which was then sealed in an evacuated quartz tube. Subsequently, the mixture was heated to 900 °C over 15 hours and maintained at that temperature for 12 hours. Finally, it was slowly cooled to 591 °C at a rate of 1 °C per hour. and annealed for at least 14 days. The crystal structure of all samples was characterized by X-ray diffraction (XRD) on a commercial Rigaku diffractometer with Cu Kα radiation (λ = 1.5403 Å). A field emission scanning electron microscope (FEI Inspect F50) equipped with an energy dispersive X-ray spectroscopy (EDS, INCA spectrometer) detector was used to visualize the morphology of the surfaces and the distribution of the elements in the composites. Transport and magnetic properties were determined using a physical property measurement system (PPMS-9, Quantum Design).

3 Results and discussion

Ge-doped MnBi₂Te₄ crystals exhibit a layered rhombohedral crystal structure with the space group R-3m [26,27], composed of stacking SLs Te−Bi−Te−X−Te−Bi−Te (X = Mn/Ge) as displayed in Fig.1(a). Fig.1(b) shows the XRD data of (Mn_1–xGe_x)Bi₂Te₄ single crystals. It can be observed that all samples display explicit reflections from the (0 0 l) plane and without any impurity peaks, confirming phase purity for all the crystals. The as-grown samples exhibit a smooth and shiny surface as displayed in the inset (left) of Fig.1(b). The inset (right) of Fig.1(b) displays the enlarging pattern of (0 0 2 1) diffraction peaks, which shift left with the Ge contents increase. The results show that Ge-doped MnBi₂Te₄ crystals have lattice expansion, which can be attributed to the larger radius of the Ge ion (0.73 Å) compared to that of the Mn ion (0.67 Å) by 9%. The Bi-normalized EDS images of (Mn_1–xGe_x)Bi₂Te₄ with different amounts of germanium substitution are shown in Fig.1(c), which shows that the stoichiometric ratio of Mn:Ge:Bi:Te is close to the nominal ratio. These results suggest that Ge successfully substitutes Mn in MnBi₂Te₄. The scanning electron microscope (SEM) image of the surface of the (Mn_0.85Ge_0.15)Bi₂Te₄ sample is shown in Fig.1(d). The crystal exhibits a smooth surface with a visible layered structure, consistent with findings reported in previous studies [10-15]. Fig.1(e) shows the corresponding EDS mapping, which reveals that Mn, Ge, Bi, and Te elements are homogeneously distributed in the crystal. Fig.1(f) demonstrates the high-resolution TEM image of the (Mn_0.85Ge_0.15)Bi₂Te₄ sample. The atomic fringes from the (110) lattice plane with a spacing of 0.215 nm are clearly shown, and the atomic fringes are relatively intact without significant deformation and dislocation. This indicates that the studied samples are high quality single crystals.

To investigate the impact of Ge doping on the magnetic properties of MnBi₂Te₄, we conducted comprehensive magnetic measurements on different Ge doping ratios. In Fig.2(a), the zero-field-cooled (ZFC) and field-cooled (FC) magnetic susceptibility (χ) is plotted against temperature for the (Mn_1–xGe_x)Bi₂Te₄ samples under out-of-plane (H//c) and in-plane (H//ab) magnetic fields. The ZFC and FC plots overlap for all materials, indicating negligible magnetic hysteresis. As displayed in the figure, the magnetic susceptibility of MnBi₂Te₄ (x = 0) rises as temperature decreases under a magnetic field of 1 T, peaking at a Néel temperature (T_N) of 24.7 K before sharply declining, which is in good consistency with previous reports [28,29]. For H//c, the magnetic susceptibility curves of samples with different ratios of Ge can clearly show peak characteristics, indicating the AFM magnetic transition with T_N in these samples. After T_N, the magnetic susceptibility decreases significantly in the H//c direction, whereas it only shows a slight decline in the H//ab direction. This notable variance in χ between the out-of-plane and in-plane orientations indicates an anisotropy in the antiferromagnetic order. Additionally, the AFM magnetic transition weakens and ultimately vanishes with increasing applied magnetic field, attributed to the suppression of inter-layer AFM coupling induced by an external magnetic field [9]. Furthermore, with increasing Ge substitution in (Mn_1–xGe_x)Bi₂Te₄, the 2D ferromagnetic sublattice becomes diluted, resulting in a gradual decrease in T_N as shown in Fig.2(d). The reduction of Néel temperature indicates an obvious weakening of inter-layer AFM coupling.

Fig.2(b) and (c) show the temperature dependence of the inverse magnetic susceptibility (χ⁻¹) with H//c and H//ab when H = 1 T. The χ⁻¹ of all samples above Néel temperature exhibits a linear relationship with temperature, conforming to the Curie−Weiss law expressed as χ = C/(T – θ_W), where C is the Curie constant and θ_W is the Curie−Weiss temperature. By linearly fitting χ⁻¹ versus T, we obtained the effective magnetic moment µ_eff = 5.5µ_B/Mn for MnBi₂Te₄, which is consistent with the theoretical value of 5.9µ_B for high-spin Mn²⁺ ions with 3d⁵ configuration [30]. The θ_W for each composition as a function of Ge concentration is plotted in Fig.2(e). Distinct θ_W temperatures were observed for the out-of-plane and in-plane field directions in samples with x = 0, 0.15, and 0.30 Ge concentrations, while at higher Ge concentrations, both θ_W approached equality, attributed to the reduction of magnetic anisotropy with increasing Ge concentration. Furthermore, the strength of ferromagnetic exchange interaction concerning antiferromagnetic can be confirmed from the ratio of θ_W/T_N, which equals (J_F + J_AF)/(J_F – J_AF) [31]. Here J_F represents the ferromagnetic exchange coupling and J_AF represents the antiferromagnetic exchange coupling. The calculated J_AF/J_F ratio as a function of doping concentration is plotted in Fig.2(f). It is obvious that with the increase of Ge concentration, the absolute value of the J_AF/J_F ratio gradually decreased, indicating a weakening of the AFM coupling in the sample. This finding is consistent with the reasons for the decrease in T_N mentioned above.​

The isothermal magnetization versus magnetic field (M−H) curves under H//c and H//ab are displayed in Fig.3(a)–(f). The M−H curve obtained for the H//ab orientation reveals lower magnetization values with a linear field dependence, implying that the c axis serves as the easy axis for magnetization. For H//c, as the field increases, all samples below T_N exhibit the evolution of the spin-structure from AFM state to canted AFM state (H_c1), and finally to a polarized FM state (H_c2). The two spin-flop transition points are marked with red and black triangles in Fig.3(a)–(f), and the positions of the transition points corresponding to each sample are extracted in Fig.3(g). It illustrates that the spin-flop transition points decrease as the Ge doping level increases, indicating a significant weakening of the antiferromagnetic exchange coupling, which corresponds with the reduction of T_N. Pb and Sn doping can also achieve the effect of reducing the spin-flop transition point of MnBi₂Te₄, suggesting that using non-magnetic ions instead of manganese is an effective strategy to reduce the spin-flop transition point [21,22]. In conclusion, substituting Ge for Mn in MnBi₂Te₄ crystals will lower the critical field of ferromagnetic ordering, which will help realize QAHE states under the low field, favoring its practical application to dissipationless electronic devices and spintronics [15-18].

For a uniaxial antiferromagnet, the saturation field under H//c and H//ab can be expressed in terms of the interlayer antiferromagnetic exchange (J_c) and single-ion anisotropy (D) as gμ_BH_c = 2zSJ_c − 2SD and gμ_BH_ab = 2zJ_c + 2SD, respectively, where g = 2, S = 5/2, and z = 6 is the coordination number for Mn to other Mn in layers above and below. Therefore, J_c and D can be calculated as SJ_c = (4z)⁻¹gμ_BJ_c(H_c + H_ab) and SD = \frac{1}{4}gμ_B(H_ab − H_c), respectively. The calculated SJ_c and SD are shown in Fig.3(h). It is obvious that both SJ_c and SD decrease with increasing Ge content, which was consistent with the situation of Sb doping [32]. The decrease of SJ_c further confirms that Ge doping reduces the interlayer antiferromagnetic coupling of the sample. In addition, the reduction of SD is consistent with the conclusion above that Ge doping reduces the magnetic anisotropy of the sample.

To further study the transport properties of the Ge-doped MnBi₂Te₄ samples, we measured the temperature dependence of resistivity over a range of 2.5 to 300 K, as depicted in Fig.4(a). The resistivity peak temperature of the sample for x = 0, 0.15, and 0.30 is consistent with T_N observed in the magnetic property measurement. This peak is caused by spin scattering due to strong spin fluctuations at temperatures approaching T_N. It is noteworthy that at x = 0.45, 0.60, and 0.75, this peak is absent in the sample and we observe an anomalous upturn in the resistivity at low temperatures. In principle, three primary reasons account for the resistance upturn: electron−electron interaction (EEI), weak localization (WL), and Kondo effect [33-36]. Among the mechanisms mentioned, the resistivity correction from EEI encompasses both singlet and triplet terms. In theory, the singlet term remains independent of the field, while the triplet term exhibits field dependency unless spin-relaxation processes are disregarded. Therefore, when strong spin scattering is present or the triplet term is significantly smaller than the singlet term, the EEI becomes insensitive to the magnetic field. Even if the triplet term contributes notably to the overall EEI correction, the magnitude of the resistance upturn can be influenced by the magnetic field but not completely suppressed. As a result, it is possible to distinguish the electron−electron interaction by comparing the temperature dependence of resistivity under varying applied magnetic fields [37,38]. Fig.4(b) presents the temperature-dependent resistivity of (Mn_0.55Ge_0.45)Bi₂Te₄ under different magnetic fields. The upturn behaviors gradually diminish with the increment of the magnetic field and vanish when the field exceeds 6 T. This observation rules out the dominance of EEI in the low-temperature transport characteristics of the sample. Traditionally, WL phenomena are observed in low-dimensional systems like thin films and nanowires owing to the higher probability of scattering rates leading to quantum interference [39]. Moreover, the conductivity (σ) does not adhere well to the weak localization formulation σ = σ₀ + kT^p/2 where k = 2e²/(ahπ²) and the factor a is defined in terms of Thoules inelastic collision length (L_Th) as L_Th = aT^−p/2 for p = 2, 3, and 3/2 [39]. Thus, the discussion can also exclude the WL effect. Finally, we conclude that the upturns of the resistance are dominated by the Kondo effect.

For systems exhibiting the Kondo effect, the resistive upturn at low temperatures can be modeled using Hamann’s equation [40,41]:

\begin{array}{rl}\rho (T)=& {\rho }_0+q{T}^2+p{T}^5+{\rho }_{\mathrm{K}}\{1-\ln (T/T_{\mathrm{K}})\\ & \cdot [{\ln }^2(T/T_{\mathrm{K}})+S(S+1){\pi }^2{]}^{-1/2}\},\end{array}

where both p and q are fitting parameters; ρ_K, T_K, and S represent the temperature-independent resistivity, the Kondo temperature, and the spin of magnetic impurities, respectively. As illustrated in Fig.4(b), the Hamann fitting provides a satisfactory description of the experimental data, resulting in T_K = 18.63 K and S = 0.13. Thus, we emphasize that the upturns of the resistance are dominated by the Kondo effect.

Fig.5(a)–(f) display the magneto-resistivity (MR) curves obtained at various temperatures. From Fig.5(a), at x = 0, there is a noticeable decrease in ρ_xx over the critical magnetic field of 3.2 T below T_N, and another change in slope occurs at a critical field of 7.3 T. These critical fields, as determined from the MR data, align closely with the values of H_c1 and H_c2 obtained from the magnetic measurement. Above the Néel temperature, noticeable negative magnetoresistivity is observed in samples with x = 0, 0.15, and 0.30 [as shown in Fig.5(a)–(c)], owing to the strong antiferromagnetic spin fluctuation. For samples with x = 0.45, 0.60, and 0.75, the parabolic field above Néel temperature is dependent on MR due to its paramagnetism.

To study the impact of Ge doping on the carrier density in the system, the Hall resistivity ρ_yx was measured for samples with varying doping ratios, as depicted in Fig.6(a)–(f). All the Hall resistivity curves have a negative slope indicating that electrons are the dominant charge carriers. The carrier density can be calculated by the equation n = 1/(eR_H), where n represents the carrier density and R_H represents the Hall coefficient. Fig.6(g) displays the carrier density of each sample at 2.5 K. It is clear that the n-type carrier density increases with the doping concentration, indicating that the carrier density of the sample is successfully modulated by Ge doping. The carrier density increase can also be identified from the plots of temperature-dependent resistivity for materials. As shown in Fig.4(a), at the same temperature, the resistivity of the sample gradually decreases with the increase of the Ge doping ratio.

Ge doping can affect not only the magnetic and transport properties but also the topological properties of MnBi₂Te₄. In the study conducted by Estyunina et al. [42], they used ab-initio calculations to determine that when the Ge concentration exceeds 50%, there is an absence of bulk band inversion at the Γ-point for the contributions of Te p_z and Bi p_z, along with significant spatial redistribution of states at the edges of the band gap into the bulk [42]. This observation suggests a topological phase transition in the system.

4 Conclusions

In conclusion, we have synthesized a series of high-quality single crystals of Ge-doped MnBi₂Te₄. We find that Ge substitutes for Mn in MnBi₂Te₄, which can effectively weaken robust AFM coupling, thereby reducing the external magnetic field that aligns the magnetic moments into the ferromagnetic state, which may provide a possible way to implement the QAHE at lower magnetic field. Electrical transport measurements suggest that the mainly transport dominated carriers are n-type, and the density of the carrier increases with the doping concentration. Additionally, the Kondo effect is observed in the samples with x = 0.45, 0.60, and 0.75. Our studies on Ge-doped MnBi₂Te₄ reveal that element doping effectively modulates the magnetic and transport properties of magnetic topological insulators. This research provides insights into optimizing and achieving the QAHE and other related quantum topological effects.

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