FI/TI heterostructures

Creating a heterostructure of a 3D TI and a FI is of great interest. Several phenomena, predicted for TIs with broken TRS, exist only at the interface. Contrary to the QAHE of magnetically doped TI films,^{Reference Chang, Zhang, Feng, Shen, Zhang, Guo, Li, Ou, Wei, Wang, Ji, Feng, Ji, Chen, Jia, Dai, Fang, Zhang, He, Wang, Lv, Ma and Xue23} a half-integer QAHE can be observed only in a FI/TI heterostructure.^{Reference Qi, Hughes and Zhang7} Furthermore, a FI layer introduces TRS locally, and thus a lithographically patterned FI thin film can open a Zeeman gap at selected regions on a TI surface, an essential prerequisite for confining Majorana fermions (fermions that are their own antiparticles) in a superconducting TI.^{Reference Fu and Kane30,Reference Akhmerov, Nilsson and Beenakker31} One of the excellent properties exhibited by adjoining the FI to a superconducting TI layer is that the local exchange field experienced by the TI is able to lift spin degeneracy without destroying the superconducting pairing, in complete contrast to magnetic impurity doping.^{Reference Hao, Moodera and Meservey32,Reference Moodera, Santos and Nagahama33} This opens up significant new avenues for functional ferromagnetic superconducting TI devices. One of the most critical factors in this proximity-induced approach is interfacial control of the TI/FI system: not only should they be closely interacting magnetically, but they should also be maintaining a chemically ‘intact’ interface; control down to a single atomic layer is necessary to achieve this.

FI/TI heterostructures have shown success in producing ferromagnetism in TIs by the proximity effect with the choice of EuS/Bi₂Se₃.^{Reference Wei, Katmis, Assaf, Steinberg, Jarillo-Herrero, Heiman and Moodera27} An induced interface magnetization was confirmed by various observations. The thickness dependence of the magnetic moment in EuS/Bi₂Se₃ bilayers measured with a SQUID magnetometer exhibited an excess moment from the ferromagnetic TI surface.^{Reference Wei, Katmis, Assaf, Steinberg, Jarillo-Herrero, Heiman and Moodera27} The ferromagnetic order in this TI was further evident from the anomalous Hall effect in the bilayers.^{Reference Wei, Katmis, Assaf, Steinberg, Jarillo-Herrero, Heiman and Moodera27} With similar objectives, Yang et al.^{Reference Yang, Dolev, Zhang, Zhao, Fried, Schemm, Liu, Palevski, Marshall, Risbud and Kapitulnik28} and Kandala et al.^{Reference Kandala, Richardella, Rench, Zhang, Flanagan and Samarth29} investigated the effects on the weak anti-localization (WAL) behavior of the TI in conjunction with an FI, where the electrons with spin-momentum locking are less likely to encounter backscattering, hence they become localized once the time reversal symmetry is preserved. The planar magnetoresistance (MR) of these heterostructures, studied using patterned Hall bars with in-plane applied magnetic field (EuS has an in-plane easy axis), showed hysteretic MR signifying proximity-induced ferromagnetic order of charge carriers in Bi₂Se₃.^{Reference Wei, Katmis, Assaf, Steinberg, Jarillo-Herrero, Heiman and Moodera27}Figure 2a shows an example of this for a 1 nm EuS/20 nm Bi₂Se₃ bilayer. The sample resistance undergoes a minimum at the bilayer’s ferromagnetic coercive field (H _C), independent of the angle between the applied in-plane field and the electric current. The large number of random magnetic domains that develops (Figure 2b) at H _C coincides with the occurrence of resistance minima (or higher electrical conduction). This unconventional behavior was attributed to the isotropic distribution of domains and hence the observed isotropic planar MR. Interestingly, the Dirac SSs along the domain wall were theoretically predicted to have zero mass carrying chiral conduction modes similar to the quantum Hall edge channels,^{Reference Hasan and Kane1,Reference Qi and Zhang2} in agreement with the experimental observations of the MR dips (increased conduction) at H _C. ^{Reference Wei, Katmis, Assaf, Steinberg, Jarillo-Herrero, Heiman and Moodera27}

Figure 2.

(a) Planar magnetoresistance of a Bi₂Se₃/EuS sample measured at T = 1.0 K indicates domain wall-assisted electron conduction. Curves are shifted along the y-axis for clarity. (b) Schematic diagram showing the inferred magnetic moment distribution between magnetic domains at the Bi₂Se₃/EuS interface. Figure adapted from Reference 27.

Generally, all the FIs have an in-plane easy magnetization axis, although canted magnetization or small perpendicular magnetic hystereses have been reported.^{Reference Wei, Katmis, Assaf, Steinberg, Jarillo-Herrero, Heiman and Moodera27–Reference Kandala, Richardella, Rench, Zhang, Flanagan and Samarth29} However, the perpendicular magnetic anisotropy (PMA) can be engineered by choosing a proper interface layer, which is attributed to the hybridization of the electronic states.^{Reference Freeman and Wu34} Strong PMA in transition metal/rare-earth multilayers has been reported.^{Reference Chappert and Bruno35,Reference Shan and Sellmyer36} Thus the proper choice of a FI and TI material combination may lead to a strong PMA. Nevertheless, it may be noted that QAHE has also been predicted in FI/TI heterostructures with an in-plane easy magnetization axis, although this is yet to be experimentally confirmed.^{Reference Liu, Hsu and Liu37}

Magnetically doped TI materials

Doping 3d TM impurities into TIs is a convenient approach to bring robust long-range ferromagnetic order, as demonstrated by the success of diluted magnetic semiconductors (DMSs).^{Reference Ohno, Chiba, Matsukura, Omiya, Abe, Dietl, Ohno and Ohtani12–Reference Dietl14} Doping TI compounds with magnetic atoms could be a straightforward way to reach the goal. However, it is important to confirm the absence of other secondary phase formation in the bulk or locally on the surface, and/or clustering or non-uniform distribution of dopants in the parent compound (all of which can yield a false magnetic signature). The results become fortuitous and unreliable, unless the above factors are carefully addressed to rule them out.

Ferromagnetism has been realized in several TI materials of the Bi₂Se₃ family doped with 3d TM ions.^{Reference Xu, Neupane, Liu, Zhang, Richardella, Wray, Alidoust, Leandersson, Balasubramanian, Barriga, Radar, Landolt, Slomski, Dil, Osterwalder, Chang, Jeng, Lin, Bansil, Samarth and Hasan15–Reference Chang, Zhang, Feng, Shen, Zhang, Guo, Li, Ou, Wei, Wang, Ji, Feng, Ji, Chen, Jia, Dai, Fang, Zhang, He, Wang, Lv, Ma and Xue23} The observation of a Zeeman gap at the SS Dirac cone, a sign of broken TRS, has been reported in Fe- or Mn-doped Bi₂Se₃.^{Reference Xu, Neupane, Liu, Zhang, Richardella, Wray, Alidoust, Leandersson, Balasubramanian, Barriga, Radar, Landolt, Slomski, Dil, Osterwalder, Chang, Jeng, Lin, Bansil, Samarth and Hasan15,Reference Chen, Chu, Analytis, Liu, Igarashi, Kuo, Qi, Mo, Moore, Lu, Hashimoto, Sasagawa, Zhang, Fisher, Hussain and Shen16} Figure 3 shows one example of ferromagnetic TI with Cr doping; the magnetic moment per Cr ion was observed to be close to 2μ_B, with an optimum hysteresis loop for a Cr ion content of 5.2%.^{Reference Haazen, Laloë, Nummy, Swagten, Jarillo-Herrero, Heiman and Moodera17} For Cr ion concentrations above or below this, hysteresis was present at lower temperatures. The participation and magnetic nature of charge carriers in the doped TI was seen in the planar MR signal (inset of Figure 3), while in a perpendicular magnetic field, no hysteresis was seen (preferentially in-plane magnetization).^{Reference Haazen, Laloë, Nummy, Swagten, Jarillo-Herrero, Heiman and Moodera17} The Hall traces exhibit a linear dependence on the perpendicular magnetic field, and the MR exhibited WAL behavior at 10 K, both of which are the characteristics of a TI with TRS. Below 10 K, a nonlinear Hall signal gradually developed, accompanied by the evolution of MR into weak localization behavior, which implies broken TRS. However, long-range ferromagnetic order with perpendicular easy axis is absent since no anomalous Hall loop was observed.^{Reference Chang, Tang, Wang, Feng, Li, Zhang, Wang, Wang, Chen, Liu, Duan, He, Ma and Xue18,Reference Liu, Zhang, Chang, Zhang, Feng, Li, He, Wang, Chen, Dai, Fang, Xue, Ma and Wang19} Comparing the in- and out-of- plane magnetization data, Cr-doped Bi₂Se₃ thin films displayed in-plane magnetization.

Figure 3.

Magnetic moment per Cr ion as a function of applied in-plane magnetic field at T = 4 K. Inset: planar magnetoresistance signal in a sample with x = 1.3% at T = 1 K, showing clear hysteresis. Adapted from Reference 17.

A well-defined anomalous Hall effect (AHE), however, was seen in Mn-doped Bi₂Te₃,^{Reference Hor, Roushan, Beidenkopf, Seo, Qu, Checkelsky, Wray, Hsieh, Xia, Xu, Qian, Hasan, Ong, Yazdani and Cava20} and Cr-doped Bi₂Te₃ or Sb₂Te₃ films.^{Reference Zhang, Chang, Tang, Zhang, Feng, Li, Wang, Chen, Liu, Duan, He, Xue, Ma and Wang21–Reference Chang, Zhang, Feng, Shen, Zhang, Guo, Li, Ou, Wei, Wang, Ji, Feng, Ji, Chen, Jia, Dai, Fang, Zhang, He, Wang, Lv, Ma and Xue23} To understand the contrasting magnetotransport properties of Cr-doped Bi₂Se₃ and Bi₂Te₃, Zhang et. al. studied eight quintuple layers (QLs) of Cr-doped Bi₂(Se_xTe_1–x)₃, an isostructural, isovalent mixture of Bi₂Se₃ and Bi₂Te₃. The Hall traces of all the films measured at T = 1.5 K are summarized in Figure 4a, revealing a highly systematic evolution of coercivity (H _C) and the AHE resistivity ρ_yx⁰ at zero applied magnetic field. They further constructed a magnetic phase diagram by plotting the ρ_yx⁰ values as a function of the Se (or Te) concentration. At the base temperature of T = 1.5 K, the phase diagram was separated into two distinct regimes: a ferromagnetic phase with positive ρ_yx⁰ and a paramagnetic phase with negative ρ_yx⁰, as shown in Figure 4b. Because the transition between the two magnetic phases occurs at the ground state, it is a quantum phase transition driven by the change in chemical composition, as confirmed by ARPES measurements and density functional theory calculations.^{Reference Zhang, Chang, Tang, Zhang, Feng, Li, Wang, Chen, Liu, Duan, He, Xue, Ma and Wang21}

Figure 4.

(a) Systematic evolution of the Hall effect for all the samples (0 ≤ x ≤ 1) in an eight quantum layer Bi_1.78Cr_0.22(Se_xTe_1–x)₃ measured at T = 1.5 K. (b) Magnetic phase diagram of Bi_1.78Cr_0.22(Se_xTe_1–x)₃ summarizing the intercept $$\rho _{yx}^0 $$ as a function of x and T. The T _C of the ferromagnetic phase (FM) is indicated by the solid symbols (PM = paramagnetic phase). Adapted from Reference 21.

Quantum anomalous Hall effect

The quantized version of AHE, QAHE, predicted to be one of the representative quantum phenomena displayed by TRS-broken TIs, was observed experimentally in a system with 5 QL Cr-doped (Bi_xSb_1–x)₂Te₃ thin films (i.e., five successive QLs were grown, which results in a film thickness of ∼5 nm).^{Reference Chang, Zhang, Feng, Shen, Zhang, Guo, Li, Ou, Wei, Wang, Ji, Feng, Ji, Chen, Jia, Dai, Fang, Zhang, He, Wang, Lv, Ma and Xue23} In order to observe QAHE in a TI, one needs three prerequisites:^{Reference Qi, Hughes and Zhang7} First, the growth of TI quantum well thin films on insulating substrates (e.g., sapphire (0001) or SrTiO₃ (111)).^{Reference Chang, He, Wang, Ma, Liu, Zhang, Chen, Wang and Xue38} Thinner TI films promote localization of dissipative channels and result in a gap between the lowest order quantum well subbands, larger than the ferromagnetic exchange gap. Second, a long-range ferromagnetic state in the TI that should continue into the insulating regime and have an easy magnetization axis perpendicular to the film plane is another necessity. Third, the chemical potential should be tunable into the magnetic gap. As discussed in the previous section, ferromagnetic Cr-doped Bi₂Se₃ has in-plane magnetization. On the other hand, Mn-doped Bi₂Te₃, Cr-doped Bi₂Te₃, and Sb₂Te₃ show perpendicular magnetic anisotropy. Among these materials, Cr-doped Sb₂Te₃ seemed to be the best material (i.e., the one with the strongest ferromagnetic properties), as it showed carrier-type and density-independent AHE, hence the QAHE.^{Reference Chang, Zhang, Feng, Shen, Zhang, Guo, Li, Ou, Wei, Wang, Ji, Feng, Ji, Chen, Jia, Dai, Fang, Zhang, He, Wang, Lv, Ma and Xue23}

The p-type conduction in Sb₂Te₃ is usually due to anti-site defects,^{Reference Jiang, Sun, Chen, Wang, Li, Song, He, Wang, Chen, Xue, Ma and Zhang39} whereas Bi₂Te₃ is intrinsically n-type and has the same structure as Sb₂Te_3.^{Reference Zhang, Chang, Zhang, Wen, Feng, Li, Liu, He, Wang, Chen, Xue, Ma and Wang40} Thus, by partially replacing Sb with Bi in Cr-doped Sb₂Te₃, the chemical potential is tunable across the Dirac point as was confirmed by ARPES measurements.^{Reference Chang, Zhang, Liu, Zhang, Feng, Li, Wang, Chen, Fang, Qi, Zhang, Wang, He, Ma and Xue22}Figure 5 shows the magnetic field dependent Hall resistance of 5QL Cr_0.22(Bi_xSb_1–x)_1.78Te₃ films grown on sapphire (0001) substrates with different Bi:Sb ratios keeping the Cr doping constant. At T = 1.5 K, all films showed near square-shaped AHE hysteresis loops, suggesting strong ferromagnetism with perpendicular axis magnetization.^{Reference Chang, Zhang, Liu, Zhang, Feng, Li, Wang, Chen, Fang, Qi, Zhang, Wang, He, Ma and Xue22} With increasing Bi concentration, the ordinary Hall effect evolved from positive to negative, showing carrier type changing from p- to n-type, with no effect on the ferromagnetism in Cr-doped (Bi_xSb_1–x)₂Te₃ despite a significant change of the carrier density as well. The Curie temperature (T _C) stayed unchanged, even in the rather insulating samples around the p- to n- transition. This showed carrier independent ferromagnetism, supporting the existence of a FI phase likely by a van Vleck mechanism (i.e. by modulation of the crystalline electric fields at magnetic ion sites due to lattice vibrations).^{Reference Qi, Hughes and Zhang7} The anomalous Hall (AH) resistance, on the other hand, exhibited a dramatic and systematic change with Bi doping. The largest AH resistance was ∼3 kΩ, when the sample had the lowest carrier density. Although this number is larger than the AH resistance observed in most ferromagnetic metals, it still is far from the quantized value (∼25.8 kΩ).^{Reference Chang, Zhang, Liu, Zhang, Feng, Li, Wang, Chen, Fang, Qi, Zhang, Wang, He, Ma and Xue22}

Figure 5.

Magnetic and electric properties of Cr-doped (Bi_xSb_1–x)₂Te₃ films. Magnetic field dependent Hall resistance R _yx of the Cr_0.22(Bi_xSb_1–x)_1.78Te₃ films with (a) x = 0, (b) x = 0.15, (c) x = 0.2, (d) x = 0.25, (e) x = 0.35, and (f) x = 0.5 at various temperatures. Adapted from Reference 22.

Further optimization of sample growth and measurements at ultralow temperature (∼30 mK) yielded QAHE in 5 QL Cr-doped (Bi_xSb_1–x)₂Te₃ thin films on SrTiO₃(111) substrates. The high dielectric constant of SrTiO₃ at low temperature allowed for the possibility of applying a sufficiently large electric field to fine tune the carrier density. Figure 6a–b shows the magnetic field dependence of the Hall resistance (ρ_yx) and longitudinal resistance (ρ_xx), respectively, measured at T = 30 mK for various gate bias (V _g). The shape and coercivity of the hysteresis loops are nearly unchanged, with V _g showing carrier independent ferromagnetism.^{Reference Qi, Hughes and Zhang7} At the saturated magnetization state, ρ_yx is nearly independent of the magnetic field, suggesting uniform ferromagnetic order and charge neutrality of the sample, whereas the AH resistance changed dramatically with V _g, with a maximum value of h/e² (25.8 kΩ) occurring at V _g ∼1.5 V. The MR curve exhibited the typical hysteretic shape as in ferromagnetic metals.^{Reference Chang, Zhang, Feng, Shen, Zhang, Guo, Li, Ou, Wei, Wang, Ji, Feng, Ji, Chen, Jia, Dai, Fang, Zhang, He, Wang, Lv, Ma and Xue23}

Figure 6.

The quantum anomalous Hall effect measured at 30 mK. (a) Magnetic field dependence of ρ_yx at different V _g values. (b) Magnetic field dependence of ρ_xx at different V _g values. (c) Dependence of ρ_yx(0) (blue squares) and ρ_xx(0) (red circles) on V _g. The vertical purple dash-dotted lines in (c) indicate V _g for the charge neutral point ($V_{\rm{g}}^{\rm{0}}$). Figure adapted from Reference 23.

The most important observation, the Hall resistance exhibiting a distinct plateau with the quantized value h/e ² at zero applied magnetic field (QAHE), is shown in Figure 6c. Complementary to this ρ_yx plateau, the longitudinal resistance ρ_xx(0) shows a dip, reaching a value of 0.098 h/e², yielding a ρ_yx(0)/ρ_xx(0) ratio (Hall angle) of 84.4°. These results demonstrated the realization of QAHE in magnetically doped TI films. It may be noted that, compared with QHE systems, all of these doped TI samples reported/displaying QAHE had a rather low mobility (<1000 cm²/Vs). The observation of QAHE not only shows the ability to obtain QHE without Landau levels but also paves a way for developing low-power future electronics. It also indicates the feasibility of discovering other predicted exotic quantum phenomena in TIs, such as the topological magnetoelectric effect^{Reference Qi, Hughes and Zhang7} and Majorana bound states.^{Reference Fu and Kane30,Reference Akhmerov, Nilsson and Beenakker31}

Conclusions and prospects

We have provided a brief review of the phenomenon of broken TRS in TIs, which is achievable both through the proximity effect in FI/TI heterostructures and magnetic impurity doping. The proximity-induced ferromagnetism originates from a uniform interface exchange field that does not structurally disturb the TI. In transition metal ions-doped TIs, long-range ferromagnetic order was found in Cr (or Mn)-doped Se- and Te-based TIs. In carefully optimized and electric field tuned Cr-doped (Bi_xSb_1–x)₂Te₃ thin films, QAHE was demonstrated, while the ferromagnetism in the system was seen to be insensitive to the carrier type and density, demonstrating a novel magnetic TI phase.

The proximity effect of a FI/TI heterostructure not only enables the creation of cleaner ferromagnetic TIs with larger surface exchange gap, but also allows locally breaking TRS in designated areas over a TI surface by lithographic patterning. This might be used to create exotic domain wall states between the TI surface regions with and without TRS. Furthermore, a FI can form a seamless interface with a topological superconductor to confine Majorana bound states by a proximity-induced Zeeman gap, whereas magnetic impurities may easily destroy the superconducting pairing.^{Reference Fu and Kane30–Reference Hao, Moodera and Meservey32} Besides, the zero-field half integer quantum Hall effect is also expected to be a hallmark of the FI/TI/FI sandwich structure.^{Reference Qi, Hughes and Zhang7} In magnetic element-doped and ferromagnetic TIs, the observation of QAHE has set the possibility and hope for observing many other exotic quantum phenomena predicted in TIs, such as a topological magnetoelectric effect,^{Reference Qi, Hughes and Zhang7} image magnetic monopoles,^{Reference Qi, Li, Zang and Zhang11} and Majorana bound states.^{Reference Fu and Kane30,Reference Akhmerov, Nilsson and Beenakker31} Importantly, since the QAHE inherits high mobility quantum Hall edge channels, low-power-consumption spintronic devices will be significantly promoted.