With molecular beam epitaxy, we grew uniformly vanadium-doped Bi2Se3 films which exhibit ferromagnetism with perpendicular magnetic anisotropy. A systematic study on the magneto-transport properties of the films revealed the crucial role of topological surface states in ferromagnetic coupling. The enhanced ferromagnetism with reduced carrier density can support quantum anomalous Hall phase in the films, though the anomalous Hall resistance is far from quantization due to high carrier density. The topological surface states of films exhibit a gap of ∼180 meV which is unlikely to be magnetically induced but may significantly influence the quantum anomalous Hall effect in the system.
Ferromagnetism can induce novel phenomena in topological insulators (TIs) such as the quantum anomalous Hall effect (QAHE) and topological magneto-electric effect.1–4 Ferromagnetic TIs exhibiting these effects could be used to develop new-concept electronic and spintronic applications.5,6 The explorations in this direction were greatly encouraged by the experimental realization of ferromagnetism and QAHE in magnetically doped three-dimensional (3D) TI films.3 Up to now the QAHE has only been observed in Cr- and V-doped (Bi,Sb)2Te3 films, and a ultralow temperature (∼0.1 K) is needed for either of the materials to reach full quantization.3,7 Further studies and applications of the QAHE and other related effects call for new magnetically doped TI materials with good ferromagnetism and different characteristics.
Bi2Se3 has long been studied as a representative 3D TI for its large bulk bandgap (300 meV) and standard Dirac-cone surface states.8 Despite many experimental efforts, one still cannot obtain a Bi2Se3-based magnetically doped TI with well-established long-range ferromagnetism.9,10 The past experimental results on the magnetism and electronic structure of magnetically doped Bi2Se3 are somewhat controversial and quite different from those of magnetically doped (Bi,Sb)2Te3. For example, gap-opening at the Dirac surface states induced by magnetic impurities were reported in several studies on magnetically doped Bi2Se3, but the ferromagnetism and anomalous Hall effect (AHE) observed are always weak.11–13 It is contrary to magnetically doped (Bi,Sb)2Te3 TIs which show clear ferromagnetism and QAHE though the magnetic gap could not be resolved.14 Therefore, the QAHE in magnetically doped Bi2Se3, once being realized, is expected to exhibit distinct features from that in magnetically doped (Bi,Sb)2Te3. In this study, we achieved uniformly V-doped Bi2Se3 thin films by molecular beam epitaxy (MBE) and observed clear long-range ferromagnetism and AHE in them. The result paves the way for the realization of a Bi2Se3-based QAHE system.
V-doped Bi2Se3 films were MBE-grown on SrTiO3(111) substrates by co-evaporation of Bi, Se, and V sources (see supplementary material). Reflective high energy electron diffraction (RHEED) and X-ray diffraction patterns of the V-doped Bi2Se3 films show decent crystalline quality and negligible phase separation induced by V doping (see Fig. S1 of the supplementary material). Figure 1(a) displays the scanning tunneling microscope (STM) topography image of a 7 QL V0.04Bi1.96Se3 film. The surface is distributed with triangle-shaped defects composed of three atoms (see the atomic-resolution image in the inset). Similar to the observations in early STM studies on magnetically doped Bi2Te3 family TIs,15,16 the triangle-shaped defects can be attributed to single V atoms occupying subsurface Bi sites. The domination of the triangle-shaped defects at the surface indicates homogeneous distribution of V dopants in Bi2Se3, which is favorable to formation of long-range ferromagnetism. The observation is similar to that of magnetically doped (Bi,Sb)2Te3 but different from that of Cr-doped Bi2Se3 in which Cr substitutional atoms aggregate into larger defects with various shapes.13,17
Figures 1(b) and 1(d) show the angle-resolved photoemission spectroscopy (ARPES) bandmaps of a 7 QL pristine Bi2Se3 film and a 7 QL V0.04Bi1.96Se3 film measured at 100 K, respectively. Figures 1(c) and 1(e) display the energy distribution curves (EDCs) of Figs. 1(b) and 1(d), respec-tively. We can see that doping a small amount of V atoms (2% of the cations) induces an energy gap of ∼180 meV at the surface states [see Fig. 1(e)]. The origin of the large surface state gap will be discussed below.
Figures 2(a) and 2(b) show the magnetoresistance (MR, defined by MR = (Rxx(H) − Rxx(0)) /Rxx(0)) curves and the Hall traces of VxBi2−xSe3 films with different V concentration x. The MR curve of the pristine Bi2Se3 film (x = 0) exhibits the typical shape of weak anti-localization (WAL). The linear Hall trace indicates the ordinary Hall effect (OHE), for which the slope of the trace is 1/ne, where n represents the two-dimensional carrier density and e represents the electron charge. Estimated from the slope, the charge carriers of the films are n-type with the density ∼2.8 × 1013/cm2. Doping a small amount of V atoms in Bi2Se3 (x = 0.002, 0.005) significantly reduces the MR as well as the phase coherence length lφ and the α coefficient (obtained by fitting the curves with the Hikami-Larkin-Nagaoka model, see supplementary material) because of magnetic scattering induced by V impurities. In the x = 0.02 sample, MR becomes negative and shows two maxima, and the Hall trace exhibits a hysteresis loop of the anomalous Hall effect (AHE) with a linear background of the OHE. These observations clearly indicate long-range ferromagnetism in the sample. The films with higher V concentrations all show ferromagnetism. Figure 2(c) plots the anomalous Hall (AH) resistance RAyx and the sheet longitudinal resistance of the samples of different V concentrations at zero magnetic field. RAyx is defined by RAyx = Ryx − ROyx, where ROyx is the ordinary Hall (OH) resistance. Both RAyx and increase with increasing V concentration. The carrier density estimated from the OHE [see Fig. 2(c)] is little influenced by V doping, staying at ∼3 × 1013/cm2. It implies that V impurities barely introduce charge carriers into Bi2Se3.
The temperature (T) dependences of RAyx [at magnetic saturation (0.7 T)] of the samples with different V concentrations are displayed in Fig. 2(d). The Curie temperature (TC), estimated from the curves, increases with increasing V concentration from 10 K (x = 0.02) to 16 K (x = 0.12). Below TC, RAyx grows with decreasing temperature without showing any tendency of saturation down to 2 K, which suggests strong magnetic disorder in the material.18,19
To understand the mechanism of the ferromagnetism in V-doped Bi2Se3 and its relationship with the electronics structure, we studied the thickness-dependent transport properties of Bi1.97V0.03Se3 films because the evolution of the band structure of Bi2Se3 with thickness has been mapped in detail by ARPES.20 Figures 3(a) and 3(b) show the AH traces (with the OH background removed) and the MR curves of the Bi1.97V0.03Se3 films with the thickness d ranging from 2 QL to 20 QL, respectively. The 2 and 3 QL thick films exhibit non-linear Hall traces without hysteresis and negative MR around zero magnetic field. Similar to the transport properties of Cr-doped Bi2Se3 films,13 the observations suggest that only short range ferromagnetic order exists in the films. The films with d ≥ 4 QL all show hysteresis in their AH traces and MR curves. The coercivity and the remanence ratio [RR = RAyx(0 T)/RAyx(0.7 T)], which characterize the ferromagnetism, both increase with increasing film thickness. In Fig. 3(c), we plot Hc and RR of the films with different thicknesses. Interestingly, in either of the thickness-dependent curves, the slope shows an obvious change at ∼7 QL (see the dashed lines). The growth of Hc and RR with increasing thickness above 7 QL is much slower. Figure 3(d) displays the thickness-dependences of the AH resistance and the longitudinal conductance. The AH resistance first increases with increasing thickness to a maximum at 7 QL and then starts decreasing. The longitudinal conductance increases monotonically with thickness but with the slope above 7 QL significantly larger than that below 7 QL.
Clearly, all the magnetic and transport properties experience a change at around 7 QL. The rapid growth of Hc and RR below 7 QL reflects the gradual formation of long-range ferromagnetic order with increasing thickness. Above 7 QL, the ferromagnetism basically reaches the bulk level and is thus less sensitive to thickness. The increasing AH resistance below 7 QL results from the enhanced ferromagnetism. After saturation of ferromagnetism above 7 QL, the AH resistance decreases with increasing thickness, as the usual 1/d dependence of Hall resistance. The formation of good ferromagnetic order above 7 QL results in a higher longitudinal conductivity than more magnetically disordered thinner films, which explains the more rapid growth of the longitudinal conductance in thicker films. Therefore, all the thickness-dependent transport properties can be attributed to the significant weakening of the ferromagnetism in the Bi1.97V0.03Se3 films below ∼7 QL. The mechanism behind will be discussed below.
The dependence of ferromagnetism on carrier density can provide information on the mechanism of magnetic coupling in a magnetically doped semiconductor. The carrier density of the V-doped Bi2Se3 films can be tuned by a bottom gate with the SrTiO3 substrate as the dielectric layer. Figure 4(a) shows the gate voltage (Vg) dependences of Hc and RR of a 7 QL Bi1.97V0.03Se3 film. Figure 4(b) exhibits the Vg dependences of RAyx/, i.e., tangent of the anomalous Hall angle, at 0 T. And Fig. 4(c) displays Vg dependence of the carrier density. Applying a negative Vg to −200 V reduces the electron density of the film down to 1.5 × 1013/cm2. Hc and RR significantly increase with the decreasing carrier density, which suggests that the ferromagnetism is enhanced as Fermi level is tuned towards the charge neutral point. The increasing anomalous Hall angle with decreasing electron density indicates that the AHE is also enhanced when Fermi level is shifted closer to charge neutral point.
To further decrease the electron density of V-doped Bi2Se3, we tried co-doping Sb atoms into it. An electron density of ∼1 × 1013/cm2 is reached with Sb doping [estimated from Fig. S5(c) of the supplementary material], and the AH resistance is enhanced to 225 Ω, about 7 times of that in the singly V-doped sample with the same V concentration [see Figs. 4(d)–4(h)]. However, the crystalline quality of the film is obviously worsened by Sb-doping, as shown in the RHEED patterns in Fig. S5(a) of the supplementary material. It is because the increase of Sb concentration in Bi2Se3 tends to change the lattice structure from rhombohedral to orthorhombic.21 Hence other methods are needed for further reduction of carrier density.
The observation of enhanced ferromagnetism with decreasing carrier density is distinct from the ferromagnetism mediated by bulk itinerant carriers which are usually observed in III–V DMSs22 and also seen in heavily p-doped Cr-doped (Bi,Sb)2Te3.23 It is however consistent with the magnetic coupling mediated by Dirac surface states in magnetically doped 3D TIs.24,25 The surface-state-mediated ferromagnetism favors longer Fermi wavelength, i.e., lower surface carrier density, which is contrary to the ferromagnetism mediated by bulk carriers. The surface-state-mediated ferromagnetism can support the QAHE because the ferromagnetism survives even when bulk and surface carriers are depleted. The role of Dirac surface states in the ferromagnetic coupling is also seen from the thickness-dependent data shown in Fig. 3. In Bi2Se3 films, the hybridization between the Dirac surface states from the top and bottom surfaces becomes significant below 6 QL.21 In the V-doped Bi2Se3 films, the significant weakening of the ferromagnetism with decreasing thickness occurs below 7 QL. The similar crossover thickness of topological surface states and ferromagnetism implies they may have close relationship. This observation and the enhanced ferromagnetism with decreasing carrier density both support surface state-mediated ferromagnetism in the material.
The QAHE can occur in a magnetic 3D TI when the Fermi level is located in the magnetically induced gap of the Dirac surface states. In Fig. 1(b), we indeed observe a gap of ∼180 meV at the Dirac surface states as the result of V doping. However, such a large gap is not likely induced by the ferromagnetism. The TC of the samples is 10 K–16 K. The corresponding exchange energy should be at most several meV, much smaller than the observed gap size. In Cr-doped Bi2Se3, aggregated Cr impurities can locally contribute to a large exchange energy and exhibit a gap-like feature at the topological surface states in ARPES measurements.13 This possibility is excluded by the STM image in Fig. 1(a), which shows that most V dopants are well separated from each other. In several early studies, gap-like features at Dirac surface states were observed in Bi2Se3 doped with non-magnetic impurities.26–33 There are several possible non-magnetic mechanisms that can explain the gap-like features observed at the Dirac surface states of Bi2Se3.10,26–33 First, dopants can reduce the spin–orbit coupling of Bi2Se3 such that a topological phase transition occurs and the Dirac surface states are removed.10,26–30 Second, the combination of dephasing and impurity scattering can induce strong backscattering of the surface states around the Dirac point, resulting in a gap-like feature here.31 Third, impurity potential can induce a resonance state near the Dirac point, which also leads to a gap-like feature at the surface states.32,33 It is to note that the above non-magnetic mechanisms can work no matter whether the dopants in Bi2Se3 are magnetic or non-magnetic. For the present material, the first case is not likely to happen because the V doping level in the sample (x = 0.04) is much lower than that required for the topological phase transition in Cr-doped Bi2Se3 (x ∼ 0.15)10,13 and In-doped Bi2Se3 (x ∼ 0.12).30 For now, we do not know whether the second or the third mechanism dominates the observed gap-like feature. In either of the cases, the QAHE can be significantly influenced since the effect is associated with the band structure at Dirac point. For the second case, the band structure of the Dirac surface states actually does not change. The QAHE might occur at higher temperature because the large backscattering promotes localization of the surface state electrons.31 For the third case, since the surface band structure near Dirac point is modified by impurity resonance, the surface state-mediated ferromagnetism might be destroyed when the Fermi level is tuned near the gap.32,33 The real magnetic gap can be filled by the resonance-induced change in the surface band structure.32 Therefore, the temperature for observation of the QAHE might be reduced. Further theoretical and experimental studies are required to reveal the exact origin of the observed gap and its influences on the QAHE.
In conclusion, we have prepared uniformly V-doped Bi2Se3 films with MBE and realized long-range ferromagnetism in them. The enhanced ferromagnetism with decreasing carrier density indicates that it is possible to realize the QAHE in the system though the AH resistance is still far from quantization. We observed an energy gap of ∼180 meV at the topological surface states which is unlikely magnetically induced but may significantly influence the QAHE in the system.
SUPPLEMENTARY MATERIAL
See supplementary material for experimental methods and supplementary data.
This work was supported by the National Natural Science Foundation of China (Nos. 11325421, 51661135024), the Ministry of Science and Technology of People’s Republic of China (No. 2013CB921702).