Engineering the breaking of time-reversal symmetry in gate-tunable hybrid ferromagnet/topological insulator heterostructures

Studying the influence of breaking time-reversal symmetry on topological insulator surface states is an important problem of current interest in condensed matter physics and could provide a route toward proof-of-concept spintronic devices that exploit spin-textured surface states. Here, we develop a new model system for studying the effect of breaking time-reversal symmetry: a hybrid heterostructure wherein a ferromagnetic semiconductor Ga1-xMnxAs, with an out-of-plane component of magnetization, is cleanly interfaced with a three-dimensional topological insulator (Bi,Sb)2(Te,Se)3 by molecular beam epitaxy. Lateral electrical transport in this bilayer is dominated by conduction through the topological insulator whose conductivity is a few orders of magnitude higher than that of the highly resistive ferromagnetic semiconductor with a low Mn concentration. Electrical transport measurements of a top-gated heterostructure device reveal a crossover from weak anti-localization (negative magneto-conductance) to weak localization (positive magneto-conductance) as the temperature is lowered or as the chemical potential approaches the Dirac point. This is accompanied by a systematic emergence of an anomalous Hall effect. These results are interpreted in terms of the opening of a gap at the Dirac point as a result of the exchange coupling between the topological insulator surface state and the ferromagnetic ordering in the Ga1-xMnxAs layer. Our study shows that this hybrid system is well suited to explore topological quantum phenomena and to realize proof-of-concept demonstrations of topological spintronic devices at cryogenic temperatures.

A three-dimensional (3D) topological insulator (TI) is characterized by its surface states which are protected by time-reversal (TR) symmetry [1][2][3][4]. The TR symmetry can be broken by doping a TI with magnetic atoms or interfacing a TI surface with a magnetic layer, causing an energy gap opening at the Dirac point [5][6][7][8]. Unique quantum phenomena resulting from the broken TR symmetry have been proposed: such as a topological magneto-electric effect [5], an image magnetic monopole effect [9], topological Kerr and Faraday rotation [5], and the quantum anomalous Hall effect [10]. Some of these phenomena have been demonstrated experimentally [11,12]. With a motivation for studying such effects, synthesis and characterization of magnetically doped 3D TIs with transition metals have been studied [7,[13][14][15][16][17][18]. Angle-resolved photoemission spectroscopy (ARPES) has suggested evidence a gap opening by breaking TR symmetry in magnetically doped TI systems, [7,8,16,19] although recent studies point out an alternative mechanism for the gap seen in such studies [20]. In addition, a spin-resolved ARPES experiment revealed the hedgehog-like spin textures in the modified surface state of Bi 2 Se 3 films by Mn doping [21].
In this paper, we focus on another way of breaking TR symmetry in the TI surface states, interfacing a TI surface to a ferromagnetic insulator (FMI) with perpendicular magnetization to evidence the broken TR symmetry and ultimately to realize topological quantum phenomena and potential spintronic applications [22][23][24][25][26][27]. The key advantage of a TI/FMI heterostructure over the magnetically doped TI system is the selective modification of one surface by an adjacent FMI. Magnetic proximity affects only the interfaced surface, and thus magnetic properties or the resulting effects are free from the magnetism of bulk or another surface of the TI layer. So far, a few TI/FMI heterostructures have been experimentally reported using FMIs interfaced with TIs where the chemical potential is located in or near the conduction band [28][29][30][31][32][33][34]. We note that all these heterostructures involve ferromagnets whose magnetization is in plane. To further separate the FMI-interfaced TI surface from the electrical coupling to the bulk or another surface, the chemical potential needs to be placed in the bulk band gap. Also, to avoid the surface-to-surface tunneling, a TI film needs to be thicker than the critical thickness for hybridization [35]. To study the magnetic proximity, a clean, well-defined TI/FMI interface is necessary, and the FMI should have a magnetization component perpendicular to the TI surface to break the TR symmetry.
We demonstrate a new approach for a TI/FMI heterostructure using a dilute magnetic semiconductor (Ga,Mn)As. The ferromagnetic Curie temperature (T C ) and resistivity as 2 well as the magnetic easy axis of (Ga,Mn)As films can be engineered by the amount of Mn-doping, annealing, and strain [36][37][38]. Here, highly resistive Ga 1−x Mn x As with an outof-plane magnetization is desired. High resistivity was achieved by using a low Mn-doping of x ≈ 0.05 and a perpendicular component of magnetization by growing the (Ga,Mn)As film (15 nm) on an InP (111)A substrate by MBE. (See supplementary information for magnetic and structural characterizations.) An advantage of using (Ga,Mn)As for the TI/FMI heterostructure is the well-defined interface, without an amorphous interfacial layer or secondary phases, as was demonstrated for epitaxial growth of Bi-chalcogenide TIs on GaAs (111) [39]. After growing the (Ga,Mn)As film in a ultrahigh vacuum chamber (low 10 −10 Torr), the substrate was transferred to another ultrahigh vacuum MBE chamber without breaking vacuum for the growth of the 3D TI (Bi,Sb) 2 (Te,Se) 3 thin film (8 nm). The Dirac fermion dynamics in Bi 2 (Te 3−x Se x ) can be engineered by varying the composition of Te (3-x) and Se (x) [40], and we chose x to be 1 (Bi 2 Te 2 Se) to place the Dirac point above the top of the valence band. Further engineering of the chemical potential was achieved by Sb-doping: with an optimal ratio of Bi and Sb (Bi:Sb ≈ 1.25:0.75) we were able to place the chemical potential into the bulk band gap, as confirmed by the electrical transport measurements.
Although the selective modification of one TI surface with an FMI is advantageous, as discussed earlier, the buried interface between TI and FMI restricts direct probing of the modified TI surface state by techniques such as ARPES or scanning tunneling microscopy.
However, electrical transport measurements do provide a route to study the modification of the surface states by quantum corrections to the magneto-conductance (MC) and by the anomalous Hall effect (AHE). For the transport measurements, we fabricated a topgated Hall-bar device with high-κ dielectric HfO 2 and Au/Ti gate metal by standard photolithography (Figs.1a and 1b). One important question for the electrical transport laterally through the heterostructure is whether a current flows only through the TI layer. The black curve in the Figs.1c and 1d represents the resistivity when the current flows through the whole TI/FMI heterostructure while the red curve shows the resistivity of only (Ga,Mn)As layer after the TI overlayer was carefully removed by mechanical scratching. Since the resistivity of the (Ga,Mn)As is more than two orders of magnitude higher than that of the heterostructure below 40 K, we conclude that the current flows mostly through the TI layer and causes a crossover between WAL and WL [42]. When the gap is  6 ture. Notably, in certain regimes of temperatures and gate voltages, we observe the unique coexistence of a WAL peak near zero magnetic field and WL behaviors at larger magnetic fields, indicating at least two decoupled transport channels with different dephasing lengths.
As the gate voltage is tuned from -5 V to 1V at 0.29 K, MC becomes negative (WL) for larger magnetic field while the positive peak (WAL) is still observed for small magnetic field near zero, as shown in Fig. 2b.
The increases as the gate voltage decreases from 1 V to -5 V (-7 V) at 0.1 K (0.29 K). This can be interpreted as E F at the bottom surface being tuned from above towards the magnetic gap, but not passing through it, as illustrated in Fig. 2f. This qualitatively agrees with the WAL-WL crossover when the Berry phase changes from π to a smaller value by tuning E F . Similarly, as we fix the gate voltage to -5 V to place E F close to the gap and vary temperature, α 1 increases with decreasing temperature (Fig. 2g) as ∆ increases at lower temperatures due to the temperature dependence of the interfacial exchange coupling with the adjacent (Ga,Mn)As layer (illustrated in Fig. 2h).
Equation (2) shows that the Hall conductivity is half-quantized in the insulating regime of a single Dirac model, and the half-integer quantum Hall conductivity monotonically decreases as E F moves above the energy gap or as the gap gradually closes with a E F fixed to a position near the gap.
Since our results are not in the regime of the quantized Hall conductivity, the observed Hall conductivity is smaller than e 2 /2h. However, it follows the qualitative behavior of Eq.
(2). Figures 3c(inset) and 3d(inset) clearly show the systematic emergence of the anomalous Hall term R AH xy with respect to the gate voltage and temperature, where R AH xy is obtained after subtracting the ordinary Hall term R OH xy from the Hall resistance as R AH xy = R xy − R OH xy . We show R AH xy instead of σ AH xy since R xx term contains a large contribution of the top surface and affects the values of σ xy = R xy /(R 2 xx + R 2 xy ). The expression for R xy from σ xy can be written as: with σ xx from the Drude model σ xx = e 2 τ n/m where n, m and τ are the carrier density, the effective mass, and the relaxation time between collisions. For E F > |∆|/2, n increases as E F increases (moves away from the gap). Similarly to the case of quantum corrections to MC, the change of R xy reveals a systematic modification of the size of the energy gap and the chemical potential. As the chemical potential lowers and approaches the energy gap by tuning the gate voltage from 1 V to -5 V, the estimated magnitude of the anomalous Hall resistance R 0 xy increases. R 0 xy is the intercept obtained by extrapolating a linear line of the high field Hall resistance. R 0 xy is zero in the case of a closed gap (∆ = 0). When a gap opens and widens, a non-zero R 0 xy monotonically increases. Figure 3c shows the evolution of the anomalous Hall resistance R 0 xy as the chemical potential lowers towards the energy gap. Similarly, Fig. 3d shows the monotonic increase of R 0 xy with decreasing temperature, interpreted as the widening of the gap with decreasing temperature. The interpretation of both gate-voltage dependence and temperature dependence of the AHE is consistent with that of the quantum corrections to the MC with varying gate voltage and temperature.
The onset temperature of both AHE and WL is much lower than the T C of the adjacent (Ga,Mn)As layer, indicating that the exchange coupling between electrons in TI bottom surface and Mn moments in (Ga,Mn)As is much weaker than the exchange coupling between Mn moments in (Ga,Mn)As (Fig. 4).
In summary, we synthesized and characterized a TI/FMI heterostructure of a TI film (Bi,Sb) 2 (Te,Se) 3 on a dilute magnetic semiconductor (Ga,Mn)As. The Ga 0.95 Mn 0.05 As layer is highly resistive with a perpendicular component of magnetization below 50 K. With an optimal Bi to Sb ratio, the chemical potential was placed in the surface state and further tuned by electrical top gating. The crossover between WAL and WL as well as the systematic emergence of AHE was observed with varying temperatures and gate voltages, interpreted as a result of a gap opening in the Dirac surface state due to the TR symmetry breaking by the exchange coupling between the TI surface state and the adjacent (Ga,Mn)As. The results suggest that the systematic changes in MC and AHE can be used as indirect probes to estimate the E F position and the existence of the magnetic gap opening for the surface state .

Acknowledgement
This work was supported in part by DARPA and C-SPIN, one of six centers of STARnet, An advantage of (Ga,Mn)As as an FM for a TI/FM heterostructure is the well-defined interface without any amorphous growth or secondary phases, as demonstrated in the previous work of epitaxial growth of Bi-chalcogenide TIs on GaAs(111) crystal [1]. The clean interfaces between adjacent layers are shown in the high-resolution transmission electron microscopy (TEM) image and energy-dispersive spectrometer (EDS) scanning transmission electron microscopy (STEM) image in Figures S2 and S3.

S2. Weak antilocalization in three-dimensional TI
In three-dimensional (3D) TIs where spin and momentum are strongly "locked", weak antilocalization (WAL) naturally arises from the  Berry phase of electrons going around the Fermi circle of the Dirac surface state [2]. The quantum corrections to the MC for the Dirac surface states are expected to follow the behavior of the equation for a conventional 2D metal with a strong spin-orbit coupling [3]: where  is a prefactor,  is the digamma function, and l  is the coherence length. WAL leads to  = -1/2 (symplectic case) while WL by constructive interference leads to  = 1 (orthogonal case). For an ideal 3D TI, when the Fermi energy E F lies in the bulk conduction band (BCB) or the bulk valence band (BVB), the top and bottom surfaces are coupled by the conducting bulk, and one can expect the prefactor  = -1/2, while  becomes -1 when E F moves into the bulk band gap where the top and bottom surfaces are decoupled by the insulating bulk [4,5]. We note that the exact value of  can depend on inter-channel scattering [4].

S3. Hall conductance with a finite energy gap
Let's consider the anomalous Hall contribution from 2D Dirac model. From a theoretical calculation of TI with a single Dirac surface state with a finite energy gap () at the  point in the Brillouin zone, the Hall conductivity is half-quantized as = 2 /2ℎ in the insulating regime (− |Δ| 2 ≤ ≤ |Δ| 2 ), with the Hamiltonian written as: where , , are the Pauli matrices with basis states of spin-up and spin-down states of real spin, and is the Fermi velocity. The Hall conductance can be evaluated from the TKNN formula [6], and for the above two-band model, a simplified version is given by  Figure S1. a, Temperature dependence of magnetization with perpendicular-to-plane magnetic field for the (Bi,Sb) 2 (Te,Se) 3 /Ga 0:95 Mn 0:05 As heterostructure by SQUID magnetometry.
T C of the (Ga,Mn)As layer is around 50 K. b, Magnetization of the (Ga,Mn)As layer as a function of perpendicular-to-plane magnetic field below T C . Clear hysteresis was observed as shown in the inset. c, XRD of the (Bi,Sb) 2 (Te,Se) 3 /(Ga,Mn)As heterostructure on InP (111)A substrate. Blue, green, and violet lines are the calculated positions of Bi 2 Te 2 Se (003), Bi 2 Te 2 Se (006), InP (111), and GaAs (111) peaks, respectively. The inset shows the typical reflection high-energy electron diffraction patterns observed while the (Bi,Sb) 2 (Te,Se) 3 film growth.