Strong spin-dephasing in a topological insulator - paramagnet heterostructure

The interface between magnetic materials and topological insulators can drive the formation of exotic phases of matter and enable functionality through manipulation of the strong spin polarized transport. Here, we report that the spin-momentum-locked transport in the topological insulator Bi$_2$Se$_3$ is completely suppressed by scattering at a heterointerface with the kagome-lattice paramagnet, Co$_7$Se$_8$. Bi$_2$Se$_{3-}$Co$_7$Se$_{8-}$Bi$_2$Se$_3$ trilayer heterostructures were grown using molecular beam epitaxy. Magnetotransport measurements revealed a substantial suppression of the weak antilocalization effect for Co$_7$Se$_8$ at thicknesses as thin as a monolayer, indicating a strong dephasing mechanism. Bi$_{2-x}$Co$_x$Se$_3$ films, where Co is in a non-magnetic $3^+$ state, show weak antilocalization that survives to $x = 0.5$, which, in comparison with the heterostructures, suggests the unordered moments of the Co$^{2+}$ act as a far stronger dephasing element. This work highlights several important points regarding spin-polarized transport in topological insulator interfaces and how magnetic materials can be integrated with topological materials to realize both exotic phases as well as novel device functionality.

highly uniform and homogeneous systems 32,33 . These respective materials enable the application of strong magnetic disorder on the TI without breaking time reversal symmetry, which allows a cleaner view of the mechanisms driving the spin polarized transport. Trilayer structures used here were composed of a 7 QL Bi2Se3 bottom layer, a variable thickness Co7Se8 layer ranging in number of monolayers from n = 1-23 ML, and a 7 QL Bi2Se3 top layer, as schematically shown in Fig. 1(c) along with a corresponding scanning transmission electron microscopy (STEM) image in Fig. 1(d). This structure was chosen since the bottom Bi2Se3 layer served as a necessary nucleation layer for Co7Se8, and the top Bi2Se3 layer preserved inversion symmetry between the Co7Se8 interfaces. Since the Bi2Se3 is in the regime where the bulk bands are occupied and the Co7Se8 is also metallic, both the top and bottom surface states can interact with the Co7Se8 through the free electrons in the bulk state of Bi2Se3. As such, this heterostructure enables probing both the nature of the spin-polarized transport as well as the topological character via ARPES on the top surface of the Bi2Se3.
Samples were grown using a home-built MBE system operating at a base pressure lower than 1×10 -9 Torr. Cobalt, bismuth, and selenium were all supplied via thermal effusion cells. The source temperature of each cell was adjusted prior to growth to give the desired flux that was measured by a quartz crystal microbalance. Bi2Se3 and Co7Se8 were both grown in a self-regulated manner, where the flux ratios between the Bi:Se and Co:Se were around 1:10. As such, the Se shutter remained open during the entire growth sequence, whereas the growth of Bi2Se3 and a Co7Se8 were, respectively, controlled by timing the opening of the shutters based on the individual fluxes. Samples were grown on 5×5 mm 2 Al2O3 (0001) substrates, which were treated prior to growth with an acetone and IPA ultrasonic bath to degrease the surface, followed by annealing in air at 1000 °C. In all cases, an initial 2 QL Bi2Se3 buffer layer was deposited at 150 °C to maintain a smooth interface 34 . The remainder of the heterostructures were grown at 200 °C, with the exception of the pure Bi2Se3 sample grown at 275 °C. Doped samples were grown by keeping the bismuth and selenium shutters open, while opening the Co shutter many times within a single monolayer to achieve homogeneous doping (see Fig. S1). X-ray diffraction measurements were performed on a Malvern Panalytical's X'Pert³ with a 4-circle goniometer using Cu kα1 radiation. Transport measurements were performed in the van der Pauw geometry using pressed indium wires as contacts and measured in a Quantum Design Physical Property Measurement System down to a base temperature of 2 K. ARPES measurements were performed on a Scienta-Omicron ARPES system with a DA30-L electron analyzer, a helium lamp source with photon energy of 21.2 eV, and base temperature <10 K. The energy resolution of the ARPES measurement is 10 meV. Due to the difficulty in preserving the quality of the 2D materials during manual sample-preparation, STEM samples were thinned using a FEI Nova 200 focused ion beam (FIB), with the initial lift-out performed at an ion accelerating voltage of 30 kV, and final thinning performed at an accelerating voltage of 2 kV. Surface gallium ion implantation from the FIB thinning was removed by argon ion milling in a Fischione 1040 Nanomill, with 5 minutes per side at a voltage of 0.9 kV, which was followed by 1 minute of milling each side at 0.5 kV. The samples were subsequently imaged using a NION UltraSTEM 100 operating at an electron accelerating voltage of 100 kV, which was corrected for fifth order spherical aberrations. The images were collected using an annular dark field detector with the collection angles from 84-200 mrad. Images were collected with a pixel dwell time of 8 μs. Overall beam exposure was minimal due to observed sensitivity to beam-damage.
To understand the global structure of the trilayer heterostructures, XRD measurements were performed to probe crystallinity, morphology, and interfacial character. 2θ-θ scans of the parent materials, Bi2Se3, and Co7Se8, as well as the trilayer heterostructures for various Co7Se8 thicknesses are shown in Fig.  2(a). The Bi2Se3 sample was 14 nm, the Co7Se8 was 10 nm, and for the trilayer heterostructures the Co7Se8 thickness ranged from n = 1-23 ML. The 2θ-θ scan of Bi2Se3 shows the 003m series of peaks (m is an integer), which are highlighted by square-symbols. The peaks due to the Al2O3 substrate are marked with asterisks. Further, for the Bi2Se3 peaks Laue oscillations due to coherent scattering off the top and bottom interfaces can be seen about the most intense peaks, which indicates the films are extremely flat. The Co7Se8 film shows only the 001 and 002 reflections, as marked by circles. The lack of Laue oscillations indicate that the films are slightly rougher or, since the intensity of the oscillations scale with the intensity of the reflection, that they are below the scan's detection threshold due to the relative weakness of Co7Se8 001 and 002 peaks. The latter point is highlighted by comparing the 0012 reflection of Bi2Se3 at around 2θ ≈ 37°, which is similar magnitude at the 002 peak of Co7Se8. Neither of these reflections show Laue oscillations, which indicates that the films are likely of similar flatness. The 2θ-θ scans of the trilayers samples, with Co7Se8 thickness ranging from n = 1-23 ML, reveal a complex array of features. For the single monolayer the data looks very similar to Bi2Se3, only with some of the reflections slightly distorted and with weak oscillations that are superimposed upon the main peaks. With increasing Co7Se8-thickness, the Bi2Se3 peaks are further distorted, and these unusual oscillations become more prominent. Moreover, at 4 ML, the Co7Se8 peaks clearly emerge and by 23 ML are relatively sharp, which indicate that a significant portion of scattering emanates solely from Co7Se8.
We further investigated the source of these intensity oscillations utilizing XRD simulations of the heterostructures for two plausible origins (see Supplementary Materials and Ref. [35] for additional details). For both cases, when the films are thick, interference should qualitatively occur if reflections from both the parent materials are close in 2θ. This occurs since the reflected X-rays can interfere constructively or destructively; away from these regions no coherent scattering should be seen. In the first scenario two pristine Bi2Se3 layers with sharp interfaces are separated by a thickness equivalent to n monolayers of Co7Se8, representing an ideal structure, shown in Fig. 2(b) for the n=8 condition labelled "ideal 8 ML". This accounts for interference off the various interfaces, and clearly reproduces the experimental data. In the second scenario, we assume some interdiffusion of Co into the Bi2Se3 and perhaps Bi into the Co7Se8 which will likely occur asymmetrically if the Bi2Se3/Co7Se8 interface is different than the subsequent Co7Se8/Bi2Se3 interface 33,36 . This would be accompanied by a modification of the out-of-plane lattice parameter in the various layers 37 , thus creating, for example, peak broadening or multiple Bi2Se3 reflections very close in 2θ depending on the degree of lattice distortion and cobalt interdiffusion. However, interference should only occur at lower 2θ where the overlap of the reflections would be maximum and would give way to a splitting of the peaks at higher 2θ. This is shown in the simulation in Fig. 2(b) labeled "slightly mixed" and "heavily mixed", where the intensity is calculated for a bilayer structure composed of two Bi2Se3 of slightly different out-of-plane lattice parameters. For the lightly mixed case, a small (1%) variation in the lattice constant from the bulk Bi2Se3 reproduced the reflections at high 2θ values, but not the interference pattern at lower 2θ. For the heavily mixed sample which had a larger (5%) variation in the lattice constant, there is some interference at low 2θ values but a large degree of peak splitting at high 2θ. Moreover, X-ray photoelectron spectroscopy (XPS) was carried out on the trilayer with n = 8 ML and doped samples and is shown in Fig. S2. No cobalt signature could be seen for the trilayer sample, confirming that there is minimal diffusion of Co into the Bi2Se3 layers and that the surface is free of Co impurities. As such, this scenario can be eliminated. Considering this and returning to the experimental data in Fig. 2(a), comparing the trilayer structures to the simulated data reveals only the ideal case closely matches the experimental data at both high and low 2θ values, confirming the global structural quality of the trilayer heterostructures. Now that the structural quality has been confirmed, we move on to magnetotransport measurements. Conductance versus magnetic field is shown in Fig. 3(a) for the trilayer samples in comparison to the 14 nm Bi2Se3 (0 ML) film measured at 2 K. With increasing magnetic field, the conductance for the Bi2Se3 sample shows a sharp drop with increasing field; at higher fields the conductance transitions to a weak B 2 dependence, where B is the magnetic field, which is characteristic of the freeelectron response. For the trilayer heterostructures, the sharp drop in the conductance is substantially suppressed even for samples with Co7Se8 thickness as thin as a single monolayer, and by 4 ML the conductance exhibits solely a B 2 dependence. Transport in TIs in low magnetic field is characterized by a sharp cusp-like feature centered around B = 0 T 38 . The origin of this feature, called weak antilocalization (WAL), is due to the magnetic field suppressing coherent backscattering. In TIs specifically, and, more generally, 2D systems with strong spin-orbit coupling, WAL is due to a reduction of the probability to backscatter, which is driven by the accumulation of phases of opposite sign for clockwise and counterclockwise backscattering loops 39 . Application of a small magnetic field, therefore, suppresses this effect, which is manifest as a sharp drop in conductance. The WAL effect can be quantified by fitting the experimental data using the Hikami-Larkin-Nagaoka (HLN) model for the change in conductance, in which ( ) is the digamma function, h is Planck's constant, e is the electron charge, and the two free parameters are α which quantifies the number of 2D channels (1 per channel; this has been rescaled by 1/(2π) relative to the original HLN formulation), and ∅ is the dephasing magnetic field 40 . The dephasing magnetic field is related to the phase coherence length ∅ by the following equation.
The data was fit using the HLN model with an additional B 2 term to account for the free electron response. The fits are shown in Fig. 3(a) as solid lines for the Bi2Se3 and the trilayer with n = 1. The resulting ∅ and α are plotted versus Co7Se8 thickness in Fig. 3(b) and (c), respectively. For larger thicknesses, the low-field kink was absent, and, therefore, we took both ∅ and α to be zero indicating that there is no spinpolarized transport. The complete quenching of this effect is surprising since the transport for TIs should be immune from such scattering events so long as time reversal symmetry is intact. This immunity is demonstrated by the magnetoconductance data shown in Fig. 3(d). This data was taken from Bi2-xCoxSe3 where x ranged from 0.07 to 0.50. For these films it is assumed that Co takes a non-magnetic 3 + valence state and predominately replaces Bi 3+ . Over this range the WAL effect can be seen clearly to survive to the highest doping range as the cusp in the conductance in the low field regime is maintained. Fitting to the HLN function shows that α is nominally constant and lϕ drops relative to the undoped materials.
To understand the data for both the trilayer structures and doped samples it is instructive to compare length scales for the scattering processes. For the trilayer samples scattering off the Co7Se8 layer provides complete dephasing, thus, the minimum length scale is then set by the Bi2Se3 thickness. Physically this implies that all backscattering loops that contribute to WAL effect contain at least one scattering event off the Co7Se8 layer. For Bi2Se3, where both the bulk and the surface states contribute to the WAL effect, scattering off the surfaces does not provide a dephasing mechanism, since WAL is observed from the thick limit of hundreds of nanometers down to the thin limit where surface scattering dominates the resistance 38,41,42 ; moreover, in Bi2Se3/(Bi1-xInx)2Se3/Bi2Se3 trilayer heterostructures, there a strong dependence on the doping levels and thickness of the (Bi1-xInx)2Se3 43 . In contrast to this, in Bi2-xCoxSe3, the length scale is approximately set by the average spacing of the dopants, which is of the order of a few nanometers for x ≈ 0.1. Therefore, scattering due to Co defects should occur at a significantly higher rate than scattering off the Co7Se8 interfaces in the trilayer heterostructures. Yet, WAL is clearly observed for the highest doped samples. It is emphasized that the Co should be in a 3 + valence state with no net moment. This highlights the extreme sensitivity of the spin-polarized transport processes to magnetic defects.
As the spin-polarized transport is fully suppressed, the question arises whether the trilayer system is topological. To answer this question in situ ARPES was performed on a trilayer sample with a Co7Se8 thickness of 8 ML at low temperature (<10 K). The spectrum for this sample is shown on the left of Fig. 4  (a). From this the linearly dispersive topological surface band is visible. This, and the degenerate Dirac point (DP), can be more clearly seen by processing the spectrum with the curvature method described in Ref. [44], as shown on the right-hand side of Fig. 4(a) and the equipotential map at various energies shown in Fig. 4(b). To further illustrate the gapless nature of the DP, we plot the stacking energy distribution curves (EDCs) in Fig. 4(c). The red curve indicates the EDC at kx = 0, which shows a single peak at ~300 meV that corresponds to the DP position in the 2D spectrum in Fig. 4(a). However, the ARPES measurement only probes the top surface of the trilayer heterostructure. The electronic structure of the interface between Co7Se8 and Bi2Se3 remains uncertain. This, however, motivates the future question regarding the nature of the states that form at the interfaces of Co7Se8. The strong magnetic moments of the Co will certainly interfere with the spin polarized states, but strong hybridization among the Co7Se8 states and the topological surface states may also inhibit its formation entirely. Since this interface is well below the escape depth for photoelectrons used here, this question will have to be addressed in the future in combination with first principles calculations.
To conclude, we have shown that spin-polarized transport is completely suppressed in the topological material Bi2Se3 by embedding an epitaxial layer of a kagome-paramagnetic material, Co7Se8, using MBE growth. Scattering off the magnetic Co 2+ in the Co7Se8 is the primary source of the strong spin dephasing. This is in stark contrast to Bi2-xCoxSe3 where spin polarized transport is found to survive the non-magnetic disorder due to Co 3+ even in doping levels as high as x = 0.5. In situ ARPES measurements show that, despite the absence of spin polarized transport, the topological band structure on the top surface remains intact. Taken with a broader prospective, the current measurements have deep implications. One of the biggest impacts comes from device functionality that relies on spin-polarization. Topological materials are supposed to be immune to disorder that obeys time reversal symmetry. Although Co7Se8 is not magnetic, it does have a net moment which causes complete spin dephasing of the charge carriers. As such, this demonstrates that in a device the materials need to be carefully chosen to avoid anything with a net moment-specifically, paramagnetic substrates with a net moment should be avoided for the growth of topological materials. Alternatively, if control over spin dephasing is desired, strong moment materials such as Co7Se8 can be incorporated epitaxially with TIs. Further questions regarding the source of dephasing in topological systems necessitates understanding and quantifying the dependence of the scattering processes on the details of the interfaces. As an example, metallic materials with a net moment, like Co7Se8, may be more susceptible to suppressing spin-polarized transport processes than an insulating material with net moments. As such, proposals for realizing novel topological phases necessitate interfacing magnetic metals, insulators, or both, thus highlighting the significance of these questions. This work brings about a broader view of spin polarized transport processes in topological materials, which is significant for realizing novel phases of matter at topological interfaces and for engineering topological devices.

Supplementary Materials
See supplementary materials for additional X-ray diffraction data, details regarding the simulations, and Xrap photoemission spectroscopy. Fig. 1. Materials and experimental schematic. (a) Crystal structure of TI Bi2Se3 showing the layered hexagonal structure consisting of 3 repeated quintuple layer (QL) units of Se-Bi-Se-Bi-Se, three of which make the unit cell. (b) Co7Se8 is characterized by an ordered vacancy structure forming a kagome network of Co atoms in layer 1 and a hexagonal structure in layer 2. This leads to a mixed valence of 2 + and 3 + states, which are shown at the bottom decorating the layers as red arrows and blue circles, respectively. The structure is formally monoclinic, however the 〈11 ̅ 0 〉 can be thought of as the pseudohexagonal 〈010 〉 direction, showing the hexagonal arrangement between the two unit cells. (c-d) Schematic of the trilayer structure (c) and accompanying scanning high-angle annular dark field (HAADF) scanning transmission electron microscopy (STEM) image (d) for a Bi2Se3 (7 QL)/Co7Se8 (23 ML)/Bi2Se3 (7 QL) trilayer sample.

Fig. 2. X-ray diffraction (XRD) measurements and simulations of trilayer heterostructures and parent materials.
(a) XRD 2θ-θ scans of the parent materials Bi2Se3 and Co7Se8 as well as trilayer heterostructures with Co7Se8 thickness ranging from n = 1-23 monolayers (ML). The Bi2Se3 peaks are marked by square-symbols, Co7Se8 peaks are marked by circles, and the Al2O3 peaks are marked by asterisks. (b) Results from simulated structures including single-layer Bi2Se3, bi-layer Bi2Se3 with differing c-axis lattice parameters labeled "lightly mixed" and "heavily mixed" (the expected splitting at large 2θ is labeled "Δ2θ",) as well as a Bi2Se3 heterostructure with spacing equivalent to 8 ML of Co7Se8 labeled "ideal 8 ML" (see Supplement Materials). X-ray diffraction of the doped samples can be found in Fig. S1.

Fig. 3. Conductance versus magnetic field for trilayer heterostructures and doped samples. (a,d)
Change in conductance versus magnetic field for the trilayer heterostructures (a) and for  where the data is shown as symbols and fit is the solid lines. Curves are offset for clarity. (b-c,e-f) Extracted α (number of conductance channels) and ∅ (phase coherence length) parameters from the HLN model are plotted for the trilayers (b-c) and Bi2-xCoxSe3 (e-f), respectively. The single Bi2Se3 layer is the black square symbol, the trilayer are blue triangles, and the Bi2-xCoxSe3 are the red circles. The dashed lines are guides-to-the-eye.

X-ray diffraction simulations of trilayer samples.
Insight into the structure of trilayer films was obtained by modeling of the specular Bragg reflections 1 . The model was written in terms of out-of-plane scattering vector qz = 4πsin(2θ/2)/λ where for the instrument used λ = 1.5406 Å. The X-ray diffraction from a thin-film epitaxial sample is given by the square modulus of the sum of amplitudes from the individual layers. The specular intensity, ISpec, is calculated using a kinematic model as a function of qz and is given by where the full structure factor of the sapphire substrate is ( ) and for the Bi2Se3 layers , ( ), which is indexed by m = 1 for the bottom layer and m = 2 for the top layer. The parameters used are as follows: In eq. (1) S is an overall scale factor, the term in the denominator of the for Al2O3 accounts for the surface truncation, and, in the third term, the phase term, ( ,1 + ) models the spatial separation among the two Bi2Se3 layers where ,1 is the total thickness of the first Bi2Se3 layer and is the thickness of the equivalent Co7Se8 layer. In eq. (2) for Al2O3 cSub = 12.991 Å is the lattice parameter along the c-axis and the terms in the parenthesis in the exponent index the atomic positions within the unit cell. For eq. (2-3) ρi is the atomic weight as an approximation to the atomic form factor. In eq (3), dBiSe = 9.526 Å, n = 7 is the number of unit cells of Bi2Se3, and again the terms in the parenthesis in the exponent index the atomic positions within the unit cell. For the simulation of the ideal structure the thickness of the Co7Se8 is 8 ML which is about 41 Å. For the lightly mixed structure dBiSe,1=dBiSe, and dBi2Se,2=0.99×dBiSe, and tCoSe = 0 Å 2 , while the heavily mixed sample is structure dBi2Se,2=0.95×dBiSe 2 . Finally, the exponential − , / 2 2 is the Debye-Waller term that was included to account for vertical fluctuations in the atomic positions that appears as a fall off of the intensity with increasing qz, and only changes the relative intensities of the reflections. The semiempirical parameters σj,Bi = 0.001 and σj,Se = 0.01 is related to the root-mean-square vertical displacements of atoms 1,3 .

Fig. S2
Surface compositional analysis by X-ray photoelectron spectroscopy (XPS) performed on the 8 ML trilayer heterostructure (bottom black curve), doped sample with x = 0.7 (middle red curve), and Co7Se8 thin film (top blue curve). Cobalt is clearly visible on the surface of the doped sample and while no cobalt peak is observed for the trilayer structure, indicating the Bi2Se3 surface is free of Co impurities.