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Observation of chiral currents at the magnetic domain boundary of a topological insulator

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Science  28 Aug 2015:
Vol. 349, Issue 6251, pp. 948-952
DOI: 10.1126/science.aaa0508

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Magnetizing a topological insulator

Inducing magnetism in a topological insulator can lead to exotic effects. The usual experimental route is to introduce magnetic dopants into the material, but that approach is intricate and creates unwanted disorder. Wang et al. used a simpler technique: They fabricated a bilayer consisting of Bi2Se3, a topological insulator, and EuS, a magnet. The physical proximity of EuS induced magnetism on the surface of Bi2Se3. This approach allowed for the creation of magnetic domains at will and the detection of characteristic current flowing along the domains' edges.

Science, this issue p. 948

Abstract

A magnetic domain boundary on the surface of a three-dimensional topological insulator is predicted to host a chiral edge state, but direct demonstration is challenging. We used a scanning superconducting quantum interference device to show that current in a magnetized topological insulator heterostructure (EuS/Bi2Se3) flows at the edge when the Fermi level is gate-tuned to the surface band gap. We further induced micrometer-scale magnetic structures on the heterostructure and detected a chiral edge current at the magnetic domain boundary. The chirality of the current was determined by magnetization of the surrounding domain, and its magnitude by the local chemical potential rather than the applied current. Such magnetic structures provide a platform for detecting topological magnetoelectric effects and may enable progress in quantum information processing and spintronics.

The metallic surface of a three-dimensional topological insulator (3D-TI) is protected by time-reversal symmetry (TRS). Breaking TRS opens a band gap on the surface Dirac cone and transforms it into a Chern insulator (14). TRS-broken surface states are predicted to exhibit topological magneto-electric effects (1) and, when coupled with a superconductor, Majorana fermions (57). Just as the surface Dirac cone is a signature of the nontrivial topological bulk band structure of a time-reversal invariant 3D-TI, bulk-boundary correspondence dictates that the TRS-broken surface states with a nonzero Chern number manifest as a gapless chiral edge state (CES) at its boundary (1).

In the special case where the boundary is the edge of the sample surface, a CES along the edge leads to a quantized Hall conductance equal to e2/h, where e is the electron charge and h is the Planck constant, even at zero magnetic field. This quantized anomalous Hall conductance was observed only in a 3D-TI doped with a high concentration of magnetic impurities to break TRS, with the measurements performed at very low temperatures to achieve ballistic transport between contacts (8, 9). More generally, a CES theoretically should exist at a magnetic domain boundary (1, 10), which does not need to be the physical boundary of the system. In this case, the presence of a CES changes only the local conductivity and therefore does not contribute to the conductance of the system (11). The CES at a magnetic domain boundary can be used to investigate 1D quantum transport without edge effects (1214), to induce a parity anomaly (4), or to realize magnetically defined quantum bits (15).

Inducing magnetism on the surface of a TI through proximity to a ferromagnet provides an alternative strategy for breaking the TRS on the surface states without disrupting the bulk. Previous bulk magnetic and transport measurements (16) revealed some evidence of enhanced magnetization at the interface of a heterostructure composed of EuS, a known ferromagnetic insulator (FMI) (1719), and Bi2Se3, a prototypical TI (2023) (Fig. 1A). For our experiments, a Hall bar was etched through the bilayer using a shadow mask (Fig. 1B) for transport measurements. The Curie temperature of the EuS (10 nm)/Bi2Se3 (5 nm) heterostructure was previously found by magnetoresistance and bulk magnetic measurement to be approximately 15 K (16, 24), comparable to that of bulk EuS (17).

Fig. 1 Scanning SQUID microscopy of a TI-FMI heterostructure shows micrometer-scale magnetic domains.

(A) Schematic of the EuS/Bi2Se3 bilayer nanostructure on the SrTiO3 substrate under the pickup loop and field coil of a SQUID. (B) Optical image of the patterned bilayer film. The Hall bar has all the layers shown in (A), and the etched area has only the SrTiO3 substrate. (C) Scanning SQUID flux (Φ) image of the green square area in (B) at 4.1 K after zero-field cooling and at 19 K (inset). The pickup loop (cyan) is shown to scale. Φ0 is the flux quantum. (D) Susceptometry (dΦ/dIF) micrograph of the area in (C). (Inset) Susceptibility as a function of distance from the surface of the film at 5 K (red) and 21 K (blue). The lower right corner of (C) and (D), which corresponds to an etched area, shows small flux and susceptibility.

We employed scanning superconducting quantum interference device (SQUID) microscopy (Fig. 1A), a sensitive probe for detecting magnetic flux from magnetic domains or current on the mesoscopic scale (25, 26), to search for the chiral edge states in a EuS/Bi2Se3 heterostructure (Fig. 1B). The pickup loop (Fig. 1A) was integrated into a two-junction SQUID that converts the flux through the loop (Embedded Image) into a voltage signal (2729). Flowing a current (IF) through the field coil (Fig. 1A) provided a local magnetic field for either susceptometry measurement (Embedded Image) or to manipulate magnetic domain structures in our bilayers (Fig. 1A). Current magnetometry (Embedded Image) was performed simultaneously with direct current (DC) magnetometry by measuring the component of the flux through the pickup loop that is locked to the frequency and in phase (Embedded Image) with the alternating current (AC) source-drain bias current (IAC).

A typical magnetometry micrograph (Fig. 1C) of the sample under zero field cooling displayed micrometer-scale patches of magnetic domains at the base temperature of 4 K. Such magnetic features disappeared at 19 K (Fig. 1C, inset), consistent with the Curie temperature of these samples (16, 24). The etched area of the Hall bar showed zero magnetization (Fig. 1C) and susceptibility (Fig. 1D). The much-reduced susceptibility of the film at 21 K (Fig. 1D, inset) was also consistent with its ferromagnetic nature. To break the TRS at the EuS/Bi2Se3 interface with magnetization, we applied a uniform out-of-plane magnetic field of 30 G while cooling the sample from 18 K to 5 K (30). After field cooling, the magnetic structure close to the edge of the Hall bar, as determined from scanning susceptometry (Fig. 2A), showed a change of magnetization from the film side to the substrate side; this indicated that the out-of-plane magnetic field induced, on average, a mixture of out-of-plane and in-plane remnant magnetization (31). The lateral variation of magnetization along the edge may be caused by the inhomogeneity of the film and some domain structure (31). The magnetic field from the magnetization is less than 1 G (31) and is too small to induce any observable Landau levels (32) at 4 K.

Fig. 2 Edge current in a magnetized topological insulator appears by tuning the back gate.

(A to C) Magnetometry images along the sample edge after cooling in a uniform 30 G out-of-plane magnetic field at various back-gate voltages VG. (D to F) are the corresponding current magnetometry (Embedded Image) images. The 0-V images [(A) and (D) insets)] were taken in a slightly shifted area. (G) Cross sections of the current magnetometry images [(D), (E), and (F)] along the direction and position shown along the arrows in (D). (H) Current density for the current magnetometry image in (E), extracted by fast Fourier transform. The arrows indicate the FWHM width of the edge current, which is likely resolution-limited.

To determine how current flows around the edge of a Hall bar when it is magnetized, we simultaneously performed magnetometry (measurement of the static magnetic field) and current magnetometry (lock-in measurement of the magnetic field produced by the applied current) at various back-gate voltages VG (Fig. 2). Although the magnetometry images did not change as a function of VG (Fig. 2, A to C), current magnetometry images strongly depended on VG (Fig. 2, D to F). We found a current magnetometry pattern with both positive and negative polarity developing along the edge as the back-gate voltage was tuned to be more negative (Fig. 2D). The current magnetometry pattern reached a maximum at VG = –220 V (Fig. 2E). The pattern became weaker with decreasing VG and completely disappeared at VG = –350 V (Fig. 2F). The cross sections normal to the edge from these images (Fig. 2G) clearly exhibited a field profile consistent with an edge current developing when the Fermi level is gate-tuned to the surface band gap induced by magnetism (25). The extracted current density from the flux image at VG = –220 V indicates that the edge current appears to be confined to the edge with a full width at half maximum (FWHM) width of 4.1 μm (Fig. 2H), which is likely resolution-limited for the 3-μm-diameter pickup loop at a scan height of ~1 μm in this particular measurement (31).

Having demonstrated the existence of edge states at the physical boundary of the heterostructure, we investigated whether there were any CESs at a magnetic domain boundary. We applied DC to the field coil at 12 K while scanning the field coil in a square (Fig. 3A) to write a magnetic structure with two opposite out-of-plane magnetizations next to each other and away from the edge (31).

Fig. 3 Chiral edge current emerges along the magnetic domain boundary induced by the field coil of a SQUID.

(A) Magnetic structure induced by applying 30-mA current to the field coil while scanning the SQUID over a 30 by 30 μm square at 12 K in the sequence indicated by the numbered dashed lines. The negative area at the top was scanned 30 μm higher with –30 mA field coil current. The field coil (orange) is sketched to scale. (B) The magnetometry image when the sample current bias IAC is reversed from (A) to be left-to-right. (C and D) Corresponding current magnetometry images of the magnetometry images in (A) and (B) at VG = –220 V. (E) is the current magnetometry image with right-to-left IAC at VG = 0 V. (F) Current density and current streamlines (black) extracted from the current magnetometry image in (D). [For details about writing the magnetic structure and applying the current bias, see (31).]

To investigate the current around this magnetic structure, we performed current magnetometry with source-drain voltage biased both ways (Fig. 3). The reversal of the bias voltage does not cause any change to the induced magnetic structure (Fig. 3, A and B). For the current flowing in a conventional metal, the direction of the current and therefore its magnetic field reverses sign when the source-drain bias is reversed (fig. S4). Such nonchiral current is present in our TI-FMI heterostructure: On the left side of the images in Fig. 3, C and D, in which average magnetization is zero (Fig. 3A), as well as in the image with VG = 0 V (Fig. 3E), there is a linear background that switches sign when the bias current is switched. This is consistent with the out-of-plane magnetic field from a uniform plane current flowing horizontally (fig. S5A) and likely comes from the bottom surface or the bulk. The background current is caused by the gradient of chemical potential across the thickness of the Bi2Se3 layer, even when the chemical potential on the top is tuned to inside the energy gap of the surface states by the back-gate voltage (33), as is also known to happen in 2D quantum spin Hall systems (25).

In addition, sharp current flux features appeared that, in contrast to the background current, did not switch sign as the voltage bias was reversed (Fig. 3, C and D). These features, reminiscent of the flux generated by an edge current (Fig. 2E), appeared along the magnetic domain wall at VG = –220 V (Fig. 3, C and D) but were absent at VG = 0 V (Fig. 3E), which is consistent with the gate dependence of the edge current (Fig. 2) and suggests their common origin from the states in the surface gap. The sign of these features is opposite (Fig. 3, C and D) along the left edges of the top and bottom domains with reversed magnetizations (Fig. 3A), indicating the chiral nature of the edge current. These chiral features in current magnetometry disappeared when the temperature was increased to 12 K, whereas the magnetization became weaker but was still present (fig. S6). This observation suggests that a strong magnetization is essential to the chiral current features and therefore only the top surface of Bi2Se3 is contributing to such features, because exchange coupling from the FMI layer is short range (34, 35). In stark contrast, current magnetometry on a trivial semimetal-FMI bilayer showed no such chiral features around a magnetic structure at base temperature, regardless of gating (fig. S4).

The average of the current magnetometry images with opposite source-drain bias canceled out the nonchiral background current and clearly reveals the chiral features along the magnetic domain boundary in the shape of a square (fig. S3B). We find that the peaks in current magnetometry were approximately described using the out-of-plane magnetic field generated by thin current wires with finite width (31). The current density (Fig. 3F) extracted from the current magnetometry image (Fig. 3D) (25) confirmed this picture of chiral edge current surrounding the magnetic domain boundary with chirality determined by magnetization of the domain. Because the magnetization that we induced with the field coil was below the saturation magnetization of similar films (16), there could be domains beyond the resolution of the pickup loop inside the magnetic structures (Fig. 3A). However, the chiral current from these smaller domains only reduces the average intensity of chiral features in current magnetometry in a similar fashion that these domains reduce the average magnitude of magnetization detected by the pickup loop (31).

To identify what determines chiral current intensity, we performed current magnetometry on the magnetic structures induced at various positions along the Hall bar, where the electrochemical potentials (μ) differ (Fig. 4). Magnetic structures were induced at different locations along the Hall bar (Fig. 4A and fig. S12) by cooling the sample from 15 K while applying DC current to the field coil (31). The current magnetometry images (Fig. 4, B to G) correspond to such structures induced on the left of the Hall bar close to the source contact (Fig. 4, B and C), in the middle of the Hall bar (Fig. 4, D and E), and on the right of the Hall bar close to the drain contact (Fig. 4, F and G). Although the sign of the current features was the same for all configurations (at VG = –200 V) (Fig. 4, B to G), as expected from a chiral effect, the intensity was strongly position-dependent. For the magnetic structure close to the source, the intensity of the current features was stronger when the voltage bias was on the source (Fig. 4B) than when the bias was on the drain (Fig. 4C). This behavior was reversed for the magnetic structure close to the drain (Fig. 4, F and G), whereas the middle structure displayed approximately equal intensity when the voltage bias was switched (Fig. 4, D and E).

Fig. 4 Chiral current intensity depends on electrochemical potential.

(A) Magnetic structure induced by the field coil when applying 30 mA of current and cooled from 15 K. The field coil (orange) is sketched to scale. (B to G) Current magnetometry images when the left side of the Hall bar is attached to a voltage lead and the right side is grounded [(B), (D), and (F)] versus the opposite lead configuration [(C), (E), and (G)]. (B) and (C), (D) and (E), and (F) and (G) are from the magnetic structures on the left, middle, and right of the Hall bar, respectively (as indicated on the sketch at the top of each panel). When the magnetic structure is closer to VAC than to the ground, the modulation of μ is larger, yielding the stronger chiral feature in current magnetometry. (H) Band structure of the surface states (SS) and the CES around a magnetic domain boundary. Arrows indicate the direction of spin polarization, and the color coding of the surface states indicates how their momentum-dependent spin texture is modified by the magnetization of the top EuS layer from in-plane (green and magenta) to out-of-plane (blue and yellow). The AC biased source-drain voltage VAC = V0 sin(ωt) modulates the electrochemical potential μ, which is proportional to the magnitude of the edge current.

Because the location of the application of the voltage bias does not change the total current flowing through the Hall bar, the position-dependent current flux intensity suggests that μ rather than the bias current IAC determined the chiral current intensity. μ at each location was linearly proportional to the position along the Hall bar because the Hall bar’s length is much longer than the typical electron mean free path (Fig. 1B and fig. S12D). This dependence on μ is reminiscent of the chiral edge current in a quantum Hall state, where the domain boundary is the edge of the sample (34). Current flowing along each edge is proportional to the μ of the contact from which the charge is emitted. Meanwhile, the total bias current depends on the difference in μ between the source and drain contacts. If the voltages on the contacts are equal, then there will be no net current, but there will be a circulating edge current with a magnitude dependent on the source-drain voltage relative to the back-gate voltage (11).

In our TI-FMI heterostructure, the drop of μ across the magnetic structure was small compared with the drop of μ across source and drain (due to the ratio of their lengths), and therefore the local μ determined the magnitude of the chiral edge current. Because current magnetometry is a lock-in measurement (31), the measured magnetic response from the chiral current is proportional to the modulation of the local μ when the Fermi level is in the surface gap. When the domain boundary is close to the alternating AC voltage bias (Fig. 4, B and G), μ is more strongly modulated than when it is close to the ground (Fig. 4, C and F), yielding a stronger chiral current intensity in current magnetometry (Fig. 4H). The magnitude of the extracted current I (fig. S5B) along the magnetic domain boundary (31) is in agreement with calculations of the current carried by one spin-polarized edge mode in the ballistic transport regime I = eμ/h (11, 35, 36).

Our results not only demonstrate the existence of CES at the magnetic domain boundary of a TI but also establish a versatile platform in scanning SQUID microscopy for imaging and manipulating broken TRS TI surface states on the mesoscopic scale. The broken TRS state and its chiral edge will be a playground for exploring interaction between TIs and FMIs (3740).

Supplementary Materials

www.sciencemag.org/content/349/6251/948/suppl/DC1

Materials and Methods

Supplementary Text

Figs. S1 to S12

Reference (42)

References and Notes

  1. It is possible to induce CES with in-plane magnetization, but the effect may be very weak in Bi2Se3 (41) because of the small warping effect (23).
  2. See the supplementary materials on Science Online.
  3. Acknowledgments: These measurements were supported by the Center for Function Accelerated nanoMaterial Engineering (FAME), one of six centers of STARnet, a Semiconductor Research Corporation program sponsored by the Microelectronics Advanced Research Corp. (MARCO) and the Defense Advanced Research Projects Agency (DARPA). Preliminary measurements and analysis were supported by the Department of Energy (DOE), Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under contract DE-AC02-76SF00515. The SQUID microscope and sensors were developed with support from NSF-NSEC 0830228 and NSF IMR-MIP 0957616. Y.H.W. is partially supported by the Urbanek Fellowship of the Department of Applied Physics at Stanford University. For sample preparation, F.K., P.J-H., and J.S.M. acknowledge support by the Massachusetts Institute of Technology’s Materials Research Science and Engineering Center (MRSEC) through the MRSEC Program of the National Science Foundation under award DMR-0819762. Partial support for sample development was provided by NSF (DMR-1207469), ONR (N00014-13-1-0301) (F.K. and J.S.M.), and by the DOE, Basic Energy Sciences Office, Division of Materials Sciences and Engineering, under award no. DE-SC0006418 (F.K. and P.J-H.). We are grateful for the assistance from G. Gibson, M. Ketchen, and M. Huber on developing the SQUID sensors and from I. Sochnikov, E. Spanton, J. Palmstrom, and K. C. Nowack on the measurement, as well as for stimulating discussions with S.-C. Zhang, X.-L. Qi, J. Wang, D. Goldhaber-Gordon, and B. I. Halperin.
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