Evidence for ferromagnetic coupling at the doped topological insulator/ferrimagnetic insulator interface

Three-dimensional (3D) TIs feature novel phases of quantum matter with an insulating bulk band gap and gapless Dirac-like band dispersion surface states (SS). Unlike the different electronic properties of the surface and the bulk universally existing in all solids owing to the inevitable termination of the periodic lattice structure near the surface, TIs present a new class of nontrivial SS arising from the intrinsic strong spin-orbital coupling.^1–3 These low-dimensional conducting states are immune to localization as long as the disorder potential is time-reversal-invariant⁴ and therefore have strong implications for emerging technologies such as dissipationless spintronics and quantum computing. Breaking time-reversal-invariance by introducing magnetic perturbation, on the other hand, reveals a complex phenomenology associated with an excitation gap of the surface spectrum, resembling that of a massive Dirac fermion.^5,6 Such a system with a tunable gap promises rich exotic topological phenomena and would allow purely electric control of the surface transport and magnetization.^7–10 

Breaking TRS can be accomplished by either doping the TI host with magnetic ions or by designing TI/magnetic heterostructures.^11–32 Within the growing family of magnetically doped TIs, ferromagnetism has been observed in Cr- and Mn-doped single crystals of Sb₂Te₃,^11–13 Fe- and Mn-doped single crystals of Bi₂Te₃,^14,15 and Mn- and Cr-doped thin films of Bi₂Se₃.^16–18 Apart from transition metals, rare-earth metals such as Gd,¹⁹ Dy, and Sm²⁰ have also been explored as an effective dopant to induce long-range magnetic ordering in Bi₂Se₃ or Bi₂Te₃.²¹ Growing TIs on top of ferromagnetic metals (FMs) and insulators (FMIs), or vice versa, has been shown to produce an exchange interaction affecting the SS of TIs. Although pioneering theoretical work on TIs has demonstrated a pronounced effect of an adjacent magnetic layer,^22–24 successful experimental demonstrations are rather limited, and include that of GdN/Bi₂Se₃ by Kandala et al.,²⁵ and EuS/Bi₂Se₃ by Yang et al.,²⁶ and Wei et al.²⁷ Moreover the effect is limited to low temperature (<  22 K) due to the low T_C of the selected FMI. The interfacial magnetism of (anti-)FM/TI heterostructures, such as Fe/Bi₂Se₃,^28–30 Co/Bi₂Se₃²⁹ and Fe/Bi_2−xMn_xTe₃³¹ has also been investigated and robust magnetism was obtained by means of proximity effects. However, it should be noted that with the presence of a metallic layer, the SS of the TI can be significantly altered, and device designs are constrained due to the short circuit caused by the metal layer.

This work focusses on a heterostructure consisting of a magnetically-doped TI interfaced with a FMI. The T_c of the magnetically doped TIs, generally less than ∼35 K, is still well below room temperature (RT).^11–20 However, very recently we published a work demonstrating enhancement of the magnetic ordering in Cr-doped Bi₂Se₃ grown on a ferrimagnetic insulator (FMI) Y₃Fe₅O₁₂ (YIG) via the proximity effect.³² Garnet-type YIG is a well-known FMI with a high T_C (∼550 K) and a long spin diffusion length. YIG is ferrimagnetic and each formula unit contains two Fe ions occupying octahedral sites and three Fe ions occupying tetrahedral sites coupled antiparallel. Proximity effects have been demonstrated in PdPt/YIG,³³ Pt/YIG,³⁴ and Nb/YIG.³⁵ Strong exchange coupling effects are anticipated in heterostructures consisting of materials with two-dimensional quantum surface states, as in our experimental system Bi_2−xCr_xSe₃/Y₃Fe₅O₁₂.³² This work demonstrated that the penetration depth of the proximity effect was large (up to 6 nm at 30 K) and decreased quickly with increasing temperature (by 80% from 30 to 50 K), compared to that of conventional dilute ferromagnetic semiconductors (DMSs), suggestive of a different mechanism for carrier propagation near the TI surface.³⁶ Here we present a further study of the interfacial magnetic interaction in this bilayer system using the synchrotron-based XMCD technique.^37–40 The unique elemental selectivity of XMCD enables unambiguous determination of the nature of magnetic coupling of the doped TI/FMI interface by measuring independently the magnetization of the doped TI and the YIG as a function of temperature.

Samples³² consisted of 50 nm YIG (111) films, which were deposited on gallium gadolinium garnet (Gd₃Ga₅O₁₂ or GGG) (111) substrates using pulsed-laser deposition (PLD),^41,42 then coated with 10 nm Bi_1.89Cr_0.11Se₃ thin films grown at 200 °C in a Perkin-Elmer molecular-beam epitaxy (MBE) system. Structural and magnetic properties of YIG were measured by X-ray diffraction (XRD) and magneto-optical Kerr effect (MOKE) magnetometry as reported previously.⁴³ Bi (99.9999%) and Cr (99.99%) were evaporated from effusion cells at 470°C and Se (99.99%) from a cracker cell at 240 °C, and growth of the Bi₂Cr_2−xSe₃ was monitored by reflection high-energy electron diffraction (RHEED). Figure 1(a)-1(b) presents a typical RHEED pattern of the Bi_1.89Cr_0.11Se₃ epitaxial thin film grown on YIG(111) compared with that on Si(111). The diffraction patterns and in-plane lattice constants are similar suggesting that the enhancement of T_C for the Bi_1.89Cr_0.11Se₃/Y IG, above that of of Bi_1.89Cr_0.11Se₃/Si (∼20 K), is more likely due to the presence of the YIG than to structural changes caused by the substrates.

The detailed interfacial topography and crystalline structure were characterized using high-angle annular dark-field (HAADF) high-resolution scanning transmission electron microscopy (STEM). Cross-sectional foils of Bi_1.89Cr_0.11Se₃/YIG(111) and YIG/GGG(111) were prepared by focused ion beam (FIB), during which all parameters were carefully optimized to avoid ion injection and specimen damage, including the accelerating voltage, beam current, and tilt angle. As presented in Figure 2(a)-2(b), the HAADF images confirm the highly ordered hexagonal and quintuple-layered structure of the Bi_2−xCr_xSe₃ thin films without detectable Cr segregation. Owing to the high stability of YIG and the relatively low growth temperature of Bi_1.89Cr_0.11Se₃, no significant intermixing occurs at the Bi_1.89Cr_0.11Se₃/Y IG and YIG/GGG interfaces.

The Bi_1.89Cr_0.11Se₃/Y IG (111) was characterized initially by 4-point magneto-transport measurements. The films were patterned into Hall bar devices by CHF₃ dry etching for 20 s and contacts were made from Ti 10nm/Au 100 nm (Figure 3(a)). An AC current of 0.05 - 0.1 μA at 1300 Hz was applied and the voltage drop across inner contacts was detected. Figure 3(b) shows the Hall resistance (R_xy) vs. perpendicular field and the anomalous Hall resistance (R_AHE) which was found from R_AHE = R_xy - R₀ ⋅ H,⁴⁴ in which the latter term represents the ordinary Hall resistance. Figure 3(c) compares R_AHE of Bi_1.89Cr_0.11Se₃ on YIG and on Si., from which it is clear that the TI/YIG has a higher T_C than TI/Si by about 20K. A similar difference was found from the longitudinal resistance R_xx. Weak anti-localization (WAL) was found for TI/YIG at low temperatures and low fields, indicative of the gapped topological surface states below T_C.^12,17,45 Up to at least 50 K the valleys of the WAL cusp exhibited a shift as the scan direction of the field was reversed, with minimum resistance at the coercive field H_c.

The magnetic moment of the Cr and Fe was measured at 6 - 300 K by X-ray absorption spectroscopy (XAS) and XMCD at the L_2,3 absorption edges, as described in Ref. 32. Beamline I10 at Diamond Light Source, UK was used with circularly polarized X-rays at normal incidence, Figure 4(a). The XAS measurements used total-electron yield detection (TEY) and the XMCD was calculated as the difference between the XAS spectra, σ^- - σ⁺, for opposite X-ray helicity at 10 kOe. Figure 4(b)-4(c) shows XAS and XMCD of the Cr and the Fe of TI/TIG. The Cr line was attributed to predominately Cr³⁺ cations by comparison with the line shape of CdCr₂Se₄⁴⁶ and CrFe₂O₄ spinels.⁴⁷ We conclude from the lineshape that Cr³⁺ is present in Bi sites in the lattice, consistent with transport data.¹⁷ 

On the other hand, the Fe XMCD shows a remarkably detailed multiplet structure and the XMCD spectrum shows alternating positive and negative peaks corresponding to the contributions of the octahedral Fe³⁺ and tetrahedral Fe³⁺ of YIG, respectively. The spin direction of the Cr³⁺ is aligned in parallel with that of tetrahedral Fe³⁺, suggesting a ferromagnetic exchange interaction between the Bi_2−xCr_xSe₃ and the YIG underlayer, as indicated by the sign of the XMCD spectra. Although no magnetic signature is distinguishable from the noise above 100 K for the Bi_1.89Cr_0.11Se₃, the YIG spectra remain strongly dichroic up to RT. The integration of the XMCD spectra or the summed peak intensity is a quantity proportional to the magnetic moment and here that of the Cr and Fe has the same sign. This means that unlike the antiphase proximity effect demonstrated by Vobornik et al.⁴⁸ with the Bi_2−xMn_xTe₃/Fe system, in which the Mn and Fe are antiferromagnetically coupled, the net spin of the Fe and the Cr in the Bi_1.89Cr_0.11Se₃/Y IG bilayer are aligned parallel, as schematically shown in Figure 4(d). Similar exchange coupling is present at the Co₂FeAl/(Ga, Mn)As interface.³⁶ 

To summarize, we have studied the exchange interaction of the Bi_1.89Cr_0.11Se₃/Y IG interface and provided direct evidence of ferromagnetic coupling in this technologically important TI/FMI bilayer system. The high quality Bi_1.94Cr_0.06Se₃/Si(111) epitaxial thin film was prepared using MBE, and characterized with STEM and magnetotransport measurements. The unique elemental selectivity of the XMCD technique enabled a direct determination of the relative magnetization of the Cr and the Fe. These results show that the Cr in the TI is coupled ferromagnetically with the net moment of the YIG, which is useful in stimulating experimental approaches to further increase the T_c in a magnetically doped TI via proximity effect. Future work to explore the tuning of the magnetization of TIs and its dependence on the band filling will have strong implications for both fundamental physics and emerging spintronics technology.

This work is supported by the State Key Programme for Basic Research of China (Grants No. 2014CB921101), NSFC (Grants No. 61274102), UK STFC, DARPA Meso program under contract No.N66001-12-1-4034 and N66001-11-1-4105. C. A. Ross and M. C. Onbasli acknowledge FAME, a STARnet Center of SRC supported by DARPA and MARCO, and the NSF. Diamond Light Source is acknowledged for beamtime on I10.