RESEARCH ARTICLE | OCTOBER 14 2020 Magnetic order in 3D topological insulators—Wishful thinking or gateway to emergent quantum effects? A. I. Figueroa  ; T. Hesjedal  ; N.-J. Steinke  Appl. Phys. Lett. 117, 150502 (2020) https://doi.org/10.1063/5.0027987 CrossMark   View Export Online Citation Downloaded from http://pubs.aip.org/aip/apl/article-pdf/doi/10.1063/5.0027987/14539464/150502_1_online.pdf Applied Physics Letters PERSPECTIVE scitation.org/journal/apl Magnetic order in 3D topological insulators—Wishful thinking or gateway to emergent quantum effects? Cite as: Appl. Phys. Lett. 117, 150502 (2020); doi: 10.1063/5.0027987 Submitted: 2 September 2020 . Accepted: 24 September 2020 . Published Online: 14 October 2020 . Corrected: 21 October 2020 A. I. Figueroa,1,a) T. Hesjedal,2,a) and N.-J. Steinke3,a) AFFILIATIONS 1 Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSICand BIST, Campus UAB, Barcelona 08193, Spain Downloaded from http://pubs.aip.org/aip/apl/article-pdf/doi/10.1063/5.0027987/14539464/150502_1_online.pdf 2 Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom 3 Institut Laue-Langevin, 71 Avenue des Martyrs, 38000 Grenoble, France a) Authors to whom correspondence should be addressed: adriana.figueroa@icn2.cat; Thorsten.Hesjedal@physics.ox.ac.uk; and steinkenj@ill.eu ABSTRACT Three-dimensional topological insulators (TIs) are a perfectly tuned quantum-mechanical machinery in which counterpropagating and oppositely spin-polarized conduction channels balance each other on the surface of the material. This topological surface state crosses the bandgap of the TI and lives at the interface between the topological and a trivial material, such as vacuum. Despite its balanced perfection, it is rather useless for any practical applications. Instead, it takes the breaking of time-reversal symmetry (TRS) and the appearance of an exchange gap to unlock hidden quantum states. The quantum anomalous Hall effect, which has first been observed in Cr-doped (Sb,Bi)2Te3, is an example of such a state in which two edge channels are formed at zero field, crossing the magnetic exchange gap. The breaking of TRS can be achieved by magnetic doping of the TI with transition metal or rare earth ions, modulation doping to keep the electronically active channel impurity free, or proximity coupling to a magnetically ordered layer or substrate in heterostructures or superlattices. We review the challenges these approaches are facing in the famous 3D TI (Sb,Bi)2(Se,Te)3 family and try to answer the question whether these materials can live up to the hype surrounding them. Published under license by AIP Publishing. https://doi.org/10.1063/5.0027987 Prototypical three-dimensional (3D) topological insulators (TIs)1 In order to observe the exciting physical phenomena TIs are syn- of the (Bi,Sb)2(Se,Te)3 family of solid solutions, most notably Bi2Se3, onymous for, such as the quantum anomalous Hall effect (QAHE),7 Bi2Te3, and Sb2Te3, had a successful career as efficient thermoelectric the topological magnetoelectric effect,8 the physics related to chiral materials2,3 before the theoretical prediction of their topological sur- edge states,9 and spintronic effects,10 TRS has to be broken and an face states (TSSs) in 2009.4 The TSS results from their large spin–orbit exchange gap introduced in the TI.11 The exchange gap was initially coupling and is made up of spin-momentum locked, counterpropagat- achieved by direct magnetic doping of the TI, by both transition- ing streams of oppositely spin-polarized electrons. Elastic backscatter- metals and rare-earth ions, in bulk crystals as well as thin films.12–20 ing by nonmagnetic impurities is forbidden by time-reversal The QAHE was recently observed in the intrinsic magnetic TI symmetry (TRS), in principle resulting in high carrier mobilities. The MnBi2Te4.21 Proximity-coupling to magnetically ordered substrates or existence of the gapless TSS in 3D TIs was first experimentally demon- layers, i.e., ferromagnets, ferrimagnets, or antiferromagnets, is another strated using angle-resolved photoemission spectroscopy,5 instead of, way to break TRS. One inherent advantage of this approach is that as one might have expected, in transport measurements. The reason there are no dopants interfering with the electrically active part of the lies in the rather poor electronic properties of (Bi,Sb)2(Se,Te)3-based TI, which could be compromised by the added impurities. Finally, the materials, which are in fact narrow-gap semiconductors with strong, combination of the different approaches in the form of heterostruc- unintentional charge doping due to chalcogen vacancies. These high tures and superlattices opens up new ways to achieve efficient TRS levels of bulk carriers can be most efficiently overcome by counter- breaking without, in principle, compromising the electronic properties doping,6 in particular in very thin films in which the relative bulk of the TI too much. Nevertheless, neither approach is yielding an carrier concentration is naturally suppressed. observable QAHE at decent (liquid He and above) temperatures Appl. Phys. Lett. 117, 150502 (2020); doi: 10.1063/5.0027987 117, 150502-1 Published under license by AIP Publishing Applied Physics Letters PERSPECTIVE scitation.org/journal/apl despite the fact the TSS is observable at room temperature. On the followed by an anneal under chalcogen flux.55,79 The growth can be other hand, the magnetic transition temperature TC itself is not setting monitored in situ by reflection high-energy electron diffraction the limit either; in fact, it can reach very high values. For instance, (RHEED). Figure 1(c) shows streaky RHEED patterns on Bi2Te3 on c- Cr0:15 ðBi0:1 Sb0:9 Þ1:85 Te3, which has been the most successful QAHE plane sapphire obtained along the ½112 0 and ½101 0 azimuths, which system so far, has a TC of 16 K, whereas very low temperatures repeat every 60 . The streaky patterns are indicative of flat, crystalline (<300 mK) are required to observe the QAHE.7,22,23 surfaces and they remain intact for doped films as well, up to the criti- There are several outstanding recent reviews of magnetic TIs, cal concentration above which the streaks become diffuse (and the their exotic phenomena, and applications, which can be found in Refs. films rough), indicative of their non-substitutional incorporation.14–16 24–26. In this review, we focus on the discussion of the various growth Note that RHEED cannot be continuously used for (Bi,Sb)2(Se,Te)3 and doping approaches for achieving an exchange gap in TI thin films, growth as the electron beam visibly damages the films, most likely due with a particular emphasis on heterostructures, and we finally try to to local heating. For the evaporation of Bi and Sb, standard effusion answer the question whether there is hope for these materials to fulfill cells are commonly used, whereas Se and Te are often (but not neces- their star potential. sarily) evaporated out of special cracker cells. For the evaporation of In the context of thermoelectric applications and fundamental dopants, high temperature effusion cells have proven advantageous studies of the (Bi,Sb)2(Se,Te)3 family of solid solutions, a number of since they are thermally better shielded, thereby reducing the uninten- single crystal,27,28 nanostructure,29–34 and thin film growth techniques Downloaded from http://pubs.aip.org/aip/apl/article-pdf/doi/10.1063/5.0027987/14539464/150502_1_online.pdf tional evaporation of the high vapor-pressure chalcogens from sur- have been employed;35–40 however, for brevity and also given the ver- rounding areas. In fact, Se is very hard to contain and some satility of the method, our review focuses solely on results obtained unintentional Se “co-evaporation” is unavoidable, as shown in high- using molecular beam epitaxy (MBE)41,42 (for reviews on TI thin film resolution compositional analysis using Rutherford backscattering growth, see, e.g., Refs. 43–45). High-quality single crystalline TI thin spectroscopy with 2.3 MeV He ions and particle-induced x-ray emis- film growth by MBE has been reported on a wide variety of single- sion with 1 MeV protons.16 crystalline substrates, e.g., Si,46–51 Al2O3,52–56 GaAs,57–60 Ge,61,62 The structural properties of the films are usually further investi- CdS,63 SrTiO3,64 graphene (on 6H-SiC),65 lattice-matched InP,66,67 gated ex-situ using x-ray diffraction (XRD) with Cu Ka1 radiation. and BaF2,68 as well as amorphous SiO2/Si for back-gated electrical Figure 1(d) shows the spectrum for a Bi2Te3 film on BaF2 (111), which transport measurements69–71 and fused silica,72 indicating that these is characterized by the (1 1 1) substrate peaks and the (allowed) (0 0 materials may grow on virtually anything.73 3l) film peaks, representative of c-axis oriented, rhombohedral single In fact, the in-plane lattice mismatch spans a remarkable range in crystalline material. Upon doping, the analysis of the resulting peak the context of conventional thin film growth (see Table I in Ref. 44), shifts and peak broadening can be used to quantify the undesired deg- reaching from 0.2% for Bi2Se3 on InP all the way up to 43.8% for radation in crystalline quality, as well as giving clues on the doping sce- Bi2Te3 on graphene.44 The reason for this enormous tolerance of lat- nario.18,80,81 Furthermore, the in-plane lattice constants, as well as the tice mismatches lies in the layered nature of the rhombohedral crystal rotational symmetry of the system, can be obtained from asymmetric structure [space group D53d (R3 m)] of the (Bi,Sb)2(Se,Te)3 compounds, 2D reciprocal space mapping or u-scans, as shown in Fig. 1(e). which is characterized by the van der Waals (vdW) gap. Figure 1(a) Whereas the in-plane orientation of vdW epitaxially grown films, in illustrates a Bi2Te3 unit cell, in which the Te–Bi–Te–Bi–Te quintuple principle, lock to the symmetry of the underlying substrate, this lock- layer (QL) building blocks are illustrated, which are separated from ing may not be perfect. In particular (Bi,Sb)2(Se,Te)3 films on c-plane one another by the vdW gap across which the Te–Te bonding is weak. sapphire are known to exhibit rotational twins, as can be seen in the In consequence, the bonding between the first QL and the substrate is 60 repeat of the streaky patterns in RHEED [cf. Fig. 1(c)]—instead of also characterized by weak vdW forces. The vdW gap can be clearly the threefold symmetry expected from the R3 m crystal structure. In seen in transmission electron microscopy images shown in Fig. 1(b). contrast, films grown on BaF2 (111) are twin-free,68 which alters the The vdW epitaxy growth mechanism74–76 does not require lattice electronic properties of the film as well.82 Figure 1(e) shows a compari- matching between the film and the substrate but is nevertheless char- son of the threefold symmetric f101 5g Bi2Te3 peaks on a smooth acterized by in-plane (rotational) alignment between the film and the BaF2 surface (120 apart) and the additional peaks due to twinning  substrate. van der Waals epitaxy has seen a renaissance with the (60 apart) on a rougher BaF2 surface (which dominates the growth advent of 2D materials, for which TIs provide a suitable substrate for on, e.g., c-plane sapphire). the direct 2D materials growth or for integration with TIs in hetero- The film morphology, and the distribution of rotational domains, structures for future electronic devices.77 The flip-side of the lack of can be conveniently visualized using atomic force microscopy (AFM) strong ionic or covalent bonding across the film-substrate interface is owing to the dominating QL-terrace structure with its 1 nm-high a lack of control over the TI film growth. steps. Figure 1(f) shows the characteristic, triangular terraced islands,  The growth of (Bi,Sb)2(Se,Te)3 thin films by MBE is usually car- which are rotated with respect to each other by 60 in a Bi2Te3 film on ried out with a considerable chalcogen overpressure on the order of c-plane sapphire. The triangular shape in the case of a hexagonal sys- >5:1 due to the high rate of re-evaporation. The growth rate of typi- tem can be understood in the framework of the Burton-Cabrera-Frank cally less than 1 nm/min is controlled by the group-V element flux theory, when for particular crystallographic orientations, the distance and varies as a function of substrate temperature. The substrate tem- between corners of the structure is larger than the diffusion length of perature, which typically lies in the range between 200  C and 300  C, the surface adatoms.36 In general, the growth is of the spiral surface has been shown to be the main parameter determining the quality of growth type.83 The growth spirals are believed to be due to the pinning the films.44,78 It has proven advantageous to first grow a seed layer at a of 2D growth fronts at irregular substrate steps.84 The formation of temperature of 50  C lower than the final growth temperature, screw dislocations in Bi2Te3 has been linked to variations in Appl. Phys. Lett. 117, 150502 (2020); doi: 10.1063/5.0027987 117, 150502-2 Published under license by AIP Publishing Applied Physics Letters PERSPECTIVE scitation.org/journal/apl Downloaded from http://pubs.aip.org/aip/apl/article-pdf/doi/10.1063/5.0027987/14539464/150502_1_online.pdf FIG. 1. Structural properties and growth of Bi2Te3 thin films by MBE. (a) Crystal structure. On the left, the unit cell consisting of three Te–Bi–Te–Bi–Te quintuple layer (QL) blocks is shown. The QL blocks (Bi and Te are shown in blue and red, respectively) are separated by the weakly bonding Te–Te van der Waals gap. (b) Cross-sectional high- angle annular dark field scanning transmission electron microscopy. The high-resolution image on the left shows the fine structure of the QL blocks and the van der Waals gap (no intensity). The overview scan on the right shows the perfectly ordered QL stack. (c) RHEED images of Bi2Te3 on c-plane sapphire along the ½1120 and ½1010 azimuths, showing streaky patterns, indicative of flat, crystalline surfaces. (d) Out-of-plane h-2h XRD spectrum of Bi2Te3 on BaF2 (111). The film peaks (red) and substrate peaks (blue) are indicated. (e) In-plane XRD u scan of a f1015g Bi2Te3 peak. On smooth substrates (black line), only one domain is found (120 apart), consistent with the threefold crystal symmetry. On rough substrates (blue line), two in-plane domains are found (60 apart). (f) The surface morphology of Bi2Te3 on c-plane sapphire, as obtained by AFM, is dom- inated by two domains of triangular islands, measuring 1 lm across. On the right, the close-up reveals details of the typical 1-QL-step terrace structure as well as the spiral- like growth center. (g) Schematic illustration of a Bi2Te3 island. The stepped structure exposes the van der Waals gap, which can act as an entry point for the efficient, but uncontrolled, diffusion of dopants into the material. stoichiometry of the deposited nucleation centers due to Te re- Fig. 1(g)]. While during standard layer-by-layer growth the dopants evaporation during the initial stages of film growth.36 can be incorporated in a deterministic way, allowing for the so-called This characteristic morphology of (Bi,Sb)2(Se,Te)3 thin films d-doping of individual layers,85,86 the exposed vdW gap of the terraced poses a major challenge for their controlled doping [see illustration in islands with its relatively weak electrostatic bonding forces and large Appl. Phys. Lett. 117, 150502 (2020); doi: 10.1063/5.0027987 117, 150502-3 Published under license by AIP Publishing Applied Physics Letters PERSPECTIVE scitation.org/journal/apl layer spacings provides an entry portal for the uncontrolled incorpora- achieved with magnetic dopants, both with transition metals (TMs) tion of dopants.87 This is particularly concerning since the diffusion and rare earths (REs). constants in these layered hosts are highly anisotropic, with the diffu- With TMs, magnetic order has been observed in Fe-, Mn-, Cr-, sion along the planes (in the vdW gap) being particularly fast.87–89 The and V-doped compounds. For Fe-doping in Sb2Te3 and Bi2Se3, the diffusing dopants are then incorporated into the (Bi,Sb)2(Se,Te)3 host, compounds remained paramagnetic while the electron concentration illustrated by the concentration gradient in Fig. 1(g), as the solubility was increased, despite successful substitutional doping94,95 and pd- limit for interstitial metal incorporation is usually low. This is cer- hybridization predicted by spin density calculations.96 In contrast, tainly no surprise and a long-standing problem87 in the thermoelec- Kulbachinskii et al. reported ferromagnetic (FM) ordering up to 12 K trics community where the electric contacting with the obvious in (Fe,Bi)2Se3 single crystals.97 choices of low electrical resistivity and high thermal conductivity In Mn-doped Tis, FM order has been observed in bulk crystals metals has been challenging (with a few exceptions such as Ta90) and thin films. In addition, there are reports on the surface magnetism mostly resulting in the degeneration (or even complete dissolu- in Mn:Bi2Se3 with observations of both an enhanced moment and TC tion91) of the electrodes in the case of, e.g., Sn,92 Ag,93 and Au.91 due to surface segregation of the Mn ions,98 as well as a diminished For instance, Cu is notorious for its high diffusivity in Bi2Te3 of surface moment and soft magnetic behavior with no hysteresis possi- 106 cm2 s1 parallel to the plane and 3  1015 cm2 s1 along the bly caused by partial antiferromagnetic (AF) ordering near the sur- Downloaded from http://pubs.aip.org/aip/apl/article-pdf/doi/10.1063/5.0027987/14539464/150502_1_online.pdf c-axis at room temperature87 and the formation of binary chalcoge- face.18 A bandgap has been observed in Mn-doped TIs, but it is likely nides. For electrodes, specific diffusion barriers have been devel- not of magnetic origin.99 oped (e.g., Ni barriers for Sn electrodes); however, some of them Of all the single-ion dopants tried so far, Cr and V possess the rely on the formation of secondary chalcogen compounds at the most robust long-range FM order with out-of-plane anisotropy and interface92 and so do not provide a solution for achieving con- a typical (doping concentration-dependent) TC of 59 K (104 K) for trolled, substitutional doping of TIs. Cr (V) concentrations of x ¼ 0.29 (0.25) in Sb2x (V/Cr)xTe3.23 In The need to break TRS in TIs led to a very active quest for suit- Table I, we summarize the properties of the most common TI able dopants to introduce magnetic order. Magnetic TIs (MTIs) were dopants. TABLE I. Summary of the physical properties of transition metal and rare earth element doped TI thin films. The doping concentration is given in % of the (BiþSb) sites for sub- stitutional (SUB) doping, unless otherwise noted [e.g., for interstitial (INT) doping]. The magnetic moment is given per doping ion (in lB ) and the transition temperature (trans. temp. TC or TN in K). The out-of-plane (OOP) magnetocrystalline anisotropy (MCA) is indicated when stated in the reference. Magnetic Doping moment Magnetic Trans. Open Dopant TI host conc. (at.%) Valence (lB ) order temp. (K) MCA loop Comments References * † ‡ * Cr Bi2Se3  5.2 <3þ 2 FM 20 … Yes Poor cryst. quality for >5% Mn 80 † Max. for 2% Mn; ‡max. for 5.2% Mn Cr Bi2Se3 12 2þ 2.1 FM … OOP Yes SUB and INT 18 Cr Bi2Se3 0.6† Mixed 2.49* FM 46* OOP † Effective conc. for modulation doping 104 2þ, 3þ 1.3‡ 31‡ * Surface value; ‡ bulk value Cr Sb2Te3 7.5–21 2þ 2.8 FM 28–125 OOP Yes SUB 105 Cr (Bi,Sb)2Te3 5 <3þ 3.19 FM 20 OOP Yes Zener-type pd-exchange interaction 106 Cr (Bi,Sb)2Te3  15 3þ 2.9 FM  59* OOP Yes * 14–59 K for 5–15% Cr 23 V Bi2Se3  12 … … FM  16* OOP Yes * 10 K for 1%, 16 K for 6% 107 V (Bi,Sb)2Te3  13 Mixed 1.5 FM  104* OOP Yes * 23–104 K for 4–13% V 23 3þ, 4þ SUB V Sb2Te3 5 <3þ 1.84 FM 45 OOP Yes Zener-type pd-exchange interaction 106 Mn Bi2Te3  10 … … FM*  17 OOP Yes SUB and INT possible; FM*:  2% Mn 108 Mn Bi2Se3 … mostly 1.6* FM 1.5 OOP No XAS:109 SUB and INT 19 2þ 5.1† * XMCD;† SQUID Mn Bi2Te3  13 … … FM*  15 OOP Yes vdW gap INT 110 * FM  3% Mn; max TC for 9% Gd Bi2Te3  30 3þ 7 AFM 2.5 … No XAS:111 SUB 14, 112 Dy Bi2Te3  36 3þ 4.3–12.6 AFM 1.2 … No XAS:111 SUB 15 Ho Bi2Te3  21 3þ 5.15 AFM 0.837 … No XAS:111 SUB 16 Eu Bi2Te3 4 2þ … … … … … SUB, EuTe for 9% Eu 113 Eu Bi2Se3  21 … … FM 8–64 … Yes Nonuniform Eu SUB; FM  10% Eu 114 Appl. Phys. Lett. 117, 150502 (2020); doi: 10.1063/5.0027987 117, 150502-4 Published under license by AIP Publishing Applied Physics Letters PERSPECTIVE scitation.org/journal/apl In line with these findings, the QAHE has been observed in both semiconductors.121,122 In addition, it seems that the introduction of Cr- and V-doped samples but not in Mn or Fe doped ones (except for Bi weakens the pd-hybridization between the 5p states and the 3d the intrinsic magnetic TIs based on MnBi2Te4).21,100 However, the fact states.101 Apart from this carrier-mediated exchange, there is evidence that even in these materials the QAHE is limited to very low tempera- of exchange interactions mediated by the host ions.118,119 tures, far below TC , calls the nature and robustness of the magnetic Notwithstanding, it is clear that the necessary tuning to reduce order into question. unwanted bulk carriers will always be detrimental to the long-range Early theoretical and experimental studies7,115,116 on Cr- and V- magnetic order in these compounds. doped TIs proposed that long-range magnetic ordering of the Van It seems that the surface magnetism can differ from the bulk Vleck type could be established.117 This type of magnetic order is sta- behavior, in particular, in Cr-based compounds. For instance, in Ref. bilized by intra-atomic mixing of the d-orbital ground state with 123, it was shown that the surface magnetization lies in-plane, rather higher energy excitations close in energy, which lead to a positive than following the bulk out-of-plane anisotropy. However, the study exchange integral. Observations of long-range magnetic order in Cr- by Ye et al. using surface-sensitive XMCD in total-electron yield mode and V-doped thin films and crystals were first investigated by super- on Cr-doped ðSb; BiÞ2 Te3 did not find any evidence for a variation of conducting quantum interference device (SQUID) magnetometry, the Cr-magnetism at the surface, neither did Duffy et al.20 In the work x-ray magnetic circular dichroism (XMCD), and polarized neutron by Liu et al.,104 it was reported that TC for modulation-doped Bi2Te3 reflectometry (PNR),18,80,105,106 which reported a clear ferromagnetic Downloaded from http://pubs.aip.org/aip/apl/article-pdf/doi/10.1063/5.0027987/14539464/150502_1_online.pdf increased if the Cr dopants were introduced at the sample surface. transition and open hysteresis loops with out-of-plane anisotropy and, Using muon spin rotation (lþ SR) techniques, the magnetic vol- crucially, a doping concentration-dependent TC . This is incompatible ume fraction can be directly tracked as a function of temperature in with the notion of magnetic order dominated by intra-atomic interac- Cr- and V-doped thin films of Sb2 Te3 and other TIs.102,124 These mea- tions and, instead, strongly hints at a magnetic ordering mechanism surements show that ferromagnetic ordering develops rather gradually that is dependent on either carrier or spin concentrations. over a wide temperature range and that for lower doping concentra- The exact features of the magnetic ordering appear to depend on tions, a significant fraction of the material remains paramagnetic. The the details of the modification of the electronic band structure due to magnetic transition can also be tracked through the slow relaxation the dopant. For instance, in V-doped samples, impurity bands caused rate during the phase transition in lSR measurements [see Fig. 2(c)]. by the V 3d states are found near the Fermi energy, EF , and Dirac This relaxation rate is a measure of the static and ls-dynamic mag- point of the system.118,119 These states appear to stabilize the magnetic netic disorder in the system. This peak is very broad, and, for lower ordering. Both V and Cr show significant pd hybridization between doping concentrations, disorder persists down to at least 4 K, the low- the host 5p states and the dopant 3d states in Sb2 Te3 based com- est temperature reachable in the system. pounds as has been observed by a number of groups using Furthermore, a change of the internal magnetic field experi- XMCD.20,101,118,120 Figure 2(a) shows the XMCD signal due to enced by the muons in the samples provides evidence for a percola- induced spin polarization in the Sb p-states for a Cr-doped Sb2Te3 tion transition, above which magnetically ordered clusters thin film. As the conduction and valence bands are mainly formed by gradually appear in a paramagnetic sea, growing and percolating as the host lattice p-states, this leads to the question if it is not the carriers the temperature is decreased.102 For lower doping concentrations, that mediate magnetic order in these systems. In the tetradymite the internal field remains shifted even at the lowest tempera- dichalcogenides, near the center of the Brillouin zone, the valence tures.102,124 This behavior is likely due to residual paramagnetic band is formed by the anion p-states of Te or Se, whereas the conduc- regions, which remain between the ferromagnetic patches. Note tion band is formed by the p-states of the Sb and Bi cations, though it that there can also be a large difference in percolation between sur- has recently been shown that the bonds of magnetically doped com- face and bulk due to different screening behaviors.125 Lachman pounds have a strong covalent character.106 et al.103 investigated the magnetic domain pattern in a Cr-doped The important role carriers play in stabilizing the magnetic order (Sb,Bi)2Te3 film using scanning SQUID-on-tip microscopy [see was shown by the gate-voltage dependence of the magnetic relaxation Fig. 2(d)]. In their measurements, the nearly non-interacting, time103 and strongly supported by the dependence of TC on the con- slowly fluctuating, superparamagnetic domains were directly centration of Bi, acting as a counter dopant, in V- and Cr-doped films. imaged. These measurements show directly that the magnetic order Ye et al. showed, by systematically varying the dopant and Bi concen- in TM-doped TIs is not robust over long lengthscales. Instead, a tration in Cr:ðSb; BiÞ2 Te3 and V:ðSb; BiÞ2 Te3 , not only that the mag- picture of superparamagnetic or superferromagnetic domains netic ordering is stabilized with the increasing doping concentration emerges, which gradually form during a broad transition, and with but also that TC is systematically suppressed when the carrier-hole con- significant disorder, and paramagnetic regions remaining intact centration is decreased by substituting Sb with Bi.101,120 Figure 2(b) until far below TC [see illustration in Fig. 2(e)]. With an increase in shows Arrott plots from which the values of TC are determined for doping concentration, the distances between the dopant ions shrink systematically varied Cr and Bi concentrations in Crx(Sb1yBiy)2xTe3 and additional carriers are introduced into the system. The net crystals. An increase in the Cr concentration stabilizes the magnetic effect is the stabilization of the magnetic order, but at the cost of order, whereas an increase in Bi strongly suppresses it. First principles severely compromising the quantum properties of the material. calculations show the extent of the magnetic coupling in the c-axis The phenomenon of nanoscale magnetic phase separation is direction across the vdW gap. The picture that emerges is that of a known from dilute magnetic semiconductors, such as GaMnAs. dominant carrier-mediated interaction based on the hybridization of There, depending on the extent of the localization of the (hole) car- the d-states of the dopants with the carrier bands formed by the riers, either the magnetic transition follows the percolation dynamics p-states of the host lattice, similar to the ordering in dilute magnetic of bound magnetic polarons in the case of strongly localized holes126 Appl. Phys. Lett. 117, 150502 (2020); doi: 10.1063/5.0027987 117, 150502-5 Published under license by AIP Publishing Applied Physics Letters PERSPECTIVE scitation.org/journal/apl Downloaded from http://pubs.aip.org/aip/apl/article-pdf/doi/10.1063/5.0027987/14539464/150502_1_online.pdf FIG. 2. Magnetic properties of MTI films. (a) X-ray absorption (XAS) and x-ray magnetic circular dichroism (XMCD) spectra at the Sb M4;5 edges of an in situ cleaved Cr:Bi2Te3 film. The measurement was carried out in a field of 8 T and at a temperature of 3 K. The XMCD signal (green) is obtained by subtracting the XAS spectrum measured with right-circularly polarized x-rays (blue) from the one measured with left-circularly polarized x-rays (red).20 (b) XMCD intensities (symbols) and SQUID magnetization data (lines) obtained for different Cr doping concentrations x and different Sb to Bi ratios in counter-doped Crx(Sb1yBiy)2x Te3 crystals.101 From the plot of the inverse intensity (i.e., magnetization) in the panel on the right, the transition temperature is estimated, which shows a clear trend: TC increases with x, whereas an increase in Bi:Sb ratio strongly reduces it. (c) Temperature-dependent transverse-field lþ SR measurement showing the magnetic transition in a Cr:Sb2Te3 film.102 The data shown in red represent the behavior of the near-surface region of the film, whereas the (higher muon energy) data shown in black include the information from the middle of the film as well. The relax- ation rate k, which is a measure of the static and dynamic (ls) magnetic disorder in the system, is very broad across the magnetic transition. (d) SQUID-on-tip microscopy showing the magnetization reversal dynamics of a Cr:(Bi,Sb)2Te3 film. (Left) magnetic images, i.e., the Bz component of the film magnetization, obtained in applied magnetic fields increasing (0.5 mT field steps) at a temperature of 250 mK. (Right) change in the film’s magnetic flux, illustrating the reversal of isolated domains.103 (e) Illustration of the magnetic order in TM-doped TIs, showing magnetically ordered and paramagnetic regions coexisting at temperatures far below TC. Panel (a) adapted from Duffy et al., Phys. Rev. B 95, 224422 (2017). Copyright 2017 Authors, licensed under a Creative Commons Attribution CC BY 4.0 license. Panel (b) reproduced with permission from Ye et al., Nat. Commun. 6, 8913 (2015). Copyright 2015 Authors, licensed under a Creative Commons Attribution CC BY 4.0. license Panel (d) adapted from Lachman et al., Sci. Adv. 1, e1500740 (2015). Copyright 2015 Authors, licensed under a Creative Commons Attribution CC BY 4.0 license. or, in the case of hole states extended over distances longer than the state of 94 (87) pm. Doping with a high moment ion has the advantage average dopant distance, the Zener model becomes valid.121 However, that as the exchange gap is dependent on the size of the magnetization, even in the Zener model description, paramagnetic regions may persist the doping concentration can be reduced for the same gap size, below TC in hole-free regions.122 thereby preserving crystal quality. Of the rare earth lanthanide series, Rare earth dopants are extremely attractive given their large, the high moment materials Gd, Dy, and Ho were all used to dope localized magnetic moments and their similarity to the Bi and Sb ions Bi2Te3.14–16 However, none of these materials display long-range mag- in the host lattice. The ionic radius of Dy3þ is 105 pm, much more netic order by themselves.14–17,127 Doping concentrations of up to 35% similar to that of Bi3þ (117 pm) than to Cr2þ in the high (low) spin were achieved in Gd-doped Bi2Te3 thin films; much above the bulk Appl. Phys. Lett. 117, 150502 (2020); doi: 10.1063/5.0027987 117, 150502-6 Published under license by AIP Publishing Applied Physics Letters PERSPECTIVE scitation.org/journal/apl solubility limit.81 The details of the magnetic configurations are given 38 K up to 90 K.136,137 The successful design of such structures in Table I. Of the investigated RE dopants, Dy shows the most interest- relies on the fact that these materials are chemically very compatible ing properties: it is the only ion that leads to a concentration- and well lattice-matched, resulting in abrupt interfaces which support dependent moment, its susceptibility is large, and thin films can be the magnetic exchange across the interface. This concept of using magnetically saturated in fields as low as 2 T. PNR measurements materials with related or at least comparable crystal structure and simi- have shown that the induced moment can be as large as 1/3 of the lar atomic compositions has also been explored, both theoretically and full Dy3þ moment at fields as low as 0.65 T.128 lþ SR measurements experimentally, in heterostructures of MnBi2Te4/Bi2Te3, MnBi2Se4/ showed that while no long-range order can be established, strong, Bi2Se3, MnSe/Bi2Se3, and similar compounds.138–141 In particular, het- short-range magnetic correlations establish themselves with decreasing erostructures of, e.g., MnBi2Te4 and Bi2Te3, which are part of the temperature.128 This makes Dy-doped TIs a prime candidate for fur- (MnBi2Te4)(Bi2Te3)m homologous series,142 are particularly suited as ther exploitation in heterostructures, where order can be introduced there are no real interfaces (the MnBi2Te4 layer is effectively termi- via proximity coupling.129,130 nated by Bi2Te3 layers). This makes the magnetic film a natural exten- Incorporating TIs into magnetic heterostructures has been sion of the TI and allows for efficient TRS breaking. In fact, some of explored both as an alternative to magnetic doping and as an added these systems exhibit ferromagnetism up to room temperature and a materials design opportunity to tune the magnetic properties. clear Dirac cone gap opening of 100 meV.140 Downloaded from http://pubs.aip.org/aip/apl/article-pdf/doi/10.1063/5.0027987/14539464/150502_1_online.pdf Magnetic heterostructures offer the advantage of, e.g., opening an The latter examples have an additional advantage in terms of the exchange gap in the TI with less disorder than in doped systems since electrical characteristic of the magnetic layer. They use magnetic insu- no extra scattering centers need to be introduced. It is proposed that lators (MIs), instead of metallic films, which preserve the band struc- when a non-magnetic TI is combined with another magnetically ture of the TI, and thus the TSS, as they avoid hybridization with the ordered material, proximity effects at the interface involving the sur- bulk states of the AF or FM in contact. Using a MI is also convenient face Dirac fermions will align spin moments of the TI band with the for the fabrication and incorporation of such structures into quantum itinerant carriers and give rise to exchange splitting. Similar exchange devices. Intensive investigation of proximity effects has been done in mechanisms are used in stacks with MTIs to alter their magnetic prop- heterostructures comprising TIs and MIs, such as EuS/Bi2Se3, EuS/ erties. Engineering heterostructures by incorporating magnetic and (Bi,Sb)2Te3, (Bi,Sb)2Te3/Y3Fe5O12, (Bi,Sb)2Te3/Tm3Fe5O12, Bi2Te3/ non-magnetic TIs has therefore opened up new avenues to access Fe3O4, (Bi,Sb)2Te3/Cr2Ge2Te6, and (Zn,Cr)Te/(Bi,Sb)2Te3/ emergent quantum phenomena. In the following, we review some of (Zn,Cr)Te.124,143–151 However, the QAHE has only been reported in these aspects of magnetic heterostructures incorporating TIs. (Zn,Cr)Te/(Bi,Sb)2Te3/(Zn,Cr)Te,150 which results from the appropri- Several strategies have been followed in order to exploit magnetic ate design of the heterostructure to guarantee smooth interfaces (as it proximity effects at the interface of such heterostructures with the goal satisfies the conditions described above), as well as the maximization of tuning and controlling the magnetic and quantum transport prop- of the exchange gap at the top and bottom surface states by using a erties of MTIs. Modulation doping in heterostructures with Cr-doped MI/TI/MI sandwich stack. (Bi,Sb)2Te3 films has increased the QAHE temperature from 30 mK Proximity effects due to exchange interactions are not the only up to 2 K.131 The designed structures are illustrated in Figs. 3(a) and interesting phenomena that emerge at TI interfaces. The helical locking 3(b), and the characteristic magnetotransport data showing the QAHE of the TSS, illustrated in Fig. 3(g), and the strong spin–orbit coupling are are plotted in Fig. 3(c). This approach has also allowed for the observa- very relevant for their application in topological spintronics. The exis- tion of the axion insulator state in MTIs132—a magnetoelectric phe- tence of such a spin texture means that an electron current flowing on nomenon characterized by a large longitudinal resistance and zero the surface of a TI can generate a non-equilibrium spin density [see Fig. Hall plateau (where both the Hall and longitudinal conductivity 3(h)] with both in-plane and out-of-plane components. The spin- become zero), which is illustrated in Fig. 3(d). polarized surface currents are expected to efficiently induce out-of-plane In order to raise the temperature at which quantum and magneto- and in-plane torques in an adjacent magnetic layer. Experiments of spin- electric effects in MTIs can be observed, it seems natural to explore ways pumping using ferromagnetic resonance (FMR) techniques in FM/TI to increase their magnetic ordering temperature by, e.g., interfacial mag- and FM/TI/FM stacks, as the one depicted in Fig. 3(i), have confirmed netic interactions. Growth of Cr-doped Bi2Se3 films onto the high TC the ability of a TI to absorb and transfer a pure spin current.152–156 (550 K) ferrimagnetic insulator Y3Fe5O12 (YIG) was found to enhance Figure 3(j) shows signatures of transfer of angular momentum between the TC of the MTI from 20 K up to 50 K.133 The evaporation of a thin the FMs Co50Fe50 and Ni81Fe19 (Py, Permalloy), mediated by Bi2Se3, as FM layer, such as Fe or Co, onto the pristine surface of in-vacuum cleaved observed in the amplitude and phase of precession of each FM layer Mn-doped Bi2Te3 crystals or Cr-doped Bi2Se3, Cr-doped Sb2Te3, and Dy- recorded in time-resolved FMR measurements.153,155 doped Bi2Te3 thin films was also demonstrated to alter their TC near the The absence of bulk conduction in ideal TIs further increases surface of the TI through proximity.20,127,134,135 Figures 3(e) and 3(f) depict their spin-charge conversion efficiency. Exceptionally large spin- the increase in TC for Cr-doped Bi2Se3 and Sb2Te3 films with a Co over- charge conversion values at TI/FM interfaces have been experimen- layer, as obtained from XMCD measurements. Growth of high-quality tally demonstrated by spin–orbit torque (SOT) measurements.157–161 Dy:Bi2Te3/Cr:Sb2Te3 heterostructures resulted in successful introduction of Figure 3(k) shows a diagram of a Py/Bi2Se3 bilayer, where the non- long-range magnetic order in Dy:Bi2Te3 as a result of proximity coupling equilibrium magnetization produced by an in-plane charge current in to the higher transition temperature Cr:Sb2Te3 layer.129 SOT measurements is represented. The measured resonance line shape Alternative approaches to raise TC of MTIs include their cou- plotted in Fig. 3(l) has two components: a symmetric or antidamping- pling to antiferromagnets. An example is superlattices of the AF CrSb like SOT (in-plane) and an antisymmetric or field-like SOT (perpen- and Cr-doped (Bi,Sb)2Te3, where TC was found to increase from dicular). Analysis of these FMR curves yields spin-charge conversion Appl. Phys. Lett. 117, 150502 (2020); doi: 10.1063/5.0027987 117, 150502-7 Published under license by AIP Publishing Applied Physics Letters PERSPECTIVE scitation.org/journal/apl Downloaded from http://pubs.aip.org/aip/apl/article-pdf/doi/10.1063/5.0027987/14539464/150502_1_online.pdf FIG. 3. Emergent phenomena in TI heterostructures. Schematic Cr-modulation-doped (a) quantum anomalous Hall and (b) axion insulators. Panels (c) and (d) show the mag- netic field (B) dependence of the Hall conductivity (rxy ) and longitudinal conductivity (rxx ) in the respective heterostructure films illustrated in (a) and (b). Panels (e) and (f) depict linear fits of parameters extracted from Arrott plots obtained from XMCD measurements in Cr-doped (e) Bi2Se3 and (f) Sb2Te3 thin films. The temperature at which the intercept goes through zero yields TC . The inset illustrates the process of in situ evaporation of a thin Co layer on top of the Cr-doped TI film. (g) Schematic illustration of the spin-momentum locked helical spin texture of the TSSs in a TI. (h) Schematic of surface spin density on two opposite surfaces of a TI thin film for a charge current flowing along the x direction and for a charge current flowing along the þx direction. (i) Schematic of a FM/Bi2Se3/FM heterostructure for spin pumping experiments with FMR and time-resolved FMR. (j) Phase (top panel) and amplitude (bottom panel) of precession of magnetization for Py (pink circles) and Co50Fe50 (green triangles) layers for tTI ¼ 4 nm. Dashed lines show the positions of the resonance amplitude peak. (k) Schematic diagram of SOT measurements in a Py/Bi2Se3 bilayer. The yellow and red arrows denote spin moment directions. (l) Measured field dependent (top panel) spin-torque FMR at room temperature for a Py (16 nm)/Bi2Se3 (8 nm) bilayer, together with fits of the symmetric and antisymmetric resonance components. Bottom panel: Measured dependence on the magnetic field angle u for the symmetric and antisymmetric resonance components. Panels (a)–(d) reprinted with permission from Mogi et al., Nat. Mater. 16, 516 (2017). Copyright 2017 Springer Nature. Panel (e) adapted and reprinted with per- mission from Baker et al., Phys. Rev. B 92, 094420 (2015).135 Copyright 2015 American Physical Society. Panel (f) adapted from Duffy et al., Phys. Rev. B 95, 224422 (2017). Copyright 2017 Authors, licensed under a Creative Commons Attribution CC BY 4.0 license. Panels (i) and (j) reprinted with permission Figueroa et al., J. Magn. Magn. Mater. 400, 178 (2016). Copyright 2016 Elsevier. Panels (k)–(l) reprinted with permission from Mellnik et al., Nature 511, 449 (2014). Copyright 2014 Springer Nature. parameters that are found to be much larger than those reported for despite the remarkable progress in the growth of thin films and com- heterostructures of FM with heavy metals.157 SOT in such FM/TI het- plex heterostructures, there are a number of limitations intrinsic to erostructures can be used to efficiently manipulate the magnetization these materials and many questions are still waiting to be addressed. of the FM—a highly relevant feature for their applications in spin- Most of the experiments reviewed here rely on highly (charge) doped tronic devices. Effective magnetization switching by SOT at room tem- TIs in which the TSS coexist with bulk bands at the Fermi level, and perature has been demonstrated in, e.g., Py/Bi2Se3,160 CoTb/Bi2Se3, for their analysis, it is assumed that the FM/TI interface is perfectly and CoTb/(Bi,Sb)2Te3 structures.162 abrupt. However, magnetic phase segregation and interdiffusion are Despite the huge effort striving to make practical use of the quan- common issues in doped TIs and at FM/TI interfaces, and only tum and spin phenomena at the surfaces and interfaces of TIs and recently, the systematic analysis of FM/TI interfaces has started, Appl. Phys. Lett. 117, 150502 (2020); doi: 10.1063/5.0027987 117, 150502-8 Published under license by AIP Publishing Applied Physics Letters PERSPECTIVE scitation.org/journal/apl including practical strategies for improving their quality.161,163 The 16 S. E. Harrison, L. J. Collins-McIntyre, S.-L. Zhang, A. A. Baker, A. I. Figueroa, fact that the QAHE and other quantum, magnetoelectric, and spin A. J. Kellock, A. Pushp, Y. Chen, S. S. P. Parkin, J. S. Harris, G. van der Laan, and T. Hesjedal, Appl. Phys. Lett. 107, 182406 (2015). phenomena continue to be only observable at very low temperatures 17 S. E. Harrison, L. J. Collins-McIntyre, P. Sch€onherr, A. Vailionis, V. Srot, P. A. can, in fact, be associated with this disorder at the topological interface. van Aken, A. J. Kellock, A. Pushp, S. S. P. Parkin, J. S. Harris, B. Zhou, Y. L. Therefore, there is a clear path to improve the quality of these systems, Chen, and T. Hesjedal, Sci. Rep. 5, 15767 (2015). 18 and there is still real potential for significantly increasing the energy L. J. Collins-McIntyre, S. E. Harrison, P. Sch€ onherr, N.-J. Steinke, C. J. and temperature scales at which these intriguing quantum effects can Kinane, T. R. Charlton, D. Alba-Veneroa, A. Pushp, A. J. Kellock, S. S. P. be observed, opening the door for useful quantum devices in the Parkin, J. S. Harris, S. Langridge, G. van der Laan, and T. Hesjedal, Europhys. Lett. 107, 57009 (2014). future.26 So, coming back to the question we raised in the abstract, i.e., 19 L. J. Collins-McIntyre, M. D. Watson, A. A. Baker, S. L. Zhang, A. I. Coldea, S. whether there is hope for magnetically doped 3D TIs in the E. Harrison, A. Pushp, A. J. Kellock, S. S. P. Parkin, G. van der Laan, and T. (Sb,Bi)2(Se,Te)3 family, we hope to have been able to provide some evi- Hesjedal, AIP Adv. 4, 127136 (2014). 20 dence for answering the question with a cautious “yes.” L. B. Duffy, A. I. Figueroa, L. Gładczuk, N.-J. Steinke, K. Kummer, G. van der Laan, and T. Hesjedal, Phys. Rev. B 95, 224422 (2017). 21 Y. Deng, Y. Yu, M. Z. Shi, Z. Guo, Z. Xu, J. Wang, X. H. Chen, and Y. Zhang, The authors express their deep gratitude to the medical care Science 367, 895 (2020). personnel during the Covid-19 pandemic. We acknowledge continuous 22 C.-Z. Chang, J. Zhang, M. Liu, Z. Zhang, X. Feng, K. Li, L.-L. Wang, X. Chen, Downloaded from http://pubs.aip.org/aip/apl/article-pdf/doi/10.1063/5.0027987/14539464/150502_1_online.pdf support for the TI project at Oxford from the John Fell Fund (Oxford X. Dai, Z. Fang, X.-L. Qi, S.-C. Zhang, Y. Wang, K. He, X.-C. Ma, and Q.-K. University Press), the synchrotron facilities Diamond Light Source, ALS, Xue, Adv. Mater. 25, 1065 (2013). 23 BESSYII, ALBA, and the ESRF and the neutron sources ISIS and ILL C.-Z. Chang, W. Zhao, D. Y. Kim, H. Zhang, B. A. Assaf, D. Heiman, S.-C. Zhang, C. Liu, M. H. W. Chan, and J. S. Moodera, Nat. Mater. 14, 473 (2015). for beamtime leading to the reported insights. A.I.F. acknowledges 24 Y. Tokura, K. Yasuda, and A. Tsukazaki, Nat. Rev. Phys. 1, 126 (2019). funding from the European Union’s Horizon 2020 research and 25 M. He, H. Sun, and Q. L. He, Front. Phys. 14, 43401 (2019). innovation program under the Marie Skłodowska-Curie Grant 26 F. Fei, S. Zhang, M. Zhang, S. A. Shah, F. Song, X. Wang, and B. Wang, Adv. Agreement No. 796925, the FET-PROACTIVE project TOCHA under Mater. 32, 1904593 (2020). 27 Grant Agreement No. 824140 and the H2020 European Research H. K€ ohler, Phys. Status Solidi B 58, 91 (1973). 28 Council PoC project SOTMEM under Grant Agreement 899896. M. D. 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