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Study of Dy-doped Bi2Te3: thin film growth and magnetic properties

This content has been downloaded from IOPscience. Please scroll down to see the full text. 2015 J. Phys.: Condens. Matter 27 245602 (http://iopscience.iop.org/0953-8984/27/24/245602) View the table of contents for this issue, or go to the journal homepage for more

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Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 27 (2015) 245602 (11pp)

doi:10.1088/0953-8984/27/24/245602

Study of Dy-doped Bi2Te3: thin film growth and magnetic properties S E Harrison1,2 , L J Collins-McIntyre1 , S-L Zhang1 , A A Baker1,3 , A I Figueroa3 , A J Kellock4 , A Pushp4 , S S P Parkin4 , J S Harris2 , G van der Laan3 and T Hesjedal1 1 2 3 4

Clarendon Laboratory, Department of Physics, University of Oxford, Oxford, OX1 3PU, UK Department of Electrical Engineering, Stanford University, Stanford, California 94305, USA Magnetic Spectroscopy Group, Diamond Light Source, Didcot, OX11 0DE, UK IBM Almaden Research Center, 650 Harry Road, San Jose, California 95120, USA

E-mail: [email protected] Received 26 March 2015, revised 15 April 2015 Accepted for publication 27 April 2015 Published 22 May 2015 Abstract

Breaking the time-reversal symmetry (TRS) in topological insulators (TIs) through ferromagnetic doping is an essential prerequisite for unlocking novel physical phenomena and exploring potential device applications. Here, we report the successful growth of high-quality (Dyx Bi1−x )2 Te3 thin films with Dy concentrations up to x = 0.355 by molecular beam epitaxy. Bulk-sensitive magnetisation studies using superconducting quantum interference device magnetometry find paramagnetic behaviour down to 2 K for the entire doping series. The effective magnetic moment, µeff , is strongly doping concentration-dependent and reduces from ∼12.6 µB Dy−1 for x = 0.023 to ∼4.3 µB Dy−1 for x = 0.355. X-ray absorption spectra and x-ray magnetic circular dichroism (XMCD) at the Dy M4,5 edge are employed to provide a deeper insight into the magnetic nature of the Dy3+ -doped films. XMCD, measured in surface-sensitive total-electron-yield detection, gives µeff = 4.2 µB Dy−1 . The large measured moments make Dy-doped films interesting TI systems in which the TRS may be broken via the proximity effect due to an adjacent ferromagnetic insulator. Keywords: topological insulators, magnetic doping, rare earth, MBE, thin films, XMCD (Some figures may appear in colour only in the online journal)

Breaking the TRS in TIs has recently become the subject of intense experimental efforts, and doping with magnetic impurities has been the most commonly employed approach in 3D TIs [7]. If the exchange coupling among neighbouring magnetic impurities is strong enough to establish long-range ferromagnetic order, the ordinarily linearly dispersed Diraccone surface states, occupied by electrons that follow the massless Dirac equation, can develop a finite gap of tens of meV at the Dirac point [8]. Electrons in these gapped surface states obey the Dirac equation which now contains an explicit mass term since the TRS-breaking can cause the TSS to be transformed from a massless to massive Dirac Fermion state [9, 10]. The development of a controlled and reliable method to induce a gap in the surface state of a TI is required for observing intriguing quantum phenomena, such as the quantum anomalous Hall effect (QAHE) [8, 11–14].

1. Introduction

Three-dimensional (3D) topological insulators (TIs) [1, 2] possess spin-momentum locked surface states arising from intrinsic spin–orbit interactions which drive band inversion at high symmetry points in the Brillouin zone [3, 4]. Unlike conventional electronic surface states, which originate from properties of the surface, e.g. dangling bonds on the surface of a semiconductor, the existence of the topological surface states (TSS) is determined entirely by the topology of the bulk bandstructure [5]. In addition, the TSS are protected by time-reversal symmetry (TRS) which further distinguishes them from conventional surface states since they are inherently robust against backscattering from non-magnetic impurities and other weak disorder which do not violate TRS [6]. 0953-8984/15/245602+11$33.00

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Establishing ferromagnetic order in the prototypical 3D TIs Bi2 Se3 and Bi2 Te3 has been achieved using 3d transition metal dopants such as Mn [15–17] and Cr [18, 19]. However, uncontrollable formation of parasitic phases and inconsistent results among various complimentary measurement techniques which probe longrange ferromagnetic order and modifications in the surface states, have been reported [9, 15, 20–22]. Cr has by far been the most successful transition metal dopant as the first experimentally detected QAHE was achieved at mK temperatures in Cr-doped (Bi,Sb)2 Te3 (TC = 15 K) [23]. However, recent studies on this system have shown that the exotic physics are more complicated than expected by extreme dopant-induced Dirac-mass disorder [24]. These findings, combined with studies which demonstrate that extremely low temperatures are needed to enhance the magnetic moments and suppress dissipative channels from bulk conduction in order to realise the QAHE [25], highlight the need for improved materials and synthesis techniques. Our approach to addressing these issues has been to utilise rare earth (RE) elements (most have a trivalent electronic configuration [Xe]4f n (5d6s)3 ) as an alternative to 3d transition metals for magnetic doping studies. The lanthanides, reaching from La to Yb, are well-established in the context of thin film growth and are, despite their airsensitivity, possible to handle in a molecular beam epitaxy (MBE) growth setting. In general, due to their well-shielded 4f shell, the expectation is that the high moment RE ions behave like localised magnetic moments in the host matrix, leading to an overall paramagnetic behaviour in the doped system. However, measurements of pure RE metals and REdoped systems have revealed a variety of magnetic properties which are often complex and unexpected [26]. Previous studies on doped 3D TIs have demonstrated that the size of the Dirac gap increases with the magnetic moment [9]. This offers motivation for large magnetic moment doping studies, using dopants such as Dy or Ho with moments 2–3 times larger than those typically used in 3d transition metal-doped systems, since increasing the gap size provides greater flexibility for exploring ferromagnetic TI physics. In addition, a few of the rare earth metals exhibit ferromagnetic states at high temperatures, in some cases up to room temperature, which may also be useful in raising the temperature scale for doped TI systems. Recently, we presented the growth of (Gdx Bi1−x )2 Te3 thin films by MBE with large concentrations of Gd (x  0.3) [27]. Rhombohedral films of high-quality were achieved for Gd concentrations much larger than the bulk solubility limit [28]. In Gd-doped Bi2 Te3 , Gd3+ ions substitute isoelectronically on Bi sites which does not introduce any additional charge carriers in the process. Angle-resolved photoemission spectroscopy (ARPES) confirmed the existence of the TSS and magnetoresistance measurements showed weak antilocalisation. All films in the series were found to have large effective magnetic moments (i.e. effective Bohr magneton numbers) µeff (∼7 µB Gd−1 ) that were independent of doping concentration and close to the maximum free ion value of 7.94 µB [29]. Nevertheless, no long-range magnetic order was observed as the films remained paramagnetic down to 2 K [29].

Aside from Gd, dysprosium is one of the most attractive dopants in the lanthanide series. Dy has an electronic configuration of 4f 9 with Hund’s rule ground state of 6 H15/2 with Land´e g-factor gJ = 4/3. This results in µeff = gJ · J = 10.64 µB , making Dy one of the elements with the largest magnetic moment in the periodic table. Here we report the structural and magnetic study of Dy-doped Bi2 Te3 thin films with Dy concentrations ranging from 0% to 35.5% (in % of the Bi sites). A combination of surface- and bulk-sensitive measurement techniques, including scanning electron microscopy (SEM), Rutherford backscattering spectrometry (RBS), particle induced x-ray emission (PIXE), x-ray diffraction (XRD), superconducting quantum interference device (SQUID) magnetometry, x-ray absorption spectroscopy (XAS) and x-ray magnetic circular dichroism (XMCD), were used to explore the structural and magnetic properties of the Dy-doped films. 2. Thin film growth and structural characterisation 2.1. MBE growth

A series of Dy-doped Bi2 Te3 thin films was grown on Al2 O3 (0 0 0 1) substrates (c-plane sapphire) using MBE. Prior to growth, the substrates were degreased and baked in ultrahigh vacuum (UHV) overnight, before being loaded into the growth chamber for an additional anneal at 450 ◦ C for ∼10 min. The base pressure of the MBE system is ∼5 × 10−11 Torr. Thin films were grown by co-evaporation from high-purity elemental sources, using standard effusion cells for Dy, Bi, and Te. The Bi and Te fluxes were calibrated using a beam flux monitor, however, the Dy concentration had to be determined post-growth due to pronounced gettering effects. The Bi and Te cell temperatures were held constant (458 ◦ C and 232 ◦ C, respectively), which resulted in a nominal Te/Bi flux ratio of 15. The Dy concentration, x, was controlled by varying the Dy effusion cell temperature (825 ◦ C–925 ◦ C). A growth recipe, similar to a well-established twotemperature step growth procedure described in [30], was used. A low temperate nucleation layer was deposited at 250 ◦ C for 33 min. Following the nucleation layer deposition, growth was paused while the substrate temperature was ramped up to 300 ◦ C at 5 ◦ C min−1 under Te flux. At 300 ◦ C, the sample was annealed for 30 min and then growth continued at 300 ◦ C for another 33 min. Note that the substrate temperatures are thermocouple readings. The film growth was monitored in situ using reflection high-energy electron diffraction (RHEED). Streak-like diffraction patterns were observed for all samples grown with Dy cell temperatures 925 ◦ C, as shown in figure 1. Two different RHEED patterns (along the [1 0 1¯ 0] and [1 1 2¯ 0] azimuths of the Al2 O3 (0 0 0 1) substrate) were found to repeat upon 30◦ rotation, which reflects the three-fold symmetry of the host Bi2 Te3 crystal [4]. For higher Dy cell temperatures, the streaks become more diffuse, which suggests a degradation in crystalline quality with increasing Dy concentration. Above 950 ◦ C, a spotty ring-like RHEED pattern is obtained which is indicative of highly textured polycrystalline growth (not shown). Therefore, films grown at temperature above 925 ◦ C were exclude from further investigations. 2

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Figure 1. RHEED patterns obtained on the c-plane sapphire substrate prior to film growth and on the Dy thin film doping series. Patterns were obtained along the [1 0 1¯ 0] (top) and [1 1 2¯ 0] azimuth (bottom) of Al2 O3 (0 0 0 1) for the (a) pristine substrate, (b) undoped Bi2 Te3 , and Dy-doped films grown with the following Dy cell temperatures: (c) 825◦ C, (d) 850◦ C, (e) 875◦ C, (f ) 900◦ C, and (g) 925◦ C. The Dy concentrations, x, are indicated in the panels.

In addition to providing feedback about the surface morphology, RHEED is also used to provide information about the in-plane lattice parameter for the growing epitaxial layer. A visual comparison of the streak spacings of the (Dyx Bi1x )2 Te3 thin films and the substrate reveals that they grow with significantly different in-plane lattice constants. Differences in the in-plane lattice constants are anticipated given that the (Dyx Bi1x )2 Te3 thin films are expected to grow via van der Waals epitaxy (vdWE) on the highly latticemismatched c-plane sapphire substrate (8.7%). The vdWE growth mechanism does not require a high degree of lattice matching between film and substrate, yet the crystallographic orientation of the deposited film is in registry with the substrate [31, 32]. Examples of substrates on which TI films were successfully grown by vdWE are Si(1 1 1) [33], SrTiO3 (1 1 1) [34], CdTe(1 1 1)B [35], and Al2 O3 (0 0 0 1) substrates [30]. A careful analysis of the streak spacings within the doping series reveals that the in-plane lattice constants of the doped films vary slightly as a function of Dy concentration. A detailed study of the in-plane lattice constants, which were also found to be influenced by Dy doping, was carried out using reciprocal space mapping x-ray diffraction and is discussed in [36].

Table 1. Composition and thickness of thin films grown at the indicated Dy cell temperatures determined by the combined RBS and PIXE measurements.

Dy T Dy x Dy (◦ C) (at-%) 0 825 850 875 900 925

0 0.024 0.055 0.113 0.183 0.355

0.0 ± 1.0 0.9 ± 1.0 2.2 ± 1.0 4.5 ± 1.0 7.3 ± 1.0 14.2 ± 1.0

Bi (at-%)

Te (at-%)

thickness t (Å)

39.2 ± 0.5 38.5 ± 1.0 37.3 ± 1.0 35.4 ± 1.0 34.2 ± 1.0 28.8 ± 1.0

60.8 ± 1.0 58.4 ± 1.5 60.5 ± 1.5 60.1 ± 1.5 58.5 ± 1.5 57.0 ± 1.5

721 ± 50 812 ± 50 788 ± 50 840 ± 50 887 ± 50 1108 ± 50

Note: Note that a small Se background is observed, which is included in the Te concentration.

films show a small level of unintentional Se doping (5 at.%) since growth was performed in a chamber primarily used for Se compounds. However, from the RBS/PIXE data it is clear that Se occupies Te positions since the combined Te and Se percentages are close to 60% for the majority of the films in the doping series. In addition, the Se signals were found to have the same widths as the Te and Bi signals which indicates that the Se atoms were uniformly incorporated throughout the film thickness. Analysis of the cation (Dy+Bi) to anion (Te+Se) ratios for the majority of the samples in the series shows a relationship of ∼2:3, within the specified error margin. A cation to anion ratio of ∼2:3, is indicative of Dy being mostly substitutional on Bi sites [27]. However, at the highest doping level (x = 0.355), the anion atomic percentage was found to be slightly less than 60% which could indicate a mixed substitutional and interstitial doping scenario [27]. No signs of compositional gradients and phase segregation were observed in RBS/PIXE for Dy concentrations of x  0.355.

2.2. Compositional analysis

The elemental compositions, as well as the thicknesses of the (Dyx Bi1−x )2 Te3 thin films, were determined from a combination of RBS (2.3 MeV Helium ions) and PIXE (1 MeV Hydrogen ions). PIXE analysis was required in order to resolve an overlap of the Dy signal with the Bi and Te signals in the RBS measurements. By fitting the combined RBS and PIXE data to structural models, the elemental compositions and film thicknesses listed in table 1 were determined. Note that all 3

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(a)

(b)

(c)

(d)

(e)

(f)

Figure 2. Scanning electron micrographs of the Dy-doped Bi2 Te3 films. Dy concentration, x: (a) 0, (b) 0.023, (c) 0.055, (d) 0.113, (e) 0.183, (f ) 0.355. The scale bar in the upper row represents 200 nm and in the lower row 1 µm, respectively. The dotted lines in (a) indicate quintuple-layer-high steps, which have an average spacing of ∼130 nm.

triangular growth features were still found to dominate the surface morphology but the characteristic concentric hillocklike growth spirals were no longer prominent features in the topography. The triangular growth features observed on higher Dy concentration samples (0.113  x  0.183) were typically composed of a series of terraces grown with quasi-parallel orientation with respect to one of the triangular domain edges (see figures 2(d)–(e)). For x = 0.355 (see figure 2(f )),

2.3. Film morphology

Scanning electron microscopy was carried out to investigate changes in the morphology of the thin films as a function of Dy doping. As shown in figures 2(a)–(c), samples with x  0.055 were found to exhibit a Bi2 Te3 -like surface morphology, consisting of triangular domains with a terrace-step structure. When the Dy doping concentration is increased to x = 0.113, 4

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the surface morphology changes once again as the domains become irregularly shaped and exhibit less faceted terraces. These observations suggest that the inclusion of Dy introduces disorder in the Bi2 Te3 crystal which causes a deviation in the growth mechanism away from spiral surface growth which typically governs the growth of the (Bi,Sb)2 (Se,Te)3 family of materials [37]. The surface roughness was also found to be affected by Dy incorporation. Pits and 3D defects were observed on samples with the higher doping levels (see figures 2(d)–(f )). These finding are consistent with the increase in surface roughness detected in the RHEED patterns. Note that the dark spotlike features observed in the SEM images are attributed to solvent residue from pre-growth sample preparation of the Al2 O3 substrates [38].

102

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101 100

20

40

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(0 0 3) (0 0 6) (0 0 9) (0 0 15) (0 0 18) (0 0 21) (0 0 30)

0.8

I(0 0 3l) / I(0 0 6)

X-ray diffraction was carried out using a Bruker D8 Discover x-ray diffraction system with Cu Kα1 emission. Figure 3(a) shows representative symmetric 2θ -ω scans obtained on a (Dyx Bi1−x )2 Te3 thin film with x = 0.355 and, for comparison, on a binary Bi2 Te3 film. Throughout the series only substrate and film peaks with relative positions consistent with the (0 0 3) family of Bi2 Te3 diffraction peaks were observed. This indicates that even at large Dy concentrations, the (Dyx Bi1−x )2 Te3 thin films are c-axis oriented and grow in a rhombohedral crystal structure. Secondary phases were not observed for concentrations up to x  0.355. However, at cell temperatures which corresponded to concentrations above 0.355 (T > 925 ◦ C), only substrate peaks were detected in the XRD spectra, which is consistent with our RHEED findings for higher Dy cell temperature growth. These results establish the high doping limit for single phase (Dyx Bi1−x )2 Te3 thin films to x = 0.355. The doping levels achieved in this study were remarkably high given that the two binary end members Bi2 Te3 and Dy2 Te3 possess different crystal structures (rhombohedral and orthorhombic, respectively) which may make the (Dyx Bi1−x )2 Te3 thin films more susceptible to phase segregation at higher Dy concentrations. Phase segregation is commonly reported in magnetically doped TI systems, often at lower doping concentrations than were achieved in this study [20]. As reported for other TI doping studies, peak broadening and variations in intensity were observed in the XRD spectra with increasing doping concentration [18, 27]. These effects are particularly evident for the high-angle reflections (2θ > 65◦ ) shown in figure 3(a) and are indicative of degradation in crystalline quality. Figure 3(b) shows the normalised peak intensities, with respect to the (0 0 6) reflection, for the doping series. Trends observed in the normalised peak intensities as a function of Dy doping suggest that the structure factors for certain lattice planes are more sensitive to doping changes and disorder than others. For example, the lattice planes responsible for the (0 0 9) and (0 0 30) reflections were found to be the most affected by Dy doping. The measured peak intensities for (0 0 9) reflections were found to increase by nearly an order of magnitude, whereas the

0.6 0.4

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30.8 30.7 30.6 30.5 30.4 0.0

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Dy concentration x Figure 3. (a) XRD 2θ-ω scans obtained on an undoped binary Bi2 Te3 thin film (black) and a (Dyx Bi1−x )2 Te3 thin film (red) with x = 0.355. (b) Plot of the (0 0 3) peak intensities obtained from 2θ-ω scans and normalised to the (0 0 6) peak of the respective film in the (Dyx Bi1−x )2 Te3 series. Note that the scale for the normalised (0 0 9) peaks is shown on the right-hand side as the normalised peak intensity is very small for all films in the doping series. (c) Out-of-plane lattice parameter c obtained from the (0 0 3) reflections.

(0 0 30) peak was found to completely vanish at higher doping concentrations. Other lattice planes affected to lesser extent include planes responsible for the (0 0 3) and (0 0 15) peaks whose normalised peak intensities were found to increase and decrease, respectively, with increasing Dy concentration. Careful analysis of the XRD spectra reveals a consistent trend of shifting of the relative peak positions toward lower diffraction angles as the Dy concentration is increased. A shift toward lower diffraction angles translates to an expansion in the out-of-plane lattice constant. The c-axis lattice constants were determined from the 2θ values of the (0 0 3) peaks, between 5◦ and 65◦ , using a nonlinear least-square cell-refinement program [39]. The individual peak positions were determined by fitting a Lorentzian. The lattice constants were found to increase from (30.39 ± 0.02) Å for the undoped Bi2 Te3 film 5

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(b) x = 0.023 x = 0.055 x = 0.113 x = 0.183 x = 0.355

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Figure 4. SQUID magnetisation measurements: (a) Magnetisation loops of films with varying Dy concentration x obtained at 2 K for the field applied in-plane. Inset: low field behaviour for films with a Dy concentration of x = 0.055 (red) and 0.113 (blue). (b) Plot of the effective magnetic moment at 2 K as a function of Dy concentration.

to (30.83 ± 0.05) Å for the highest concentration investigated (x = 0.355); an increase of ∼1.45%. This observation is somewhat unexpected based on examination of the ionic radii. Comparing the ionic radius of Bi3+ (117 pm) [40] with that of the smaller Dy3+ (105 pm) [41], and assuming substitutional incorporation, a decrease in the c-axis lattice constant could be expected. Such an increase in the c-axis is indeed found for some transition metal-doped bismuth chalcogenide systems [18, 42, 43], where the dopants are known to be incorporated in the van der Waals gap. However, no increase in the c-axis lattice parameter was found for substitutional Cr doping of Bi2 Se3 [19]. In addition, transmission electron microscopy on Dy-doped films with x  0.113 found no evidence of Dy incorporation in the van der Waals gap despite a marked increase in the observed c-axis lattice parameter [36].

examples of the low field behaviour observed for films with Dy concentrations of x = 0.055 (red plot) and x = 0.113 (blue plot). Note that the magnetisation curves pass directly through the origin, i.e. no remanent magnetisation is observed. Similar paramagnetic responses were also observed in magnetisation measurements performed with the applied field parallel to the c-axis, i.e. perpendicular to surface of the sample (not shown). The concentration dependence of µeff , presented in figure 4(b), shows a decrease from (12.63 ± 0.64) µB Dy−1 for x = 0.023 to (4.29 ± 0.16) µB Dy−1 for samples with x = 0.355. Such a doping concentration dependence of µeff was not found for Gd-doped Bi2 Te3 thin films [29], which makes Dy unique among the explored RE series. As discussed previously, Gd-doped samples were found to yield effective magnetic moments of ∼7.0 µB Gd−1 , which were close to the full moment expected from Hund’s rules, independent of the doping concentration for 0.1  x  0.3. Figure 5 shows a typical example of the magnetic susceptibility χ as a function of temperature for a Dy-doped film with x = 0.113, measured in an applied magnetic field of 100 mT. The inset to figure 5 shows the inverse magnetic susceptibility 1/χ as a function of temperature. Note that no difference between zero-field-cooled and field-cooled data is observed. The inverse magnetic susceptibility data can be fitted using the Curie-Weiss dependence χ = C/(T −) (red dotted line), where C is a constant and  is the Weiss temperature. At low temperatures, no deviations from the linear behaviour are found. Fitting to the Curie-Weiss dependence reveals a negative Weiss temperature ( = −1.2 K), which suggests the possibility of an antiferromagnetic phase transition at lower temperatures. Similar results were found for all samples in the doping series, whereby the slope of 1/χ reduces throughout the series as expected from the increasing Dy concentration, whereas the Weiss temperature remains roughly the same and slightly negative (between −0.36 K and −1.2 K). The observed paramagnetic behaviour of the Dy doping series can be attributed to the strongly localised 4f electrons in Dy which have only a small overlap with the wave

3. Bulk magnetisation measurements

The magnetic properties of the (Dyx Bi1−x )2 Te3 thin films were investigated using bulk-sensitive magnetometry with a 7 T Quantum Design MPMS SQUID VSM. Figure 4(a) shows magnetisation curves obtained at 2 K for the (Dyx Bi1−x )2 Te3 series with the applied field perpendicular to the c-axis. The diamagnetic background of the Al2 O3 substrate was removed using high-field linear fitting in the range of 6 T to 7 T. At low temperatures, all magnetisation curves were found to saturate at high magnetic fields, i.e. ∼4 T at 2 K. The effective magnetic moments, µeff , for the Dy series were calculated using measurements of the sample mass along with values for the Dy concentration and thickness determined from RBS/PIXE (see table 1). µeff as a function of the Dy doping is plotted in figure 4(b). The stated errors are determined by uncertainty in the determination of sample volume from the RBS/PIXE data. No evidence of hysteretic magnetic behaviour was observed for the entire Dy series, which points towards the absence of long-range ferromagnetic ordering of the Dy dopants in the films. The inset in figure 4(a) shows typical 6

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the multi-electronic configuration of the Dy3+ , the transitions 4f 9 → 3d 9 4f 10 are calculated using atomic multiplet theory, in which spin–orbit and electrostatic interactions are treated on an equal footing [48, 49]. The intra-atomic electrostatic interactions include the 3d–4f and 4f –4f Coulomb and exchange interactions. The wave functions of the initialand final-state configurations are calculated in intermediate coupling using Cowan’s atomic Hartree–Fock code with relativistic corrections [50, 51]. To account for interatomic interactions, the parameters of the Slater integrals for the Coulomb and exchange interactions were reduced to 65%, while the spin–orbit interaction was kept at 100% [48]. The Dy M5 (M4 ) line spectra were broadened by a Lorentzian of  = 0.25 eV (0.5 eV) for intrinsic lifetime broadening and a Gaussian of σ = 0.35 eV for instrumental broadening. The 4f wave function contraction in the lanthanide series makes these orbitals atomic-like, with negligible influence on the local environment. The spectral shape of the core spectra are characteristic for the Dy3+ 4f 9 (6 H15/2 ) configuration [48]. The LS-coupled ground state gives a spin moment of Sz = 2.5 µB , an orbital moment of Lz  = 5 µB , which combine to a total angular magnetic moment of Jz = Lz +Sz = 7.5 µB , which gives an effective 4f magnetic moment of µeff = gJ ·J = 10 µB per Dy3+ , and a magnetic dipole moment Tz  = −0.33 µB [52]. Unlike the 5d and 6s electrons in Dy, the 4f electrons are not directly involved in the chemical bonding. Therefore, the Dy M4,5 spectrum is essentially the same for the metal and alloys, as well as oxides and compounds, apart from small differences in line broadening. Since the additional 4f electron is effectively screening the 3d hole, the chemical shift in the M4,5 spectra is small, so that no chemical information is obtained from the XAS and XMCD spectra. Due to its shellspecificity, the XMCD signal is directly proportional to the 4f magnetic moment [48, 49].

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Temperature (K) Figure 5. Plot of the magnetic susceptibility (zero-field-cooled) of a Dy-doped film with x = 0.113 in the temperature range from 2 K to 100 K. The inset shows the inverse magnetic susceptibility in the temperature range from 2 K to 15 K. The red line represents the linear Curie–Weiss fit to the data yielding a Weiss temperature of θ = −1.2 K.

functions of neighbouring atoms and therefore show no, or only weak, direct interactions. This behaviour is well-known for the dysprosium-tellurium compounds DyTe, Dy3 Te4 , Dy4 Te7 , Dy4 Te9 , and Dy4 Te11 [44], whereas Dy2 Te3 is known to be antiferromagnetic with a N´eel temperature of 4.1 K [45]. Magnetic ordering in rare earth elements typically occurs through an indirect exchange or Ruderman–Kittel– Kasuya–Yosida (RKKY) interaction involving the conduction electrons [26]. 4. Synchrotron-based magnetic studies

The element-specific technique of XMCD was used to probe the local electronic character of the magnetic ground state [46]. This technique allows an unambiguous determination of the electronic and magnetic state of transition metal and rare earth magnetic dopants in TIs [16, 29, 47].

Determination of spin moment – While in principle sumrule analysis [53–55] can be used to obtain the magnetic moment in rare earths, the large jj mixing between the 3d5/2 and 3d3/2 core levels, as well as a non-negligible magnetic dipole moment make it more complicated to extract the spin moment, compared to 3d transition metals. Alternatively, since the effective magnetic moment is proportional to the peak asymmetry, A = (I + −I − )/(I + +I − ), its value can be obtained by comparing the measured and calculated intensities of the spectra [29]. However, if there is an unaccounted fraction of non-magnetic or antiferromagnetic Dy, the effective magnetic moment will be accordingly reduced.

Experimental – X-ray absorption spectra (XAS) at the Dy M4,5 edges were measured at a temperature of 5 K on beamline I10 (BLADE) at the Diamond Light Source (Oxfordshire, UK) using a 14 T superconducting magnet. XAS measurements were made on the x = 0.113 sample in total-electron-yield (TEY) and fluorescence yield (FY) modes. The XMCD is obtained from the difference between two XAS spectra recorded with the x-ray helicity vector and applied magnetic field parallel and anti-parallel, respectively. The magnetic field is always parallel to the x-ray beam and the samples (with the normal  c-axis) were measured at both normal ( c-axis) and (nearly) grazing (⊥ c-axis) incidence. The XMCD is measured by reversing the polarisation of the incident x-rays to avoid changing the magnetic field of the superconducting magnet.

Experimental spectra – Figure 6 shows the Dy M4,5 XAS and XMCD measured in an applied field of 7 T at temperature of 5 K. By sweeping the applied field at the energy of the Dy M5 peak maximum, we obtain an XMCD hysteresis loop, which reveals the field dependent magnetisation of the Dy moments. XAS loops were recorded in FY detection for both left- and right-circularly polarised x-rays. The hysteresis loop in figure 6 (inset) measured at grazing incidence shows that the Dy moment saturates at 2 T, above which the magnetisation becomes flat. No loop opening was found, but it has to be

Calculational description – Electric-dipole transitions from the 3d core level in the rare earths are allowed to empty 4f states, but forbidden to 5d and 6s valence states. For 7

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8 6

0.25

Pos. helicity

0.20

Neg. helicity

Intensity (arb. units)

4 2 0 -2 -4

XMCD (arb. u.)

Intensity (arb. units)

0.30

XAS XMCD

-6 -8 -10

8 4

ramp down ramp up

0

0.15 0.10 Sum

0.05 Difference

-4 -8

0.00 -8 -6 -4 -2 0 2 4 6 8

µ H (T) -12 1270 1280 1290 1300 1310 1320 1330 1340 0

-0.05 1285

Photon energy (eV) Figure 6. Grazing incidence Dy M4,5 XMCD measured in an applied field of 7 T at temperature of 5 K for a sample with x = 0.113. Inset: XMCD hysteresis loop at Dy M5 edge measured at grazing incidence.

1295

1300

Figure 8. Experimental Dy M5 spectra (drawn red lines) of the x = 0.113 sample for positive and negative helicity and their sum and difference spectra compared with the calculated spectra (dash-dotted blue lines). The experimental spectra were fitted with the IL , IZ , and IZ spectra from figure 7, yielding the intensity ratios given in equation (1), which amounts to an XMCD effect equal to 42% of the value for the Hund’s rule ground state.

0.20 R iso = (L+Z+R)

0.15

energy by ∼2 eV each. Figure 7 shows that the main peak at 1292 eV contains 85% IR and 15% IZ . The Dy M5 spectra measured with positive and negative helicity, I ± , were fitted using the calculated IL , IZ , and IR spectra from figure 7. For normal incidence, the results are shown in figure 8, where the fitting gives

Z

Intensity (arb. units)

1290

Photon energy (eV)

0.10 L 0.05 0.00

+ Inorm.inc. = 13.8% IL + 34.5% IZ + 51.7% IR ,

-0.05

− Inorm.inc. = 57.3% IL + 33.9% IZ + 8.8% IR .

xmcd = (L-R)

-0.10

This shows that the polarised spectra are far from pure IR and IL . Despite this, the spectra are very similar to polarised Dy spectra in the literature [57]. As a possible explanation, it could be that the Dy exhibits a strong linear dichroism, IL + IR − 2IZ , due to a crystal-field electrostatic interaction. Such a linear dichroism has been reported for Dy overlayers in the absence of any magnetic field [58–60]. This leads to an increase in IX + IY (= IL + IR ), compensated by a decrease in IZ , while the opposite effect occurs at grazing angle. However, fitting the polarised spectra at grazing incidence (not shown) gives

-0.15 1285

1290

1295

(1)

1300

Photon energy (eV) Figure 7. Calculated XAS at the Dy M5 edge for left circular (L), right circular (R) and linear polarisation along the beam direction (Z), together with the resulting isotropic spectrum (L + R + Z) and XMCD spectrum (L–R).

noted that the superconducting magnet’s remanent field has been determined to be 30 mT. This suggests the Dy-doped Bi2 Te3 film is paramagnetic at 5 K.

+ Igraz.inc. = 17.3% IL + 34.6% IZ + 48.1% IR , − Igraz.inc. = 60.3% IL + 31.2% IZ + 8.4% IR ,

Calculational results – Figure 7 shows the calculated spectra for left circular (IL ), right circular (IR ), and linear polarisation along the beam direction (IZ ), together with the resulting isotropic spectrum (IL +IR +IZ ) and XMCD spectrum (IL −IR ). Using the standard convention [56], the integrated intensity for IR is larger than for IL , so that the overall sign of the XMCD is negative. The Dy M5 spectrum is ideally suited to determine the relative contributions of the three fundamental spectra, IL , IZ , and IR , since their respective peaks are separated in photon

(2)

Fitting the linear polarisation gives Ilinear = 44.3% IL + 34.1% IZ + 21.6% IR .

(3)

Since both IL +IR and IZ remain almost constant in these three cases, we can conclude that linear dichroism plays only a minor role. Hence the influence of any crystalline anisotropy is small (note that the magnetic field rotates together with the beam 8

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direction). The systematically lower value of IR compared IL in all cases can be due to the increased x-ray absorption saturation effect for the higher peak intensity and/or a ‘leakage’ of intensity into the broad structure around 1295 eV. From the coefficients in equations (1) and (2) we obtain an XMCD intensity equal to 42% of the calculated value for the Hund’s rule 4f state of µeff , which means an effective magnetic moment of 4.2 µB /Dy3+ . For comparison, the same x = 0.113 film at 5 K shows an effective magnetic moment of ∼5.5 µB Dy−1 in the SQUID data, however, this also includes a possible contribution of 5d electrons. The remaining intensity in the polarised spectra is due to an isotropic contribution. The results can also not be explained by a reduction in the degree of polarisation of the x-rays, which is >95%, as this would not give an IZ contribution. Therefore, the isotropic contribution must be due to non-magnetic or antiferromagnetic Dy sites. This could be oxidation since the TEY detection is rather surface sensitive, with a sampling depth of 3– 5 nm [56]. Simultaneously with the TEY, we also measured in fluorescence yield detection. However, these spectra were strongly saturated, which makes it difficult to extract any quantitative information about the magnetic moment. Hence, it makes sense to assume that only 42% of the Dy sites give a magnetic response.

arising from a spin polarisation of the Bi2 Te3 matrix by the Dy atoms. Giant magnetic moments, which exceed free ion values, arising from matrix polarisation of the host material have been reported in some rare earth-doped dilute magnetic semiconductors, such as Eu-doped GaN [65] and Gd-doped GaN [66], where in case of Gd doping effective magnetic moments of 4000 µB have been reported. Investigations into the local electronic structures of the rare earth dopants in 3D TIs using extended x-ray absorption fine structure (EXAFS) may be useful in revealing the origin of these discrepancies, especially if they are related to differences in electronic configuration. 6. Conclusions and outlook

A systematic study of the structural and magnetic properties of MBE-grown Dy-doped Bi2 Te3 thin films was performed. Detailed XRD measurements revealed that large concentrations of Dy (x  0.355) were incorporated into the host Bi2 Te3 crystal lattice without the formation of secondary phases. This is quite remarkable as secondary phases are common for rare earth-doped dilute magnetic semiconductors [67]. No detectable evidence for the existence of long-range ferromagnetic order was observed in bulk-sensitive SQUID magnetisation measurements. All samples in the series displayed paramagnetic behaviour down to 2 K, however, temperature-dependent measurements showed the possibility of antiferromagnetic order at lower temperatures. The effective magnetic moment is doping concentration-dependent, possibly indicating the presence of matrix polarisation of the host material at low Dy concentrations (x  0.023), and generally a more complex chemical bonding scenario as compared to Gd-doped films. The XMCD measurements at the Dy M4,5 edge are in excellent agreement with calculated multiplet spectra, which allows for the accurate determination of the magnetic moment. For the x = 0.113 sample at 5 K and 7 T we obtain an effective magnetic moment of 4.2 µB /Dy3+ . This moment arises uniquely from the 4f since XMCD is not sensitive to the polarisation of the surrounding electrons, such as the 5d. Furthermore, total-electron-yield detection measures only the top 3–5 nm of the sample, which might show some oxygen build up over time [68]. In principle, the element specificity of surface-sensitive XMCD should be able to conclusively establish the magnetic properties of the Dy-doped Bi2 Te3 films, if environmental contamination can be avoided through in situ cleaving [68] or decapping [69] in the measurement chamber. In addition, more detailed investigations into the chemical state and structural environment of the Dy dopants using EXAFS are needed, as this would allow for a determination of the exact location in the Bi2 Te3 lattice. As for many rare earth-doped systems, theoretical simulations are still lacking owing to the challenges posed by their highly localised 4f shells. Further theoretical and experimental studies will be useful for gaining a better understanding of rare earth doping in TIs.

5. Discussion

The goal of ferromagnetic doping of topological insulators is to induce a Dirac-mass gap in the topological surface state band structure at the Dirac point. From bulk magnetisation measurements, no long-range ferromagnetic order was detected for the entire Dy doping series down to the lowest temperature investigated (2 K). However, it should be noted that there is the possibility of TSS-mediated, longrange surface magnetism as the RKKY interaction induced by the Dirac fermions is generally ferromagnetic when the Fermi energy (EF ) is close to the Dirac point [61]. From scanning tunnelling microscopy studies of Dirac fermionmediated magnetic order, it was concluded that the anisotropy of the dopant and their consequences for the Fermi level are crucial [62]. In some systems, the TSS-mediated RKKYtype interaction has been used as a possible explanation for the inconsistencies between surface-sensitive and bulk-sensitive measurements [22]. The unexpected concentration dependence of the effective magnetic moment observed in the (Dyx Bi1−x )2 Te3 series may indicate the presence of complex and competing interactions. For Dy concentrations of x  0.055, the effective magnetic moments were found to be less than the free ion value of 10.64 µB Dy−1 . These low values may arise from the onset of antiferromagnetic ordering at higher Dy concentrations [18, 45, 63, 64]. Crystal-field effects and surface effects can be excluded as these are not expected to be strongly concentration dependent. Similar concentration dependent trends for µeff have been observed in 3d transition metal-doped TIs [18]. On the other hand, samples with Dy concentrations of x < 0.055 exhibited magnetic moments that were larger than expected which may be related to additional contributions 9

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Acknowledgments

This publication arises from research funded by the J Fell Oxford University Press (OUP) Research Fund and RCaH is acknowledged for their hospitality. This work was also supported by a DARPA MESO Project (No. N66001-11-1-4105). SEH was supported by the VPGE (Stanford University), SZ by the Semiconductor Research Corporation (SRC), and LCM and AAB acknowledge support by EPSRC. Diamond Light Source is acknowledged for beamtime allocated on I10 (SI9234). We thank A Vailionis and Y Huo for helpful discussions throughout the course of this work.

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Study of Dy-doped Bi₂Te₃: thin film growth and magnetic properties.

Breaking the time-reversal symmetry (TRS) in topological insulators (TIs) through ferromagnetic doping is an essential prerequisite for unlocking nove...
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