Infrared electrodynamics and ferromagnetism in the topological semiconductors Bi 2 Te 3 and Mn-doped Bi 2 Te 3
B. C. Chapler, K. W. Post, A. R. Richardella, J. S. Lee, J. Tao, N. Samarth, D. N. Basov
IInfrared electrodynamics and ferromagnetism in the topological semiconductorsBi Te and Mn-doped Bi Te B. C. Chapler, K. W. Post, A. R. Richardella, J. S. Lee, J. Tao, N. Samarth, and D. N. Basov Physics Department, University of California-San Diego, La Jolla, California 92093, USA Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA Brookhaven National Laboratory, Upton, New York 11973 USA (Dated: August 24, 2018)We report on infrared (IR) optical experiments on Bi Te and Mn-doped Bi Te epitaxial thinfilms. In the latter film, dilute Mn doping (4.5%) of the topologically nontrivial semiconductor hostresults in time-reversal-symmetry-breaking ferromagnetic order below T C =15 K. Our spectroscopicstudy shows both materials share the Bi Te crystal structure, as well as classification as bulk de-generate semiconductors. Hence the Fermi energy is located in the Bi Te conduction band in bothmaterials, and furthermore, there is no need to invoke topological surface states to describe theconductivity spectra. We also demonstrate that the Drude oscillator strength gives a simple metricwith which to distinguish the possibility of topological surface state origins of the low frequencyconductance, and conclude that in both the pristine and Mn-doped Bi Te samples the electromag-netic response is indeed dominated by the bulk material properties, rather than those of the surface.An encouraging aspect for taking advantage of the interplay between nontrivial topology and mag-netism, however, is that the temperature dependence of the Mn-doped Bi Te film suggests bulkcharge carriers do not play a significant role in mediating ferromagnetism. Thus, a truly insulatingbulk may still be suitable for the formation of a ferromagnetic ground state in this dilute magnetictopological semiconductor. PACS numbers:
I. INTRODUCTION
A topological insulator (TI) is a material with an en-ergy gap in the bulk. However, unlike conventional insu-lators or semiconductors, TIs are topologically inequiva-lent to the vacuum. A primary consequence of topolog-ical inequivalence is the requirement that the “gappedregion” in the band structure of the TI is filled with gap-less surface state (SS) bands confined to the interfacebetween the bulk TI and a topologically trivial insulator.However, when time reversal symmetry (TRS) is broken,an energy gap can be opened in the SSs. The break-ing of TRS is predicted to have a number of interest-ing consequences in TIs including magnetic monopoles ,the topological magnetoelectric effect, and quantizedKerr/Faraday rotation . Research along these lines, forexample, has recently led to the prediction and first ex-perimental observation of the quantum anomalous Halleffect .One path to breaking TRS in TIs is to introduce longrange ferromagnetic order. Ferromagnetism has beendemonstrated in a number of TI candidates doped withtransition metal elements in this new class of dilutemagnetic semiconductors: the dilute magnetic topologi-cal insulator. Potential TI phenomena related to the in-terplay between magnetism and topological SSs is an ex-tremely challenging experimental problem, however. Forinstance, it remains to be seen if upon transition metaldoping, TIs can retain their topological SSs to achieve agap at the Dirac point. It is theoretically anticipated thatthis is indeed possible . Experimentally, however,while SSs have been observed in ferromagnetic transition metal-doped TI hosts, they are significantly broadenedand not well defined compared to pure samples . Fur-thermore, data have suggested there is a crossover from aTI to a topologically trivial dilute magnetic semiconduc-tor driven by magnetic impurities . A further roadblock,and that most relevant to this work, is that TI materialshave been plagued by extrinsic defect induced charge car-riers. Thus the bulk charge carriers will need to be con-trolled and eliminated to achieve films that are insulatingin the bulk. However, the FM mechanism in canonicaldilute mangetic semiconductors such as (Ga,Mn)As and(In,Mn)As is carrier mediated . A bulk carrier medi-ated mechanism in transition metal doped TIs would beincompatible with the parallel goal of elimanating bulkcharge carriers.In our investigation we report the infrared (IR) con-ductivity and Raman spectra of epitaxial thin films ofBi Te and Mn-doped Bi Te with Curie temperature T C =15 K. IR spectra of a second Mn-doped Bi Te filmthat does not exhibit ferromagnetism is also discussed(Sec. V B), but is not a focus of this paper. The IR energyrange is commensurate with a multitude of electronic pro-cesses vital to understanding the physics of these mate-rials. These processes include the excitation of IR activeand Raman active phonons, the electrodynamic responseof charge carriers, both those in the bulk and potentiallythose on the surface, optical transitions initiated frommid-gap defect states, and excitations across the bulk en-ergy gap. More importanly, however, IR spectroscopy isa well established tool for investigating ferromagnetismin semiconductors . In particular, carrier mediatedmechanisms have specific signatures in the IR.The inclusion of Bi Te in this work is two-fold. First, a r X i v : . [ c ond - m a t . m t r l - s c i ] M a y the IR response of Bi Te serves as the basis for under-standing the effect of magnetic dopants and ferromag-netism on the IR electrodynamics of Mn-doped Bi Te ,and potentially other related TI candidates. Second, theso called “second generation materials” (Bi Se , Bi Te ,and Sb Te ) are thought to be most promising for un-veiling exotic effects predicted for TIs . Improvementsin isolating the surface state electrodynamic response inoptical experiments has previously been demonstrated inBi Se thin films, in contrast to bulk crystals . Thusthere is clear utility in performing similar IR studies onBi Te thin films.Here, spectroscopic features show both Bi Te andMn-doped Bi Te to be degenerate semiconductors, withno need to invoke topological surface states to describethe IR data. In the case of Bi Te , this conclusion isreached despite an optical band gap that is lower thanthat revealed in photoemission, and a Drude oscillatorstrength of simlilar magnitude as that observed in Bi Se thin films . Instead, a simple f -sum rule based ar-gument is introduced to put an upper limit on the SSconductance and demonstrate that what we observe inBi Te must be a bulk response. Our experiments in-dicate a significantly larger bulk charge carrier concen-tration in the Mn-doped film than that of the pristineBi Te film. However, despite the large charge carrierconcentration, our data suggest bulk charge carriers donot play a significant role in mediating ferromagnetism inMn-doped Bi Te . This latter conclusion is evidenced bythe fact that the IR spectrum exhibits remarkably littlechange upon cooling across the FM transition.The paper is organized as follows. First, we providedetails of our sample growth and initial characterizationin Sec. II. Following that, Sec. III describes the exper-imental methods used in our IR probe. In Sec. IV wepresent our main results on the IR optical properties ofour samples, which is broken in to two sections. Sec. IV Aaddresses the phonon spectra of our films, while Sec. IV Bcovers the IR electronic response. Discussion of key as-pects of these results is found in Sec. V. Sec. V A pro-vides conclusions drawn from our data regarding Bi Te .Sec. V B considers the effect of magnetic dopants andferromagnetism on the IR electrodynamics of Mn-dopedBi Te . Finally, concluding statements are found inSec. VI. II. SAMPLES GROWTH ANDCHARACTERIZATION
The films in this study were prepared using molecularbeam epitaxy (MBE) with the growth direction paral-lel to the c axis on GaAs (111)B substrates, with filmthicknesses of 70 nm and 68 nm for Bi Te and Mn-doped Bi Te , respectively. The films are characterizedusing x-ray diffraction (XRD), Rutherford backscattering(RBS), secondary ion mass spectroscopy (SIMS), scan-ning transmission electron microscopy (STEM), low tem- perature magneto-transport and superconducting quan-tum interference (SQUID) magnetometry. Details of theMBE growth and characterization measurements are pro-vided elsewhere . XRD data on the Bi Te film is in-dicative of typical c axis oriented Bi Te . Hall effectdata (Fig. 1a) shows a relatively temperature indepen-dent electron charge carrier density n of roughly 4.3 × cm − (Fig. 1c).The Mn concentration of the magnetically doped filmis 4.5 atomic % with 20% relative error, as determinedfrom RBS and SIMS. The Curie temperature for the on-set of ferromagnetism in the Mn-doped Bi Te film is T C =15 K, as established by SQUID magnetometry andby the appearance of a hysteretic anomalous Hall effectbelow T C (Fig. 1b). The Mn-doped Bi Te film shows alinear Hall effect above T C , and at magnetic fields outsidethe hysteretic regime below T C . Fig. 1c shows the elec-tron charge carrier density extracted from the Hall effectdisplay very little temperature dependence, with a valueof roughly 4.5 × cm − . TEM measurements of theMn-doped film, completed at Brookhaven National Lab-oratory using a double Cs corrected microscope, reveal astructure consistent with that of Bi Te (Fig. 1e). Thesedata also reveal dislocations of the crystal structure tobe prevalent in the Mn-doped film. Earlier work on bulkcrystals also suggest the possibility of randomly dispersedBi-bilayers . Analysis of the TEM data suggests Mnsubstitutes either at Bi sites or interstitially, with no ob-vious evidence of Mn clustering. Though not a mainfocus this paper, a second Mn-doped Bi Te film thatdoes not exhibit ferromagnetism is discussed in Sec. V B.Based on the growth parameters, and measurements onsamples with similar parameters, we estimate that theMn content is roughly 9 atomic % in this latter film.Detailed characterizations of the electronic and crystalstructure as a function of Mn concentration can be foundin Ref. . III. EXPERIMENTAL METHODS
The samples were probed optically by normal in-cidence transmission Fourier transform infrared spec-troscopy (FTIR) and Raman spectroscopy ( E -field ⊥ c axis). The Raman experiments are performed in thebackscattering configuration with a 532 nm laser. Inthe transmission experiment, unpolarized broad-band IRlight with electric field perpendicular to the c axis is inci-dent on the sample. The frequency dependent transmis-sion spectrum is recorded and then normalized by thetransmission spectrum of the bare substrate. The rawtransmission spectra of both our films, normalized to theGaAs substrate, are shown in Fig. 2. The transmissionspectra are then modeled in order to extract the opticalconstants of the films, which is imperative to a quantita-tive understanding of IR data, and is described below.Transmission spectra are dependent on, aside fromthicknesses, both the real and imaginary components of a -60 -30 0 30 60-150-100-50050100
45 K 7 K 5 K 1.5 K 0.4 K R xy ( ) H (kOe) -10 -5 0 5 10-4-2024
45 K 26 K 22 K 18 K 16 K 14 K 12 K 10 K 8 K 6 K 2 K R xy ( ) H (kOe) b e
0 1 3 Mn-doped Bi Te Bi Te n ( c m - ) T (K) c Mn-doped Bi Te Bi Te R S ( / s q ) T (K) d FIG. 1: (a) Hall resistivity of the Bi Te film. (b) Hall resistivity of the Mn-doped Bi Te film. (c) Electron charge carrierdensity extracted from the Hall effect for both films. (d) Sheet resistance as a function of temperature for both films. (e)High-angle annular dark-field STEM image of a Mn-doped Bi Te film. Top right inset shows the intensity profile along thedashed yellow line in the main panel. Bottom right inset is a schematic of the Bi Te crystal structure. the complex dielectric function (cid:15) ( ω ) = (cid:15) ( ω ) + i(cid:15) ( ω ).Importantly, these two components are not independent,but linked through the Kramers-Kronig (KK) relations .A convenient method for overcoming the complicationsof multi-layer systems, and extracting (cid:15) ( ω ) for a singlelayer in a multi-layer sample, is via multi-oscillator mod-eling. In the case of the film on substrate systems stud-ied here, (cid:15) ( ω ) of the film can be extracted through aKK consistent, multi-oscillator model fit, provided thesubstrate is measured and modeled separately or (cid:15) ( ω )of the substrate is previously determined . By incor-porating many oscillators, we make the functional formfor the dielectric function more flexible, and thus lessmodel dependent. By constraining the fitting to be KKconsistent, we inherit the ability of the KK analysis toextract both the real and imaginary parts of the dielec-tric function from a single spectrum ( e.g. transmissionintensity). The fundamental limitations of our techniqueare thus the experimental error bars and the quality ofour least square fitting. This technique has been shownto accurately reproduce optical constants obtained alter-nately through direct KK analysis of reflectivity, THztime domain spectroscopy, and ellipsometry . TheIR conductivity spectrum σ ( ω ) can then be found sim-ply from σ ( ω ) = i ω (1 − (cid:15) ( ω ))60Ω . The thick gray lines in Fig. 2represent the model fits at room temperature and 6 K.The resulting σ ( ω ) spectra, which describe dissipativeprocesses, are displayed at select temperatures in Fig. 4. IV. OPTICAL PROPERTIESA. Phonon spectrum
From symmetry considerations of the crystal lattice ofBi Te there are 15 lattice dynamical modes at momen-tum q =0: 3 acoustical modes, and 12 optical modes .Group theory classifies the 12 optical phonon modes into2A , 2E g , 2A , and 2E u . As this system has an inver-sion center, these optical modes are exclusively Raman- T( w )/T( w )GaAs a B i T e M n - d o p e d B i T e w ( c m - 1 ) FIG. 2: The panels show the raw transmission spectra ofour samples normalized to that of the GaAs substrate, withBi Te in panel a and Mn-doped Bi Te in panel b. The thickgray lines are the model fits of the transmission data for ex-traction of the optical constants, as described in the text, andshown only at room temperature and 6 K for clarity. The dataare cut near 300 cm − due to a phonon in the GaAs substratethat eliminates transmission over this frequency range. or IR-active, as listed in Table I. The E u modes are ex-cited by electric fields polarized perpendicular to the c -axis, while the A modes are excited only by electricfields polarized parallel to the c -axis. Therefore we arenot sensitive to the A modes.The Raman spectra of our films are shown in Fig. 3a.Three prominent peaks in each film are clearly observed.The three peaks are readily identified by comparing tothe literature as the 2A modes and one E g mode .The peak frequencies of these 3 modes are listed in Ta-ble I. We note the other E g mode, E , is expected near 35cm − in Bi Te , which is the low frequency limit of ourdetection. Furthermore, the E mode, if observed at all inBi Te , has been a very weak feature in the Raman spec- TABLE I: Center frequency, in units of cm − , of Ramanand IR active phonons observed at room temperature in ourBi Te and Mn-doped Bi Te films. These data are comparedto those observed in Raman studies of bulk Bi Te crystalsin Ref. . † The value listed for the E Raman mode is fromRef. Bi Te Mn-doped Ref. Raman E - - 36.5 † A
61 60.5 62.5E
101 101.5 103A
12 5 0 1 0 0 1 5 01 0123 5 0 1 0 012
M n - d o p e d
B i T e w ( c m - 1 ) E B i T e w ( c m - 1 ) T = 2 9 5 K A
21 g E Intensity (arb.) A
11 g
M n - d o p e d
6 K2 9 5 K 6 K h E s w ) (cm-1) dc ba T ( K ) w E u 1 ( B i T e ) E u 2 ( B i T e ) E u 1 ( M n - d o p e d ) h ( M n - d o p e d ) w p (cm-2) T ( K )
FIG. 3: (a) Room temperature Raman spectra of our films.Gray dashed lines are guides to the eye to identify categorizedRaman active modes (see Table I and discussion in text). (b)Infrared conductivity σ ( ω ) over the phonon region of thespectra of our films. IR data are shown at room temperatureand 6 K. Gray dashed lines are again guides to the eye toidentify categorized IR active modes (Table I and discussionin text). (c) Temperature dependence of the center frequency( ω ) of IR active phonon modes. (d) Temperature dependenceof the oscillator strength ( ω p ) of IR active phonon modes. trum compared to the 2A modes and the E mode .The remarkable similarity of the Raman spectra of thetwo films supports the conclusion that the Mn-doped filmshares the same crystal structure as the Bi Te film.The IR active modes detected in our experiments areshown in Fig. 3b in terms of the IR conductivity ( σ ( ω ))at room temperature and 6 K. These data were ex- tracted from our raw transmission data as described inSec. III. The IR active modes modes are all described byLorentzian oscillators given by, (cid:15) ( ω ) = ω p ω − ω − i Γ ω , (1)where ω p quantifies the oscillator strength, ω the centerfrequency, and Γ the linewidth. Readily apparent is adistinct mode near 60 cm − observed in both films, withprecise frequencies listed in Table I. This mode is iden-tified as the E mode. The oscillator strength of the E mode in the Bi Te film is much larger than that of theMn-doped film. Further differences between Bi Te filmand the Mn-doped film are noted by the relatively weakE mode observed near 100 cm − in Bi Te , which isabsent in the Mn-doped film (Table I). Moreover, a peakappears in the IR spectra of the Mn-doped film with cen-ter frequency ω near 60 cm − , which we refer to as the η mode. The origin of the η mode is unclear. Further-more, this mode may be a result of a different physicalprocess, such as a low energy interband transition, ratherthan a phonon. The temperature dependence of ω andoscillator strength ω p of the IR active modes observedin our spectra are plotted in Figs. 3c and d, respectfully.The close agreement of the observed ω , both in Ramanand IR spectra, with those of bulk Bi Te as shown inTable I demonstrates that our epitaxial films share theBi Te crystal structure. B. Infrared electrodynamics
The full frequency range of our IR conductivity spec-tra at select temperatures for the Bi Te and Mn-dopedBi Te films are shown in Figs. 4a and b, respectively.We first discuss the spectra of the Bi Te film in Fig. 4a.At an energy ∼ − , we observe the onset of op-tical transitions across the bulk gap of Bi Te ,followed by higher energy interband excitations. A broad(relative to phonon modes) Drude-like feature is observedbelow ∼
300 cm − at all temperatures in the Bi Te film.The Drude peak (half-Lorentzian centered at zero fre-quency) semi-classically describes the characteristic re-sponse of free charge carriers in a metal or degeneratesemiconductor. As revealed in the figure, the Drude-likefeature becomes more prominent upon cooling. The tem-perature dependence of key parameters of the featuresdescribed above are shown in Fig. 5, and are discussedlater.The σ ( ω ) spectra of the Mn-doped film are shown forselect temperatures in Fig. 4b. Like the pristine Bi Te film, the Mn-doped sample reveals a clear onset of inter-gap excitations on the order of 10 cm − , which sharpensupon cooling. Again similar to the undoped film, thereis a Drude-like feature at the intragap frequency scale.Distinct from the pristine Bi Te film, however, is the b B i T e s w ) (103 W- cm-1) w ( c m - 1 ) a M n - d o p e d B i T e ( T C = 1 5 K ) 2 9 5 K 1 5 0 K 3 0 K 6 K w ( c m - 1 ) FIG. 4: Infrared conductivity spectra σ ( ω ) of Bi Te (a), and the Mn-doped Bi Te sample (b) at select temperatures. Thedata are cut near 300 cm − due to a phonon in the GaAs substrate that eliminates transmission over this frequency range. observation of a broad intragap resonance that lies be-tween the GaAs phonon (where data in the figure is cut)and the onset of intergap excitations in the Mn-dopedfilm.In Fig. 5, we show the temperature dependence of sev-eral key parameters of the electrodynamic response of oursamples. The method for determining these parametersis discussed sequentially below. We begin by discussingthe frequency of the onset of intergap excitations ω g . Thevalue of ω g for our films at all temperatures was deter-mined from linear fits of the square of the imaginary partof the dielectric function (cid:15) ( ω ) near the gap edge. Thislinear trend of (cid:15) ( ω ) well describes the onset of directinterband excitations . In contrast, indirect excitationsscale with (cid:112) (cid:15) ( ω ) near the gap edge . A distinct linearregime in the (cid:112) (cid:15) ( ω ) spectra was not observed.As shown in Fig. 5a, ω g in the Bi Te film is rel-atively temperature independent, falling in a range ofroughly 1100–1200 cm − . This range of ω g is lowerthat the band gap observed in photoemission experi-ments , and near the lower end of the range typically ex-tracted for the band gap E G of Bi Te (1050–1330 cm − (Refs. ), represented by the gray bar in Fig. 5a).Conversely, Fig. 5a shows the Mn-doped film has ω g thatis larger than E G / ¯ h of Bi Te at all temperatures. The ω g feature in the Mn-doped film also exhibits a distinctblue shift as the sample is cooled. At 6K, ω g of the Mn-doped film is 765–1045 cm − larger than E G / ¯ h typicallyextracted for Bi Te , and 950 cm − larger than the 6K ω g found in our Bi Te film. As will be discussed be-low, the Mn-doped film also exhibits a significantly largerDrude oscillator strength than that of the pristine Bi Te film. Therefore the correspondingly larger ω g values canbe understood as a Burstein–Moss shift resulting from E F residing deeper in the conduction band due to anincrease in the carrier density .We now discuss the temperature dependence of the Drude oscillator strength D of our films, shown in Fig. 5b.We quantify D of our films by integration of the intragapspectral weight via the sum rule: D = 30Ω π (cid:90) ω c σ ( ω ) dω, (2)where, guided by the ω g values, we use a cutoff frequency ω c =1000 cm − for the Bi Te film, and ω c =1200 cm − for the Mn-doped Bi Te film. For the Bi Te film, D stays roughly constant throughout the measured temper-ature range, with a value of roughly 8 × cm − . Theconservation of Drude oscillator strength with tempera-ture observed in our Bi Te film is typical of metals. Thiscan be understood by realizing that D is directly relatedto the carrier density n , which is largely temperature in-dependent in metallic systems, by D = e πc nm ∗ , where e is the electron charge, c is the speed of light in vacuum,and m ∗ is the effective carrier mass ( e , c , and m ∗ are in cgs units).Fig. 5b shows D of the Mn-doped Bi Te film staysroughly constant throughout the measured temperaturerange as well. The figure also shows that the Mn-dopedfilm has much larger ( ∼ × ) D than that of the Bi Te sample. From the standpoint of D as a measure of n ,this latter fact is indicative that the Mn-doped film hasmuch larger n than the pristine Bi Te film, consistentwith the Hall effect data (Fig. 1c).We show the temperature dependence of the free car-rier scattering rate 1/ τ , in Fig. 5c. We quantify 1 /τ by1 /τ = D σ ( ω ) σ ( ω ) + σ ( ω ) (cid:12)(cid:12)(cid:12)(cid:12) ω (cid:48) , (3)where ω (cid:48) is the low frequency cutoff of our data. As canbe seen in the figure, 1/ τ of the Bi Te film is roughly D (106 cm-2) cba T ( K ) t (cm-1) G a A s p h o n o n M n - d o p e d B i T e B i T e w g (cm-1) B i T e b u l k g a p FIG. 5: Temperature dependence of ω g (a), Drude oscillatorstrength D (b), and free carrier scattering rate 1/ τ (c). Thegray region in panel a covers the frequency (energy) rangeof values reported in the literature for the bulk band gap ofBi Te . − , and shows a slight narrowing as the filmis cooled. This latter trend is characteristic of metallictransport. The Mn-doped sample shows a significantlylarger scattering rate ( ∼
300 cm − ) than that of the pris-tine Bi Te film. The enhanced scattering rate with re-spect to the pristine film is indicative of increased dis-order in the Mn-doped film, consistent with the lowermobility extracted from Hall effect measurements. V. DISCUSSIONA. Bi Te It is tempting to consider the possibility that theDrude-like response of the Bi Te sample, or at leasta portion of it, originates from topologically protectedmetallic SSs; a fundamental consequence and principalexperimental indicator of nontrivial topology. Such a sce-nario is even more intriguing given that ω g falls withinthe range of E G values found in Bi Te , suggesting that E F may actually lie within the bulk gap. Thus it is usefulto consider the magnitude of D expected for the Druderesponse of topological SSs in Bi Te .In strong TIs, the SSs are predicted to form Dirac- like bands with a universal background conductance of0.25 πe h (1.52 × − Ω − ). This background conductancewill be completely suppressed, however, at frequenciesbelow 2 E F . The f -sum rule dictates that this “missing”spectral weight from the universal background will ap-pear instead in the Drude portion of the Dirac band con-ductivity . In this picture, the Drude spectral weightis directly proportional to the location of E F with re-spect to the Dirac point. Assuming E F is 1200 cm − (0.15 eV) above the Dirac point yields an upper limit forthe Drude response of the Dirac band charge carriers,which expressed in 2D units of D is 0.36 cm − . We notethat we may observe a Drude response from both top andbottom SSs, suggesting that experimentally a D roughlytwice as large ( ∼ − ) could still be consistent withthe combined Drude response of the Dirac charge carri-ers from the two surfaces. If the hexagonal warping ofthe Bi Te SS band structure is taken into account ,this upper limit for D of SSs increases slightly to 0.08cm − . Averaging D over all measured temperatures inour Bi Te film and expressing the average in 2D unitsgives 10.2 ± − .From the discussion above, it is clear the observed D is much too large to be considered originating froma topological surface state response, and indicate whatwe observe is dominated by the bulk. We further notethe above argument is idependent of details such as theFermi velocity, and thus can be applied broadly to TIs.For our data, it could perhaps be considered that theDrude-like response has contributions from both bulkand surface charge carriers. Unfortunately, it is unclearhow to uniquely identify or isolate surface state conduc-tance from our measurements. An added complicationto the problem of distinguishing topological surface stateconduction from that of the bulk is the dramatic bandbending in TI materials that has been observed to pro-duce a quantized 2 dimensional electron gas (2DEG) atthe surface . In any case, it is clear the dominantcontribution to the Drude response is from bulk chargecarriers, which establishes that E F resides in the Bi Te conduction band. This latter fact cements the categoriza-tion of our Bi Te film as a degenerate semiconductor. B. Mn-doped Bi Te The degenerate semiconductor interpretation is con-sistent with data for the Mn-doped film as well. This isevidenced by the relatively large D that shows no signsof thermal activation. We also note, the increase in ω g with respect to that of pristine Bi Te coupled with thecorrespondingly larger D in the Mn-doped film impliesthat there is no reason to expect any discernable contri-bution to the conduction from topological SSs. A some-what mysterious aspect of the Mn-doped film is that it is n -type rather than p -type. Mn dopants are anticipatedboth theoretically and experimentally to substitutefor Bi as single acceptors in a Bi Te host. Bi Te filmsand crystals on the other hand, are typically n -type, andthis is supported by the Hall and IR data of our Bi Te film.The IR spectra of Mn-doped Bi Te do show a featureconsistent with excitations from mid-gap defect statesto unoccupied states above E F in the conduction band.Namely, there is a broad and relatively weak intragap res-onance that lies between the GaAs phonon (where datain the Fig. 4b is cut) and the onset of intergap excita-tions in the Mn-doped film. The width of this broadfeature covers an energy scale spanning ranges consistentwith optical excitations initiated from both donor and acceptor levels within the bulk band gap. Thus unfortu-nately, it is difficult to determine if Mn is acting as anacceptor, donor, or is neutral when doped into our films.For instance, the intragap spectral weight represented bythe broad resonance could be coming from a combina-tion of Mn acceptor levels and Te vacancy donors and orother unintentional donors. We speculate that disloca-tions found in the TEM data of Mn-doped films, whichoccur at much lower densities in undoped Bi Te , mayact as an additional source of donor defects resulting inthe large electron carrier density of the Mn-doped film.An additional key observation is that the σ ( ω ) spectraof the Mn-doped Bi Te film exhibits remarkably littlechange as it is cooled across the FM transition. This is instark contrast to the canonical dilute magnetic semicon-ductor Ga − x Mn x As. In this latter system, holes origi-nating from Mn acceptors are the principal mediators offerromagnetism . Hallmark signs of itinerant FM ob-served in IR spectra of Ga − x Mn x As include an increaseof the low energy “Drude” spectral weight with the devel-opment of magnetization , and scaling of T C with theIR spectral weight over the intragap energy range .We do not observe an increase of the low energy spec-tral weight upon crossing T C in our Mn-doped sample.This fact is supported by the resistance data in Fig. 1d.Furthermore, the spectroscopic features of the Mn-dopedfilm are remarkably similar to a second Mn-doped sam-ple we investigated, with the key distinction that the lat-ter sample showed no signs of a ferromagnetic transitiondown to below 4 K. The σ ( ω ) spectra of the PM Mn-doped film is plotted at room temperature and 6 K withthose of the FM film in Fig. 6. Key parameters of theelectrodynamic response for these two samples at roomtemperature and 6 K are also shown in Table II. Thesimilarity of the IR response of these two Mn-doped sam-ples, particularly in the intragap region, coupled with thecomplete absence of ferromagnetism in one of the sam-ples, implies T C is insensitive to the intragap spectralweight in Mn-doped Bi Te . We add that neutron re-flectivity measurements are consistent with a uniformlymagnetized bulk, and STEM shows no evidence for Mnclustering, supporting that the FM film has true longrange FM order .A difference between the two Mn-doped samples thatmay explain the absence of FM in the one is that the PMfilm was grown with larger Mn content. While the elim- b a T = 2 9 5 K
P M M n - d o p e d B i T e F M M n - d o p e d B i T e s w ) (103 W -1cm-1) T = 6 K w ( c m - 1 ) FIG. 6: Infrared conductivity spectra σ ( ω ) of the FM Mn-doped Bi Te film and a PM Mn-doped Bi Te film at 6 K(a) and room temperature (b).TABLE II: Key parameters of the electrodynamic responsefor the FM and PM Mn-doped Bi Te films, denoted as FMand PM respectively, at 6 K and room temperature.6 K 295 KPM FM PM FM ω g [cm − ] 2665 2095 1603 1337 D [cm − ] 5.5 × × × × /τ [cm − ] 251 303 307 318 ination of T C with an increase in Mn may be initiallycounter-intuitive, we speculate that the increase of Mnin the PM film may increase the density of dislocationscommon to Mn-doped Bi Te films, possibly associatedto the formation of Bi-bilayers akin to the Bi Te crystalstructure . This disruption to the translational symme-try and change in electronic properties due to conductiveBi-layers may have reached such an extent as to destroylong range FM order in the PM sample. Detailed char-acterizations of the electronic and crystal structure as afunction of Mn concentration can be found in Ref. . VI. CONCLUSION AND OUTLOOK
Our IR probe of Bi Te and Mn-doped Bi Te epitax-ial thin films show both these samples to be degener-ate semiconductors. E F resides just above the conduc-tion band minimum in the Bi Te film, falling within therange of E G values reported in the literature. The Mn-doped film on the other hand has E F located roughly1000 cm − larger than the Bi Te host conduction bandminimum due to a Burstein–Moss shift.For our Bi Te and Mn-doped Bi Te films, we find noneed to invoke topological SSs to describe the IR data.This is likely due to the relatively large bulk charge car-rier density that masks or destroys potential hallmarksof SS conduction. Although these signatures are absentfrom our data, there is evidence that THz/IR probes canbe sensitive to topological SS conduction . Still,other IR experiments have failed to see signatures thatcould uniquely identify SS conductance , even in TIcandidates that are quite insulating . Here we havedemonstrated that the Drude oscillator strength gives asimple metric to distinguish the (im)possibility of topo-logical SS origins of the low frequency conductance.Earlier reports have suggested that ferromagnetism inMn-doped TIs should be analogous to Mn-doped III-Vsemiconductors . However, our results suggest that,unlike in other Mn-doped FM semiconductors , chargecarriers do not play a significant role in mediating ferro-magnetism in Mn-doped Bi Te . Alternatively, superex-change or an enhanced Van Vleck susceptibility havebeen theoretically proposed as FM mechanisms for TIsdoped with transition metal elements. These latter mech-anisms do not rely on itinerant charge carriers to mediateFM, and thus can be considered to be consistent with thedata from our IR experiments. The bulk charge carrierswill of course need to be controlled and eliminated toachieve films that are insulating in the bulk. 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