Optical properties and electronic structure of BiTeCl and BiTeBr ...

ISSN 0030-400X, Optics and Spectroscopy, 2016, Vol. 121, No. 3, pp. 364–370. © Pleiades Publishing, Ltd., 2016. Original Russian Text © A.A. Makhnev, L.V. Nomerovannaya, T.V. Kuznetsova, O.E. Tereshchenko, K.A. Kokh, 2016, published in Optika i Spektroskopiya, 2016, Vol. 121, No. 3, pp. 395–401.

CONDENSED-MATTER SPECTROSCOPY

Optical Properties and Electronic Structure of BiTeCl and BiTeBr Compounds A. A. Makhneva, *, L. V. Nomerovannayaa, T. V. Kuznetsovaa, e, O. E. Tereshchenkob, c, and K. A. Kokhc, d a Mikheev b

Institute of Physics of Metals, Ural Branch, Russian Academy of Sciences, Yekaterinburg, 620990 Russia Institute of Semiconductor Physics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia c Novosibirsk State University, Novosibirsk, 630090 Russia d Sobolev Institute of Geology and Mineralogy, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia e Ural Federal University, Yekaterinburg, 620002 Russia *e-mail: [email protected] Received July 22, 2015

Abstract—Optical properties of BiTeCl and BiTeBr compounds with a strong Rashba spin–orbit coupling are studied in the 0.08–5.0 eV range using the optical ellipsometry method. Fundamental characteristics of the electronic structure are obtained. Similarly to BiTeI, spectra of the imaginary part of dielectric permittivity constant ε2(E) in the energy interval between the plasma edge and the threshold of an intense interband absorption (0.7 eV in BiTeCl and 0.6 eV in BiTeBr) display a fine structure of electronic transitions at 0.25 and 0.55 eV in BiTeCl and 0.20 and 0.50 eV in BiTeBr. These features are assigned to electronic transitions between the bulk conduction zones split by the Rashba spin–orbit interaction. The parameters of the electronic structure of BiTeCl and BiTeBr are compared with the BiTeI compound that was studied earlier. In the BiTeCl–BiTeBr–BiTeI row, the absorption edge and main features of the fundamental absorption exhibit a shift to low energies. DOI: 10.1134/S0030400X16090137

INTRODUCTION Currently, the physical properties of a new class of bulk semiconductor materials BiTeX, X = (Cl, Br, I), with a large spin–orbit interaction are being intensively studied. These compounds are promising for development of spintronics devices. The magnitude of spin splitting of the bulk states is characterized by Rashba energy ER, and Rashba coupling parameter αR, which determines the strength of spin splitting. The maximum splitting was found for the BiTeI compound (ER = 100 meV, αR = 3.8 eV Ǻ) [1]. The necessary conditions for the giant Rashba splitting in bulk systems were formulated as follows: a large spin–orbit splitting in atoms of a system with the inversion asymmetry, a narrow band gap, and the same type of the symmetry for the electronic states on the top of the valence band and bottom of the conduction band [2]. As a result, the valence electronic states and conduction band states exhibit energy and momentum splittings. The Rashba effect leads to a shift of zones with different spin polarizations in opposite directions. The effect of Rashba spin-splitting for the bulk carriers in BiTeX were confirmed experimentally in studies of photoemission spectroscopy with the angular and spin

resolutions (SRARPES) and in calculations of the electronic band structure [3–7]. A detailed review of electronic structure studies with the use of the ARPES method is given in [7]. The band structure of BiTeBr differs from BiTeI in having a somewhat smaller Rashba splitting. For the lighter X atoms the band gap increases while splitting αR for the bulk conduction and valence bands decreases [5]. The BiTeCl compound is of particular interest. Unlike the (0001) surface of the BiTeI compound containing areas terminated by atoms of different types (tellurium and iodine), the surface of BiTeCl is homogeneous and is terminated only by tellurium or chlorine atoms [4]. Moreover, ARPES studies also showed that, for the surface terminated by Te atoms, the charge of carriers near the surface corresponds to the n-type and to the p-type for the surface terminated by Cl atoms [8]. The BiTeX compounds are self-doped (due to antisite defects) n-type semiconductors having a layered structure without an inversion center and consist of three successive close-packed layers of Bi, Te, and X atoms. The structures of The BiTeCl and BiTeBr crystals have different structures. Like BiTeI compound, BiTeBr crystallizes in a hexagonal cell (space

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Fig. 1. Spectra of the real ε1(E) and imaginary ε2(E) parts of the complex dielectric permittivity of the BiTeCl monocrystal at 300 K. The inset shows the ε1(E) and ε2(E) spectra in the low-energy region.

group P3m1). The Te and Br atoms are distributed statistically. In BiTeCl compound, tellurium and chlorine atoms are aligned along the c axis, leading to the cell doubling and space group P63mc [9]. Bismuth forms covalent bonds with Te and X atoms, and the interaction between Te and X is much weaker. The optical properties of BiTeI are well studied [10–15]. The first study of the optical properties of BiTeI monocrystals revealed a number of features in the infrared region, which were assigned to electronic transitions between the spin-split branches of the conduction band [10]. The ground for this assignment was the magneto-optical effect in nonmagnetic BiTeI semiconductor, which was experimentally observed in the 0.08–0.55 eV spectral range [11]. To date, we are aware of only one work concerning experimental studOPTICS AND SPECTROSCOPY

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ies of the electronic structure of BiTeCl and BiTeBr monocrystals by the optical spectroscopy method [16]. Spectra of the optical conductivity were obtained by measuring reflection and transmission and the Kramers–Kronig transformation for data processing. In this work, we report ellipsometric measurements of complex permittivity components for BiTeCl and BiTeBr monocrystals in the 0.08–5.0 eV spectral range. The present results are compared with BiTeI compound, which was studied earlier [15]. EXPERIMENT The BiTeCl and BiTeBr monocrystals were grown by a modified Bridgeman method using a rotating thermal field. Details of the preparation techniques

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ε1, ε2 20

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Fig. 2. Spectra of the real ε1(E) and imaginary ε2(E) parts of the complex dielectric permittivity of the BiTeBr monocrystal at 300 K. The inset shows the ε1(E) and ε2(E) spectra in the low-energy region.

are described in [17, 18]. The crystals had dimensions of 3 × 5 mm. A fresh and clean (0001) surface for optical measurements was obtained by cleavage of the bulk monocrystals. It was shown that, in contrast to the (0001) surface of BiTeI, which contains areas terminated by atoms of different types (tellurium and iodine), the cleaved surface of BiTeCl has a homogeneous morphology and is terminated only by tellurium or chlorine atoms [19]. The presence of two different endings is associated with packaging defects because the unit cell has no symmetry center. For each compound, we studied two different samples of freshly cleaved crystals and obtained a similar dispersion of the optical functions for each compound, although the spectral intensities were somewhat differed.

method at room temperature with a single reflection from the sample plane in the range 0.08–5.0 eV at an incidence angle of 67° and polarizer azimuths of 45° and 40°. Our automatic ellipsometer is build on the basis of a universal computing spectral complex KSVU-12 [20]. The measuring error of optical constants n and k is 2–4% (∼6% in the mid-IR region). The values of n and k are used to calculate the

The optical constants—refractive index n and extinction coefficient k—were measured by the Beatty

energy Im [− 1 ε ( E )] = ε 2 (ε12 + ε 22 ) .

real ε1(E ) = n 2 − k 2 and imaginary ε 2 ( E ) = 2nk parts of complex permittivity ε, real part of the complex optical conductivity σ1 ( E ) = nk ω/2π (ω is the cyclic frequency of light wave), reflection capacity

R ( E ) = [( n − 1) + k 2 ] [( n + 1) + k 2 ], and volumetric function of the characteristic losses of the electrons 2

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R 0.55 BiTeCl BiTeBr 0.50 2 0.45 1 0.40

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Fig. 3. Spectra of reflectivity R(E): (1) BiTeCl and (2) BiTeBr monocrystals. The inset shows the spectra of the reflectivity and functions of volumetric characteristic electron energy losses in the low-energy region of the spectrum.

RESULTS AND DISCUSSION Experimental spectra of real ε1(E) and imaginary ε2(E) parts of the complex dielectric permittivity of BiTeCl and BiTeBr crystals are shown in Figs. 1 and 2, respectively. The insets show the low-energy region of the spectrum. Dielectric function ε2(E) of BiTeCl in the range of the fundamental absorption (above the absorption edge) displays two bright peaks centered at 1.6 and ∼2.55 eV and a shoulder at ∼4.25 eV. The spectrum of BiTeBr shows features at 1.45 and ∼2.5 eV and a structure at ∼4.3 eV. The absorption edge is more clearly evident in the spectrum of ε1(E) at an energy of 0.7 eV in BiTeCl and at 0.6 eV in BiTeBr. Although the energy positions of the peaks of two bright structures are close, the intensities in the interband spectra are different. The difference is associated with a higher value of the refractive index of BiTeBr as compared to OPTICS AND SPECTROSCOPY

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BiTeCl crystal at similar values of extinction coefficient k, which may be related to a less perfect surface of the BiTeCl crystal. The spectrum of function ε2(E) in the mid-IR region between the absorption edge and plasma edge (inserts in Figs. 1 and 2) shows a broad plateau with two broad features which are somewhat less pronounced as compared to BiTeI [15]. In the ε2(E) spectrum of BiTeCl, the features are seen at ∼0.55 and ∼0.25 eV, while they are seen at ∼0.50 and ∼0.20 eV in the spectrum of BiTeBr. It is likely that each feature can be resolved into several peaks at low temperatures. We observed similar features for BiTeI [15]. The presence of several real electronic transitions is manifested to a different extent in the dispersion pattern of all optical functions ε1(E), R(E), ε2(E), σ1(E), and Im [− 1 ε ( E )] in the spectral region between the onset of the contribution from free carri-

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A (L) 0.8 (H) 0.6 0.4 β 0.2 0 α −0.2 ED γ −0.4 −0.6 −0.8 −1.0 −1.2 −0.2 −0.1 0 0.1 0.2 k, Å−1

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Fig. 4. Spectra of the real part of optical conductivity σ1(E) of BiTeCl, BiTeBr, and BiTeI monocrystals. Inset (a) shows a fragment of the calculated electronic band structure of BiTeI near the point (point A) of the high symmetry of the Brillouin zone. Arrows indicate optical transitions α, β, and γ (in the notation of [10]). Inset b shows spectra of σ1(E) for BiTeCl and BiTeBr in the low-energy region of the spectrum.

ers (E ∼ 0.1 eV) and the interband absorption threshold. The upper valence bands predominantly have the Te(5p)-character, while the low-lying states of the conduction zone have the Bi(6p)-character. Spin– orbit interaction creates conditions for optical transitions between the zones with different spin angular momentum, reflecting the complex nature of electronic excitations near EF [3]. For comparison with the published work on the optical properties of BiTeCl and BiTeBr, which were calculated using Kramers–Kronig relations from measurements of transmission and reflection [16], Figs. 3 and 4 show spectra of reflectivity R(E) and the real part of optical conductivity σ1(E).

Figure 4 (inset a) shows a fragment of the energy band dispersion for BiTeI compound obtained in ab initio relativistic calculations of the electronic band structure for the upper valence bands and lower conduction bands near a high symmetry point A along the direction H–A–L of the Brillouin zone (figure from [11]). The possible optical transitions are indicated by vertical arrows α, β, and γ (in the notation of [10]). Electronic transition γ is related to an interband transition (the threshold of interband absorption), while transitions α and β are attributed to intraband transitions between spin-split conduction bands. Observation of the magneto-optical effect for BiTeI has been


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possible owing to the strong spin–orbit interaction [11]. In contrast to BiTeI and BiTeBr, for our BiTeCl crystal, we did not observe a plasma edge (a deep minimum in the R(E) spectrum followed by a sharp growth) or passage of the ε1(E) function through zero, that would indicate the onset of a predominant contribution from the free carriers. However, a significant decline of ε1(E) in the E < 0.1 eV range indicates the onset of contribution from the free carriers. The plasma frequency for conductivity electrons can be estimated from the characteristic electron energy loss function Im [− 1 ε ( E )] (due to limitation on the spectral range of ellipsometric measurements in the IR region). In the optical spectrum, the electron energy loss function reveals longitudinal modes, such as plasmons. In the case of a simple (Drude–Lorentz) character of ε1(ω) and ε2(ω) dependences, the bulk plasmon is seen in close proximity to ϖ p = ω p ε ∞ (ϖ p is the screened plasma frequency), when the conditions for plasma resonance (ε1 ~ 0 , ε 2 ! 1) are satisfied. In addition, the asymmetry of the peak function may indicate (as in the case of BiTeI [15]), the charge nonhomogenecity of this compound. We emphasize that, in the spectral region below the threshold, our samples exhibit a fairly large absorption (measured values of ε2 ∼ 6–11), which indicates a superposition of several contributions: the interband transitions, intraband transitions, and a contribution from free charge carriers which decreases with increasing energy. This circumstance does not satisfy the ideal condition for the plasma resonance. For BiTeBr crystal, the maximum of the Im [− 1 ε ( E )] function is located at ∼0.1 eV, that is close to the energy of the deep minimum in the R(E) function, and, therefore, to the value of the screened plasma frequency of charge carriers ϖ p ∼ 0.1 eV. For BiTeCl crystal, growth of the Im [− 1 ε ( E )] function is observed in the E < 0.1 eV range and we can assume that ϖ p < 0.1 eV. As shown earlier, ϖ p = 0.13 eV for the BiTeI crystal [15]. Figure 4 shows spectra of the optical conductivity for three BiTeX compounds. The spectra have different intensities. This is likely due to the different surface quality, because the ratio of the intensities of the main peaks of fundamental absorption is comparable. To estimate the displacement of the fundamental absorption as a whole, we used a simple extrapolation of the sharp decline of the σ1(E) function with decreasing energy (Fig. 4, inset b). For the studied crystals, the value of the energy at the interception point is ∼0.2 eV, while for BiTeI compound it is 0.33 eV [15]. OPTICS AND SPECTROSCOPY

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CONCLUSIONS Comparison of the optical response of the BiTeХ compounds in the 0.08–5.0 eV spectral range reveals a similarity in the dispersion patters of the optical functions, proximity in the energy positions of the spectral features below and above the fundamental absorption threshold. At the same time, we may note a difference in the behavior of the spectra of dielectric function ε2(E) in the series BiTeCl–BiTeBr–BiTeI: a shift to the lower energies range is seen for the absorption threshold (0.7, 0.6, 0.44 eV) and for the features below absorption thresholds α (0.25, 0.20, 0.20 eV) and β (0.55, 0.50, 0.30 eV), as well as for the low energy peak of the fundamental absorption (1.6, 1.45, 1.1 eV).

ACKNOWLEDGMENTS This work was performed in the framework of an assignment of the Federal Agency for Scientific Organizations of Russia (project “Electron,” no. 01201463326) with support from Ural Branch of Russian Academy of Sciences (grant no. 15-9-2-46) and the Russian Foundation for Basic Research (grant no. 15-02-01797). REFERENCES 1. K. Ishizaka, M. S. Bahramy, H. Murakawa, M. Sakano, T. Shimojima, T. Sonobe, K. Koizumi, S. Shin, H. Miyahara, A. Kimura, K. Miyamoto, T. Okuda, H. Namatame, M. Taniguchi, R. Arita, et al., Nat. Mater. 10, 521 (2011). 2. M. S. Bahramy, R. Arita, and N. Nagaosa, Phys. Rev. B 84, 041202(R) (2011). 3. M. Sakano, J. Miyawaki, A. Chainani, Y. Takata, T. Sonobe, T. Shimojima, M. Oura, S. Shin, M. S. Bahramy, R. Arita, N. Nagaosa, H. Murakawa, Y. Kaneko, Y. Tokura, and K. Ishizaka, Phys. Rev. B 86, 085204 (2012). 4. G. Landolt, S. V. Eremeev, O. E. Tereshchenko, S. Muff, B. Slomski, K. A. Kokh, M. Kobayashi, T. Schmitt, V. N. Strocov, J. Osterwalder, E. V. Chulkov, and J. H. Dil, New J. Phys. 15, 085022 (2013). 5. S. V. Eremeev, I. A. Nechaev, Y. M. Koroteev, P. M. Echenique, and E. V. Chulkov, Phys. Rev. Lett. 108, 246802 (2012). 6. I. P. Rusinov, I. A. Nechaev, S. V. Eremeev, C. Friedrich, S. Blugel, and E. V. Chulkov, Phys. Rev. B 87, 205103 (2013). 7. L. Moreschini, G. Autes, A. Crepaldi, S. Moser, J. C. Johannsen, K. S. Kim, H. Berger, Ph. Bugnon, A. Magrez, J. Denlinger, E. Rotenberg, A. Bostwick, O. V. Yazyev, and M. Grioni, J. Electron Spectrosc. Rel. Phenom. 201, 115 (2015). 8. Y. L. Chen, M. Kanou, Z. K. Liu, H. J. Zhang, J. A. Sobota, D. Leuenberger, S. K. Mo, B. Zhou, S-L. Yang, P. S. Kirchmann, D. H. Lu, R. G. Moore, Z. Hussain, Z. X. Shen, X. L. Qi, and T. Sasagawa, Nat. Phys. 9, 704 (2013). 9. A. V. Shevelkov, E. V. Dikarev, R. V. Shpanchenko, and B. A. Popovkin, J. Solid State Chem. 114, 379 (1995).

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Translated by V. Alekseev

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