Bi layer properties in the Bi-FeNi GMR-type structures probed by spectroscopic ellipsometry

Bismuth (Bi) having a large atomic number is characterized by the strong spin-orbit coupling (SOC) and is a parent compound of many 3D topological insulators (TIs). The ultrathin Bi films are supposed to be 2D TIs possessing the nontrivial topology, which opens the possibility of developing new efficient technologies in the field of spintronics. Here we aimed at studying the dielectric function properties of ultrathin Bi/FeNi periodic structures using spectroscopic ellipsometry. The [Bi(d)-FeNi(1.8 nm)]N GMR-type structures were grown by rf sputtering deposition on Sitall-glass (TiO2) substrates. The ellipsometric angles Psi(omega) and Delta(omega) were measured for the grown series (d=0.6,1.4,2.0,2.5 nm, N=16) of the multilayered film samples at room temperature for four angles of incidence of 60, 65, 70, and 75 degrees in a wide photon energy range of 0.5-6.5 eV. The measured ellipsometric angles, Psi(omega) and Delta(omega), were simulated in the framework of the corresponding multilayer model. The complex (pseudo)dielectric function spectra of the Bi layer were extracted. The GMR effects relevant for the studied Bi-FeNi MLF systems are estimated from the optical conductivity zero-limit (optical GMR effect). The obtained results demonstrate that the Bi layer possesses the surface metallic conductivity induced by the SOC effects, which is strongly enhanced on vanishing the semimetallic-like phase contribution on decreasing the layer thickness, indicating its nontrivial 2D topology properties.


I. INTRODUCTION
The relativistic effect of spin-orbit (SOC) coupling is involved in the so-called Rashba effect [1]. This phenomenon arises from the apparent loss of crystalline inversion symmetry near the surface or heterojunction leading to the lifting of the spin degeneracy and generating spin-polarized surface metallic states. In this respect, 3D (2D) topological insulators (TIs) also exhibit spin-polarized surface metallic states due to SOC. However, contrary to the Rashba effect, the surface metallic bands of a TI are determined by its bulk characteristics.
The TIs host metallic surface states in a bulk energy gap, which are topologically protected.
The surface (or interface) states of TIs can be topologically trivial or nontrivial. In the latter case, for example, electrons cannot be backscattered by impurities. Bismuth (Bi) having a large atomic number is characterized by the strong SOC and is a parent compound of many 3D TIs, such as Bi 1−x Sb x or Bi 2 Se 3 , even although 3D bulk Bi itself is topologically trivial.
The specific feature of the electronic band structure of bulk Bi having R3m rhombohedral symmetry [2][3][4] is its inverted band gaps at both the Γ and M points of the Brillouin zone due to the strong SOC. The uniqueness of Bi films associated with the surface metallic states [5,6] and the semiconductor-to-metal transition [7,8] are well documented in the literature.
Theoretical analyses predict a 1-bilayer (BL) Bi(111) film to be a 2D TI [9,10]. If there is no or weak inter-BL coupling, a stack of the odd-even 1-BL films will exhibit nontrivial to trivial oscillations of topology (where the topological number ν [11] is equal to 1 or 0, respectively). However, for the nontrivial topology in a stack of the 1-BL films, here we aimed at studying the dielectric function properties of ultrathin periodic structures Bi/Ni 79 Fe 21 , prepared by rf sputter deposition, which is one of the most common technologies used to grow coatings and multilayered films (MLFs) exhibiting a giant magnetoresistance (GMR) effect for various existing and modern nanotechnological applications. Earlier, we have demonstrated that electronic band structure and surface electronic properties of ultrathin Bi layers in real GMR-type (Bi-FeNi) N MLF structures incorporating nanoisland FeNi layers can be successfully studied by spectroscopic ellipsometry (SE) [13]. Here, by applying the elaborated SE approach, we investigate (Bi-FeNi) MLFs, where the thickness of the FeNi layer was 1.8 nm, corresponding to the FeNi layer structural percolation threshold [14,15], and the Bi spacer layer was 0.6, 1.4, 2.0, and 2.5 nm thick, incorporating about 2, 4, 6, and 8 Bi(012)-type planes, respectively. We found that the Bi spacer layers have the metallic surface conductivity, which demonstrates strongly enhanced metallicity properties on vanishing the Bi semimetallic-like phase contribution on decreasing the layer thickness, which can be constructive in finding new nontrivial 2D topology properties of the (Bi-FeNi) GMR-type structures for their different nanotechnological applications.

II. MATERIALS AND METHODS
The (Bi-FeNi) N MLFs were prepared in a sputter deposition system by cathode sputtering from 99.95% pure Bi and Fe 21 Ni 79 targets in an alternative way. The base pressure in a sputter deposition chamber was 2×10 −6 Torr. The multilayers were deposited at approximately 80 • C in an argon atmosphere of 6× 10 −4 Torr on to insulating glassy Sitall (TiO 2 ) substrates. We utilized the substrates having typical dimensions 15 × 5 × 0.6 mm 3 .
The nominal thicknesses of the FeNi and Bi layers were controlled by the layer deposition times in accordance with the material deposition rates. A series consisting of four MLF samples was prepared. In the series of the grown (Bi-FeNi) N samples, the nominal thickness of the FeNi layer was 1.8 nm and the Bi layer thickness was of 0.6, 1.4, 2.0, and 2.5 nm, the number N of the periodically repeated Bi/FeNi layers was 16. The thickness of the FeNi layer was chosen to be 1.8 nm matching the structural percolation threshold [14,15]. The Bi layer thicknesses were chosen in such a way that the conditions for ferromagnetic (FM) or antiFM coupling in the GMR-type structures would be optimized. To prevent degradation, the deposited (Bi-FeNi) 16   where the interlayer distance is 3.28Å. It follows from this that in the studied MLF structures the Bi layers with a thickness corresponding to 0.6, 1.4, 2.0, and 2.5 nm incorporate two, four, six, and eight Bi(012)-type planes, respectively.
In the present study, the surface morphology of the Bi-FeNi(1.8 nm) MLF samples, prepared by rf sputtering deposition on the Sitall (TiO 2 ) substrates, was studied at room temperature using an ambient AFM (Bruker, Dimension Icon) in the Peak Force Tapping mode with ScanAsyst Air tips (Bruker, k=0.4 N/m, nominal tip radius 2 nm). The SE measurements for the investigated Al 2 O 3 /(Bi-FeNi) 16 /Sitall samples were performed at room temperature in a wide photon energy range of 0.5 -6.5 eV using a J.A. Woollam VUV-VASE ellipsometer (see the scheme illustrating the SE study of the (Bi-FeNi) N MLFs in Fig. 1(a) of Ref. [13]). The measured ellipsometry spectra are represented by real values of the angles Ψ(ω) and ∆(ω), which are defined through the complex Fresnel reflection coefficients for light-polarized parallel r p and perpendicular r s to the plane of incidence, tan Ψ e i∆ = rp rs . The ellipsometric angles, Ψ(ω) and ∆(ω), measured for the Bi-FeNi MLF samples were simulated using the multilayer model simulation available in the J.A. Woollam VASE software [16]. From the multilayer model simulations, the (pseudo)dielectric function spectra of the ultrathin 0.6, 1.4, 2.0, and 2.5 nm Bi layers and 1.8 nm FeNi layer inside the Bi-FeNi MLF structures were extracted. The corresponding calculated optical conductivity spectra were analyzed.

A. Atomic force microscopy study
The retrieved 5×5 µm 2 and 1×1 µm 2 AFM images of the  16 /Sitall MLF sample. The smaller-scale (1 × 1 µm 2 ) images clearly recognize a fine grainy-like structure of the surface morphology, which seems to be characteristic for all studied film samples (see Figure 1e-h).
The typical grain size, being of about 50 nm, is notably larger for the FeNi(1.8 nm) -Bi MLF sample incorporating the 2.5 nm-thick Bi layers, and, following the estimated RMS roughness values, the average grain size decreases to about 20 nm with decreasing the Bi layer thickness to 1.4 nm. As one can see from the typical height profiles presented in Figure 1i,j, with decreasing the Bi layer thickness from 2.5 to about 0.6 nm, the surface morphology becomes highly irregular due to the formation of conglomerates of nanoislands separated by rather flat (relatively small roughness) areas of about 20 nm.

B. Spectroscopic ellipsometry study of the ultrathin Bi-FeNi multilayer film samples
The ellipsometric angles Ψ(ω) and ∆(ω) were measured for the prepared Al 2 O 3 /(Bi-FeNi) 16 /Sitall MLF samples at the angles of incidence of 60 • , 65 • , 70 • , and 75 • . Figure 2 demonstrates the ellipsometric angles Ψ(ω) and ∆(ω) recorded at 65 • and 70 • . To model the contributions from free charge carriers and interband optical transitions, the complex dielectric functionε(ω) = ε 1 (ω) + iε 2 (ω) of the Bi and FeNi layers was interpreted in terms of the Drude and Lorentz parts, respectively, where ε ∞ is the high-frequency dielectric constant, which takes into account the contribution from the higher-energy interband transitions. The fitted Drude parameters were A D and free charge carrier's scattering rate γ D . The fitted parameters of Lorentz bands were E j , γ j , and A j of the band maximum energy, the full width at half maximum, and the ε 2 band height, respectively. The obtained ellipsometric angles Ψ(ω) and ∆(ω) measured at different angles of incidence of 60 • , 65 • , 70 • , and 75 • were fitted for each sample simultaneously using the J.A. Woollam VASE software [16] in the framework of the designed multilayer model. The multilayer model for the studied Al 2 O 3 /(Bi-FeNi)/Sitall multiayers was constructed as it is schematically presented in Figure 3, exactly so as the layers were deposited. In addition, we attempted to take into account the roughness properties of the surface by using the conventional approach of effective medium approximation (EMA) based on the (50% Al 2 O 3 -50% Sitall substrate derived from our earlier SE studies [18,19] were introduced to the elaborated multilayer model. The dielectric response of the Al 2 O 3 capping layer was represented by the tabular complex dielectric function spectra [20].  Tables I and II, and the resulting ε 1 (ω) and ε 2 (ω) parts of the Bi and FeNi (pseudo)dielectric function spectra are presented in Figure 4.   Table II).   dently demonstrated. The optical conductivity spectra of the Bi and FeNi layers follow the main trends identified in their complex dielectric function spectra presented in Figure 4.

IV. DISCUSSION
Initially, we would like to discuss GMR effects relevant for the studied MLF systems. Our simulations of the dielectric functions for the 1.  Table II). From the corresponding optical conductivity spectra presented in Figure 5e-h one can notice that the associated Drude dc limit, σ 1ω→0 , displays an oscillating character (in agreement with the results deduced for the corresponding Drude parameter A D , see Table II and Figure 6). We  Using a simple model of a two-current series resistor [22], the magnetoresistance ∆R R can be estimated as where d Bi and d F eN i are the thicknesses of Bi and FeNi layers, and α = ↓ ρ F eNi ρ Bi and β = ↑ ρ F eNi ρ Bi are the ratios of the resistivity in the FeNi layer to that in the Bi layer in the spin down and spin up current channel, respectively. Exploiting values for ρ = σ −1 1ω→0 estimated for the 1.4 nm Bi and 1.8 nm FeNi layers from the current model simulations (see Table I and II), namely, ρ Bi = 1 8970 Ω·cm, ↓ ρ F eN i = 1 2020 Ω·cm and ↑ ρ F eN i = 1 4540 Ω·cm (the latter estimate is given by the FM coupling for the 0.6 nm Bi spacer), we obtain α=4.4 and β=2.0. Then, using Equation (2) we have ∆R R =10%. This means that the 1.4 nm Bi spacer corresponds to the second antiFM maximum. Following the same approach for the 2.5 nm Bi spacer, where ρ Bi = 1 3370 Ω·cm, ↓ ρ F eN i = 1 1760 Ω·cm and ↑ ρ F eN i = 1 2920 Ω·cm (corresponding to the FM coupling for the 2.0 nm Bi spacer), we obtain α=1.9 and β=1.2. Using Equation (2), we have ∆R R =1.4%, which may correspond to the very weakly pronounced third antiFM maximum. From the analysis presented above, we may expect that the first antiFM maximum corresponding to the magnetoresistance of about 20% occurs for the Bi spacer thickness of about 0.9 nm, which is in agreement with the results presented in Ref. [21].  Table I). The Drude and Lorentz contributions are more clearly pronounced in the corresponding optical conductivity spectra (see Figure 5a,b). The obtained Drude and Lorentz parameters are in excellent agreement with those deduced in our previous study [13] for the Bi spacer layer incorporated in the [Bi(2.5, 2.0 nm)-NiFe(1.2 nm)] 16 structures under study. The pronounced Lorentz band found at low photon energies for Bi single crystals (rhombohedral symmetry, space group R3m) [24,25] and bulk Bi layers [26,27] is characteristic of the semimetallic-like electronic band structure due to the contributions from the interband transitions near the Γ point, Γ + 6 -Γ − 6 and Γ + 45 -Γ − 6 [2], and near the T point, T − 6 -T − 45 [4]. The estimated values (see Table I Table I).
Thus, we have discovered that, on the one hand, the optical conductivity spectra spectra of the 2.0 and 2.5 nm thick Bi spacer layers in the (Bi-FeNi) MLFs incorporating 8 and 6 Bi(012)-type monolayers, respectively, have contributions from the pronounced low-energy Lorentz oscillator and from the free charge carrier Drude term (for details, see Figure 5a,b and Table I). Here, the presence of the low-energy Lorentz band points on the Bi semimetallic phase contribution, and the parameters obtained for the Drude conductivity indicate that its origin can be associated with the surface metallic states [6]. Therefore, the 2.0 and 2.5 nm Bi layers can be associated with the semimetallic Bi phase sandwiched between two metallic layers on the top and bottom surfaces. On the other hand, the contribution from the intrinsic Lorentz band is strongly suppressed for the 1.4 and 0.6 nm layers, where the Drude conductivity displays notably improved metallicity properties, as one can see from the optical conductivity spectra shown in Figure 5c,d (for details, see Table I).
From the above discussion of the obtained results, we can conclude that the Bi layer consisting of 4 Bi(012)-type monolayers represents a kind of crossover regarding the contributions from the semimetallic Bi phase and/or surface metallic-like states. Here we noticed some similarity with the theory results presented for the ultrathin Bi(111) layers by Liu et al. [12]. There, it was established that below 4 Bi(111) BLs the film is a semiconductor with the direct gap open at the Γ point and the positive indirect band gap, leading to nontrivial Z 2 topology (ν=1) peculiar for an intrinsic 2D TI. Hovewer, above 4 Bi (111) BLs, the indirect band gap becomes negative resulting in a semiconductor-semimetal transition due to overlapping of two bands at the Fermi level around the Γ and M points. It is argued by Liu et al. [12] that the Bi layers consisting of 5 to 8 Bi(111) BLs represent a 2D TI suited between two "trivial" metallic surfaces [12]. This means that for the surface considered as an individual 2D system its Z 2 number is trivial (ν=0). The surface bands have no contribution to the nontrivial Z 2 topology and, therefore, these trivial metallic surfaces are not robust and can easily be removed by surface defects or impurities. It was found by us [13] that the Bi layers in the [Bi(2.0, 2.5 nm)-NiFe(0.8 nm)] multilayers, incorporating the nanoisland permalloy layer, exhibit bulk-like semimetallic properties of the electronic band structure, although the surface (Drude) metallic conductivity is absent there (see Fig. 4(d) of Ref. [13]). Indeed, strong magnetic and spatial disorder induced by magnetic FeNi nanoislands, as well as long-range many-body interactions between magnetic moments of permalloy nanoislands [17], may lead to specific localization of free charge carriers [28]. However, the surface conductivity (or interface) states for the 1.4 nm layer in the Bi-FeNi(1.8 nm) multilayers may be topologically nontrivial and, in this case, the electrons cannot be backscattered by impurities. Here, the Drude dc limit is 8970±540 Ω·cm −1 and the scattering rate γ D =1.5±0.06 eV. We found that the 0.6 nm thick Bi layer exhibits somewhat different Drude dc limit (6300±540 Ω·cm −1 ) and γ D (1.2±0.1 eV), see Table I and Figure 6, which can be attributed to the discontinuous nanoisland structure of this layer.
Finally, we would like to note that it will be challenging to investigate dc transport and superconductivity properties of the ultrathin Bi films possessing 2D TI surface states following the approach presented in Ref. [29], where the subkelvin superconductivity without any external stimuli was discovered in 3D TI Cd 3 As 2 films [30,31].

V. CONCLUSIONS
In summary, using wide-band (0.5-6.5 eV) spectroscopic ellipsometry we studied the optical properies of the [Bi(0.6, 1.4, 2.0, 2.5 nm)-NiFe(1.8ṅm)] 16 MLFs prepared by rf sputtering. The XRD analysis suggested that the 0.6, 1.4, 2.0, and 2.5 nm Bi layers in the  Bi(012)-type monolayers represents a kind of crossover regarding the contributions from the semimetallic Bi phase and/or surface metallic-like states. Therefore, the properties of Bi layers below 4 monolayers may be associated with nontrivial topology (where the topology number ν=1) peculiar for an intrinsic 2D TI. We expect that the Bi layers having thickness of 0.9 nm will exhibit maximal GMR effect of about 20% in the (Bi-FeNi) MLFs, where the Drude dc limit is about 8970±540 Ω·cm −1 . These states may be protected from backscattering, which makes them promising in spintronic devices and quantum computing.