# Bi Layer Properties in the Bi–FeNi GMR-Type Structures Probed by Spectroscopic Ellipsometry

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

## 3. Results

#### 3.1. Atomic Force Microscopy Study

#### 3.2. Spectroscopic Ellipsometry Study of the Ultrathin Bi–FeNi Multilayer Film Samples

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Sample Availability

## Abbreviations

GMR | Giant magnetoresistance |

SOC | Spin–orbit coupling |

TI | Topological insulator |

MLF | Multilayered film |

SE | Spectroscopic ellipsometry |

AFM | Atomic force microscopy |

FM | Ferromagnetic |

XRD | X-ray diffraction |

XRR | X-ray reflectivity |

## References

- Bychkov, Y.A.; Rashba, E.I. Properties of a 2D electron gas with lifted spectral degeneracy. JETP Lett.
**1984**, 39, 78–81. [Google Scholar] - Golin, S. Band Structure of Bismuth: Pseudopotential Approach. Phys. Rev. B
**1968**, 166, 643–651. [Google Scholar] [CrossRef] - Gonze, X.; Michenaud, J.-P.; Vigneron, J.-P. First-principles study of As, Sb, and Bi electronic properties. Phys. Rev. B
**1990**, 41, 11827–11836. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Liu, Y.; Allen, R.E. Electronic structure of the semimetals Bi and Sb. Phys. Rev. B
**1995**, 52, 1566–1577. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Hofmann, P. The surfaces of bismuth: Structural and electronic properties. Prog. Surf. Sci.
**2006**, 81, 191–245. [Google Scholar] [CrossRef] - Yokota, Y.; Takeda, J.; Dang, C.; Han, G.; McCarthy, D.N.; Nagao, T.; Hishita, S.; Kitajima, K.; Katayama, I. Surface metallic states in ultrathin Bi(001) films studied with terahertz time-domain spectroscopy. Appl. Phys. Lett.
**2012**, 100, 251605. [Google Scholar] [CrossRef] - Hoffman, C.A.; Meyer, J.R.; Bartoli, F.J. Semimetal-to-semiconductor transition in Bismuth thin films. Phys. Rev. B
**1993**, 48, 11431–11434. [Google Scholar] [CrossRef] - Koroteev, Y.M.; Bihlmayer, G.; Chulkov, E.V.; Blugel, S. First-principles investigation of structural and electronic properties of ultrathin Bi films. Phys. Rev. B
**2008**, 77, 045428. [Google Scholar] [CrossRef] [Green Version] - Wada, M.; Murakami, S.; Freimuth, F.; Bihlmayer, G. Localized edge states in two-dimensional topological insulators: Ultrathin Bi films. Phys. Rev. B
**2011**, 83, 121310(R). [Google Scholar] [CrossRef] [Green Version] - Murakami, S. Quantum Spin Hall Effect and Enhanced Magnetic Response by Spin-Orbit Coupling. Phys. Rev. Lett.
**2006**, 97, 236805. [Google Scholar] [CrossRef] [Green Version] - Fu, L.; Kane, C.L.; Mele, E.J. Topological Insulators in Three Dimensions. Phys. Rev. Lett.
**2007**, 98, 106803. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Liu, Z.; Liu, C.-X.; Wu, Y.-S.; Duan, W.-H.; Liu, F.; Wu, J. Stable nontrivial Z
_{2}topology in ultrathin Bi(111) films: A first principles study. Phys. Rev. Lett.**2011**, 107, 136805. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Kovaleva, N.N.; Chvostova, D.; Pacherova, O.; Muratov, A.V.; Fekete, L.; Sherstnev, I.A.; Kugel, K.I.; Pudonin, F.A.; Dejneka, A. Bismuth layer properties in the ultrathin Bi–FeNi multilayer films probed by spectroscopic ellipsometry. Appl. Phys. Lett.
**2021**, 119, 183101. [Google Scholar] [CrossRef] - Sherstnev, I.A. Electronic Transport and Magnetic Structure of Nanoisland Ferromagnetic Systems. Ph.D. Thesis, P.N. Lebedev Physical Institute, Moscow, Russia, 2014. [Google Scholar]
- Boltaev, A.P.; Pudonin, F.A.; Shertnev, I.A.; Egorov, D.A. Detection of the metal-insulator transition in disordered systems of magnetic nanoislands. JETP
**2017**, 125, 465–468. [Google Scholar] [CrossRef] - Woollam, J.A. VASE Spectroscopic Ellipsometry Data Analysis Software; J.A. Woollam, Co.: Lincoln, NE, USA, 2010. [Google Scholar]
- Stupakov, A.; Bagdinov, A.V.; Prokhorov, V.V.; Bagdinova, A.N.; Demikhov, E.I.; Dejneka, A.; Kugel, K.I.; Gorbatsevich, A.A.; Pudonin, F.A.; Kovaleva, N.N. Out-of-plane and in-plane magnetization behaviour of dipolar interacting FeNi nanoislands around the percolation threshold. J. Nanomater.
**2016**, 3190260. [Google Scholar] [CrossRef] - Kovaleva, N.N.; Chvostova, D.; Bagdinov, A.V.; Petrova, M.G.; Demikhov, E.I.; Pudonin, F.A.; Dejneka, A. Interplay of electronic correlation and localization in disordered β-tantalum films: Evidence from dc transport and spectroscopic ellipsometry study. Appl. Phys. Lett.
**2015**, 106, 051907. [Google Scholar] [CrossRef] - Kovaleva, N.; Chvostova, D.; Dejneka, A. Localization phenomena in disordered tantalum films. Metals
**2017**, 7, 257. [Google Scholar] [CrossRef] - Palik, E.D. Handbook of Optical Constants of Solids; Elsevier Science: San Diego, CA, USA, 1991. [Google Scholar]
- Hütten, A.; Mrozek, S.; Heitmann, S.; Hempel, T.; Brückl, H.; Reiss, G. Evolution of the GMR-Effect Amplitude in Copper-Permalloy-Multilayered Thin Films. Acta Mater.
**1999**, 47, 4245–4252. [Google Scholar] [CrossRef] - Mathon, J. Exchange Interactions and Giant Magnetoresistance in Magnetic Multilayers. Contemp. Phys.
**1991**, 32, 143–156. [Google Scholar] [CrossRef] - Nagao, T.; Sadowski, J.T.; Saito, M.; Yaginuma, S.; Fujikawa, Y.; Kogure, T.; Ohno, T.; Hasegawa, S.; Sakurai, T. Nanofilm allotrope and phase transformation of ultrathin Bi film on Si(111) − 7 × 7. Phys. Rev. Lett.
**2004**, 93, 105501. [Google Scholar] [CrossRef] [Green Version] - Wang, P.Y.; Jain, A.L. Modulated Piezoreflectance in Bismuth. Phys. Rev. B
**1970**, 2, 2978–2983. [Google Scholar] [CrossRef] - Lenham, A.P.; Treherne, D.M.; Metcalfe, R.J. Optical Properties of Antimony and Bismuth Crystals. J. Opt. Soc. Am.
**1965**, 55, 1072–1074. [Google Scholar] [CrossRef] - Hunderi, O. Optical properties of crystalline and amorphous bismuth films. J. Phys. F
**1975**, 5, 2214–2225. [Google Scholar] [CrossRef] - Toudert, J.; Serna, R. Interband transitions in semi-metals, semiconductors, and topological insulators: A new driving force for plasmonics and nanophotonics [Invited]. Opt. Mater. Express
**2017**, 7, 2299–2325. [Google Scholar] [CrossRef] - Kovaleva, N.N.; Kusmartsev, F.V.; Mekhiya, A.B.; Trunkin, I.N.; Chvostova, D.; Davydov, A.B.; Oveshnikov, L.N.; Pacherova, O.; Sherstnev, I.A.; Kusmartseva, A.; et al. Control of Mooij correlations at the nanoscale in the disordered metallic Ta-nanoisland FeNi multilayers. Sci. Rep.
**2020**, 10, 21172. [Google Scholar] [CrossRef] [PubMed] - Suslov, A.V.; Davydov, A.B.; Oveshnikov, L.N.; Morgun, L.A.; Kugel, K.I.; Zakhvalinskii, V.S.; Pilyuk, E.A.; Kochura, A.V.; Kuzmenko, A.P.; Pudalov, V.M.; et al. Observation of subkelvin superconductivity in Cd
_{3}As_{2}thin films. Phys. Rev. B**2019**, 99, 094512. [Google Scholar] [CrossRef] [Green Version] - Kochura, A.V.; Zakhvalinskii, V.S.; Htet, A.Z.; Ril’, A.I.; Pilyuk, E.A.; Kuz’menko, A.P.; Aronzon, B.A.; Marenkin, S.F. Growth of thin cadmium arsenide films by magnetron sputtering and their structure. Inorg. Mater.
**2019**, 55, 879–886. [Google Scholar] [CrossRef] - Kovaleva, N.; Chvostova, D.; Fekete, L.; Muratov, A. Morphology and Optical Properties of Thin Cd
_{3}As_{2}Films of a Dirac Semimetal Compound. Metals**2020**, 10, 1398. [Google Scholar] [CrossRef]

**Figure 1.**AFM images (

**a**–

**d**) 5 × 5 $\mathsf{\mu}$m${}^{2}$ and (

**e**–

**h**) 1 × 1 $\mathsf{\mu}$m${}^{2}$ of the Al${}_{2}$O${}_{3}$/(Bi–FeNi)${}_{16}$/Sitall MLF samples, where the nominal Al${}_{2}$O${}_{3}$ and FeNi layer thicknesses are 2.1 and 1.8 nm and the nominal Bi layer thicknesses are 0.6, 1.4, 2.0, and 2.5 nm, respectively. The estimated surface RMS roughness values are in (

**a**–

**d**), 3.6, 3.0, 3.1, and 5.2 nm, and in (

**e**–

**h**), 3.2, 2.6, 2.7, and 5.3 nm, respectively. (

**i**,

**j**) The typical height profiles for the MLF samples with the nominal Bi layer thicknesses of 0.6 and 2.5 nm, respectively.

**Figure 2.**(

**a**–

**d**) Ellipsometric angles, $\Psi \left(\omega \right)$ and $\Delta \left(\omega \right)$ (symbols), measured at the angles of incidence of 65${}^{\circ}$ and 70${}^{\circ}$ for the Al${}_{2}$O${}_{3}$/[Bi(d)–NiFe(1.8 nm)]${}_{16}$/Sitall multilayered films where the Bi spacer layer thicknesses d = 0.6, 1.4, 2.0, and 2.5 nm, respectively. The solid red, blue, green, and black curves show the corresponding simulation results for a 65${}^{\circ}$ angle by the dielectric function model using Equation (1).

**Figure 3.**The multilayer model applied for the simulation of the Al${}_{2}$O${}_{3}$/[Bi(0.6, 1.4, 2.0, and 2.5 nm)–FeNi(1.8 nm)]${}_{16}$/Sitall samples. The Bi and FeNi thicknesses estimated from the model simulations are (

**a**) 0.684 ± 0.037 nm and 2.082 ± 0.116 nm, (

**b**) 1.408 ± 0.574 nm and 1.780 ± 0.65 nm, (

**c**) 1.764 ± 0.194 nm and 1.825 ± 0.358 nm, and (

**d**) 2.387 ± 0.128 nm and 1.782 ± 0.171 nm. Note the good agreement between the thicknesses of the FeNi and Bi layers estimated from the model simulations and their respective nominal thickness values. The roughness and Al${}_{2}$O${}_{3}$ capping layer thicknesses estimated from the model simulations are (

**a**) 0.00 ± 3.85 nm and 1.283 ± 2.37 nm, (

**b**) 0.000 ± 4.97 nm and 4.967 ± 2.17 nm, (

**c**) 0.848 ± 5.86 nm and 4.738 ± 2.92 nm, and (

**d**) 0.000 ± 2.95 nm and 5.389 ± 1.23 nm.

**Figure 4.**The complex (pseudo)dielectric function spectra, ${\epsilon}_{2}\left(\omega \right)$ and ${\epsilon}_{1}\left(\omega \right)$, of the (

**a**,

**b**) Bi layers and (

**c**,

**d**) FeNi layers in the [Bi(d)–FeNi(1.8 nm)]${}_{16}$ structures shown for the Bi layer nominal thickness values $d=$ 0.6, 1.4, 2.0, and 2.5 nm by solid red, blue, green, and black curves, respectively.

**Figure 5.**The intralayer optical conductivity, ${\sigma}_{1}\left(\omega \right)={\epsilon}_{2}\left(\omega \right)\omega [{\mathrm{cm}}^{-1}]/60$, for the (

**a**–

**d**) Bi layers and (

**e**–

**h**) FeNi layers in the [Bi(d)–FeNi(1.8 nm)]${}_{16}$ structures shown for the Bi layer nominal thickness values $d=$ 2.5, 2.0, 1.4, and 0.6 nm by solid curves (

**a**,

**e**) black, (

**b**,

**f**) green, (

**c**,

**g**) blue, and (

**d**,

**h**) red, respectively. The contributions from the Drude term and the Lorentz oscillator in (

**a**–

**d**) are displayed by the yellow- and cyan-shaded areas. In (

**e**–

**h**), the Drude term for the FeNi layers is displayed by the magenta-shaded area. Shown by the dotted curves are the summary of the Drude and Lorentz contributions.

**Figure 6.**(

**a**,

**b**) Parameters of the Drude term (${A}_{D}$ and ${\gamma}_{D}$) for the Bi (filled symbols) and FeNi (empty symbols) layers in the [Bi(0.6, 1.4, 2.0, 2.5 nm)–FeNi(1.8 nm)] MLF structures.

**Table 1.**Drude–Lorentz parameters for the Bi spacer layer in the [Bi(0.6, 1.4, 2.0, 2.5 nm)–NiFe(1.8 nm)]${}_{16}$-multilayered films obtained from the model simulations of the dielectric functions by using Equation (1). The values of ${E}_{j}$, ${\gamma}_{j}$, and ${\gamma}_{D}$ are given in eV and optical conductivity limit ${\sigma}_{1(\omega \to 0)}$ in ${\Omega}^{-1}\xb7$cm${}^{-1}$.

Parameters | 0.6 nm | 1.4 nm | 2.0 nm | 2.5 nm | |
---|---|---|---|---|---|

Drude | ${A}_{D}$ | 46.(9) ± 4 | 66.(7) ± 4 | 24.(5) ± 4 | 25.(1) ± 2 |

${\gamma}_{D}$ | 1.2(5) ± 0.09 | 1.51(0) ± 0.06 | 2.7(2) ± 0.4 | 3.1(3) ± 0.2 | |

${\sigma}_{1(\omega \to 0)}$ | 6300 ± 540 | 8970 ± 540 | 3290 ± 540 | 3370 ± 270 | |

Lorentz | ${E}_{1}$ | – | 0.45(8) ± 0.05 | 0.35(9) ± 0.01 | 0.38(6) ± 0.004 |

oscillator | ${A}_{1}$ | – | 15.(0) ± 6 | 96.(0) $\pm 10$ | 70.(8) ± 2 |

${\gamma}_{1}$ | – | 0.52(6) ± 0.09 | 0.79(1) ± 0.02 | 0.67(6) | |

Lorentz | ${E}_{2}$ | 4.67 | 5.31(5) ± 0.03 | 5.08(7) ± 0.04 | 4.77(5) ± 0.04 |

oscillator | ${A}_{2}$ | 10.2(7) ± 0.6 | 2.53(2) ± 0.05 | 1.2(5) ± 0.1 | 0.67(6) ± 0.08 |

${\gamma}_{2}$ | 4.2(1) ± 0.07 | 3.99(3) ± 0.07 | 3.4(7) ± 0.2 | 2.5(5) ± 0.2 | |

Lorentz | ${E}_{3}$ | 11.1 | 7.8 | 7.7 | 7.7 |

oscillator | ${A}_{3}$ | 7.2 | 4.1 | 4.1 | 4.1 |

${\gamma}_{3}$ | 8.9 | 2.8 | 2.8 | 2.8 |

**Table 2.**Drude–Lorentz parameters for the 1.8 nm thick NiFe layer in the [Bi(0.6, 1.4, 2.0, 2.5 nm)–NiFe]${}_{16}$-multilayered films obtained from the simulations of the model dielectric function described by Equation (1). The values of ${E}_{1}$, ${\gamma}_{1}$, and ${\gamma}_{D}$ are given in eV and optical conductivity limit ${\sigma}_{1(\omega \to 0)}$ in ${\Omega}^{-1}\xb7$cm${}^{-1}$.

Parameters | 0.6 nm | 1.4 nm | 2.0 nm | 2.5 nm | |
---|---|---|---|---|---|

Drude | ${A}_{D}$ | 33.(8) ± 2 | 15.(0) ± 1 | 21.(7) ± 2 | 13.(1) ± 2 |

${\gamma}_{D}$ | 0.876(5) ± 0.04 | 2.8(2) ± 0.3 | 3.4(2) ± 0.4 | 3.1(3) ± 0.2 | |

${\sigma}_{1(\omega \to 0)}$ | 4540 ± 270 | 2020 ± 130 | 2920 ± 270 | 1760 ± 270 | |

Lorentz | ${E}_{1}$ | 1.87 | 3.32 | 3.32 | 3.32 |

oscillator | ${A}_{1}$ | 14.76 | 14.28 | 15.23 | 14.74 |

${\gamma}_{1}$ | 3.62 | 5.88 | 5.65 | 5.95 |

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**MDPI and ACS Style**

Kovaleva, N.; Chvostova, D.; Fekete, L.; Dejneka, A.
Bi Layer Properties in the Bi–FeNi GMR-Type Structures Probed by Spectroscopic Ellipsometry. *Coatings* **2022**, *12*, 872.
https://doi.org/10.3390/coatings12060872

**AMA Style**

Kovaleva N, Chvostova D, Fekete L, Dejneka A.
Bi Layer Properties in the Bi–FeNi GMR-Type Structures Probed by Spectroscopic Ellipsometry. *Coatings*. 2022; 12(6):872.
https://doi.org/10.3390/coatings12060872

**Chicago/Turabian Style**

Kovaleva, Natalia, Dagmar Chvostova, Ladislav Fekete, and Alexandr Dejneka.
2022. "Bi Layer Properties in the Bi–FeNi GMR-Type Structures Probed by Spectroscopic Ellipsometry" *Coatings* 12, no. 6: 872.
https://doi.org/10.3390/coatings12060872