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Measurements of Surface Impedance in MgB_{2} in DC Magnetic Fields: Insights in Flux-Flow Resistivity

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## Abstract

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## 1. Introduction

## 2. Surface Resistance in the Mixed State

## 3. Measurement Technique

## 4. Experimental Section

#### 4.1. Sample Preparation

#### 4.2. Surface Resistance

#### 4.3. Vortex Parameters

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Buzea, C.; Yamashita, T. Review of the Superconducting Properties of MgB
_{2}. Supercond. Sci. Technol.**2001**, 14, R115–R146. [Google Scholar] [CrossRef] [Green Version] - Choi, H.J.; Roundy, D.; Sun, H.; Cohen, M.L.; Louie, S.G. The Origin of the Anomalous Superconducting Properties of MgB
_{2}. Nature**2002**, 418, 758–760. [Google Scholar] [CrossRef] [PubMed] - Szabó, P.; Samuely, P.; Kačmarčík, J.; Klein, T.; Marcus, J.; Fruchart, D.; Miraglia, S.; Marcenat, C.; Jansen, A.G.M. Evidence for Two Superconducting Energy Gaps in MgB
_{2}by Point-Contact Spectroscopy. Phys. Rev. Lett.**2001**, 87, 137005. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Sarti, S.; Amabile, C.; Silva, E.; Giura, M.; Fastampa, R.; Ferdeghini, C.; Ferrando, V.; Tarantini, C. Dynamic Regimes in MgB
_{2}Probed by Swept Frequency Microwave Measurements. Phys. Rev. B**2005**, 72, 024542. [Google Scholar] [CrossRef] - Babaev, E. Vortices with Fractional Flux in Two-Gap Superconductors and in Extended Faddeev Model. Phys. Rev. Lett.
**2002**, 89, 067001. [Google Scholar] [CrossRef] [Green Version] - Moshchalkov, V.; Menghini, M.; Nishio, T.; Chen, Q.; Silhanek, A.; Dao, V.; Chibotaru, L.; Zhigadlo, N.; Karpinski, J. Type-1.5 Superconductivity. Phys. Rev. Lett.
**2009**, 102, 117001. [Google Scholar] [CrossRef] [Green Version] - Dao, V.H.; Chibotaru, L.F.; Nishio, T.; Moshchalkov, V.V. Giant Vortices, Rings of Vortices, and Reentrant Behavior in Type-1.5 Superconductors. Phys. Rev. B
**2011**, 83, 020503. [Google Scholar] [CrossRef] [Green Version] - Silaev, M.; Babaev, E. Microscopic Theory of Type-1.5 Superconductivity in Multiband Systems. Phys. Rev. B
**2011**, 84, 094515. [Google Scholar] [CrossRef] [Green Version] - Gutierrez, J.; Raes, B.; Silhanek, A.V.; Li, L.J.; Zhigadlo, N.D.; Karpinski, J.; Tempere, J.; Moshchalkov, V.V. Scanning Hall Probe Microscopy of Unconventional Vortex Patterns in the Two-Gap MgB
_{2}Superconductor. Phys. Rev. B**2012**, 85, 094511. [Google Scholar] [CrossRef] [Green Version] - Lin, S.Z.; Bulaevskii, L.N. Dissociation Transition of a Composite Lattice of Magnetic Vortices in the Flux-Flow Regime of Two-Band Superconductors. Phys. Rev. Lett.
**2013**, 110, 087003. [Google Scholar] [CrossRef] - Aguirre, C.; Martins, Q.; Barba-Ortega, J. Vortices in a superconducting two-band disk: Role of the Josephson and bi-quadratic coupling. Phys. C Supercond. Its Appl.
**2021**, 581, 1353818. [Google Scholar] [CrossRef] - Jorge, T.N.; Aguirre, C.; de Arruda, A.; Barba-Ortega, J. Two-band superconducting square with a central defect: Role of the deGennes extrapolation length. Eur. Phys. J. B
**2020**, 93, 1–7. [Google Scholar] [CrossRef] - Aguirre, C.; Joya, M.; Barba-Ortega, J. On the vortex matter in a two-band superconducting meso-prism. Phys. C Supercond. Its Appl.
**2021**, 585, 1353867. [Google Scholar] [CrossRef] - Flükiger, R. MgB
_{2}Superconducting Wires: Basics and Applications; World Scientific Series in Applications of Superconductivity and Related Phenomena; World Scientific Publishing Company Pte. Limited: Singpore, 2016. [Google Scholar] - Ballarino, A.; Flükiger, R. Status of MgB
_{2}Wire and Cable Applications in Europe. J. Phys. Conf. Ser.**2017**, 871, 012098. [Google Scholar] [CrossRef] [Green Version] - Gozzelino, L.; Gerbaldo, R.; Ghigo, G.; Torsello, D.; Bonino, V.; Truccato, M.; Grigoroscuta, M.A.; Burdusel, M.; Aldica, G.V.; Sandu, V.; et al. High Magnetic Shielding Properties of an MgB
_{2}Cup Obtained by Machining a Spark-Plasma-Sintered Bulk Cylinder. Supercond. Sci. Technol.**2020**, 33, 044018. [Google Scholar] [CrossRef] - Fracasso, M.; Gömöry, F.; Solovyov, M.; Gerbaldo, R.; Ghigo, G.; Laviano, F.; Napolitano, A.; Torsello, D.; Gozzelino, L. Modelling and Performance Analysis of MgB
_{2}and Hybrid Magnetic Shields. Materials**2022**, 15, 667. [Google Scholar] [CrossRef] - Iwasa, Y. Towards Liquid-Helium-Free, Persistent-Mode MgB
_{2}MRI Magnets: FBML Experience. Supercond. Sci. Technol.**2017**, 30, 053001. [Google Scholar] [CrossRef] [Green Version] - Yamamoto, A. Advances in MgB
_{2}Superconductor Applications for Particle Accelerators. arXiv**2022**. [Google Scholar] [CrossRef] - Takano, Y.; Takeya, H.; Fujii, H.; Kumakura, H.; Hatano, T.; Togano, K.; Kito, H.; Ihara, H. Superconducting Properties of MgB
_{2}Bulk Materials Prepared by High-Pressure Sintering. Appl. Phys. Lett.**2001**, 78, 2914–2916. [Google Scholar] [CrossRef] [Green Version] - Tampieri, A.; Celotti, G.; Sprio, S.; Caciuffo, R.; Rinaldi, D. Study of the Sintering Behaviour of MgB
_{2}Superconductor during Hot-Pressing. Phys. C Supercond.**2004**, 400, 97–104. [Google Scholar] [CrossRef] - Schmidt, J.; Schnelle, W.; Grin, Y.; Kniep, R. Pulse Plasma Synthesis and Chemical Bonding in Magnesium Diboride. Solid State Sci.
**2003**, 5, 535–539. [Google Scholar] [CrossRef] - Aldica, G.; Batalu, D.; Popa, S.; Ivan, I.; Nita, P.; Sakka, Y.; Vasylkiv, O.; Miu, L.; Pasuk, I.; Badica, P. Spark Plasma Sintering of MgB
_{2}in the Two-Temperature Route. Phys. C Supercond.**2012**, 477, 43–50. [Google Scholar] [CrossRef] - Badica, P.; Aldica, G.; Ionescu, A.; Burdusel, M.; Batalu, D. The influence of different additives on MgB
_{2}superconductor obtained by ex situ spark plasma sintering: Pinning force aspects. In Correlated Functional Oxides; Springer: Berlin, Germany, 2017; pp. 75–116. [Google Scholar] [CrossRef] - Sandu, V.; Aldica, G.; Grigoroscuta, M.; Burdusel, M.; Pasuk, I.; Ching, Y.; Ionescu, A.; Badica, P. Effect of polysilane addition on spark plasma sintering and superconducting properties of MgB
_{2}bulks. Ceram. Int.**2022**, 48, 31914–31922. [Google Scholar] [CrossRef] - Maeda, A.; Kitano, H.; Inoue, R. Microwave Conductivities of High-T
_{c}Oxide Superconductors and Related Materials. J. Phys. Condens. Matter**2005**, 17, R143–R185. [Google Scholar] [CrossRef] - Grigoroscuta, M.; Aldica, G.; Burdusel, M.; Sandu, V.; Kuncser, A.; Pasuk, I.; Ionescu, A.; Suzuki, T.; Vasylkiv, O.; Badica, P. Towards high degree of c-axis orientation in MgB
_{2}bulks. J. Magnes. Alloys**2022**, 10, 2173–2184. [Google Scholar] [CrossRef] - Sandu, V.; Aldica, G.; Popa, S.; Enculescu, M.; Badica, P. Tellurium Addition as a Solution to Improve Compactness of Ex-Situ Processed MgB
_{2}-SiC Superconducting Tapes. Supercond. Sci. Technol.**2016**, 29, 065012. [Google Scholar] [CrossRef] - Jin, B.; Klein, N.; Kang, W.; Kim, H.J.; Choi, E.M.; Lee, S.I.; Dahm, T.; Maki, K. Energy Gap, Penetration Depth, and Surface Resistance of MgB
_{2}Thin Films Determined by Microwave Resonator Measurements. Phys. Rev. B**2002**, 66, 104521–1/104521–6. [Google Scholar] [CrossRef] [Green Version] - Ghigo, G.; Botta, D.; Chiodoni, A.; Gozzelino, L.; Gerbaldo, R.; Laviano, F.; Mezzetti, E. Effective Gap at Microwave Frequencies in MgB
_{2}Thin Films with Strong Interband Scattering. Phys. Rev. B**2005**, 71, 214522. [Google Scholar] [CrossRef] [Green Version] - Lee, S.Y.; Lee, J.H.; Han, J.H.; Moon, S.H.; Lee, H.N.; Booth, J.C.; Claassen, J.H. Effects of the Two-Gap Nature on the Microwave Conductivity of Polycrystalline MgB
_{2}Films with a Critical Temperature of 39 K. Phys. Rev. B**2005**, 71, 104514. [Google Scholar] [CrossRef] - Ghigo, G.; Ummarino, G.A.; Gerbaldo, R.; Gozzelino, L.; Laviano, F.; Mezzetti, E. Effects of Disorder on the Microwave Properties of MgB
_{2}Polycrystalline Films. Phys. Rev. B**2006**, 74, 184518. [Google Scholar] [CrossRef] - Oates, D.E.; Agassi, Y.D.; Moeckly, B.H. Microwave Measurements of MgB
_{2}: Implications for Applications and Order-Parameter Symmetry. Supercond. Sci. Technol.**2010**, 23, 034011. [Google Scholar] [CrossRef] - Gallitto, A.A.; Camarda, P.; Vigni, M.L.; Albisetti, A.F.; Saglietti, L.; Giunchi, G. Microwave Response of Coaxial Cavities Made of Bulk Magnesium Diboride. IEEE Trans. Appl. Supercond.
**2014**, 24, 1500109. [Google Scholar] [CrossRef] [Green Version] - Pompeo, N.; Alimenti, A.; Torokhtii, K.; Silva, E. Physics of Vortex Motion by Means of Microwave Surface Impedance Measurements (Review Article). Low Temp. Phys.
**2020**, 46, 343–347. [Google Scholar] [CrossRef] - Shibata, A.; Matsumoto, M.; Izawa, K.; Matsuda, Y.; Lee, S.; Tajima, S. Anomalous Flux Flow Resistivity in the Two-Gap Superconductor MgB
_{2}. Phys. Rev. B**2003**, 68, 060501. [Google Scholar] [CrossRef] [Green Version] - Dulčić, A.; Paar, D.; Požek, M.; Williams, G.; Krämer, S.; Jung, C.; Park, M.s.; Lee, S.i. Magnetization and Microwave Study of Superconducting MgB
_{2}. Phys. Rev. B**2002**, 66, 014505. [Google Scholar] [CrossRef] [Green Version] - Sarti, S.; Amabile, C.; Fastampa, R.; Giura, M.; Pompeo, N.; Silva, E. Vortex Motion and Quasiparticle Resistivity in MgB
_{2}at Microwave Frequencies. J. Supercond. Nov. Magn.**2007**, 20, 51–57. [Google Scholar] [CrossRef] - Zaitsev, A.; Schneider, R.; Hott, R.; Schwarz, T.; Geerk, J. Effect of a Dc Magnetic Field on the Microwave Losses in MgB
_{2}Thin Films. Phys. Rev. B**2007**, 75, 212505. [Google Scholar] [CrossRef] - Bardeen, J.; Stephen, M. Theory of the Motion of Vortices in Superconductors. Phys. Rev.
**1965**, 140, 1197–1207. [Google Scholar] [CrossRef] - Goryo, J.; Matsukawa, H. Flux Flow Resistivity in Two-Gap Superconductor. J. Phys. Soc. Jpn.
**2005**, 74, 1394–1396. [Google Scholar] [CrossRef] - Tinkham, M. Introduction to Superconductivity, 2nd ed.; McGraw-Hill, Inc.: New York, NY, USA, 1996. [Google Scholar]
- Coffey, M.W.; Clem, J.R. Unified Theory of Effects of Vortex Pinning and Flux Creep upon the Rf Surface Impedance of Type-II Superconductors. Phys. Rev. Lett.
**1991**, 67, 386–389. [Google Scholar] [CrossRef] - Brandt, E. Linear a.c. Response of High-T
_{c}Superconductors and the Irreversibility Line. Phys. Scr.**1992**, T45, 63–68. [Google Scholar] [CrossRef] - Pompeo, N.; Silva, E. Reliable Determination of Vortex Parameters from Measurements of the Microwave Complex Resistivity. Phys. Rev. B
**2008**, 78, 094503. [Google Scholar] [CrossRef] [Green Version] - Goryo, J.; Saito, T.; Matsukawa, H. Vortex Pinning in Two-Gap Superconductors. J. Phys. Conf. Ser.
**2007**, 89, 012022. [Google Scholar] [CrossRef] - Alimenti, A.; Torokhtii, K.; Silva, E.; Pompeo, N. Challenging Microwave Resonant Measurement Techniques for Conducting Material Characterization. Meas. Sci. Technol.
**2019**, 30, 065601. [Google Scholar] [CrossRef] - Torokhtii, K.; Pompeo, N.; Silva, E.; Alimenti, A. Optimization of Q-factor and Resonance Frequency Measurements in Partially Calibrated Resonant Systems. Meas. Sens.
**2021**, 18, 100314. [Google Scholar] [CrossRef] - Torokhtii, K.; Alimenti, A.; Pompeo, N.; Silva, E. Estimation of Microwave Resonant Measurements Uncertainty from Uncalibrated Data. Acta IMEKO
**2020**, 9, 47–52. [Google Scholar] [CrossRef] - Torokhtii, K.; Alimenti, A.; Pompeo, N.; Leccese, F.; Orsini, F.; Scorza, A.; Sciuto, S.A.; Silva, E. Q-Factor of Microwave Resonators: Calibrated vs. Uncalibrated Measurements. J. Phys. Conf. Ser.
**2018**, 1065, 052027. [Google Scholar] [CrossRef] [Green Version] - Pompeo, N.; Torokhtii, K.; Alimenti, A.; Silva, E. A Method Based on a Dual Frequency Resonator to Estimate Physical Parameters of Superconductors from Surface Impedance Measurements in a Magnetic Field. Measurement
**2021**, 184, 109937. [Google Scholar] [CrossRef] - Pompeo, N.; Alimenti, A.; Torokhtii, K.; Bartolomé, E.; Palau, A.; Puig, T.; Augieri, A.; Galluzzi, V.; Mancini, A.; Celentano, G.; et al. Intrinsic Anisotropy and Pinning Anisotropy in Nanostructured YBa
_{2}Cu_{3}O_{7-δ}from Microwave Measurements. Supercond. Sci. Technol.**2020**, 33, 044017. [Google Scholar] [CrossRef] - Fuchs, G.; Müller, K.H.; Handstein, A.; Nenkov, K.; Narozhnyi, V.N.; Eckert, D.; Wolf, M.; Schultz, L. Upper Critical Field and Irreversibility Line in Superconducting MgB
_{2}. Solid State Commun.**2001**, 118, 497–501. [Google Scholar] [CrossRef] [Green Version] - Handstein, A.; Hinz, D.; Fuchs, G.; Müller, K.H.; Nenkov, K.; Gutfleisch, O.; Narozhnyi, V.N.; Schultz, L. Fully Dense MgB
_{2}Superconductor Textured by Hot Deformation. J. Alloys Compd.**2001**, 329, 285–289. [Google Scholar] [CrossRef] [Green Version] - Alimenti, A.; Torokhtii, K.; Grigoroscuta, M.; Badica, P.; Crisan, A.; Silva, E.; Pompeo, N. Microwave Investigation of Pinning in Te- and Cubic-BN- Added MgB
_{2}. J. Phys. Conf. Ser.**2020**, 1559, 12039. [Google Scholar] [CrossRef] - Mazin, I.I.; Andersen, O.K.; Jepsen, O.; Dolgov, O.V.; Kortus, J.; Golubov, A.A.; Kuz’menko, A.B.; van der Marel, D. Superconductivity in MgB
_{2}: Clean or Dirty? Phys. Rev. Lett.**2002**, 89, 107002. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Bonura, M.; Gallitto, A.A.; Vigni, M.L.; Ummarino, G.A. Field-Induced Suppression of the π-Band Superconductivity and Magnetic Hysteresis in the Microwave Surface Resistance of MgB
_{2}at Temperatures near T_{c}. Supercond. Sci. Technol.**2009**, 22, 055010. [Google Scholar] [CrossRef] - Alimenti, A.; Pompeo, N.; Torokhtii, K.; Spina, T.; Muzzi, L.; Silva, E. Surface Impedance Measurements on Nb
_{3}Sn in High Magnetic Fields. IEEE Trans. Appl. Supercond.**2019**, 29, 3500104. [Google Scholar] [CrossRef] - Alimenti, A.; Pompeo, N.; Torokhtii, K.; Spina, T.; Flükiger, R.; Muzzi, L.; Silva, E. Microwave Measurements of the High Magnetic Field Vortex Motion Pinning Parameters in Nb
_{3}Sn. Supercond. Sci. Technol.**2021**, 34, 014003. [Google Scholar] [CrossRef] - Silaev, M.; Vargunin, A. Vortex Motion and Flux-Flow Resistivity in Dirty Multiband Superconductors. Phys. Rev. B
**2016**, 94, 224506. [Google Scholar] [CrossRef] [Green Version] - Takahashi, H.; Okada, T.; Imai, Y.; Kitagawa, K.; Matsubayashi, K.; Uwatoko, Y.; Maeda, A. Investigation of the Superconducting Gap Structure in SrFe
_{2}(As_{0.7}P_{0.3})_{2}by Magnetic Penetration Depth and Flux Flow Resistivity Analysis. Phys. Rev. B**2012**, 86, 144525. [Google Scholar] [CrossRef] [Green Version] - Okada, T.; Imai, Y.; Takahashi, H.; Nakajima, M.; Iyo, A.; Eisaki, H.; Maeda, A. Penetration Depth and Flux-Flow Resistivity Measurements of BaFe
_{2}(As_{0.55}P_{0.45})_{2}Single Crystals. Phys. C Supercond.**2014**, 504, 24–27. [Google Scholar] [CrossRef] - Okada, T.; Nabeshima, F.; Takahashi, H.; Imai, Y.; Maeda, A. Exceptional Suppression of Flux-Flow Resistivity in FeSe
_{0.4}Te_{0.6}by Back-Flow from Excess Fe Atoms and Se/Te Substitutions. Phys. Rev. B**2015**, 91, 054510. [Google Scholar] [CrossRef] [Green Version] - Pompeo, N.; Torokhtii, K.; Alimenti, A.; Sylva, G.; Braccini, V.; Silva, E. Pinning Properties of FeSeTe Thin Film through Multifrequency Measurements of the Surface Impedance. Supercond. Sci. Technol.
**2020**, 33, 114006. [Google Scholar] [CrossRef] - Pompeo, N.; Alimenti, A.; Torokhtii, K.; Sylva, G.; Braccini, V.; Silva, E. Microwave Properties of Fe(Se, Te) Thin Films in a Magnetic Field: Pinning and Flux Flow. J. Phys. Conf. Ser.
**2020**, 1559, 012055. [Google Scholar] [CrossRef] - Xu, M.; Kitazawa, H.; Takano, Y.; Ye, J.; Nishida, K.; Abe, H.; Matsushita, A.; Kido, G. Single crystal MgB
_{2}with anisotropic superconducting properties. arXiv1**2001**, arXiv:cond-mat/0105271. [Google Scholar] - Lee, S.; Mori, H.; Masui, T.; Eltsev, Y.; Yamamoto, A.; Tajima, S. Growth, structure analysis and anisotropic superconducting properties of MgB
_{2}single crystals. J. Phys. Soc. Jpn.**2001**, 70, 2255–2258. [Google Scholar] [CrossRef]

**Figure 2.**Surface resistance ${R}_{s}$ vs. T measured with different applied magnetic fields ${\mu}_{0}H$ at the frequencies of ${\nu}_{1}=16.5$ GHz in (

**a**) and ${\nu}_{2}=26.7$ GHz in (

**b**). In the inset of (

**a**), the procedure used for the determination of the critical temperature ${T}_{c}$ at different applied fields is shown.

**Figure 3.**${H}_{c2}$ as derived from the surface resistance data of Figure 2, compared to reported data in the literature as measured in polycrystalline samples [53,54] and in single crystals; in the latter case, with the applied magnetic field oriented both parallel to the a–b planes and the c axis. The continuous lines were the fit of anisotropic data, taken from [1]. The data obtained on the polycrystalline sample studied in this work were consistent with the values measured in other polycrystals and fell well between the two limits of ${H}_{c2}$ measured on oriented single crystals.

**Figure 4.**Ratio of the surface resistance measured at ${\nu}_{2}=26.7$ GHz and ${\nu}_{1}=16.5$ GHz, ${r}_{21}={R}_{s2}/{R}_{s1}$ in MgB${}_{2}$ at different applied magnetic fields.

**Figure 5.**Surface resistance ${R}_{s}\left({\nu}_{2}\right)$ vs. ${R}_{s}\left({\nu}_{1}\right)$ with T and B as parameters. In particular, curves wre drawn by varying T, while different curves correspond to distinct B values.

**Figure 6.**${\rho}_{ff}$ vs. H at various T, with fits according to Equation (9) reported as dashed lines.

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**MDPI and ACS Style**

Alimenti, A.; Torokhtii, K.; Vidal García, P.; Silva, E.; Grigoroscuta, M.A.; Badica, P.; Crisan, A.; Pompeo, N.
Measurements of Surface Impedance in MgB_{2} in DC Magnetic Fields: Insights in Flux-Flow Resistivity. *Materials* **2023**, *16*, 205.
https://doi.org/10.3390/ma16010205

**AMA Style**

Alimenti A, Torokhtii K, Vidal García P, Silva E, Grigoroscuta MA, Badica P, Crisan A, Pompeo N.
Measurements of Surface Impedance in MgB_{2} in DC Magnetic Fields: Insights in Flux-Flow Resistivity. *Materials*. 2023; 16(1):205.
https://doi.org/10.3390/ma16010205

**Chicago/Turabian Style**

Alimenti, Andrea, Kostiantyn Torokhtii, Pablo Vidal García, Enrico Silva, Mihai Alexandru Grigoroscuta, Petre Badica, Adrian Crisan, and Nicola Pompeo.
2023. "Measurements of Surface Impedance in MgB_{2} in DC Magnetic Fields: Insights in Flux-Flow Resistivity" *Materials* 16, no. 1: 205.
https://doi.org/10.3390/ma16010205