Sains Malaysiana 55(2)(2026): 327-337

http://doi.org/10.17576/jsm-2026-5502-12

 

Modulus Kekenyalan dan Pemalar Gandingan Elektron-Fonon Superkonduktor NdBa₂Cu_3-xFe_xO₇_-δ

(Elastic Moduli and Electron-Phonon Coupling Constant of NdBa₂Cu_3-xFe_xO₇_-δ  Superconductor)

 

R. ABD-SHUKOR^1,*, C.M. CHEW¹, M.S. TANG¹, N.J. NOR-AZAH², W.S. CHIU³, S.K. CHEN⁴, M.N. MOHD NASIR¹ & DANIYAR USKENBAEV⁵

 

¹Department of Applied Physics, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia

²Pusat PERMATA@Pintar Negara, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia

³Low Dimensional Materials Research Centre, Department of Physics, Faculty of Science Universiti Malaya, 50603 Kuala Lumpur, Malaysia

⁴Department of Physics, Universiti Putra Malaysia 43400 UPM Serdang, Selangor, Malaysia

⁵Institute of Energy, S. Seifullin Kazakh Agrotechnical Research University

Astana, Kazakhstan

 

Received: 15 December 2025/Accepted: 27 January 2026

 

Abstrak

Kaedah ultrasonik amat sensitif untuk mengesan peranan fonon dalam mekanisme superkonduktor. Dalam kajian ini, halaju bunyi bujur, v_L dan ricih, v_s bagi superkonduktor NdBa₂Cu₃_-xFe_xO₇_-δ dengan x = 0, 0.02 dan 0.05 telah diukur daripada 80 K hingga sekitar 220 K dan frekuensi 10 MHz. NdBa₂Cu₃O₇ menunjukkan suhu genting mula, T_c-mula 93 K dan sampel x = 0.02 menunjukkan T_c-mula 58 K, manakala sampel x = 0.05 tidak menunjukkan sifat superkonduktor. Halaju bunyi bujur dan ricih meningkat secara monotonik apabila suhu diturunkan hingga ke 80 K. Suhu Debye, θ_D menurun apabila Fe didopkan ke dalam NdBa₂Cu₃O₇. θ_D adalah 370 K bagi NdBa₂Cu₃O₇ dan 314 K dan 265 K masing-masing bagi x = 0.02 dan 0.05. Ini menunjukkan pelembutan kekisi berlaku apabila sifat mensuperkonduksi bahan berkurangan. Pemalar gandingan elektron-fonon bagi superkonduktor NdBa₂Cu₃O₇ mengikut teori BCS tiga dimensi dalam had gandingan lemah ialah λ_BCS = 0.67, manakala dalam senario van Hove dua dimensi, λ_vH2 = 0.023. Bagi sampel x = 0.02, λ_BCS = 0.55 dan λ_vH2 = 0.020. Nilai λ_vH2 ini adalah selaras dengan nilai yang diukur dan dilaporkan dalam superkonduktor oleh penyelidik lain. Kajian ini menunjukkan bahawa gandingan elektron-fonon serta ketumpatan keadaan yang tidak terhingga pada aras Fermi seperti yang dicadangkan oleh model van Hove dua dimensi dapat menerangkan mekanisme superkonduktor suhu tinggi dalam NdBa₂Cu₃O₇.

Kata kunci: Halaju bujur; halaju ricih; senario van Hove; suhu Debye

 

Abstract

The ultrasonic method is very sensitive in determining the role of phonons in the mechanism of superconductivity. In this research, the longitudinal velocity, v_L and shear velocity, v_s for NdBa₂Cu₃_-xFe_xO₇_-δ superconductors with x = 0, 0.02 and 0.05 have been measured between 80 K and around 220 K at a frequency of 10 MHz. NdBa₂Cu₃O₇ exhibited an onset transition temperature, T_c-onset of 93 K and the x = 0.02 sample showed T_c-onset of 58 K while the x = 0.05 showed no transition temperature. The longitudinal and shear velocities increased monotonically with decreasing temperature down to 80 K. The Debye temperature, θ_D, decreased with Fe doping. For NdBa₂Cu₃O₇, θ_D is 370 K, while for the Fe-doped samples it is reduced to 314 K (x = 0.02) and 265 K (x = 0.05), respectively. This decrease showed lattice softening when the superconducting property was suppressed. The electron-phonon coupling constant of NdBa₂Cu₃O₇ according the weak coupling limit of the BCS theory is λ_BCS = 0.67, while in the two-dimensional van Hove scenario, λ_vH2 = 0.023. For the x = 0.02 sample, λ_BCS = 0.55 and λ_vH2 = 0.020. These λ_vH2 values are consistent with the measured values reported in superconducting cuprates reported by other researchers. This work showed that the electron-phonon coupling together with the infinite density of states at the Fermi level as suggested in the two-dimensional van Hove scenario can be used to explain high temperature superconductivity in the NdBa₂Cu₃O₇ superconductor.

Keywords: Debye temperature; longitudinal velocity; shear velocity; van Hove scenario

 

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*Corresponding author; email: ras@ukm.edu.my