Multigap superconductivity in ThAsFeN investigated using $\mathbf{\ensuremath{\mu}}\mathbf{SR}$ measurements

Multigap superconductivity in ThAsFeN investigated using $μ SR$ measurements

Devashibhai Adroja, Amitava Bhattacharyya, Pabitra Kumar Biswas, Michael Smidman, Adrian D. Hillier, Huican Mao, Huiqian Luo, Guang-Han Cao, Zhicheng Wang, and Cao Wang

Phys. Rev. B 96, 144502 – Published 3 October 2017

Abstract

We have investigated the superconducting ground state of the newly discovered superconductor ThFeAsN with a tetragonal layered crystal structure using resistivity, magnetization, heat capacity, and transverse-field muon-spin rotation ( $TF - μ SR$ ) measurements. Our magnetization and heat-capacity measurements reveal an onset of bulk superconductivity with $T_{c} \sim 30 K$ . A nonlinear magnetic-field dependence of the specific heat coefficient $γ (H)$ has been found in the low-temperature limit, which indicates that there is a nodal energy gap. Our analysis of the $TF - μ SR$ results shows that the temperature dependence of the superfluid density is better described by a two-gap model either isotropic $s + s$ wave or $s + d$ wave than a single-gap isotropic $s$ -wave model for the superconducting gap, consistent with other Fe-based superconductors. The combination of $γ (H)$ and $TF - μ SR$ results suggest that the ( $s + d$ )-wave model is the most consistent candidate for the gap structure of ThFeAsN. The observation of two gaps in ThFeAsN suggests a multiband nature of the superconductivity possibly arising from the $d$ bands of Fe ions. Furthermore, from our $TF - μ SR$ study we have estimated the magnetic penetration depth in the polycrystalline sample of $λ_{L} (0) = 375 nm$ , superconducting carrier density $n_{s} = 4.97 \times 10^{27} m^{- 3}$ , and carrier's effective-mass $m^{*} = 2.48 m_{e}$ . We compare the results of our present paper with those reported for the Fe-pnictide families of superconductors.

Received 9 June 2017
Revised 11 September 2017

DOI:https://doi.org/10.1103/PhysRevB.96.144502

Physics Subject Headings (PhySH)

Superconducting gap Superconducting order parameter Superconducting phase transition Superconductivity

Muon spin relaxation & rotation

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Devashibhai Adroja^1,2,*, Amitava Bhattacharyya^1,3,†, Pabitra Kumar Biswas¹, Michael Smidman⁴, Adrian D. Hillier¹, Huican Mao⁵, Huiqian Luo⁵, Guang-Han Cao⁶, Zhicheng Wang⁶, and Cao Wang⁷

¹ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot Oxon OX11 0QX, United Kingdom
²Highly Correlated Matter Research Group, Physics Department, University of Johannesburg, P.O. Box 524, Auckland Park 2006, South Africa
³Department of Physics, Ramakrishna Mission Vivekananda University, Howrah 711202, India
⁴Center for Correlated Matter and Department of Physics, Zhejiang University, Hangzhou 310058, China
⁵Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
⁶Department of Physics, State Key Laboratory of Silicon Materials, Zhejiang University, Hangzhou 310027, China
⁷Department of Physics, Shandong University of Technology, Zibo 255049, China

^*devashibhai.adroja@stfc.ac.uk
^†amitava.bhattacharyya@rkmvu.ac.in

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Vol. 96, Iss. 14 — 1 October 2017

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Figure 1
X-ray powder-diffraction pattern (at 300 K) with the Rietveld refinement fit of the data of ThFeAsN. The line drawn through the data points corresponds to the calculated pattern, and the cross symbols represent observed data. The vertical bars show the Bragg peaks' positions, and the blue line at the bottom shows the difference plot. The inset shows the tetragonal crystal structure [26].
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Figure 2
(a) Temperature dependence of electrical resistivity, (b) Low-field dc-magnetic susceptibility measured in zero-field cooled (ZFC) and FC modes in an applied field of 5 G. (c) The isothermal field dependence of magnetization at 5 K. (d) The isothermal field dependence of magnetization at low field at 2, 5, and 10 K. (e) Temperature dependence of the heat capacity divided by temperature in a zero field and in an applied field of 16 T, and the inset shows the difference of the heat-capacity data 0–16 T plotted as $C / T$ vs $T$ . The blue vertical arrow shows the jump in $C / T$ at $T_{c}$ . (f) The magnetic-field dependence of the electronic specific heat coefficient $Δ γ [= γ (H) - γ (0)]$ extrapolated to $T \sim 0$ and 7 K. The solid lines show a power-law fit $γ (H) \sim H^{n}$ .
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Figure 3
Transverse-field $μ SR$ asymmetry spectra for ThFeAsN collected (a) at $T = 1.5 K$ and (b) at $T = 32.5 K$ (i.e., below and above $T_{c}$ ) in an applied magnetic field of $H = 400 G$ . For the sake of clarity we present here the time-dependent asymmetry in the short-time region. The solid line shows a fit using Eq. (1).
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Figure 4
(a) Temperature dependence of the muon depolarization rate $σ_{s c} (T)$ of ThFeAsN collected in an applied magnetic field of 400 G in a FC mode. $σ_{s c} (T)$ of the FC mode (symbols) where the lines are the fits to the data using Eq. (2) for various gap models. The dotted magenta line shows the fit using an isotropic single-gap $s$ -wave model with $Δ (0) = 5.1 \pm 0.1$ meV, the dashed red line and blue solid line show the fit to a two-gap model, the $s + s$ wave and $s + d$ wave, respectively, with $Δ_{1} (0) = 5.2 \pm 0.1$ meV and $Δ_{2} (0) = 0.3 \pm 0.1$ meV (for both models). The green long-dashed line shows the fit using an anisotropic $s$ -wave model, and the solid purple line shows the fit using the $d$ -wave model. (b) Temperature dependence of the internal field.
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Figure 5
A schematic of the plot of Uemura et al. [55] of superconducting transition temperature $T_{c}$ against effective Fermi temperature $T_{F}$ . The big solid red square and small blue square (on top of the red square) show the points calculated using the ( $s + d$ )- and ( $s + s$ )-wave models, respectively, for ThFeAsN. The “exotic” superconductors fall within a common band for which $1 / 100 < T_{c} / T_{F} < 1 / 10$ , indicated by the region between two red color dashed lines in the figure. The solid black line corresponds to the Bose-Einstein condensation temperature ( $T_{B}$ ) [56].
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Physical Review B

covering condensed matter and materials physics

Multigap superconductivity in ThAsFeN investigated using $μ SR$ measurements

Devashibhai Adroja, Amitava Bhattacharyya, Pabitra Kumar Biswas, Michael Smidman, Adrian D. Hillier, Huican Mao, Huiqian Luo, Guang-Han Cao, Zhicheng Wang, and Cao Wang

Phys. Rev. B 96, 144502 – Published 3 October 2017

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Physical Review B

covering condensed matter and materials physics

Multigap superconductivity in ThAsFeN investigated using μSR measurements

Devashibhai Adroja, Amitava Bhattacharyya, Pabitra Kumar Biswas, Michael Smidman, Adrian D. Hillier, Huican Mao, Huiqian Luo, Guang-Han Cao, Zhicheng Wang, and Cao Wang

Phys. Rev. B 96, 144502 – Published 3 October 2017

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Multigap superconductivity in ThAsFeN investigated using $μ SR$ measurements