Microscopic study of the impurity effect in the kagome superconductor $\mathrm{La}{({\mathrm{Ru}}_{1\ensuremath{-}x}{\mathrm{Fe}}_{x})}_{3}{\mathrm{Si}}_{2}$

Microscopic study of the impurity effect in the kagome superconductor $La {({Ru}_{1 - x} {Fe}_{x})}_{3} {Si}_{2}$

C. Mielke, III, D. Das, J. Spring, H. Nakamura, S. Shin, H. Liu, V. Sazgari, S. Jöhr, J. Lyu, J. N. Graham, T. Shiroka, M. Medarde, M. Z. Hasan, S. Nakatsuji, R. Khasanov, D. J. Gawryluk, H. Luetkens, and Z. Guguchia

Phys. Rev. B 109, 134501 – Published 1 April 2024

Abstract

We report on the effect of magnetic impurities on the microscopic superconducting (SC) properties of the kagome-lattice superconductor $La {({Ru}_{1 - x} {Fe}_{x})}_{3} {Si}_{2}$ using muon spin relaxation/rotation. A strong suppression of the superconducting critical temperature $T_{c}$ , the SC volume fraction, and the superfluid density was observed. We further find a correlation between the superfluid density and $T_{c}$ which is considered a hallmark feature of unconventional superconductivity. Most remarkably, measurements of the temperature-dependent magnetic penetration depth $λ$ reveal a change in the low-temperature behavior from exponential saturation to a linear increase, which indicates that Fe doping introduces nodes in the superconducting gap structure at concentrations as low as $x = 0.015$ . Our results point to a rare example of unconventional superconductivity in the correlated kagome lattice and accessible tunability of the superconducting gap structure, offering new insights into the microscopic mechanisms involved in superconducting order.

Received 17 September 2023
Revised 26 November 2023
Accepted 4 March 2024

DOI:https://doi.org/10.1103/PhysRevB.109.134501

Physics Subject Headings (PhySH)

Superconductivity

Kagome lattice Unconventional superconductors

Muon spin relaxation & rotation

Condensed Matter, Materials & Applied PhysicsAccelerators & Beams

Authors & Affiliations

C. Mielke, III ^1,2,*, D. Das¹, J. Spring ², H. Nakamura³, S. Shin ⁴, H. Liu ², V. Sazgari ¹, S. Jöhr², J. Lyu⁴, J. N. Graham¹, T. Shiroka¹, M. Medarde⁴, M. Z. Hasan^5,6,7,8, S. Nakatsuji^9,3,10,11,12, R. Khasanov¹, D. J. Gawryluk⁴, H. Luetkens¹, and Z. Guguchia^1,†

¹Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland
²Physik-Institut, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
³Institute for Solid State Physics (ISSP), University of Tokyo, Kashiwa, Chiba 277-8581, Japan
⁴Laboratory for Multiscale Materials Experiments, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland
⁵Laboratory for Topological Quantum Matter and Advanced Spectroscopy (B7), Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
⁶Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08540, USA
⁷Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
⁸Quantum Science Center, Oak Ridge, Tennessee 37831, USA
⁹Department of Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan
¹⁰Trans-scale Quantum Science Institute, University of Tokyo, Bunkyo-ku, Tokyo 113-8654, Japan
¹¹Institute for Quantum Matter and Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
¹²Canadian Institute for Advanced Research, Toronto, Ontario M5G 1Z7, Canada

^*charles-hillis.mielke-iii@psi.ch
^†zurab.guguchia@psi.ch

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Vol. 109, Iss. 13 — 1 April 2024

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Figure 1
(a) Magnetic susceptibility vs temperature scans for an applied field of 5 mT highlighting the suppression of superconductivity with increasing Fe concentration. ZFC and FC conditions are denoted by closed and open symbols, respectively. The onset of the superconducting transition, defined as the intersection between the line tangent at the midpoint of the superconducting transition and the slope of the magnetization in the normal state, has been indicated by an arrow. (b) Sample specific heat divided by the temperature vs temperature, showing clear peaks for undoped, $x = 0.015$ , and $x = 0.01$ samples and a noticeable anomaly for the $x = 0.02$ sample, which is however embedded in a large increase in $C_{p} / T$ with decreasing temperature. Fits have been overlaid as solid black lines. (c) Extracted $Δ C_{p}$ jump vs $T_{c}$ from heat capacity measurements for each dopant concentration. Data from the current study are represented by the orange diamonds. Red triangles represent the characteristic scaling relation found for Fe-based superconductors [30]. It has been fitted with a linear relation on a logarithmic plot, giving a $T^{4.2}$ relation, notably steeper than the BNC $T^{3}$ relation. Data have been reproduced from [30].
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Figure 2
(a) ZF- $μ SR$ spectra, recorded for undoped and $x = 0.03$ Fe-doped samples, at 300 K and 10 K. The black line indicates the fit to the data using Eq. (2) [32, 33]. (b) Temperature dependence of the exponential relaxation rate in the undoped, $x = 0.03$ , and $x = 0.05$ Fe-doped samples. The Gaussian Kubo-Toyabe was fitted with a global $Δ_{GKT}$ parameter for each dopant concentration, which all refined to similar values (0.04–0.05 $µ s^{- 1}$ ). (c) Characteristic $μ SR$ time spectra for the $x = 0.01$ Fe-doped sample under 20 mT applied field in the normal state (at 10 K; red points) and in the superconducting state (at 0.15 K; blue points). Fits are shown as solid lines. The Fourier transformations showing field distribution can be found in the Supplemental Material [34].
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Figure 3
(a) The temperature dependence of the superconducting muon-spin depolarization rate $σ_{SC}$ (left axis) and the superfluid density (i.e., $\frac{1}{λ^{2}}$ ) (right axis) for all doped samples including the undoped polycrystalline sample, taken from [21]. The solid (dashed) lines correspond to fits using a model with nodeless (nodal) gap superconductivity. (b) Temperature dependence of $σ_{SC}$ for the $x = 0.02$ Fe-doped sample under various applied hydrostatic pressures. The arrow indicates $T_{c}$ , which remains unchanged under pressure.
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Figure 4
(a) The doping evolution of the superconducting muon-spin depolarization rate $σ_{SC}$ , normalized superconducting $T_{c}$ , and superconducting volume fraction $V_{SC}$ , extracted from the $μ SR$ results. The light green–to–red shaded region indicates the crossover around $x = 0.015$ from nodeless superconducting gap structure (light green) to a nodal structure (red). (b) The $T_{c}$ vs superfluid density ratio has been plotted for the different dopant concentrations of $La {({Ru}_{1 - x} {Fe}_{x})}_{3} {Si}_{2}$ compared with other known conventional and unconventional superconductors [18, 43, 44, 45, 46, 47]. While all dopant concentrations lie far from the elemental conventional superconductors, they fall almost entirely along the same line as several example transition metal dichalcogenides [46, 47] and other kagome superconductors [18]. Only the 3% Fe-doped sample falls a bit away from this line, and falls instead on the same line as the electron-doped cuprates, similarly to ${RbV}_{3} {Sb}_{5}$ and ${KV}_{3} {Sb}_{5}$ under ambient pressure.
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Physical Review B

covering condensed matter and materials physics

Microscopic study of the impurity effect in the kagome superconductor $La {({Ru}_{1 - x} {Fe}_{x})}_{3} {Si}_{2}$

C. Mielke, III, D. Das, J. Spring, H. Nakamura, S. Shin, H. Liu, V. Sazgari, S. Jöhr, J. Lyu, J. N. Graham, T. Shiroka, M. Medarde, M. Z. Hasan, S. Nakatsuji, R. Khasanov, D. J. Gawryluk, H. Luetkens, and Z. Guguchia

Phys. Rev. B 109, 134501 – Published 1 April 2024

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Physical Review B

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Microscopic study of the impurity effect in the kagome superconductor La(Ru1−xFex)3Si2

C. Mielke, III, D. Das, J. Spring, H. Nakamura, S. Shin, H. Liu, V. Sazgari, S. Jöhr, J. Lyu, J. N. Graham, T. Shiroka, M. Medarde, M. Z. Hasan, S. Nakatsuji, R. Khasanov, D. J. Gawryluk, H. Luetkens, and Z. Guguchia

Phys. Rev. B 109, 134501 – Published 1 April 2024

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Microscopic study of the impurity effect in the kagome superconductor $La {({Ru}_{1 - x} {Fe}_{x})}_{3} {Si}_{2}$