Nodeless superconductivity in the noncentrosymmetric Mo{}_{3}Rh{}_{2}N superconductor: a SR study

Nodeless superconductivity in the noncentrosymmetric MoRhN superconductor: a SR study

T. Shang tian.shang@psi.ch Laboratory for Multiscale Materials Experiments, Paul Scherrer Institut, Villigen CH-5232, Switzerland Swiss Light Source, Paul Scherrer Institut, Villigen CH-5232, Switzerland Institute of Condensed Matter Physics, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne CH-1015, Switzerland.    Wensen Wei Anhui Province Key Laboratory of Condensed Matter Physics at Extreme Conditions, High Magnetic Field Laboratory of the Chinese Academy of Sciences, Hefei 230026, People’s Republic of China    C. Baines Laboratory for Muon-Spin Spectroscopy, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland    J. L. Zhang Anhui Province Key Laboratory of Condensed Matter Physics at Extreme Conditions, High Magnetic Field Laboratory of the Chinese Academy of Sciences, Hefei 230026, People’s Republic of China    H. F. Du Anhui Province Key Laboratory of Condensed Matter Physics at Extreme Conditions, High Magnetic Field Laboratory of the Chinese Academy of Sciences, Hefei 230026, People’s Republic of China    M. Medarde Laboratory for Multiscale Materials Experiments, Paul Scherrer Institut, Villigen CH-5232, Switzerland    M. Shi Swiss Light Source, Paul Scherrer Institut, Villigen CH-5232, Switzerland    J. Mesot Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland Institute of Condensed Matter Physics, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne CH-1015, Switzerland. Laboratorium für Festkörperphysik, ETH Zürich, CH-8093 Zurich, Switzerland    T. Shiroka Laboratorium für Festkörperphysik, ETH Zürich, CH-8093 Zurich, Switzerland Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland
Abstract

The noncentrosymmetric superconductor MoRhN, with  K, adopts a -Mn-type structure (space group 432), similar to that of MoAlC. Its bulk superconductivity was characterized by magnetization and heat-capacity measurements, while its microscopic electronic properties were investigated by means of muon-spin rotation and relaxation (SR). The low-temperature superfluid density, measured via transverse-field (TF)-SR, evidences a fully-gapped superconducting state with , very close to 1.76  – the BCS gap value for the weak coupling case, and a magnetic penetration depth  nm. The absence of spontaneous magnetic fields below the onset of superconductivity, as determined by zero-field (ZF)-SR measurements, hints at a preserved time-reversal symmetry in the superconducting state. Both TF-and ZF-SR results evidence a spin-singlet pairing in MoRhN.

preprint: Preprint: July 19, 2019, 18:26.

Introduction. The current research interest in superconductivity (SC) involves either studies of high temperature superconductors (such as cuprates or iron pnictides), or investigations of unconventional superconducting states. Superconductors with centrosymmetric crystal structures are bound to have either pure spin-singlet or spin-triplet pairings.Anderson (1984) On the other hand, due to the relaxed space-symmetry requirement, noncentrosymmetric superconductors (NCSCs) may exhibit unconventional pairing.Bauer and Sigrist (2012); Smidman et al. (2017) A lack of inversion symmetry leads to internal electric-field gradients and, hence, to antisymmetric spin-orbit coupling (ASOC), which lifts the spin degeneracy of the conduction-band electrons. As a consequence, the superconducting order can exhibit a mixture of spin-singlet and spin-triplet pairing.Bauer and Sigrist (2012); Smidman et al. (2017); Gor’kov and Rashba (2001)

Of the many NCSCs known to date, however, only a few exhibit a mixed singlet-triplet pairing. LiPtB and LiPdB are two notable examples, where the mixture of singlet and triplet states can be tuned by modifying the ASOC through a Pd-for-Pt substitution.Yuan et al. (2006); Nishiyama et al. (2007) LiPdB behaves as a fully gapped -wave superconductor, whereas the enhanced ASOC turns LiPtB into a nodal superconductor, with typical features of spin-triplet pairing. Other NCSCs may exhibit unconventional properties besides mixed pairing. For instance, CePtSi,Bonalde et al. (2005) CeIrSi,Mukuda et al. (2008) and KCrAs,Pang et al. (2015); Adroja et al. (2015) exhibit line nodes in the gap, while others such as LaNiCChen et al. (2013) and (La,Y)C,Kuroiwa et al. (2008) show multiple nodeless superconducting gaps. In addition, due to the strong influence of ASOC, their upper critical fields can exceed the Pauli limit, as has been found in CePtSiBauer et al. (2004) and (Ta,Nb)RhB.Carnicom et al. (2018)

MoAlC forms a -Mn-type crystal structure with space group 432. Muon-spin rotation/relaxation (SR), nuclear magnetic resonance (NMR), and specific heat studies have revealed that MoAlC is a fully-gapped, strongly-coupled superconductor, which preserves time-reversal symmetry (TRS) in its superconducting state.Bauer et al. (2010, 2014) The recently synthesized MoRhN NCSC, a sister compound to MoAlC, has been studied via transport and specific-heat measurements.Wei et al. (2016) Yet, to date the microscopic nature of its SC state remains largely unexplored. DFT calculations suggest a strong hybridization between the Mo and Rh 4-orbitals, reflecting the extended nature of the latter.Li et al. (2016) The density of states (DOS) at the Fermi level , arising from the Rh and Mo 4-orbitals, are comparable. This is in strong contrast with the MoAlC case, where the DOS at is mostly dominated by Mo 4-orbitals.Bauer et al. (2010); Karki et al. (2010) In the MoRhN case, the SOC is significantly enhanced by the replacement of a light element, such as Al, with one with a strong SOC, such as Rh. Considering that already MoAlC exhibits unusual properties,Bauer et al. (2010, 2014) we expect the enhanced SOC to affect the superconducting properties of MoRhN, too. In Re (= transition metal) alloys,Singh et al. (2014, 2017); Shang et al. (2018); Barker et al. (2018) whose DOS is dominated by the Re 5-orbitals (with negligible contributions from the metal orbitals), even a robust increase in SOC — from 3 Ti to 5 Ta — is shown to not significantly affect the superconducting properties. Conversely, similarly to the Li(Pd,Pt)B case, SOC effects are expected to be more important in MoRhN. Therefore, a comparative microscopic study of MoRhN vs. MoAlC is very instructive for understanding the (A)SOC effects on the superconducting properties of NCSCs. Another goal of this study was the search for a possible TRS breaking in the superconducting state of MoRhN.

In this paper, we report on the systematic magnetization, thermodynamic, and SR investigation of the recently discovered MoRhN NCSC. In particular, zero- (ZF) and transverse-field (TF) SR measurements allowed us to study the microscopic superconducting properties and to search for a possible TRS breaking below in MoRhN.

Experimental details. Polycrystalline MoRhN samples were synthesized by solid-state reaction and reductive nitridation methods, whose details are reported elsewhere.Wei et al. (2016) The room-temperature x-ray powder diffraction confirmed the -Mn-type crystal structure, with no detectable extra phases.Wei et al. (2016) The magnetization and heat capacity measurements were performed on a 7-T Quantum Design Magnetic Property Measurement System (MPMS) and a 9-T Physical Property Measurement System (PPMS). The bulk SR measurements were carried out using the general-purpose surface-muon (GPS) and the low-temperature facility (LTF) instruments of the M3 beamline at the Swiss muon source of Paul Scherrer Institut, Villigen, Switzerland. For measurements on LTF, the samples were mounted on a silver plate using diluted GE varnish. The SR data were analyzed by means of the musrfit software package.A. Suter and Wojek (2012)

(a) The Mo
Temperature dependence of (a) the muon-spin relaxation rate
 Superfluid density vs. temperature, as determined from TF-
 Coinciding
ZF-
Temperature 1.5 K 8 K
0.24814(83) 0.24833(73)
(s) 0.0366(69) 0.0379(58)
(s) 0.0069(32) 0.0047(28)
0.01985(83) 0.01987(73)

This lack of evidence for an additional SR relaxation below , implies that TRS is preserved in the superconducting state of MoRhN. Since TRS is preserved also in the MoAlC sister compound, this explains the many common features shared by these two -Mn-type NCSCs.Bauer et al. (2014)

Discussion. Since the admixture of spin-singlet and spin-triplet pairing depends on the strength of ASOC,Gor’kov and Rashba (2001) the latter plays an important role in determining the superconducting properties of NCSCs. An enhanced ASOC can turn a fully gapped -wave superconductor into a nodal superconductor, with typical features of spin-triplet pairing, as exemplified by the Li(Pd,Pt)B case. However, a larger SOC is not necessarily the only requirement for a larger ASOC and an enhanced band splitting , since the latter two depend also on the specific crystal- and electronic structures. All 4-Rh, -Ru and 5-Ir are heavy SOC metals, but their ASOC-related band splittings are relatively small in some materials. For example, the expected values for Ce(Rh,Ir)Si, LaRhSi, RhGa, and RuB are less than 20 meV (i.e., ten times smaller than in CePtSi or LiPtB). Smidman et al. (2017) Therefore, their pairing states remain in the spin-singlet channel and all of them behave as fully-gapped superconductors. In -Mn-type materials, like MoRhN, the replacement of a light metal such as Al by the heavy Rh does indeed increase the SOC, yet the still remains weak. Hence, the superconducting pairing is of spin-singlet type, in good agreement with both TF- and ZF-SR results. Further band structure calculations, which explicitly take into account the SOC effects, are needed to clarify this behavior.

Summary. We perfomed comparative SR experiments to study the superconducting properties of NCSC MoRhN. Bulk superconductivity with  K was characterized by magnetization and heat capacity measurements. The temperature variation of the superfluid density reveals nodeless superconductivity in MoRhN, which is well described by an isotropic -wave model and is consistent with a spin-singlet pairing. The lack of spontaneous magnetic fields below indicates that time-reversal symmetry is preserved in the superconducting state of MoRhN.

This work was supported by the Schweizerische Nationalfonds zur Förderung der Wissenschaftlichen Forschung, SNF (Grants 200021-169455 and 206021-139082) and the National Natural Science Foundation of China (Grant No. 11504378).

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Table 1.: Fit parameters extracted from ZF-SR data for MoRhN (collected above and below ) by using the Eq. (5) model.
Figure 5. : Coinciding ZF-SR spectra in the superconducting (1.5 K) and the normal state (8 K) show that in MoRhN the TRS is preserved. Both spectra show only a weak muon-spin depolarization, but no visible differences. The solid line is a fit to the 1.5-K spectra by means of Eq. (5), as described in the text.
Figure 5. : Coinciding ZF-SR spectra in the superconducting (1.5 K) and the normal state (8 K) show that in MoRhN the TRS is preserved. Both spectra show only a weak muon-spin depolarization, but no visible differences. The solid line is a fit to the 1.5-K spectra by means of Eq. (5), as described in the text.
Figure 4. : Superfluid density vs. temperature, as determined from TF-SR measurements. The different lines represent fits to various models, including -, -, and -wave pairing (see text for details).
Figure 4. : Superfluid density vs. temperature, as determined from TF-SR measurements. The different lines represent fits to various models, including -, -, and -wave pairing (see text for details).
Figure 3. : Temperature dependence of (a) the muon-spin relaxation rate and (b) diamagnetic field shift for MoRhN measured in an applied field of 30 mT. Here , where is the same as the applied magnetic field.
Figure 3. : Temperature dependence of (a) the muon-spin relaxation rate and (b) diamagnetic field shift for MoRhN measured in an applied field of 30 mT. Here , where is the same as the applied magnetic field.
Figure 2. : (a) The MoRhN TF-SR time spectra, collected at 0.02 K and 6.4 K in an applied field of 30 mT, show very different relaxation rates. Fourier transforms of the above time spectra at 6.4 K (b) and 0.02 K (c). The solid lines are fits to Eq. (1) using a single Gaussian relaxation; the dashed lines indicate the applied magnetic field. Note the clear diamagnetic shift below in (c).
Figure 2. : (a) The MoRhN TF-SR time spectra, collected at 0.02 K and 6.4 K in an applied field of 30 mT, show very different relaxation rates. Fourier transforms of the above time spectra at 6.4 K (b) and 0.02 K (c). The solid lines are fits to Eq. (1) using a single Gaussian relaxation; the dashed lines indicate the applied magnetic field. Note the clear diamagnetic shift below in (c).
Figure 1. : (a) Temperature dependence of magnetic susceptibility and (b) of specific heat for MoRhN. The inset in (a) shows the estimated vs. temperature up to , the solid-line being a fit to . For each temperature, was determined from the value where deviates from linearity. The inset in (b) shows , as determined from heat-capacity measurements in various applied fields, with the solid-line being a fit to the WHH model without spin-orbit scattering.
Figure 1. : (a) Temperature dependence of magnetic susceptibility and (b) of specific heat for MoRhN. The inset in (a) shows the estimated vs. temperature up to , the solid-line being a fit to . For each temperature, was determined from the value where deviates from linearity. The inset in (b) shows , as determined from heat-capacity measurements in various applied fields, with the solid-line being a fit to the WHH model without spin-orbit scattering.
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