Superconductivity in a new layered triangular-lattice system Li2IrSi2

We report on the crystal structure and superconducting properties of a novel iridium-silicide, namely Li2IrSi2. It has a Ag2NiO2-type structure (space group R-3m) with the lattice parameters a = 4.028 30(6) Å and c = 13.161 80(15) Å. The crystal structure comprises IrSi2 and double Li layers stacked alternately along the c-axis. The IrSi2 layer includes a two-dimensional Ir equilateral-triangular lattice. Electrical resistivity and static magnetic measurements revealed that Li2IrSi2 is a type-II superconductor with critical temperature (Tc) of 3.3 K. We estimated the following superconducting parameters: lower critical field Hc1(0) ∼ 42 Oe, upper critical field Hc2(0) ∼ 1.7 kOe, penetration depth λ0 ∼ 265 nm, coherence length ξ0 ∼ 44 nm, and Ginzburg–Landau parameter κGL ∼ 6.02. The specific-heat data suggested that superconductivity in Li2IrSi2 could be attributed to weak-coupling Cooper pairs.


Introduction
Owing to their unique physical properties, including charge and spin ordering, colossal magnetoresistance, and high-T c superconductivity, 3d transition-metal compounds have attracted considerable attention. These physical properties emerge from the interplay between spin, charge, and orbital degrees of freedom. On the contrary, 5d transition-metal compounds are expected to exhibit exotic phenomena, because their spin-orbit coupling (SOC) is significantly stronger than that of 3d transition-metal compounds. The non-centrosymmetric superconductivity discovered in CePt 3 Si [1] and UIr [2] is a typical example of effective physical property enhancement by SOC, wherein Cooper pairs develop a spontaneous magnetic moment below the superconducting transition temperature (T c ), breaking the time-reversal symmetry. The superconducting wave function is described as a mixed-parity state of spin-singlet and triplet Cooper pairs. Another typical case is the spin-orbit Mott state in Sr 2 IrO 4 proposed by Kim et al, wherein an effective total angular moment j eff =1/2 Kramers doublet state is produced by an on-site Coulomb repulsion U associated with strong SOC in a 5d electron system [3]. Watanabe et al theoretically predicted that the electron-doped SO Mott state would exhibit d-wave superconductivity due to the pseudospin of the j eff =1/2 Kramers doublet [4]. In recent angle-resolved photoemission spectroscopy experiments, d-wave symmetry in the superconducting gap order parameter was observed in electron-doped Sr 2 IrO 4 [5]. Therefore, 5d electron systems, particularly in Ir compounds, involve rich physics, which are interesting research subjects for the exploration of novel exotic superconductivity.
Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. electron-phonon coupling [25]. In general, Si often reacts with 4d-or 5d-elements (M) to form a variety of silicide intermetallics because the energy levels of the Si 3p and M 4d or 5d orbitals are close together, resulting in orbital hybridization and unfilled metallic bands near E F . Orbital hybridization generates M-Si covalent bonding network in the structure. In Sc 5 Ir 4 Si 10 , a Co 4 Sc 5 Si 10 -type structure, the three-dimensional network comprised an Ir-Si cyclic octagonal lattice. A two-dimensional (2D) network is formed by Ir-Si tetrahedral linkage in LaIr 2 Si 2 , a ThCr 2 Si 2 -type structure. A metallic state with a large DOS at E F is expected in iridium silicides. This would be advantageous for the development of new superconductors because large electron densities can lead to Cooper pairing coherency. In fact, several Ir-Si superconductors, such as Sc 5 Ir 4 Si 10 (T c ∼8.5 K), Lu 2 Ir 3 Si 5 (T c ∼5.6 K), CaIrSi 3 (T c ∼3.6 K), and HfIrSi (T c ∼3.5 K), have been reported [26][27][28][29]. These superconductors comprised primarily of rare-earth or alkali-earth compounds. To the best of our knowledge, Li 2 IrSi 3 (T c =∼3.8 K) is the only alkali-metal compound reported till date. Therefore, the alkali-metal Ir-Si ternary system is an unexplored subject in new materials research, which motivated us to perform this study.
After numerous attempts to synthesize new alkali-metal iridium silicides, we recently produced a new superconductor, Li 2 IrSi 2 , using a high-pressure synthesis technique. Li 2 IrSi 2 has a layered structure composed of planar equilateral triangular Ir lattices and it exhibits a superconducting transition at ∼3.3 K. Therefore, Li 2 IrSi 2 is a rare superconductor with a 2D Ir triangular lattice. Its crystal structure, a triangular Ir lattice, is similar to that of IrTe 2 . However, in contrast to Ir 1−x Pt x Te 2 (T c =∼3.1 K), superconductivity in Li 2 IrSi 2 occurs at low temperatures without breaking chemical bonds [10]. Herein, we report the crystal structure and superconducting properties of Li 2 IrSi 2 and present its superconducting parameters estimated from experimental critical field measurements. We also comment briefly on another new superconductor, Li 2 RhSi 2 , which is isostructural to Li 2 IrSi 2 . Furthermore, we discuss the relation between the SOC and superconductivity in this material.

Experimental procedures
Polycrystalline samples of Li 2 IrSi 2 were prepared using a solid-state reaction with a high-pressure synthesis technique. Commercial chemicals, Ir (4N) and Si (4N) powders, and handmade precursor (Li 12 Si 7 ) were used as starting materials. The precursor Li 12 Si 7 was prepared from a stoichiometric mixture of Li lumps and Si powder in a solid-sate reaction at 800°C for 30 min, which was post-annealed at 450°C for 16 h in an evacuated quartz tube. The starting materials were mixed in an agate mortar at a molar ratio of Li:Ir:Si=2:1:2 and then pressed into a disk shape with a diameter and thickness of 6.9 and ∼3.5 mm, respectively. The chemicals in these procedures were handled in a glove box filled with dry argon gas. The pellets were put in a high-pressure cell with a pressure medium of hexagonal boron nitride (h-BN) powder. Then, they were reacted at 1250°C for 15 min under 3 GPa using a flat-belt-type high-pressure apparatus installed at the National Institute for Materials Science (NIMS) in Japan, followed by quenching to room temperature before pressure release [30].
Powder x-ray diffraction (XRD) data were collected at room temperature using a conventional diffractometer (Rigaku; RINT-TTR III) with Bragg-Brentano geometry and a Cu-K α radiation source. The collected Bragg peak positions were analyzed using the TREOR97 indexing program [31]. Synchrotron powder XRD experiments were conducted using a diffractometer equipped with Debye-Scherrer geometry and curvedsurface imaging-plate detector installed at the SPring-8 BL12B2 beamline. The incident beam, with a wavelength (λ)=0.6857 Å, was focused in a 250 μm 2 size using a toroidal mirror. A capillary with a diameter of 0.5 mm was used for a powder-sample holder. The synchrotron XRD data were analyzed using the Rietveld method with the software RIETAN2000 [32].
Magnetic measurements were performed using a superconducting quantum interference device magnetometer (Quantum Design, MPMS-R2). The magnetic data were collected for a pulverized sample encapsulated by nonmagnetic material. Electrical resistivity was measured with the standard DC four-probe method using a commercial apparatus (Quantum Design, PPMS). The excitation current was set to either 1.0 or 5.0 mA. The data were collected at temperatures between 1.9 and 200 K under various magnetic fields up to 2 kOe. Specific heat was measured with the PPMS according to the time-relaxation method. The data were collected with a small bulk specimen at temperatures between 2 and 10 K under magnetic fields of 0 and 90 kOe.

Results and discussion
3.1. Crystal structure Figure 1(a) shows the powder XRD patterns. The top pattern (red) is that of Li 2 IrSi 2 sample. The middle (blue) pattern was a calculated based on the Li 2 IrSi 2 phase with the structural model shown in figure 2(a) (v.i.). The bottom (green) pattern is that of the known phase, Li 2 IrSi 3 [23,24]. The observed Li 2 IrSi 2 pattern (top) could be reproduced from the calculated pattern (middle), and they were undoubtedly different from that of Li 2 IrSi 3 . The  XRD pattern observed for the Li 2 IrSi 2 sample indicates a new phase, which is not in the PDXL (Rigaku) database. Majority of the Bragg reflections can be indexed to a trigonal unit cell with lattice parameters a and c as∼4.03 and c∼13.16 Å, respectively. The extinctions are -h+k+l=3n for hkl and l=3n for 00l reflections, where n is an integer. Therefore, the potential space groups are centrosymmetric R-3m (No. 166) and R-3 (148) and non-centrosymmetric R32 (155), R3m (160), and R3 (146). Li 2 IrSi 2 has rhombohedral symmetry. The sample also contains a small amount of a secondary phase, non-superconducting IrSi 3 .
Herein, we propose a crystal structure model for Li 2 IrSi 2 with the space group R-3m, which is the group with the highest symmetry of those mentioned above, as shown in figure 2(a). This is the Ag 2 NiO 2 -type structure. The structure model comprised closed-packed stacking of equilateral-triangle lattice planes of Ir, Si, and Li atoms with rhombohedral symmetry. The atomic layer sequence in a period along the c-axis is KIr Based on the structural model in figure 2(a), the atomic coordinates were refined by Rietveld analysis of the synchrotron XRD data. Figure 1(b) shows the synchrotron XRD pattern. A multiphase pattern-fitting method was used for the analysis of the primary (Li 2 IrSi 2 ) and secondary (IrSi 3 ) phases. The resultant reliability factors were R wp =3.72%, R P =2.46%, and S=R wp /R e =1.2559, which were satisfactorily low. The mass fraction of the secondary phase (IrSi 3 ) included in the sample was estimated to be ∼9.3%. We also performed Rietveld refinement of the Li site occupancy, and we could refine ∼10% of the Li vacancies in the structure. However, our refinement could not determine the thermal factor B (we fixed B=1) which is strongly correlated with the occupancy of atom and the reliability factor of this defect model was nearly identical to that of the non-defect model. The chemical formula thus needs to be confirmed with another method, such as energy dispersive x-ray spectroscopy. For this reason, we do not address Li vacancy quantitatively in this report. The refined structural parameters for Li 2 IrSi 2 are listed in table 1.
We tested the other space groups R-3, R32, R3m, and R3 to describe the Ag 2 NiO 2 -type structural model. These space groups have a lower symmetry than R-3m. Since the space groups R-3 and R32 give the same structural model as R-3m, these space groups can be excluded from the candidates. The non-centrosymmetric space groups R3m and R3 give a structural model similar to that of R-3m. They give additional structural parameters describing the asymmetry of the atomic position. However, it was found that these space groups did not effectively lower the reliability factors. Therefore, it is unlikely that the space groups R3m and R3 actually describe the structure. Furthermore, we tested other possible cases of the structural model, which were relates to Li defects in the structure because Li is a volatile and light element and is insensitive to detection by XRD measurements. If the structure contains heavy Li defects, the Li atomic layer may be a monolayer rather than a bilayer. In this case, the atomic layer sequence would be KIr, Si)-(Li)-(Si, Ir, Si)-(Li)-(Si, Ir, Si)-(Li)-(Si, IrK, therefore, the molecular formula is actually LiIrSi 2 . Figure 2(b) illustrates a structural model for the CuCrSe 2 -NaVS 2 -type structure (space group R3m), where Li has a prismatic (six-fold) coordination with adjacent Si atoms. We analyzed the XRD data with this structural model and found that it gave a rather similar XRD pattern to the observed one. However, it was less satisfactory for reliability factors than the Ag 2 NiO 2 -type structure. Therefore, it seemed unlikely that the CuCrSe 2 -NaVS 2 -type structural model fully described the actual structure. For LiIrSi 2 , another possible structural model was delafossite-type NaCrS 2 (R-3m), which had a different stacking manner for the IrSi 2 layer block than the CuCrSe 2 -NaVS 2 type. We confirmed that the XRD pattern calculated with this structural model was essentially different from the observed pattern. Therefore, delafossite-type NaCrS 2 apparently did not represent LiIrSi 2 .
Resultantly, we concluded that the structural model with the Ag 2 NiO 2 type (space group R-3m) in figure 2(a) was the most suitable for the crystal structure in Li 2 IrSi 2 . Li 2 IrSi 2 with quasi-2D layer structure, including Ir equilateral-triangular lattice planes. This structure strongly contrasted with the quasi-1D columnar structure of Li 2 IrSi 3 [23,24]. The Ir-Si bond lengths in Li 2 IrSi 2 (2.495 Å) and Li 2 IrSi 3 (2.463 Å) were nearly the same. The atomic compositions of the compounds were similar; however, their structures were essentially different.

Superconducting properties
Superconductivity in Li 2 IrSi 2 was observed in magnetic and electrical resistivity measurements. Figure 3(a) shows the temperature (T) dependence of the magnetic susceptibility (χ) taken under a magnetic field (H) of 10 Oe. Diamagnetic Meissner signals were observed below 3.6 K (∼T c onset ). The magnitude of the superconducting signal at 2 K was ∼47% of the full Meissner volume fraction (−1/4π) for the field-cooling (FC) condition and ∼131% for zero-field-cooling (ZFC). The signal was sufficiently large to indicate that superconductivity was a natural property of the bulk material. The value in excess of 100% suggested that the observed signal was affected by demagnetization and magnetic penetration under the magnetic field. Figure 3 (b) shows the T-dependence of the electrical resistivity (ρ) of Li 2 IrSi 2 . The T-dependence between 4 and 50 K in the normal state followed the T-square law, ρ=ρ 0 +AT 2 , suggesting Fermi-liquid behavior. The inset in figure 3 shows the low-temperature resistivity data. At ∼3.6 K, the resistivity started to drop due to the superconducting transition. The observed critical temperature, T c onset =3.6 K, was consistent with that of the magnetic susceptibility measurements. The bulk T c defined as the midpoint of resistive transition was 3.3 K. Figure 4 (a) shows initial magnetization (M-H) curves measured at various temperatures below T c onset (=3.6 K), which exhibited type-II superconductor behavior. The lower critical field H c1 (T) at each temperature was defined as the magnetic field at which the magnetization began to deviate from the straight line tangent to the curve at H=0 in figure 4(a). The H c1 values are plotted as a function of temperature in figure 4(c). Based on the Ginzburg-Landau (GL) theory, the H c1 (T) curve was numerically fitted using the following equation: where H c1 (0)=42 Oe. Figure 4(b) shows the T-dependence of the electrical resistivity below 5 K under various magnetic fields. The onset and midpoint T c values are plotted as a function of the magnetic field in figure 4(d).
H c2 (T) monotonically increased with decreasing temperature. The upper critical fields H c2 (0) determined from the linear extrapolation of the observed onset and midpoint T c data were estimated to be ∼2.6 and 1.28 kOe, respectively. To determine H c2 more precisely, we measured the specific-heat in this system. Figure 5 shows the specific-heat data for Li 2 IrSi 2 , specifically C p /T versus T 2 plots measured at H=0 and 90 kOe. At H=0, a specific-heat jump was observed around ∼3.5 K, indicating that the superconductivity is a bulk property. The phase-transition temperature is consistent with the T c values determined from the electrical resistivity and the magnetic susceptibility measurements. At H=90 kOe, the specific-heat jump disappeared completely. The normal-state specific heat (at H=90 kOe) can be given by where γ N is the Sommerfeld constant of the normal state, and β is the specific-heat coefficient of the lattice part. The Debye temperature can be written as Θ D =(12π 4 NR/5β) 1/3 , where N is the number of atoms in a formula unit and R is the gas constant. By numerically fitting the dataset in equation (2), the initial values, γ N0 and β 0 , were first determined. Since γ N0 and β 0 include the contribution from the secondary phase IrSi 3 , we corrected the values by subtracting the impurity contribution to estimate intrinsic γ N and β for Li 2 IrSi 2 . Herein, we used the parameters reported in [24] for IrSi 3   Assuming that the conventional phonon-mediated Cooper pairing mechanism is realized in Li 2 IrSi 2 , we evaluated the strength of the electron-phonon coupling. According to McMillan's theory [33], the electronphonon coupling constant λ ep is written as follows: where μ * is the Coulomb pseudo-potential parameter. By substituting the experimental Θ D value (∼373 K) and standard value of μ * =0.1 into equation (3), we estimated λ ep ∼0.5, which suggests that Li 2 IrSi 2 is a weakcoupling superconductor. The electronic DOS at the Fermi level N(E F ) can be given by as follows: For Li 2 IrSi 2 , by substituting the obtained γ N and λ ep values into equation (4), N(E F ) was estimated to be ∼1.2 states/eV/f.u. This value is close to the DOS value (N(E F )∼1.1 states/cell/f.u.) of the Ir-Si superconductor BaIrSi 2 (T c ∼6 K) [34].
We are curious how the SOC affects the superconducting properties. From this viewpoint, it is interesting to clarify the relation between the SOC and superconductivity by substituting Rh for Ir in Li 2 IrSi 2 . In general, Rh (4d element) provides more moderate SOC than Ir (5d element). Recently, we succeeded in synthesizing a new  rhodium silicide superconductor Li 2 RhSi 2 that is isostructural to Li 2 IrSi 2 . Its critical temperature T c onset is ∼3.0 K, which is a little lower than the T c onset (∼3.6 K) of Li 2 IrSi 2 . It is important to clarify whether or not the difference between the T c values is due to the difference in the SOC of Rh and Ir. Therefore, it is necessary to precisely evaluate the superconducting parameters and gap structure in Li 2 RhSi 2 , which is the focus of further studies that are now in progress.

Summary
We successfully discovered a new Ir-Si superconductor, Li 2 IrSi 2 , with T c =3.3 K. The crystal structure is a rhombohedral system with the lattice constants a and c of 4.028 30(6) and 13.161 80(15) Å, respectively. We have proposed a structural model with space group R-3m ( figure 2 (a)), which comprises edge-shared IrSi 2 layers interleaved with a Li bilayer. The IrSi 2 layer includes a quasi-2D Ir equilateral triangular lattice as an electron conduction plane. Superconductivity in Li 2 IrSi 2 is type-II and is a bulk property. The superconducting parameters are as follows: lower critical field H c1 (0)∼42 Oe, upper critical field H c2 (0)∼1.7 kOe, penetration depth λ 0 ∼265 nm, coherence length ξ 0 ∼44 nm, Ginzburg-Landau parameter κ GL ∼6.02, and electronphonon coupling constant λ ep ∼0.5. It seems that Li 2 IrSi 2 is a conventional weak-coupling superconductor. The influence of SOC on its superconductivity is still unclear.