Non-centrosymmetric superconductor Th[Formula: see text]Be[Formula: see text]Pt[Formula: see text] and heavy-fermion U[Formula: see text]Be[Formula: see text]Pt[Formula: see text] cage compounds.

Unconventional superconductivity in non-centrosymmetric superconductors has attracted a considerable amount of attention. While several lanthanide-based materials have been reported previously, the number of actinide-based systems remains small. In this work, we present the discovery of a novel cubic complex non-centrosymmetric superconductor [Formula: see text] ([Formula: see text] space group). This intermetallic cage compound displays superconductivity below [Formula: see text] K, as evidenced by specific heat and resistivity data. [Formula: see text] is a type-II superconductor, which has an upper critical field [Formula: see text] T and a moderate Sommerfeld coefficient [Formula: see text] mJ [Formula: see text] [Formula: see text]. A non-zero density of states at the Fermi level is evident from metallic behavior in the normal state, as well as from electronic band structure calculations. The isostructural [Formula: see text] compound is a paramagnet with a moderately enhanced electronic mass, as indicated by the electronic specific heat coefficient [Formula: see text] mJ [Formula: see text] [Formula: see text] and Kadowaki-Woods ratio [Formula: see text] [Formula: see text] [Formula: see text] cm [Formula: see text] [Formula: see text] (mJ)[Formula: see text]. Both [Formula: see text] and [Formula: see text] are crystallographically complex, each hosting 212 atoms per unit cell.

Introduction

The absence of inversion symmetry in non-centrosymmetric superconductors (NCSCs) allows an electronic asymmetric spin–orbit coupling (ASOC) to exist. This, in turn, may cause normally forbidden mixing of the spin-singlet and spin-triplet components into a new superconducting pairing state[1,2]. Broken inversion symmetry also opens up a possibility for unusual effects in areas of superconducting magnetic response, electromagnetic effects, superconducting finite moment states, as well as unusual surface states[1,2]. Among NCSCs, previous studies have concentrated on heavy-fermion materials such as Si, [3-6], and [7-12], in which superconductivity coexists with antiferromagnetic order. However, in these materials it is impossible to disentangle the effects of non-centrosymmetricity from those of strong electron correlations. A possible solution to this issue is an in-depth investigation of weakly correlated NCSCs, such as B[13-16], [17-20], and [21-25].

Interestingly, even though the presence of Th has been suggested to enhance ASOC[28,29], only a handful of Th-based NCSCs are known. Crystallographically, it is possible to classify them into three groups according to the number of atoms per primitive unit cell, as shown in Fig. 1. The first group contains -based superconductors (structure type ), namely stoichiometric , and its substitutional derivates C for [30,31], LaThNiC[32,33], YThNiC[34]. The second group includes superconductors with the LaPtSi structure type, namely ThMSi ( Ir, Co, Ni, Pt)[28,29,35-38]. The third group contains ThC[39-41] (structure type PuC) and the partially Th-substituted La and Y analogues, as well as superconductors with the ThM (ThFe structure type ( Fe, Co, Ni, Ru, Rh, Os, and Ir)[42-46] and the derived Th(Co,Fe) pseudobinaries[47]. What all previously reported Th-based NCSCs have in common is their relative structural simplicity, as evidenced by the small number of atoms per primitive unit cell.

Figure 1

Crystallographic complexity and superconductivity in Th-based compounds. Left: The relation between the number of atoms per unit cell, i.e., structural complexity[26,27], and the superconducting temperature for the three previously reported classes of Th-based NCSCs and for the newly discovered NCSC (structure type ). Right: Coordination polyhedra around the Th/U and Pt atoms in Th/.

In this work, we present the discovery and characterization of a novel structurally complex NCSC ThBePt. This compound is isostructural to the previously reported family of intermetallic cage compounds BePt (R = Y, La–Nd, Sm–Lu), which host a wide range of physical properties[48,49]. The ThBePt compound displays type-II superconductivity below  K, as inferred from the specific heat and electrical resistivity data. The upper critical field T is comparable to that of other conventional superconductors. In the normal state, ThBePt displays metallic electrical resistivity and Sommerfeld coefficient  mJ mol K, which are in good agreement with non-zero density of states at the Fermi level, illustrated by band structure calculation. With 212 atoms per unit cell, the ThBePt compound is the most complex Th-based NCSC reported to date, see Fig. 1 for an overview. We also report synthesis and characterization of the isostructural UBePt and (LaTh)BePt phases. No ordering has been observed in the U compound down to  mK. The specific heat data yield the electronic specific heat coefficient  mJ mol , which classifies UBePt as a moderately heavy heavy-fermion compound. The effective mass enhancement in the UBePt compound is less than that, observed in unconventional superconductor UBe[50-52]—another heavy-fermion system containing Be and U. What both compounds have in common is a very strong coupling between minute changes in crystal chemistry and resultant physical properties[53].

Results

Materials synthesis and characterization.

The results of the single crystal X-ray diffraction analysis of UBePt and ThBePt are summarized in Tables SI and SII of the “Supplementary Information”. As reported earlier for the isostructural BePt compounds[48], they crystallize in the non-centrosymmetric space group and can be thought of as an arrangement of rod-like structures along the 3-fold [111] directions of the unit cell, consisting of interpenetrating coordination polyhedra centered on the Th and Pt1 atoms (see Fig. 1 (right)). The Th atoms are located at the center of a 20-atom polyhedra, consisting of Pt and Be (see Fig. 1 (right)). The Pt atoms have environment derived from Frank–Kasper polyhedrons and have coordination numbers of 14 (Pt1) and 13 (Pt2). With 212 atoms per unit cell, UBePt and ThBePt are classified as complex metallic alloys[27].

As is the case for BePt[49], both series of ThBePt and UBePt samples include minority secondary phases, see Figs.  S1–S4. The determined lattice parameters reveal clear differences between the samples, caused most probably by Be vacancies, like it was observed for Al in the UBeAl material[53]. The possible vacancies in the Be sublattice are evident from the enhanced displacement of the Be1 and Be2 positions (Table SIIS). The exact homogeneity ranges of ThBePt and UBePt are difficult to describe quantitatively, due to the analytical problems in establishing the exact Be content. In particular, the superconducting temperature of the ThBePt compound is strongly affected by the magnitude of the lattice parameter a. Although a varies by only ( Å  Å), changes over a range of (Fig. 2). For UBePt, the change in the lattice parameter a is also on the same order of magnitude ( Å  13.5033 Å).

Figure 2

Relationship between crystallinity and superconducting properties of ThBePt. The critical temperature versus the lattice parameter a for six ThBePt samples. The values of were taken from the equal entropy construction (red symbols) and as the minimum in the first derivative of the specific heat data (gray symbols). The variation of a is two orders of magnitude less, compared to the corresponding variation of .

Superconductivity in ThBePt

A first indication of bulk superconductivity in ThBePt is an anomaly, observed in the specific heat data (Fig. 3a–c and Fig. S6). A BCS-like transition occurs around  K, with its sharpness, height, and width varying slightly among the three samples. This variation can be attributed to the presence of impurity phases and an appreciable homogeneity range of ThBePt, as deduced from the powder X-ray diffraction data and energy dispersive micrographs, presented in Figs. S1 and S3, respectively. The two impurity phases, observed in ThBePt samples are BePt (superconductor,  K[54]) and ThPt (paramagnet[55]) in the amount of at. The physical properties of ThBePt can therefore be decoupled from those of the impurity phases.

Figure 3

Superconducting properties of ThBePt. (a)–(c) The electronic specific heat of three ThBePt samples, measured in . Note that a feature, associated with transition into superconducting state is observed around  K for all three samples. Vertical solid lines are equal entropy construction. The horizontal dashed line corresponds to the Sommerfeld coefficient . The red curve is a fit . (d)–(f) Temperature-dependent specific heat data, scaled by temperature, as a function of temperature squared for three ThBePt samples, measured in various magnetic fields.

Upon subtraction of the phononic contribution to the specific heat ( mJ mol K,  mJ mol K), the electronic specific heat data, shown in Fig. 3a–c, are fit with (red line). Since the sharpness of the transition is sample-dependent, the value of was taken from the derivative of the specific heat data, shown in Fig. S6. The value of is comparable to the BCS value of [56]. Using the McMillan formula, the magnitude of the Debye temperature  K yields a moderate value of the electron–phonon coupling (for )[57]. Upon application of magnetic field, the superconducting transition is gradually suppressed, as summarized in Fig. 3d–f. The corresponding values of are given in the phase diagram, shown Fig. 5a (circles). Based on the specific heat data, the behavior of ThBePt is similar to that of a conventional, type-II superconductor. However, given that SR (muon spin rotation, relaxation, and resonance) experiments can frequently reveal complex nature of NCSCs[58-61], a future, in-depth SR study of ThBePt, is likely to be very fruitful.

Figure 5

Evolution of superconducting properties in ThBePt as a function of a tuning parameter. (a) The H–T phase diagram of ThBePt. The dashed black line corresponds to the Ginzburg–Landau fit of the data, while the red line is a linear fit around needed for the WHH extrapolation. (b) The value of the superconducting critical temperature as a function of x in (LaTh)BePt.

The electrical resistivity of ThBePt, shown in Fig. 4a, classifies this material as a metal. At lower temperatures, a transition into superconducting state is observed around  K (Fig. 4b). A second, weaker transition, which occurs at  K, can be attributed to the BePt superconductor ( K[54]). Upon application of magnetic field, both transitions shift down in temperature, allowing to extract values for ThBePt in each respective magnetic field. The resultant values are summarized in Fig. 5a (squares). Given considerable overheating of the ThBePt samples, the error bars for the values of , extracted from the resistivity data are larger, than those for the values, extracted from the specific heat data. The magnetic susceptibility data, collected on all ThBePt samples (not shown), classify this compound as a paramagnet with temperature-independent magnetic susceptibility between  K and  K. Pauli paramagnetic susceptibility in ThBePt is consistent with metallic resistivity and non-zero density of states (DOS) at the Fermi level , as evidenced by band structure calculations (see below).

Figure 4

Electrical resistivity of ThBePt. (a) and (b)  mT data. High-temperature region indicates metallic behavior of ThBePt, while a drop around  K marks entrance into superconducting state. The additional transition around  K can be attributed to the secondary phase BePt.

Chemical substitution in Th-based NCSCs can sometimes lead to interesting results. For example, in unconventional NCSC ThCoNiC with –0.5, the superconducting transition temperature increases from 2.65 K at –12.1 K at [31]. A similar trend was also observed in (LaTh)NiC with –0.8, where varies from to 7.70 K, with the maximum observed at [32]. Given that we have previously reported superconductivity in LaBePt at  K[49], we have investigated the (LaTh)BePt pseudo-ternary in hopes of increasing the value of . As can be seen in Fig. 5b, the maximum value of  K is achieved for the sample. We have therefore been able to achieve a enhancement of nearly , compared to the (LaBePt) value or , compared to the (ThBePt) value. This indicates that future chemical substitution experiments among the isostructural rare-earth- and actinide-based BePt compounds are likely of interest, especially between superconducting and magnetic members of the series.

The values of in various fields for three ThBePt samples are summarized in the H–T phase diagram (Fig. 5). The fit to the Ginzburg–Landau relation yields  K and T. An extrapolation using the Werthamer–Helfand–Hohenberg approximation[62,63] also gives similar values  K and  T. The magnitude of is below the paramagnetic limit and is similar to that of other Th-based NCSCs–ThNiSi (0.058 or 0.126 T[28]), ThCoSi (4.5 T[29]), ThCoC ( T[30]), ThCo ( T[43]), and ThCoNiC (1–10 T[31]).

The spin un-polarized scalar relativistic calculations place the Fermi level near a local minimum of the DOS with  states eV f.u.. In contrast, at the same level of calculation the Fermi level was found near a local maximum in YBePt[48]. The spin polarized calculations at both scalar and fully-relativistic levels converged to zero spin magnetic moment solution—also for all individual atoms. The orbital moments, too, were zero in the fully relativistic calculation. The total, atom-, and atomic orbital-resolved DOS, computed at the fully relativistic level for ThBePt, are shown in Fig. 6. The value of is 19.92 states eV f.u., yielding  mJ mol  ), which is similar to , extracted from the specific heat data. Similarly to the case of YBePt, three energy regions can be recognized in the occupied part. The lower-energy region (below  eV) is dominated by Be 2s and Pt 6s contributions with Be 2p and Pt 5d states becoming also important above  eV. The middle-energy region (between and  eV) consists mainly of Pt 5d contributions. The upper-energy region, dominated by Be 2p states, contains contributions from Pt 5d and Th 6d as well as Th 5f, Pt 6s and Be 2s. The unoccupied part features two pseudo gaps at 0.40 and 1.04 eV, the latter originating from a band (Fig. S5) very similar to the one observed in YBePt[48]. The Th 5f states behave band-like with an occupancy of about 0.45 electrons, therefore, there is no need for a correlated system treatment. The splitting of the 6p semi-core energies due to the spin–orbit coupling is about 7.36 eV. The states are located between and  eV with a narrow band width of 0.03 eV, while the states have a wider spread of 0.29 eV (between and   eV). The weighted average of these values is  eV, which is very close to the energy of the 6p states in the scalar relativistic calculation,  eV.

Figure 6

Computed electronic density of states at the fully-relativistic level for ThBePt: total and atom-resolved density of states (left), as well as projected density of states showing the contributions of the most relevant orbitals (right).

Heavy-fermion behavior in UBePt

The physical properties of the isostructural UBePt compound were also investigated. The magnetic susceptibility data, shown in Fig. 7a indicate paramagnetic behavior for the temperature range between  K and  K. The zero-field-cooled (ZFC) (full symbols) and field-cooled (FC) (open symbols) data show a small bifurcation around  K. The origin of the ZFC/FC splitting is a small ferromagnetic impurity, present in elemental uranium. The linear fit to the inverse magnetic susceptibility data above  K (right axis, straight line) yields Weiss temperature  K and effective moment . The value of is smaller than that expected for U and U configurations ( and , respectively), suggesting possible delocalization of 5f orbitals and their hybridization with conduction electrons. The value of  emu mol is rather small compared to that of compounds, located close to a ferromagnetic quantum critical point—for example, UNiAl ( emu mol[64]) and UCoAl ( emu mol[65]). Instead, the value of M/H in UBePt is similar to that of UAu ( emu mol[66]).

Figure 7

(a) Zero-field-cooled and field-cooled magnetic susceptibility (left axis) and inverse magnetic susceptibility (right axis) data for UBePt in  T. The solid line is a Curie–Weiss fit to the inverse susceptibility. (b) Low-temperature specific heat data exhibit logarithmic divergence over more than a decade in temperature (red line). Inset: vs. with the solid line representing the fit from which the value of was extracted. (c) Temperature-dependent resistivity data for UBePt in . (d) The low-temperature region of the vs. plot.

While no ordering has been observed down to  mK, the low-temperature specific heat data show logarithmic divergence over a decade in temperature—see Fig. 7b. The specific heat data are fit to the function, yielding an enhanced value of the electronic specific heat coefficient  mJ mol K. The possibility of the electron mass enhancement arising from the small atomic percentage of U atoms can be eliminated by considering that while of isostructural ThBePt is only  mJ mol K, the corresponding value for UBePt is larger by more than one order of magnitude. Therefore, UBePt is classified as a moderately heavy heavy-fermion system.

The electrical resistivity of UBePt exhibits a drop around  K, marking the onset of Kondo scattering (Fig. 7c). The residual resistivity ratio (RRR) of 5.1 is similar to what is typically seen in polycrystalline samples and larger than that observed in systems with disorder[67]. In Fig. 7d, the resistivity is plotted as a function of , allowing to extract the value of coefficient  cm K. The resultant Kadowaki–Woods ratio  cm K mol (mJ) supports correlated electron behavior in UBePt[68-70].

Discussion and conclusions

In this work we present two isostructural compounds—ThBePt and UBePt—that show drastically different properties. The ThBePt compound is a NCSC with a transition temperature of  K and upper critical field T. The bulk superconductivity in ThBePt is confirmed by measurements of specific heat and resistivity, which identify it as a weakly-coupled BCS-like superconductor. Metallic behavior above the superconducting transition is consistent with non-zero density of states at the Fermi level, as inferred from electronic band structure calculations. Negligible mass enhancement in ThBePt is evident from the electronic specific heat coefficient  mJ  mol K. The UBePt compound, on the other hand, shows a large  mJ mol K and Kadowaki–Woods ratio  cm K mol (mJ), indicating heavy-fermion behavior in this system.

Methods

All sample preparation was performed in the specialized laboratory, equipped with an argon-filled glove box system (MBraun,  ppm)[71]. Polycrystalline samples of UBePt and ThBePt were prepared by arc-melting U (wires, Good Fellow, ) or Th (foil, Good Fellow, ) with Be (sheet, Heraeus, ) and Pt (balls, Chempur, ) with the compositions, shown in Table 1. The melting temperature of the ThBePt compound is  C, while that of UBePt is  C. Therefore, all samples were annealed for 4 days at  C. Small inclusions of secondary phases were identified by several experimental methods, see Figs. S1–S4. Based on these data, only three out of six ThBePt samples (samples 1, 4, and 5) and one out of six UBePt (sample 3), which show the least amount of impurities, were characterized in-depth in the present study. Since the amount of Be is hard to quantify analytically (see below), and given that the evaporation losses of Be are unavoidable, the only way to keep control of the sample composition is to follow a careful weighing protocol. None of the samples exhibited any marked air or moisture sensitivity.

Table 1

Sample summary for UBePt and ThBePt samples.

Sample number	Th_4Be_33Pt_16		U_4Be_33Pt_16
	Nominal composition	Resultant compositiona	Nominal composition	Resultant compositiona
1	Th_9.8Be_60.8Pt_29.4	Th_10.0Be_59.9Pt_30.1	U_8.0Be_67.8Pt_24.2	U_10.0Be_59.9Pt_30.1
4	Th_6.0Be_70.1Pt_23.9	Th_6.9Be_65.4Pt_27.7	U_6.3Be_68.6Pt_25.1	U_7.4Be_63.1Pt_29.5
2	Th_6.4Be_67.8Pt_25.8	Th_7.3Be_63.4Pt_29.3	U_6.1Be_69.4Pt_24.5	U_7.1Be_64.4Pt_28.5
3	Th_6.2Be_68.8Pt_25.0	Th_7.1Be_64.4Pt_28.5	U_6.0Be_70.3Pt_23.7	U_6.8Be_65.9Pt_27.3
6	Th_5.6Be_72.1Pt_22.3	Th_6.5Be_67.4Pt_26.1	U_5.8Be_71.1Pt_23.1	U_6.7Be_66.4Pt_26.9
5	Th_5.8Be_71.2Pt_23.0	Th_6.7Be_66.3Pt_27.0	U_5.6Be_72.0Pt_22.4	U_6.6Be_67.2Pt_26.2

aEstimated assuming that the mass, lost during arc-melting, is solely that of Be.

Powder X-ray diffraction was performed on a Huber G670 Image plate Guinier camera with a Ge-monochromator (CuK, = 1.54056 Å). Phase identification was done using the WinXPow software[72]. The data for all ThBePt and UBePt samples are shown in Figs. S1 and S2, respectively. The lattice parameters were determined by a least-squares refinement using the peak positions, extracted by profile fitting (WinCSD software[73]). Single crystal diffraction data were collected using a Rigaku AFC7 diffractometer, equipped with a Saturn 724+ CCD detector and a MoK radiation source ( = 0.71073 Å). The SHELXL software was used for data analysis. The results of the crystallographic characterization are provided in Tables SI and SII.

Chemical composition of polished samples was studied using energy-dispersive X-ray spectroscopy with a Jeol JSM 6610 scanning electron microscope equipped with an UltraDry EDS detector (ThermoFisher NSS7). The semi-quantitative analysis was performed with 25 keV acceleration voltage and  nA beam current. Small inclusions of secondary phases are also visible from back-scatter scanning electron micrographs, presented in Figs. S3 and S4. However, it has to be emphasized that the Be content cannot be reliably analyzed by this method.

The magnetic properties were studied using a Quantum Design (QD) Magnetic Property Measurement System for the temperature range from  K to  K and for applied magnetic fields up to  T. The inverse magnetic susceptibility data were fit to the Curie–Weiss law, after a temperature-independent contribution  emu mol has been subtracted. The specific heat data were collected on a QD Physical Property Measurement System (PPMS) in the temperature range from  K to  K for magnetic fields up to  T. The dc resistivity measurements in a temperature range from  K to  K were carried out using the standard four-probe method in the QD PPMS. Platinum wires were attached to the polished surfaces of bar-shaped sample using silver epoxy.

First-principles electronic structure calculations were carried out by using the all-electron full-potential local orbital (FPLO) method[74]. Exchange-correlation effects were taken into account by the local density approximation to the density functional theory as parametrized by Perdew and Wang[75]. Both scalar and fully-relativistic treatments were employed. The implementation of the latter in the FPLO method is based directly on the Dirac equation[76,77]. Brillouin zone integrations were evaluated using a k-mesh and the linear tetrahedron method.

Supplementary Information.