Type-II superconductivity in W5Si3-type Nb5Sn2Al

TL;DR

This paper reports the discovery of multiband, type-II superconductivity below 2.0 K in Nb5Sn2Al with a W5Si3-type structure, and compares it to related compounds to understand the factors influencing Tc.

Contribution

It is the first report of superconductivity in Nb5Sn2Al, revealing its multiband nature and providing detailed superconducting parameters and comparisons with similar compounds.

Findings

Superconductivity below 2.0 K confirmed by specific heat jump.

Nb5Sn2Al exhibits multiband, weakly coupled, type-II superconductivity.

Tc correlates with the average valence electrons per atom in W5Si3-type compounds.

Abstract

We report the discovery of superconductivity in the ternary aluminide Nb$_{5}$Sn$_{2}$Al, which crystallizes in the W$_{5}$Si$_{3}$-type structure with one-dimensional Nb chains along the $c$-axis. It is found that the compound has a multiband nature and becomes a weakly coupled, type-II superconductor below 2.0 K. The bulk nature of superconductivity is confirmed by the specific heat jump, whose temperature dependence shows apparent deviation from a single isotropic gap behavior. The lower and upper critical fields are estimated to be 2.0 mT and 0.3 T, respectively. From these values, we derive the penetration depth, coherence length and Ginzburg-Landau parameter to be 516 nm, 32.8 nm and 15.6, respectively. By contrast, the isostructural compound Ti$_{5}$Sn$_{2}$Al dose not superconduct above 0.5 K. A comparison of these results with other W$_{5}$Si$_{3}$-type superconductors suggests that $T_{\rm c}$ of these compounds correlates with the average number of valence electrons per atom.

Tables

Table 1. Table 1: Refined structural parameters of M 𝑀 M 5 Sn 2 Al ( M 𝑀 M = Nb, Ti). Here a 𝑎 a and c 𝑐 c are the lattice parameters, V 𝑉 V the unit cell volume, R wp subscript 𝑅 wp R_{\rm wp} and R p subscript 𝑅 p R_{\rm p} the weighted and unweighted R 𝑅 R factors.

		Nb5Sn2Al	Ti5Sn2Al
	Space group	$I$4/$mcm$
	$a$ (Å)	10.638(1)	10.558(2)
	$c$ (Å)	5.225(1)	5.262(1)
	$V$ (Å3)	591.46	586.57
	$R_{\mathrm{wp}}$	8.1%	12.9%
	$R_p$	5.7%	9.6%
0 Atoms	000 site	00 $x$	00 $y$	00 $z$
00 $M$1	000 16k	0.07308	0.2134	00 0
00 $M$2	000 4b	00 0	0 0.5	0 0.25
00 Sn	000 8h	0.1683	0.6683	00 0
00 Al	000 4a	00 0	00 0	0 0.25

Table 2. Table 2: Physical parameters of Nb 5 Sn 2 Al and Ti 5 Sn 2 Al. Here T c subscript 𝑇 c T_{\rm c} is the superconducting transition temperature, B c1 subscript 𝐵 c1 B_{\rm c1} (0) and B c2 subscript 𝐵 c2 B_{\rm c2} (0) the zero-temperature lower and upper critical fields for type-II superconductors, λ eff subscript 𝜆 eff \lambda_{\rm eff} the effective penetration depth, ξ GL subscript 𝜉 GL \xi_{\rm GL} (0) the Ginzburg-Landau coherence length, κ GL subscript 𝜅 GL \kappa_{\rm GL} the Ginzburg-Landau parameter, Θ D subscript Θ D \Theta_{\rm D} the Debye temperature, γ 𝛾 \gamma the Sommerfeld coefficient, λ ph subscript 𝜆 ph \lambda_{\rm ph} the electron-phonon coupling constant.

00Parameters	Nb5Sn2Al	000Ti5Sn2Al
00$T_c$ (K)	00 2.0	000000 $-$
00$B_{\mathrm{c1}}$(0) (mT)	00 2.0	000000 $-$
00$B_{\mathrm{c2}}$(0) (T)	00 0.3	000000 $-$
00${\lambda }_{\mathrm{eff}}$ (nm)	00 516	000000 $-$
00${\xi }_{\mathrm{GL}}$(0) (nm)	00 32.8	000000 $-$
00${\kappa }_{\mathrm{GL}}$	00 15.6	000000 $-$
00${\Theta }_D$ (K)	00 340	00000 386
00$\gamma$ (mJ mol-1 K-2)	00 19.0	00000 31.5
00${\lambda }_{\mathrm{ph}}$	00 0.46	000000 $-$

Equations

$${\lambda }_{\mathrm{ph}}=\frac{1.04+{\mu }^{\ast }\ln ({\mathrm{\Theta }}_{\mathrm{D}}/1.45{\text{T}}_{\mathrm{c}})}{(1-0.62{\mu }^{\ast })\ln ({\mathrm{\Theta }}_{\mathrm{D}}/1.45{\text{T}}_{\mathrm{c}})-1.04},$$

Full text

1 Introduction

Some structural types have been shown to favor the occurrence of superconductivity (SC) in intermetallic compounds [1]. A well-known example is the cubic $A$15 materials with the general formula $A$3$B$, in which nearly fifty superconductors were found and the highest $T_{\rm c}$ reaches above 20 K [2]. Recently, the $A$5$B$3 compounds and their derivatives emerge as another fertile ground for SC [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]. These materials mainly crystallize in three different structural types, namely, tetragonal Cr5B3-type [17], W5Si3-type [18], and hexagonal Mn5Si3-type [19]. In particular, the W5Si3 and $A$15 types are similar in that they both consist of one dimensional chains of the $A$ atoms, which could give rise to a large density of states at the Fermi level [$N$($E_{\rm F}$)] [20]. So far, except for W5Si3 itself [9], superconductors of this structural type include Nb5$X_{3}$ ($X$=Si, Ge and Ga) [3, 4, 5], Nb5Sn2Ga [7], Ta5Ga2Sn [8], Hf5Sb2.5Ru0.5 [13], and Zr5Sb2.4Ru0.6 [14]. The exploration and study of new member will help to identify the factors that govern $T_{\rm c}$ in these materials.

Ternary aluminides Nb5Sn2Al and Ti5Sn2Al were first synthesized in 1990s and found to adopt the W5Si3-type structure [21]. However, to our knowledge, their physical properties have not been investigated to date. In this paper, we present measurements of resistivity, Hall coefficient, magnetic suceptibility and specific heat on high-quality polycrystalline samples of Nb5Sn2Al and Ti5Sn2Al. We show that Nb5Sn2Al is a type-II superconductor with $T_{\rm c}$ of 2.0 K, and the behavior of its specific heat jump is inconsistent with Bardeen-Cooper-Schreiffer (BCS) prediction for a single isotropic gap. Nevertheless, the isostructural Ti5Sn2Al with remains normal down to 0.5 K, albeit with a larger Sommerfeld coefficient. We compare these results with other W5Si3-type superconductors and discuss the dependence of their $T_{\rm c}$ on the valence electron count.

2 Experimental

Polycrystalline $M_{5}$Sn2Al ($M$= Nb, Ti) samples were synthesized by using a solid state reaction method, similar to the previous report [21]. High purity powders of $M$ (99.99%), Sn (99.99%) and Al (99.999%) with the stoichiometric ratio of 5:2:1 were homogenized and pressed into pellets in an argon-filled glove-box. The pellets were then loaded in an alumina crucible, which was sealed in a tantalum (Ta) tube. The Ta tube was protected in a argon-filled sealed quartz tube, which was heated to 900-1000 oC in a muffle furnace. After maintaining for 10 days, the quartz tube was quenched into cold water. The reaction was repeated for several times with intermediate grinding to ensure sample homogeneity.

The purity of the resulting $M_{5}$Sn2Al samples was checked by powder X-ray diffraction (XRD) using a PANalytical x-ray diffractometer with a monochromatic Cu-Kα1 radiation at room temperature. The chemical compositions of these samples were measured with an energy-dispersive X-ray (EDX) spectrometer (Model Octane Plus). The spectra were collected on different locations of each sample, and the Al content was not included in the analysis due to contribution from Al sample holders. For consistency reason, all the physical property measurements were performed on samples derived from the same pellet. A part of the pellet was cut into regular-shaped samples for transport and specific heat measurements, and the remaining part was crushed into powders. The electrical resistivity was measured using a standard four-probe method. Resistivity, Hall coefficient and specific heat measurements down to 1.8 K were performed on a Quantum Design PPMS-9 Dynacool. Measurements of resistivity and specific heat down to 0.5 K were carried out on a Quantum Design PPMS-9 Evercool II. The two sets of specific-heat data agree well within 5% in the overlapped temperature range. The dc magnetization was measured on crushed powders with a commercial SQUID magnetometer (Quantum Design MPMS3).

3 Results

3.1 Crystal Structure and chemical composition

The structure of $M$5Sn2Al is sketched in Fig. 1(a) and (b). All the atoms are distributed orderly in the lattice, and there are two distinct crystallographic sites for the $M$ atoms, namely $M$(1) at 16$k$ site and $M$(2) at 4$b$ site. Notably, these atoms form linear and zigzag chains along the $c$-axis, respectively. For Nb5Sn2Al, this one dimensional arrangement of Nb atoms is reminiscent of that observed in Nb3Sn. Figure 1(c) shows the XRD patterns of the Nb5Sn2Al and Ti5Sn2Al samples at room temperature, together with structural refinement profiles using the GSAS program. The observed and calculated diffraction patterns show a good agreement for both cases, demonstrating that they adopt the tetragonal W5Si3-type structure. As can be seen in Table 1, the refined lattice parameters are $a$ = 10.638 Å, $c$ = 5.225 Å for Nb5Sn2Al and $a$ = 10.558 Å, $c$ = 5.262 Å for Ti5Sn2Al, which are in good agreement with the previous report [21]. It is also noted that, for Ti5Sn2Al, there exists additional diffraction peaks due to unknown impurities, whose maximum intensity is around one tenth that of the main phase. This suggests that the impurity phases occupy $\sim$10% of the sample volume. On the other hand, EDX measurements yield the Nb:Sn molar ratio of 5:2.06(6) and Ti:Sn ratio of 5:2.09(3) for the Nb5Sn2Al and Ti5Sn2Al samples, respectively. These results indicate that both compounds are stoichiometric within the experimental error. In addition, a Ti:Sn ratio in the range of 5:2.55$-$2.80 is observed in a small part of the Ti5Sn2Al sample, which is presumably ascribed to the impurities detected in XRD.

3.2 Resistivity and Hall coefficient

Figure 2(a) shows the temperature dependence of resistivity for Nb5Sn2Al and Ti5Sn2Al. For both samples, the resistivity shows a weak metallic behavior with a concave curvature, similar to that observed in other $A$5$B$3 compounds [10, 11, 12, 15]. Actually, the data of Nb5Sn2Al is an almost rigid upward shift of that of Ti5Sn2Al, pointing to essentially the same temperature-dependent electron scattering mechanism for the two samples. However, their low temperature behavior is quite different. As can be seen in the inset of Fig. 2(a), when cooling below 2.5 K, the resistivity of Nb5Sn2Al drops rapidly to zero, evidencing a superconducting transition. By contrast, for Ti5Sn2Al, the decrease in resistivity tends to saturate and no SC is observed down to 0.5 K.

Figure 2(b) shows the temperature dependence of 1/(e$R_{\rm H}$) for the two samples, where $e$ is the electron charge and $R_{\rm H}$ is the low-field Hall coefficient. The $R_{\rm H}$ of Nb5Sn2Al is negative at room temperature and becomes positive below 200 K. A similar sign reversal in $R_{\rm H}$ is observed for Ti5Sn2Al, but its $R_{\rm H}$ changes back to negative again at $\sim$100 K. These results provide clear evidence that these materials are multiband systems with both electrons and holes. Nevertheless, at temperatures below 50 K, $R_{\rm H}$ is nearly temperature independent and the Hall resistivity is linear with magnetic field [see the inset of Fig. 2(b)] for both samples. Hence it appears that, in this temperature range, their electrical transport is dominated by a single type of carriers. Assuming a one-band model, the hole and electron densities are estimated to be 1.3 $\times$ 1022 cm*-3* and 1.5 $\times$ 1022 cm*-3* for Nb5Sn2Al and Ti5Sn2Al, respectively.

3.3 Magnetic susceptibility

The occurrence of SC in Nb5Sn2Al is corroborated by the magnetic susceptibility results of powder samples shown in Fig. 3. Here the demagnetization effect is taken into consideration assuming that the powders consist of cubic-shaped grains with the demagnetization factor $N_{\rm d}$ = 0.3. A strong diamagnetic signal is observed in both field-cooling (FC) and zero-field cooling (ZFC) data. In addition, a divergence is seen between the ZFC and FC curves, which is characteristic of a type-II superconducting behavior. The linear extrapolation of the initial ZFC diamagnetic transition intersects with the baseline at 2.0 K (see the inset of Fig. 3), which coincides with the onset of zero resistivity. In light of this coincidence, we determine $T_{\rm c}$ as 2.0 K for Nb5Sn2Al. At 0.4 K, the ZFC and FC data correspond to shielding and Meissner fractions of 85% and 22%, respectively, and hence clearly indicate bulk SC.

3.4 Specific heat

Figure 4(a) shows the low temperature specific heat data for Nb5Sn2Al and Ti5Sn2Al. A strong anomaly is observed in Nb5Sn2Al near its $T_{\rm c}$, which further confirms the bulk nature of SC. On the other hand, its normal state data can be well described by the Debye model $C_{\rm p}$/$T$ = $\gamma$ + \beta$$T^{2}, where $\gamma$ and $\beta$ are the Sommerfeld and phonon specific heat coefficients, respectively. The fit yields $\gamma$ = 19.0 mJ mol*-1* K*-2* and $\beta$ = 0.396 mJ mol*-1* K*-4*. The Debye temperature $\Theta_{\rm D}$ is then calculated as $\Theta_{\rm D}$ = (12\pi^{4}$$N$$R/5$\beta$)${}^{\frac{1}{3}}$ = 340 K, where $N$ = 8 and $R$ is the molar gas constant 8.314 J mol*-1* K*-1*. Applying the same analysis to the data of Ti5Sn2Al gives $\gamma$ = 31.5 mJ mol*-1* K*-2*, $\beta$ = 0.2709 mJ mol*-1* K*-4*, and $\Theta_{\rm D}$ = 386 K. Compared with Nb5Sn2Al, the larger $\Theta_{\rm D}$ of Ti5Sn2Al is as expected, but its larger $\gamma$ value is somewhat surprising.

Figure 4(b) shows the normalized electronic specific heat of Nb5Sn2Al at zero field after subtraction of the phonon contribution, plotted a function of reduced temperature $T$/$T_{\rm c}$. One can see that the normalized specific heat jump \Delta$$C_{\rm el}/\gamma$$T_{\rm c} $\sim$ 0.86 is considerably smaller than the BCS value of 1.43 [22]. Furthermore, the temperature dependence of the specific heat jump shows a significant deviation from the BCS theory, especially in the low temperature region. Note that an extrapolation of $C_{\rm el}$/\gamma$$T to 0 K yields a negative value. This, together with the absence of additional XRD peaks from impurities [see Fig. 1(c)], suggests that the sample has a superconducting volume fraction close to 100%. It therefore appears that the small specific heat jump is of intrinsic origin, which points to the presence of multiple gaps as in MgB2 [23] and Lu2Fe3Si5 [24], or even gap nodes. Nevertheless, the $C_{\rm el}$/\gamma$$T data at 0.5 K is still as large as 50% of its normal-state value, and hence to distinguish these scenarios, $C_{\rm p}$/$T$ measurements down to mK range would be needed.

Assuming that SC in Nb5Sn2Al is mediated by electron-phonon coupling, the corresponding constant, $\lambda_{\rm ph}$, can be estimated by using the inverted McMillan formula [25],

[TABLE]

where $\mu^{\ast}$ is the Coulomb repulsion pseudopotential. Taking an empirical $\mu^{\ast}$ value of 0.13, we obtain $\lambda_{\rm ph}$ = 0.46, which implies weak coupling SC in Nb5Sn2Al. This is consistent with the low value of \Delta$$C_{\rm el}/\gamma$$T_{\rm c}.

3.5 Critical fields and superconducting parameters

Figure 5(a) shows the isothermal magnetization curves at various temperatures for Nb5Sn2Al. The effective lower critical field $B_{\rm c1}^{\ast}$ at each temperature is defined as the value at which the curve deviates from its initial linear behavior. The resulting $B_{\rm c1}^{\ast}$ is plotted as a function of temperature in Fig. 5(b), and the extrapolation of the data to zero temperature yields $B_{\rm c1}^{\ast}$(0) = 1.4 mT [26]. After correction for the demagnetization factor, we obtain the zero-temperature lower critical field $B_{\rm c1}$(0) = $B_{\rm c1}^{\ast}$(0)/(1 $-$ $N_{\rm d}$) = 2.0 mT. Figure 5(c) shows the temperature dependence of resistivity for Nb5Sn2Al under various magnetic fields. With increasing field, the resistive transition is gradually suppressed to lower temperatures, as expected. Following the same criterion as shown above (see Subsection 3.2.), we determine $T_{\rm c}$ for each field as the temperature at which zero resistivity is achieved, and plot the data in Fig. 5(d). Extrapolation of the upper critical field $B_{\rm c2}$ to zero temperature, using the Wathamer-Helfand-Hohenberg (WHH) theory [27], gives $B_{\rm c2}$(0) = 0.3 T.

With $B_{\rm c1}$(0) and $B_{\rm c2}$(0) determined, we can estimate various superconducting parameters of Nb5Sn2Al. The Ginzburg-Landau (GL) coherence length $\xi_{\rm GL}$(0) as $\xi_{\rm GL}$(0) = $\sqrt{\Phi_{0}/2\pi B_{\rm c2}(0)}$ = 32.8 nm, where $\Phi_{0}$ = 2.07 $\times$ 10*-15* Wb is the flux quantum. Then from the equations $B_{\rm c1}$(0)/$B_{\rm c2}$(0) = (ln$\kappa_{\rm GL}$ + 0.5)/(2$\kappa_{\rm GL}^{2}$) [28] and $B_{\rm c1}$(0) = ($\Phi_{0}$/4\pi$$\lambda_{\rm eff}^{2})(ln$\kappa_{\rm GL}$ + 0.5), $\kappa_{\rm GL}$ = 15.6 and $\lambda_{\rm eff}$ = 516 nm are obtained.

4 Discussion

Now let us compare the physical properties of isostructural Nb5Sn2Al and Ti5Sn2Al, which are summarized in Table 2. As noted above, the $\gamma$ value of Ti5Sn2Al is $\sim$60% larger than that of Nb5Sn2Al. This means that Ti5Sn2Al has a considerably higher $N$($E_{\rm F}$), yet no SC is observed. To gain more insight, we plot the $T_{\rm c}$ against the average number of valence electrons per atom ratio ($e$/$a$) for all known ”W5Si3”-type superconductors. According to the empirical rule proposed by Matthias [29], $T_{\rm c}$ of intermetallic superconductors is expected to exhibit two maxima at $e$/$a$ close to 5 and 7 [29]. Indeed, as can be seen from the figure, most of the ”W5Si3”-type superconductors have $e$/$a$ in the range between 4.25 and 4.625, although $T_{\rm c}$ is generally higher for superconductors containing group IVB elements than those containing group VB elements. Furthermore, in the latter case, a $T_{\rm c}$ maximum is found at $e$/$a$ $\sim$ 4.5, which is slightly lower than the empirical value of 4.7 [29]. These results suggest that this family of superconductors follows the Matthias rule and their $T_{\rm c}$ is mainly controlled by the band filling rather than $N$($E_{\rm F}$). In this respect, the absence of SC in Ti5Sn2Al can be explained since its $e$/$a$ of 3.875 appears to fall below the lower bound for SC. On the other hand, the $e$/$a$ of W5Si3 exceeds the above range and reaches 5.25, hinting at the existence of another $T_{\rm c}$ maximum at higher valence electron account.

Finally, we note that, despite similar Nb atom chains, the $T_{\rm c}$ of Nb5Sn2Al is nearly one order of magnitude smaller than that of Nb3Sn. This corroborates the previous notion that the presence of these one-dimensional chains is not a sufficient condition for achieving high $T_{\rm c}$ [4, 5]. Instead, it is pointed out that the $\lambda_{\rm ph}$ value of Nb5Sn2Al is only about one-third that of Nb3Sn [30], which highlights the importance of electron phonon interaction in enhancing $T_{\rm c}$.

5 Conclusion

In summary, we have studied the transport, magnetic and thermodynamic properties of isostructural Nb5Sn2Al and Ti5Sn2Al. The results demonstrate that Nb5Sn2Al is a type-II superconductor with a bulk $T_{\rm c}$ of 2.0 K and a non-BCS gap, while Ti5Sn2Al remains metallic down to 0.5 K. Surprisingly, compared with Nb5Sn2Al, Ti5Sn2Al has a even larger Sommerfeld coefficient, suggesting that the absence of SC is not due to a reduction in $N$($E_{\rm F}$). Nevertheless, these results are in line with the empirical rule based on the average number of valence electrons per atom, and at the value of $\sim$4.5 a $T_{\rm c}$ maximum is found for the ”W5Si3”-type superconductors. Further studies to increase the number of valence electrons and electron phonon coupling, which may result in higher $T_{\rm c}$, are highly desirable in future.

Acknowledgments

This work is supported by the National Key Research and Development Program of China (No.2017YFA0303002) and the Fundamental Research Funds for the Central Universities of China.