Effect of low-temperature thermal annealing on the vortex dynamics of metastable β-Bi2Pd single crystals

doi:10.1016/j.physc.2022.1354051

Physica C: Superconductivity and its Applications

Volume 598, 15 July 2022, 1354051

https://doi.org/10.1016/j.physc.2022.1354051 Get rights and content

Abstract

We study the vortex dynamics on β-Bi₂Pd single crystals with a superconducting critical temperature of 5.1 K. The upper critical fields and magnetic penetration depth are determined from magnetization measurements. At low temperatures, the self-field critical current density (J_c) is ≈ 20 kA/cm². The vortex pinning energy, extracted from an Anderson-Kim approximation, is between 340 K and 140 K for fields between 100 G and 600 G. Differential scanning calorimetric measurements show that the crystals start to transform into the alpha-phase at temperatures as low as 60 °C. Short annealing at 100 °C modifies the pinning landscape increasing J_c mainly at temperatures below 3 K. The angular dependence of J_c from electrical transport experiments shows a broad peak when the magnetic field is parallel to the crystallographic c-axis, indicating the presence of correlated disorder.

Introduction

The Bi₂Pd system presents two distinct crystallographic structures that display superconductivity at low temperatures: α-PdBi₂ (T_c ≈ 1.7 K) and β-PdBi₂ (T_c ≈ 5.4 K) [1,2]. The α-phase, with a monoclinic structure, is thermodynamically stable at temperatures below 380 °C. The β-phase, with a tetragonal structure, is stabilized at low temperatures by rapid quenching at temperatures between 380 and 500 °C [3,4]. Both phases have received attention due to topological [4,5] and multiband superconductivity [2,3,6,7]. In addition to these remarkable superconducting particularities, β-PdBi₂ single crystals characterize for presenting unexpected vortex configurations at low magnetic fields. Unlike most systems in which the disorder produces glassy phases with a homogenous distribution in the vortex density [[8], [9]–10], β-PdBi₂ displays a wide distribution of inter-vortex separation due to the preferred arrangement of vortices close to linear defects [11]. The latter relates to spatial variations in the penetration generated by strained regions. The origin of these variations could be associated with the nucleation of the stable α-phase. Indeed, the unit cell volume per chemical formula for the α- phase is ≈ 3% larger than the β- phase [12]. Furthermore, T_c is reported to decrease under external pressure [13]. The high sensitivity of the vortex configuration to internal strain and the metastable character of the β-phase suggests that the pinning landscape will change easily by modifying the crystal growth procedure or by performing post-thermal annealing.

Vortex pinning arises from the interplay of several competing energies, namely the self-energy of the flux lines, the vortex-vortex and vortex-defect interactions, and the thermal excitations. The geometry and density of pinning centers impact the angular (θ) and magnetic field (H) dependence of the critical current density (J_c) [14]. The strength of the vortex fluctuations correlates with the Ginzburg number $G i = 1 / 2 {(γ T_{c} / H_{c}^{2} (0) ξ^{3} (0))}^{2}$ , where H_c is the thermodynamic critical field, γ the anisotropy, and ξ the coherence length. Considering a penetration depth λ(0) ≈ 172 nm - 263 nm [11,15], ξ (0) ≈ 23.5 nm and γ ≈ 1.1 [13], we obtain Gi ≈ 2 × 10⁻⁸ - 9 × 10⁻⁸. This value is within the expectations for conventional low-temperature superconductors (LTS) with low thermal fluctuations. Moreover, it is possible to make a rough estimate of the pinning energy scale by considering the condensation energy in a coherence volume $U_{0} \approx H_{c}^{2} / 8 π (\frac{4}{3} ξ^{3})$ ≈ 2000 K [16]. The value of $U_{0}$ in conventional LTS with relaxation following an Anderson-Kim mechanism determines the flux creep rate as $S = T / U_{0}$ [17].

Here, we analyze the vortex dynamics of β-Bi₂Pd single crystals through magnetization and electrical transport measurements. The thermal stability of the metastable β-phase is evaluated using differential scanning calorimetric (DSC). Based on these results, we compare the superconducting properties of an as-quenched single crystal with one in which a small fraction of α-phase was induced by thermal annealing at 100 °C. Superconducting parameters such as upper critical fields and λ are compared with the values previously reported in the literature. The angular and magnetic field dependences of J_c are evaluated from irreversible magnetization and by electrical transport measurements in thin strips. The time decay of the persistent currents ( $S = - δ lnJ / δ lnt$ ) is analyzed within the Anderson–Kim framework from which the vortex pinning energy is obtained.

Section snippets

Experimental

β-Bi₂Pd single crystals were grown as described in Refs. [3,11]. Stoichiometric amounts of Bi (99.999) and Pd (99.99) were encapsulated in a quartz tube sealed in argon. The capsule was heated over 3 h to 900 °C. This temperature was held for 24 h to facilitate the dissolution of Pd and the formation of a homogeneous solution. The mixture was then ramped over 96 h to 490 °C and finally over 200 h from the latest to 395 °C. Finally, the ampoule was quenched from the high-temperature β-Bi₂Pd

Results and discussion

Fig. 1 shows the XRD pattern of a β-Bi₂Pd single crystal. The peaks were indexed according to a tetragonal lattice with c = 1.29 (0.01) nm, in good agreement with previous reports [3,11]. The inset in Fig. 1 shows the ϕ scan for the (101) reflection. The data display a periodicity of 90° as expected for a cubic symmetry.

The superconducting critical temperature T_c was obtained through magnetization and transport measurements (see Fig. 2). The value from the magnetization curve (after zero-field

Conclusions

We have studied the superconducting parameters of β-Bi₂Pd single crystals with T_c = 5.1 K. The samples show λ_ab (0) ≈ 180 nm, λ_c (0) ≈ 230 nm, $ξ_{a b}$ (0)= 23.8 nm and $ξ_{c}$ (0)= 20.3 nm. The upper critical field anisotropy is ≈ 1.2. The crystals display small J_c at self-field and fast decay in their values as the magnetic field increases. The angular dependence of J_c shows signatures of correlated pinning, possibly originated by nucleation of α-phase during the thermal quench. Moreover, the β-phase

Declaration of Competing Interest

The work described has not been published previously.

The article is not under consideration for publication in elsewhere.

The publication has been approved by all authors.

If accepted, it will not be published elsewhere in the same form, in English or in any other language.

Acknowledgment

The authors acknowledge M. Isla and F. Castro for technical assistance. This work was partially supported by the ANPCYT (PICT2019–02396), U. N. de Cuyo (SIIP 06/C559). NH is member of the of the Instituto de Nanociencia y Nanotecnología, CNEA-CONICET.

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Effect of low-temperature thermal annealing on the vortex dynamics of metastable β-Bi2Pd single crystals

Abstract

Introduction

Section snippets

Experimental

Results and discussion

Conclusions

Declaration of Competing Interest

Acknowledgment

Intermetallics

Solid State Commun.

Solid State Commun

J. Less Common Met.

Probing the superconducting gap symmetry of α-PdBi2. A penetration depth study

Phys. Rev. B

Superconductivity at 5.4K in β-Bi2Pd

J. Phys. Soc. Jpn.

Magnetic field dependence of the density of states in the multiband superconductor β-Bi2Pd

Phys. Rev. B

Topologically protected surface states in a centrosymmetric superconductor β-PdBi2

Nat. Commun.

Unconventional pressure dependence of the superfluid density in the nodeless topological superconductor α-PdBi2

Phys. Rev. Lett.

Dirac state in a centrosymmetric superconductor α−PdBi2

Phys. Rev. B

Order-disorder phase transition in NbSe2: absence of amorphous vortex matter

Phys. Rev. B

Visualizing the morphology of vortex lattice domains in a bulk type-II superconductor

Nat. Commun.

Vortex matter freezing in Bi2Sr2CaCu2O8 samples with a very dense distribution of columnar defects

Phys. Rev. B

Observation of a gel of quantum vortices in a superconductor at very low magnetic fields

Phys. Rev. Res.

Pressure-induced irreversible evolution of superconductivity in PdBi2

Phys. Rev. B

Effect of low-temperature thermal annealing on the vortex dynamics of metastable β-Bi₂Pd single crystals

Probing the superconducting gap symmetry of α-PdBi₂. A penetration depth study

Superconductivity at 5.4K in β-Bi₂Pd

Magnetic field dependence of the density of states in the multiband superconductor β-Bi₂Pd

Topologically protected surface states in a centrosymmetric superconductor β-PdBi₂

Unconventional pressure dependence of the superfluid density in the nodeless topological superconductor α-PdBi₂

Dirac state in a centrosymmetric superconductor α−PdBi₂

Order-disorder phase transition in NbSe₂: absence of amorphous vortex matter

Vortex matter freezing in Bi₂Sr₂CaCu₂O₈ samples with a very dense distribution of columnar defects