Competition of superconductivity with the structural transition in $\mathrm{M}{\mathrm{o}}_{3}\mathrm{S}{\mathrm{b}}_{7}$

Competition of superconductivity with the structural transition in $M o_{3} S b_{7}$

G. Z. Ye, J.-G. Cheng, J.-Q. Yan, J. P. Sun, K. Matsubayashi, T. Yamauchi, T. Okada, Q. Zhou, D. S. Parker, B. C. Sales, and Y. Uwatoko

Phys. Rev. B 94, 224508 – Published 14 December 2016

Abstract

Prior to the superconducting transition at $T_{c} \approx 2.3 K, M o_{3} S b_{7}$ undergoes a symmetry-lowering, cubic-to-tetragonal structural transition at $T_{s} = 53 K$ . We have monitored the pressure dependence of these two transitions by measuring the resistivity of $M o_{3} S b_{7}$ single crystals under various hydrostatic pressures up to 15 GPa. The application of external pressure enhances $T_{c}$ but suppresses $T_{s}$ until $P_{c} \approx 10 GPa$ , above which a pressure-induced first-order structural transition takes place and is manifested by the phase coexistence in the pressure range $8 \leq P \leq 12 GPa$ . The cubic phase above 12 GPa is also found to be superconducting with a higher $T_{c} \approx 6 K$ that decreases slightly with further increasing pressure. The variations with pressure of $T_{c}$ and $T_{s}$ satisfy the Bilbro-McMillan equation, i.e. ${T_{c}}^{n} {T_{s}}^{1 - n} =$ constant, thus suggesting the competition of superconductivity with the structural transition that has been proposed to be accompanied with a spin-gap formation at $T_{s}$ . Our first-principles calculations suggest the importance of magnetism that competes with the superconductivity in $M o_{3} S b_{7}$ .

Received 20 September 2016
Revised 9 November 2016

DOI:https://doi.org/10.1103/PhysRevB.94.224508

Physics Subject Headings (PhySH)

Superconductivity

Type-II superconductors

Pressure effects Resistivity measurements

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

G. Z. Ye^1,2, J.-G. Cheng^1,3,*, J.-Q. Yan⁴, J. P. Sun¹, K. Matsubayashi^3,5, T. Yamauchi³, T. Okada³, Q. Zhou², D. S. Parker⁴, B. C. Sales⁴, and Y. Uwatoko³

¹Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
²School of Physical Science and Astronomy, Yunnan University, Kunming 650091, China
³Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan
⁴Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
⁵Department of Engineering Science, University of Electro-Communications, Chofu, Tokyo 182-8585, Japan

^*jgcheng@iphy.ac.cn

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Vol. 94, Iss. 22 — 1 December 2016

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Figure 1
The Mo sublattice of $M o_{3} S b_{7}$ that consists of Mo6 octahedral cages at the body-center positions formed by the NNN Mo-Mo bond of $\sim 4.6 Å$ and connected via the NN Mo-Mo bond of $\sim 3 Å$ in the cubic (left) and tetragonal (right) phase. The NN Mo-Mo bond length along the $c$ axis is about 0.3% shorter than those within the $a b$ plane in the tetragonal phase [21].
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Figure 2
Temperature dependence of resistivity $ρ (T)$ for (a) and (b) the sample #1 between 2 and 8 GPa, and (c) and (d) the sample #2 between 6 and 12 GPa, both measured with the constant-force cubic-anvil-cell apparatus, and (e) and (f) the sample #3 between 3.5 and 15 GPa measured with the Palm cubic-anvil-cell apparatus. The top panels of (a), (c), and (e) display the temperature derivative $d ρ / d T$ to show the variation of $T_{s}$ as a function of pressure. (b), (d), and (f) highlight the low-temperature superconducting transition. In (e), the $ρ (T)$ at 15 GPa can be described excellently by $ρ (T) = ρ_{0} + A T^{β}$ with $β = 1.52 (2)$ in a large temperature range $7 < T < 55 K$ , shown as the broken curve.
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Figure 3
Temperature-pressure phase diagram of $M o_{3} S b_{7}$ . The circle, square, and triangle symbols represent the transition temperatures for samples #1, #2, and #3, respectively. The solid black curve denotes the calculated ${T_{c}}^{calc}$ according to the Bilbro-McMillan equation, i.e. ${T_{c}}^{n} {T_{s}}^{1 - n} = T_{c 0}$ , as detailed in the main text. Note that both the experimental $T_{c}$ and ${T_{c}}^{calc}$ have been scaled by a factor of two.
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Figure 4
Magnetic-field dependence of the superconducting transition at different pressures: (a) 3.5 GPa, (b) 6.0 GPa, (c) 12 GPa, and (d) 15 GPa. These data were used to obtain the upper critical fields $μ_{0} {H_{c}}_{2}$ shown in (e), where a linear fitting has been used to extract the values of initial slope $- d {H_{c}}_{2} {/ d T |}_{T_{c}}$ .
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Figure 5
Pressure dependence of the initial slope of upper critical field $η \equiv - d {H_{c}}_{2} {/ d T |}_{T_{c}}$ . Since η is proportional to electronic specific-heat coefficient γ and thus the DOS at Fermi level $N (E_{F})$ , we employed the obtained η values below 10 GPa to estimate the portion of electronic states forming the FS $n \equiv η / η_{12 GPa}$ as shown in the inset. Here, we assume all electronic states at 12 GPa participate in the formation of FS since the spin-singlet states vanish at this pressure.
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Figure 6
The calculated FS of band 291 for $M o_{3} S b_{7}$ in the tetragonal state [the tetragonal distortion is small so that the Brillouin zone depicted is effectively the body-centered cubic (bcc) zone]. There is a possibility of nesting between the parallel faces.
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Physical Review B

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Competition of superconductivity with the structural transition in $M o_{3} S b_{7}$

G. Z. Ye, J.-G. Cheng, J.-Q. Yan, J. P. Sun, K. Matsubayashi, T. Yamauchi, T. Okada, Q. Zhou, D. S. Parker, B. C. Sales, and Y. Uwatoko

Phys. Rev. B 94, 224508 – Published 14 December 2016

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Physical Review B

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Competition of superconductivity with the structural transition in Mo3Sb7

G. Z. Ye, J.-G. Cheng, J.-Q. Yan, J. P. Sun, K. Matsubayashi, T. Yamauchi, T. Okada, Q. Zhou, D. S. Parker, B. C. Sales, and Y. Uwatoko

Phys. Rev. B 94, 224508 – Published 14 December 2016

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Competition of superconductivity with the structural transition in $M o_{3} S b_{7}$