Sharp magnetization jump at the first-order superconducting transition in ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$

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Sharp magnetization jump at the first-order superconducting transition in ${Sr}_{2} {RuO}_{4}$

Shunichiro Kittaka, Akira Kasahara, Toshiro Sakakibara, Daisuke Shibata, Shingo Yonezawa, Yoshiteru Maeno, Kenichi Tenya, and Kazushige Machida

Phys. Rev. B 90, 220502(R) – Published 1 December 2014

Abstract

The magnetization and magnetic torque of a high-quality single crystal of ${Sr}_{2} {RuO}_{4}$ have been measured down to 0.1 K under precise control of the magnetic-field orientation. When the magnetic field is applied exactly parallel to the $a b$ plane, a sharp magnetization jump $4 π δ M$ of $(0.74 \pm 0.15)$ G at the upper critical field $H_{c 2, a b} \sim 15$ kOe with a field hysteresis of 100 Oe is observed at low temperatures, evidencing a first-order superconducting-normal transition. A strong magnetic torque appearing when $H$ is slightly tilted away from the $a b$ plane confirms an intrinsic anisotropy $Γ = ξ_{a} / ξ_{c}$ of as large as 60 even at 100 mK, in contrast with the observed $H_{c 2}$ anisotropy of $\sim 20$ . The present results raise fundamental issues in both the existing spin-triplet and spin-singlet scenarios, providing, in turn, crucial hints toward the resolution of the superconducting nature of ${Sr}_{2} {RuO}_{4}$ .

Received 26 September 2014
Revised 13 November 2014

DOI:https://doi.org/10.1103/PhysRevB.90.220502

Authors & Affiliations

Shunichiro Kittaka¹, Akira Kasahara¹, Toshiro Sakakibara¹, Daisuke Shibata², Shingo Yonezawa², Yoshiteru Maeno², Kenichi Tenya³, and Kazushige Machida⁴

¹Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan
²Department of Physics, Kyoto University, Kyoto 606-8502, Japan
³Faculty of Education, Shinshu University, Nagano 310-8512, Japan
⁴Department of Physics, Okayama University, Okayama 700-8530, Japan

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Vol. 90, Iss. 22 — 1 December 2014

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Figure 1
Field dependence of the magnetization $M_{SC} = M - χ_{n} H$ at 0.1 K for $H ∥ a b$ , where $χ_{n} H$ is the normal-state contribution. The solid line represents the $M_{av}$ data obtained by averaging the increasing- and decreasing-field data ( $M_{SC}^{u}$ and $M_{SC}^{d}$ ). The upper inset is an enlarged view near $H_{c} 2$ . The lower inset shows $d M_{av} / d H$ , compared with the previous results [24] (crosses).
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Figure 2
Field dependence of (a) a raw-capacitance data measured in 0 Oe/cm, $Δ C_{0}$ , where the normal-state value has been subtracted, and (b) $d (Δ C_{0}) / d H$ at 0.1 K. Numbers labeling the curves represent the field angle $θ$ measured from the $a b$ plane in degrees. Each data in (a) and (b) is vertically shifted by $\pm 2 \times 10^{- 4}$ pF and $\pm 1 \times 10^{- 7}$ pF/Oe, respectively, for clarity. (c) Angle $θ$ dependence of the intensity of a peak in $d (Δ C_{0}) / d H (H)$ appearing near $H_{c} 2$ .
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Figure 3
(a), (b) Field-angle $θ$ dependence of the raw-capacitance data $Δ C_{0}$ at various fields for $T = 0.1$ K. Each data is vertically shifted by $- 4 \times 10^{- 4}$ pF for clarity. Numbers labeling the curves show the applied field in kG. The dashed lines are the calculated results using Eq. (1). (c) Angle $θ$ dependence of $| Δ C_{0} |$ normalized by its value at $1 . 5^{\circ}$ , $| Δ C_{0}^{*} |$ , at 0.1 K (circles) and the vortex-lattice form factor $F^{2} (θ)$ at 40 mK (squares) in 7 kOe [25]. Triangles are the calculated data of the magnetic torque normalized by its maximum value $| τ_{c}^{*} |$ on the basis of the microscopic theory for a spin-singlet superconductor [30]. The behavior for a spin-triplet superconductor with conventional orbital limiting is expected to be essentially the same. (d) Angle $θ$ dependence of $H_{c} 2$ (circles) plotted with a contour map of $Δ C_{0} (H, θ)$ . The open (solid) circles represent the first- (second-) order S-N transition. The peak position in $| Δ C_{0} (H, θ) |$ at 0.1 K (cross) and that in $F^{2} (H, θ)$ detected from SANS experiments at 40 mK (squares [25]) are also shown.
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Figure 4
(a) Field dependence of the total magnetization $M_{t}$ , the spin magnetization $M_{s}$ , and the orbital diamagnetism $M_{dia}$ at $T = 0.1 T_{c}$ and $θ = 0$ , obtained from the microscopic calculation for a Pauli-limited spin-singlet superconductor [30] with the same parameters for the calculation of $| τ_{c}^{*} |$ . Here, the calculated magnetizations are normalized by $M_{0}$ , defined as $χ_{n} H_{c} 2$ in (a). (b) $M_{dia}$ calculated for a chiral- $p$ -wave superconductor [34] with $Γ = 60$ , $κ = 162$ , $T = 0.1 T_{c}$ , and $θ = 0$ , normalized by $M_{0}$ , the same parameter in (a). For (b), $M_{s}$ shall follow $χ_{n} H$ in (a).
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Physical Review B

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Sharp magnetization jump at the first-order superconducting transition in ${Sr}_{2} {RuO}_{4}$

Shunichiro Kittaka, Akira Kasahara, Toshiro Sakakibara, Daisuke Shibata, Shingo Yonezawa, Yoshiteru Maeno, Kenichi Tenya, and Kazushige Machida

Phys. Rev. B 90, 220502(R) – Published 1 December 2014

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Physical Review B

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Sharp magnetization jump at the first-order superconducting transition in Sr2RuO4

Shunichiro Kittaka, Akira Kasahara, Toshiro Sakakibara, Daisuke Shibata, Shingo Yonezawa, Yoshiteru Maeno, Kenichi Tenya, and Kazushige Machida

Phys. Rev. B 90, 220502(R) – Published 1 December 2014

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Sharp magnetization jump at the first-order superconducting transition in ${Sr}_{2} {RuO}_{4}$