Field-induced reentrant superconductivity driven by quantum tricritical fluctuations in URhGe

doi:10.1016/j.physb.2017.09.022

Physica B: Condensed Matter

Volume 536, 1 May 2018, Pages 122-124

https://doi.org/10.1016/j.physb.2017.09.022 Get rights and content

Abstract

We review our ⁵⁹Co NMR study in a URhGe single crystal doped with 10% cobalt. The spin-spin relaxation time $(T_{2})$ measurements have revealed a divergence of electronic spin fluctuations in the vicinity of a field-induced tricritical point (TCP) locating around 13 T. The fluctuations is developed in the same limited field region around the TCP as that where a reentrant superconductivity (RSC) is observed in URhGe. The finding strongly suggests these quantum fluctuations as the pairing glue responsible for the RSC.

Introduction

Quantum critical points (QCPs) are of great current interest in modern condensed matter physics because of their singular ability to influence the finite temperature properties of materials. In the vicinity of a QCP, the strong fluctuations induced by quantum mechanics are thought to promote a reorganization of the electrons into new quantum phases, such as superconductivity (SC) in high temperature superconductors, or field-induced reentrant superconductivity (RSC) in the case of the uranium-based ferromagnetic (FM) superconductor URhGe.

Fig. 1(a) shows the temperature-field phase diagram of URhGe. At zero field, U 5f moments $(0.4 μ_{B})$ are ordered ferromagnetically along the c axis below the Curie temperature $T_{Curie} = 9.5 K$ [1]. A magnetic field applied along the b-axis $(H_{b})$ gradually decreases the $T_{Curie}$ , and eventually aligns the U moments along the b-axis at a critical field $H_{R} \sim 12 T$ [2], [3], [4], [5]. The transition is thus reminiscent of the textbook example of a field-induced quantum phase transition in a transverse Ising chain [6], however, the observation of first-order-like behaviors near $H_{R}$ implies that the transition is not an ordinary QCP, but involves a tricritical point (TCP) [5], [7], [8], [9], [10], [11]. Recent thermoelectric power measurement has estimated the TCP at $T = 2 K$ and $H = 11.5 T$ [11]. The RSC emerges around $H_{R}$ [2], [7], [8]. The RSC shows a maximum transition temperature of $T_{SC} = 0.42 K$ at the $H_{R}$ , which is higher than that observed for the lower field SC below 2 T $(\sim 0.25 K)$ .

For the mechanism of the RSC, it was naively believed from the beginning that FM quantum critical fluctuations may play a key role [2]. However, microscopic insight on the nature of these fluctuations was not disclosed. In this paper, we review our Co NMR study performed in URh_0.9Co_0.1Ge. The experiments have revealed a divergence of longitudinal ( $H ∥ b$ ) component of spin fluctuations around the field-induced QCP [12]. Comparison with resistivity measurements demonstrates that the FM quantum critical fluctuations are at the origin of the occurrence of the RSC.

Section snippets

Experimental

Since both Rh and Ge nuclei have poor NMR sensitivity, we studied ⁵⁹Co NMR in a URhGe single crystal doped with 10% cobalt (= URh_0.9Co_0.1Ge) [the inset to Fig. 1(a)]. URhGe and UCoGe have the same crystal structure of the orthorhombic TiNiSi type [Fig. 1(b)] and are both itinerant ferromagnet. The substitution of Co for Rh is thus isostructural and it only minimally affects the magnetic properties [13], [14]. The spin system retains its strong Ising character along the c axis, and the

Results and discussion

The upper panels of Fig. 2(a) and (b) show the field dependence of $1 / T_{2}$ . Here $1 / T_{2}$ values reflect the magnitude of the longitudinal component (parallel to the applied field) of slow spin fluctuations near zero frequency $(ω \sim 0)$ . That is, $1 / T_{2} \propto G_{∥} (0)$ , where $G_{α} (ω) = \int_{- \infty}^{\infty} 〈 h_{α} (t) h_{α} (0) 〉 \exp (i ω t) dt$ is the spectral density of the fluctuating hyperfine field [12]. As seen in Fig. 2(a), $1 / T_{2}$ for $θ = 0 °$ $(H ∥ b)$ shows strong field dependence associated with a divergence of the longitudinal component of the

Summary

The ⁵⁹Co NMR experiments in URh_0.9Co_0.1Ge have revealed the close interplay between the RSC and field-induced quantum fluctuations, which involve a strong component perpendicular to the Ising axis due to the tricritical nature of the phase transition. Our finding strongly suggests these quantum fluctuations as the pairing glue responsible for the RSC.

Recently, using the same single crystal, we have extended our ⁵⁹Co NMR study to high fields up to 30 T in the $(ab)$ -magnetic plane. The experiment

Acknowledgements

We are grateful for stimulating discussions with R.E. Walstedt, J. Flouquet, N. Tateiwa, K. Kubo, K. Hattori, H. Ikeda, K. Aoyama, and V.P. Mineev. A part of this work was supported by JSPS KAKENHI Grant nos. 26400375, 15H05745 and 15K05884 (J-Physics), ERC starting grant (NewHeavyFermion), ICC-IMR, and the REIMEI Research Program of JAEA.

References (31)

S. Sakarya et al.
J. Alloy. Compd.
(2008)
N.T. Huy et al.
Solid State Commun.
(2009)
D. Aoki et al.
Nature
(2001)
F. Lévy et al.
Science
(2005)
F. Hardy et al.
Phys. Rev. B
(2011)
D. Aoki et al.
J. Phys. Soc. Jpn.
(2012)
D. Aoki et al.
J. Phys. Soc. Jpn.
(2014)
See, for example, S. Sachdev, Quantum Phase Transitions, Cambridge Univ. Press,...
F. Lévy et al.
Nat. Phys.
(2007)
F. Lévy et al.
J. Phys. Condens. Matter
(2009)

A. Huxley et al.

J. Phys. Soc. Jpn.

(2007)

H. Kotegawa et al.

J. Phys. Soc. Jpn.

(2015)

A. Gourgout et al.

Phys. Rev. Lett.

(2016)

Y. Tokunaga et al.

Phys. Rev. Lett.

(2015)

A. Miyake et al.

J. Phys. Soc. Jpn.

(2008)

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Physica B: Condensed Matter

Field-induced reentrant superconductivity driven by quantum tricritical fluctuations in URhGe

Abstract

Introduction

Section snippets

Experimental

Results and discussion

Summary

Acknowledgements

J. Alloy. Compd.

Solid State Commun.

Nature

Science

Phys. Rev. B

J. Phys. Soc. Jpn.

J. Phys. Soc. Jpn.

Nat. Phys.

J. Phys. Condens. Matter

J. Phys. Soc. Jpn.

J. Phys. Soc. Jpn.

Phys. Rev. Lett.

Phys. Rev. Lett.

J. Phys. Soc. Jpn.