Reentrant superconductivity induced by strong magnetic field in uranium based
heavy-fermion compound URhGe

Y. Tokunaga1), H. Sakai1), T. Hattori1), S. Kambe1), D.Aoki2,3), H. Mayaffre4),
S. Krämer4), M.-H. Julien4), C. Berthier4), M. Horvatić4), and S. Araki2,5)1): R. G. for Materials Physics for Heavy Element Systems, ASRC, JAEA
2): CEA-Grenoble 3): Tohoku Univ. 4): LNCMI-CNRS 5): Okayama Univ.

Fig.1 Temperature-field phase diagram of URhGe under themagnetic field applied along the b-crystal axis.

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Magnetic field along the b-axis (T)161/T2 (msec )Ferromagnetism is incompatible in general withsuperconductivity (SC) with singlet spin pairs, since astrong exchange field in ferromagnetic state forces thespin pairs to align in the same direction. In contrast,
fluctuation of ferromagnetic moments has been supposedto create a binding force between quasi-particles withtriplet spin, in the same manner as in the mechanism of
superfluid pairing in 3He. Such an unconventional spintriplet state, mediated by ferromagnetic fluctuations, isnow expected to be realized in a family of uranium based
compounds, UGe2, URhGe and UCoGe, so far the only
fully
establishedexamplesofferromagnetic
superconductors in which uniform SC is realized deep
inside the ferromagnetic states.
The field-induced re-entrant superconductivity (RSC)
discovered in URhGe [1] highlights the close interplay
between SC and ferromagnetism in these exotic
superconductors. Applied magnetic fields along the bcrystal axis first suppress the SC around 2 T, but then reinduce it between 10 and 13.5 T (Fig.1) [2]. At a similarfield of HR〜12 T, the ferromagnetic moments (which areparallel to the c crystal axis in zero field) are forced to bealigned along the field direction; the transition is thus
reminiscent of the textbook example of a quantum phasetransition in a transverse Ising chain. The phase diagramof URhGe thus implies the existence of novel SC
mechanism associated with the quantum phase transition,and the understanding of it will increase the possibility
for developing new SC devices controlled by strong
magnetic fields.
To elucidate the mechanism of the RSC, we have
prepared a 10% Co-doped URhGe single crystal andperformed Co nuclear magnetic resonance (NMR)
experiments. Figure 2 shows the contour plot of thetransverse NMR relaxation rate, 1/T2, measured at 1.6 K,
which reveals how ferromagnetic quantum fluctuations
are developed in the proximity of quantum critical point(HR) in the plane (Hb, Hc) of the magnetic fieldcomponents [3]. In the same figure, we also show theregion where the RSC has been observed by resistivity
measurements in a single crystal of URhGe [4]. We cansee that the RSC appears almost in the same limited
region as that where we have observed the strong
quantum fluctuations in the (Hb, Hc) plane. This close
overlap between RSC and the quantum fluctuations
provide strong evidence that the pairing mechanism of
RSC is mediated by these fluctuations in this system [3].

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2.0 1.5 1.0 0.5

00.5 1.0 1.5

Magnetic Field along the c-axis (T)Fig.2 Map of the magnetic fluctuations amplitude in the (Hb,Hc)
plane around HR [3]. The open squares indicate the region whereRSC has been observed at T=40 mK in a single crystal of URhGe[4]. Since URhGe has a lower HR (12 T) than URh0.9Co0.1Ge(13.4 T), the data for URhGe are plotted here with the fieldvalues scaled proportionally to the corresponding HR values.

References[1] F. Lévy et al., Science 309, 1343 (2005).
[2] D. Aoki et al., J. Phys. Soc. Jpn. 81, 011003 (2012).
[3] Y. Tokunaga et al., Phys. Rev. Lett. 114, 216401 (2015).
[4] F. Lévy et al., J. Phys. Condens. Matter 21, 164211 (2009).