Ⅲ-2. Atomic & Solid State Physics (Muon)

RIKEN Accel. Prog. Rep. 47 (2014)µSR study of heavy fermion superconductor URu2 Si2
I. Kawasaki,∗1 I. Watanabe,∗1 A. D. Hillier,∗2 and D. Aoki∗3,∗4

Normalized Asymmetry

0.04

-1

λ (µs )

0.06

0.02

005

10

1.0

19.5 K

0.8

11 K

0.6
0.4

Pµ || a0.2
0.0

0T05

1015Time (µs)

15 20T (K)2520∗2∗3∗4

0.8

0.620 Oe
10 Oe
5 Oe
3 Oe
0 Oe

05T = 11 K

Pµ || a1015Time (µs)

Fig. 2. The LF-µSR spectra at 11 K under several longitudinal fields.

A0 exp(−λZF t) over the temperature range presentlyinvestigated. We observed an enhancement of λZF in
the HO phase, which reﬂects a development of the TRS
breaking magnetic ﬁeld. Figure 1 exhibits the temperature dependence of λZF , and a sharp increase is clearlyobserved at T0 . λZF shows a saturated feature around
10 K, but it exhibits an additional increase with further
decreasing temperature and keeps increasing down tothe lowest temperature.
In order to investigate the dynamics of the internal
magnetic ﬁeld in the HO phase, we performed LF-ﬁeldexperiments where LF was applied parallel to the aaxis. Figure 2 shows the LF-µSR spectra measured at
11 K. The long tails of relaxation spectra are strongly
aﬀected by applying tiny LFs. This is a characteristic feature in the presence of a static ﬁeld distribution at muon sites. In this case, the exponential relaxation in the ZF experiments reﬂects the presenceof a Lorentzian ﬁeld distribution at muon sites. Since
the relaxation rate under LFs is a measure of transverse components of ﬁeld ﬂuctuations at muon sites,
the observed decoupling behavior implies the absenceof measurable ﬁeld ﬂuctuations along both the a and cdirections. Hence, we conclude that measurable magnetic ﬂuctuations do not exist along any directions atmuon sites, and the internal magnetic ﬁeld developedin the HO phase is static on the time scale of µSR.
References

30Fig. 1. Temperature dependence of the ZF-relaxation rate.
The inset shows the ZF-µSR spectra measured at 11
and 19.5 K.
∗11.0Normalized Asymmetry

Despite intensive studies for more than two decades,
the order parameter of the mysterious phase transition
at T0 = 17.5 K1) in URu2 Si2 has not been identiﬁedyet, and thus the ordered phase is referred to as thehidden order (HO) phase.
The symmetry of the HO phase is crucial information for the identiﬁcation of its order parameter.
Recent Shubnikov-de Haas experiments have revealed
that the Fermi surfaces in the HO phase are very similar to those of the pressure induced antiferromagnetic
phase.2) This conﬁrms that translational symmetry is
broken in the HO phase, and the ordering vector is
QHO = (1, 0, 0). In addition, in the HO state, NMR
and magnetic torque experiments have shown that thefour-fold rotational symmetry in the (001) plane is broken.3,4) On the other hand, the time-reversal symmetry (TRS) is still a controversial issue, since we canﬁnd two types of very recent theoretical models for theHO transition: some of the theoretical models assume
that the TRS is conserved in the HO phase,5) while
the others assume that TRS is broken.6) Therefore,
although the previous NMR and µSR studies have reported the development of tiny internal magnetic ﬁelds
below T0 7,8) and indicate the breaking of the TRS in
the HO phase, further characterization of the internal magnetic ﬁeld in the HO phase is required. In
the present study, we performed zero-ﬁeld (ZF) andlongitudinal-ﬁeld (LF) µSR experiments on a single
crystal of URu2 Si2 in order to characterize the internal magnetic ﬁelds in the HO state.
The inset of Fig. 1 shows ZF-µSR spectra at 11and 19.5 K, which are below and above T0 . The ZFspectra were well ﬁtted by a single exponential function

RIKEN Nishina Center
ISIS Facility, STFC Rutherford Appleton Laboratory
SPSMS, UMR-E CEA/UJF-Grenoble 1, INAC
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