A High Field 29Si NMR Study of URu 2 Si 2 : A Novel Emergent Phase Out of the“Hidden-Order” State

H. Sakai1), Y. Tokunaga1), S. Kambe1), R. R. Urbano2,3), M.-T. Suzuki4), P. L. Kuhns3), A. P. Reyes3),
P. H. Tobash5), F. Ronning5), E. D. Bauer5), and J. D. Thompson5)1)
R. G. for Condens. Matter Phys. Heavy Element Systems, ASRC, JAEA
2)
IFGW, UNICAMP, Brazil 3) National High Magnetic Field Laboratory, FSU, USA
4)
CCSE, JAEA 5) Los Alamos National Laboratory, USA

The so-called “hidden-order” (HO) state, which emerges in
the URu 2 Si 2 heavy-fermion superconductor below a zero field
phase transition at T O =17.5 K, has posed a long-standing
mystery, particularly because of the inconclusive nature of its
order parameter [1]. URu 2 Si 2 is also a very attractive material
displaying intriguing T-H phase diagrams (see Fig. 1(b))
determined by the electronic transport measurements such as
resistivity and Hall effect. In particular, an anomaly in the Hall
resistivity around H*~22 T has been reported within the HO
phase [2]. It is also reported that the critical field of the HO
phase is about H c =35 T by means of resistivity andmagnetization measurements [3, 4]. Such electronic states inhigh fields are still unrevealed, let alone uncertain about therelationship with the HO state. Nuclear magnetic resonance(NMR) is a very suitable microscopic technique to investigate
such anomalies in URu 2 Si 2 . Since we cannot reach the highmagnetic field above 35 T for NMR purpose domestically atpresent, we have collaborated internationally with the researchgroups of National High Magnetic Field Laboratory and Los
Alamos National Laboratory in USA. The single crystals
studied in this project were enriched with 99.8% of 29Si isotope,
a very NMR sensitive nucleus, whose natural abundance is only
4.7%. High field NMR experiments in NHMFL were accepted
to go up to 45 T, which is world record’s static magnetic field.
We have performed NMR experiments to take NMR shifts andspectrum just above H c [5].
It is worth briefly mentioning few striking NMR results: thelow-temperature 29Si-NMR shift (K) anomaly around H* and thecritical increase of K towards H c ~35.6 T. Both observations
must be related to crucial changes in the Fermi surface of
URu 2 Si 2 . In general, K is proportional to static susceptibility χvia hyperfine coupling constant A, i.e., K=Aχ. By comparison
with the magnetization M=χH data [4], A=3.4 kOe/μ B is
obtained in the HO state, which is consistent with the reported
values of 3.3-3.6 kOe/μ B in the paramagnetic (PM) state.
Consequently, this is also in agreement with the conclusionfrom recent low-field 29Si-NMR measurements [6, 7] that thereis no ordered magnetic moment in the HO state. From amagnetic point of view, the HO phase can thus be viewed as aPauli-PM-like state. Therefore, now K ∝ χ is proportional to thetotal density of states at Fermi level D(E F ). Indeed, the changeof K is qualitatively consistent with the change of D(E F ) byexternal field, which has been calculated with internal
collaboration of CCSE, JAEA. In the magnetic field scan
procedure (A) in Fig. 1(b) at T=0.4 K, the transition between theHO and the magnetic II phases is also found to be of first order,
since the 29Si-NMR signal was gone suddenly just above H c .
In the T-lowering (B) procedure in Fig. 1(b) at H~35.6 T, wehave succeeded the first observation of the 29Si NMR spectrum
in the high field PM phase at 40 T as well as the complex 29Si
NMR spectrum in the magnetic II phase displayed in Fig. 1(a).
This spectral shape for the II phase can be understood by aFig. 1 (a) 29Si NMR spectra in the paramagnetic (PM) and themagnetic II phases, (b) T-H phase diagram for URu2Si2, and(c) schematic spin structure in the II phase.
ferrimagnetic (or antiferromagnetic) ordering of Ising-type
localized spin arrays, as illustrated in Fig. 1(c). Interestingly, thepropagation vector is perpendicular to the symmetrical c axis
(the external field direction). This magnetic structure violates
the four-fold rotational symmetry in the crystal lattice. The
estimate of Ising moments is uniformly about 0.6 μ B per eachuranium site.
Our high field NMR results provide the first microscopic
evidence of the change in the magnetic susceptibility around H*,
which, in turn, could not be unveiled by previous transportmeasurements. The U localized moments with Ising character
suddenly emerge in the II phase from non-magnetic itinerant
HO state. This behaviour may find some connection with arecent proposed theoretical model [8]: the HO state might be an
antiferro-ordered phase of extremely higher-order multipolar
moments, i.e., dotriacontapole. Further investigations will
clarify it more in the near future.
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