New aspects on URu2Si2 and CeTIn5 (T=Rh, Ir, Co) observed by high pressure NMR and NQR

Abstract

NMR and NQR studies on two interesting systems (URu2Si2, CeTIn5) were performed under high pressure. (1) URu2Si2: In the pressure range 3.0 to 8.3 kbar, we have observed new 29Si NMR signals arising from the antiferromagnetic (AF) region besides the previously observed 29Si NMR signals which come from the paramagnetic (PM) region in the sample. This gives definite evidence for spatially-inhomogeneous
development of AF ordering below T
0 of 17.5 K. The volume fraction is enhanced by applied pressure, whereas the value of internal field (∼91 mT) remains constant
up to 8.3 kbar. In the AF region, the ordered moment is about one order of magnitude larger than 0.03 µB. (2) CeTIn5: The pressure and temperature (T) dependences of nuclear spin-lattice relaxation rate 1/T
1 of 115In in CeTIn5 have shown that the superconductivity (SC) occurs close to an AF instability. From the T dependences of 1/T
1 and Knight shift below T
c. CeTIn5 has been found to exhibit non-s wave (probable d wave) SC with even parity and line nodes in the SC energy gap.

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PRAMANA
— journal of
physics
c ? Indian Academy of SciencesVol. 58, Nos 5 & 6
May & June 2002
pp. 755–760
New aspects on URu2Si2and CeTIn5
(T = Rh, Ir, Co) observed by high
pressure NMR and NQR
T KOHARA1,∗
Department of Material Science, Himeji Institute of Technology, Kamigori,
Akogun, Hyogo 678-1297, Japan
∗Email: kohara@sci.himeji tech.ac.jp
Abstract.
under high pressure. (1) URu2Si2: In the pressure range 3.0 to 8.3 kbar, we have observed new29Si
NMR signals arising from the antiferromagnetic (AF) region besides the previously observed29Si
NMR signals which come from the paramagnetic (PM) region in the sample. This gives definite ev-
idence for spatially-inhomogeneous development of AF ordering below T0of 17.5 K. The volume
fraction is enhanced by applied pressure, whereas the value of internal field (∼91 mT) remains con-
stant up to 8.3 kbar. In the AF region, the ordered moment is about one order of magnitude larger
than 0.03 µB. (2) CeTIn5: The pressure and temperature (T) dependences of nuclear spin-lattice re-
laxation rate 1/T1of115In in CeTIn5have shown that the superconductivity (SC) occurs close to an
AF instability. From the T dependences of 1/T1and Knight shift below Tc, CeTIn5has been found
to exhibit non-s wave (probable d wave) SC with even parity and line nodes in the SC energy gap.
NMR and NQR studies on two interesting systems (URu2Si2, CeTIn5) were performed
Keywords. URu2Si2; CeTIn5; high pressure; NMR; NQR.
PACS Nos 74.70.Tx; 75.40.-s; 76.60.-k; 76.60.Gv
1. Introduction
Accordingtotherecentstudiesonf-electronsystems,mostoftheceriumanduraniumcom-
pounds with heavy electron mass indicate unusual phenomena including magnetic and/or
quadrupolar orderings, spin and/or valence fluctuations and anisotropic superconductivity
by the application of pressure and substitution of constituent elements. Among them we
performed NMR and NQR measurements on URu2Si2and CeTIn5(T=Rh, Ir, Co) under
high pressure for the purpose based on the following backgrounds.
1In collaboration with K Matsuda and Y Kohori (Himeji Inst. of Tech., Japan), H Amitsuka
(Hokkaido Univ., Japan), E D Bauer and M B Maple (UC San Diego, USA) and J L Sarrao (LANL,
USA)
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T Kohara
1. URu2Si2: In the heavy-fermion compound URu2Si2, two successive phase transitions
occur at 17.5 K and 1.4 K. The transition at 1.4 K is recognized as the onset of uncon-
ventional superconductivity (SC) [1]. All the basic properties (resistivity, specific heat,
magnetization, thermal expansion) of URu2Si2exhibit a clear mean-field-like transition at
T0= 17.5 K independent of the sample quality. The neutron diffraction (ND), however,
revealed that a simple type-I antiferromagnetic (AF) ordering with U moments develops
along c-axis below T0and the observed extremely weak Bragg peak intensities are inter-
preted as originating from a ‘tiny staggered moment’ of only 0.03 µB/U [2]. Thus, uncon-
ventional phase transition at T0has remained a mystery for almost 15 years. Recently, the
ND experiment performed under pressure up to 28 kbar has shown that the magnitude of
the staggered moment (µ) increase linearly up to 0.25 µB/U at 10 kbar and then shows a
tendencyto be saturated at 13 kbar [3]. Since our previous29Si NMR carried out at ambient
pressure could not detect any evidence for AF ordering [4], high pressure29Si NMR has
been performed.
2. CeTIn5: The occurrence of SC in strongly correlated f-electron systems has been an
active area of research for several decades.
Since 1995, most AF Ce compounds such as CePd2Si2, CeRh2Si2, CeIn3and CeNi2Ge2
have been shown to become superconductors under high pressure [5]. Unfortunately, lit-
tle knowledge of SC was revealed in these systems from NMR/NQR owing to the severe
experimental conditions of lower superconducting transition temperature (Tc) and higher
superconducting critical pressure (Pc). However, new pressure-induced superconductor
CeRhIn5with higher Tcand lower Pchas recently been reported [6]. Besides CeCoIn5
and CeIrIn5heavy-fermion superconductors, we have performed the115In NMR/NQR and
59Co NMR on CeTIn5(T=Rh, Co, Ir) to examine the possibility of unusual SC mediated
by AF spin fluctuations near AF instability.
2. Results and discussion
1. URu2Si2: The Si NMR spectra with no quadrupolar effect because of I = 1/2 for29Si,
were measured under pressure up to 8.3 kbar by sweeping the frequency at Hex= 4.3 T.
Figure 1 presents the temperature (T) evolution of29Si NMR spectrum at 8.3 kbar for
Hex ? c-axis. As seen in this figure, just single resonance line was observed at high T,
whereas two symmetric resonance lines with respect to the main one appeared below T0.
The result of no splitting for the resonance line for Hex⊥ c-axis (not shown in the figure)
indicates that the internal field (Hin) at Si site is parallel to the c-axis. Up to now, this
AF ordering has been believed to develop uniformly throughout the sample at low T. As
is clearly seen from figure 1, the main resonance line decreases drastically upon cooling
while the intensity of two Hin-split resonance lines increases, suggesting that the AF region
increases in volume. At 6 K, the volume fraction of the AF region attains 85% of the whole
volume. Figure 2a shows the T variation of Hindeducedfrom the Hin-split lines at 8.3 kbar.
The Hinincreases rapidly below T0, and keeps almost constant at low T. As seen in
figure 2b, the estimated AF volume fraction at 6 K increases with increasing pressure
whereas Hin(∼ 91 mT) remains constant up to 8.3 bar. Assuming a homogeneous AF
ordering throughout the sample, the ND results show that the µ value attains 0.25 µB/U at
10 kbar. Moreover, the correct ordered moment is estimated to be 0.3 µB/U below 8.3 kbar,
using the AF volume fraction obtained by the Si NMR. The present Si NMR results show
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New aspects on URu2Si2and CeTIn5
Figure 1. T evolution of29Si NMR spectrum for Hex? c-axis at 8.3 kbar.
Figure 2. (a) T dependence of Hinat 8.3 kbar. (b) Hinand AF volume fraction vs.
applied pressure.
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T Kohara
Figure 3. T dependence of 1/T1in CeTIn5.
that the AF region increases in volume with increasing applied pressure at the expense of
paramagnetic (PM) region, where a hidden order parameter develops. Consequently, these
two types of order compete with each other for volume fraction below T0. As one of the
possibilities for the hidden order parameters, there are some models based on quadrupolar
ordering. In models with a doublet ?5ground state of 5 f2configuration, the quadrupolar
and dipolar orderings intrinsically compete with each other owing to the incommutability
of theseoperators. The quadrupolarordering model qualitativelyexplainsthe presentNMR
results, although the mechanism by which the magnetic ground state is determined remains
unclear.
2. CeTIn5: Distinct In NQR lines could be observed owing to huge quadrupole moment
of115In (I = 9/2) in CeTIn5with a tetragonal HoCoGa5structure. Four ‘allowed’ transi-
tions would be expected when asymmetric parameter η is small. Thus, two sets of sharp
NQR signals (eight signals) corresponding to two crystallographically inequivalent In sites
were observed in the paramagnetic T range (not shown in the figure).
Figure 3 shows the T dependence of nuclear spin-lattice relaxation rate (1/T1) in
CeRhIn5at P =27 kbar, and CeCoIn5and CeIrIn5at ambient pressure. In the normal state
1/T1varies close to T1/2in CeRhIn5and CeIrIn5, and close to T1/4in CeCoIn5, which
are qualitatively explained by the spin fluctuations developed around the AF instability,
following SCR theory by Ishigaki and Moriya [7]. Below Tc(2.3 K for CeCoIn5, 0.3 K
for CeIrIn5, 2.2 K for CeRhIn5at P = 27 kbar), 1/T1decreases nearly proportionally to
T3at low T, indicating the energy gap with line nodes, which is reminiscent of relaxation
behavior in many heavy-fermion superconductors such as UPt3, URu2Si2, UPd2Al3etc.
Assuming a simple polar model ? = ?0cosθ, the calculated T1values reproduce well the
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New aspects on URu2Si2and CeTIn5
Figure 4. T dependence of Knight shifts59K and115K in CeCoIn5. Tc(H) stands for
Tcunder the external field applied for the NMR measurements.
experimental ones by evaluating tentatively ?0=10 kBTc, 8 kBTcand 5 kBTcfor CeCoIn5,
CeRhIn5and CeIrIn5, respectively.
Next, the T evolution of115In and59Co Knight shifts (abbreviated as115K and59K,
respectively) below 4 K are shown in figure 4. As clearly seen in this figure, a large de-
crease of115K below Tcwas observed for parallel and perpendicular directions to c-axis
and a decrease of59K was observed only for parallel component, which has inferred the
SC of even parity. No decrease of59K perpendicular to c-axis is expected mainly due to
the large Co orbital contribution. The calculated T dependence of K by using the same
energy gap value for T1analysis is also plotted in figure 2. The nearly T linear variation
for K at very low T, which arises from the low energy excitation of quasi-particles in the
superconducting state, has also clearly been measured. Thus, both T variations of 1/T1
and K are successfully explained by the polar model, indicating strongly the appearance
of anisotropic even parity (probably d-wave) SC in CeTIn5.
3. Summary
We observed29Si NMR signals arising from the AF region besides the previously observed
29Si NMR signals which come from the PM region in the sample. This gives definite evi-
dence for spatially-inhomogeneous development of AF ordering below T0of 17.5 K. The
present Si NMR results indicate that the weakness of AF Bragg peak at ambient pres-
sure originates not from the extremely small magnitude of magnetic moment, but from
the smallness of the AF region in the sample. Next, in the normal state of CeTIn5, the
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