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101Ru NQR study of antiferromagnetic superconductor URu2Si2
IWIII ELSEVIER
Physica B 230-232 (1997) 351-353
101RuNQR study of antiferromagnetic superconductorURu2Si2 K a z u y u k i M a t s u d a , Y o h K o h o r i *, T a k a o K o h a r a Department of Material Science, Faculty of Science, Himeji Institute of Technology, Ako-gun, Hyo9o 678-12, Japan
Abstract
We have carried out I°IRu NQR measurement of URu2Si2 in zero magnetic field in the temperature (T) range from 0.16 to 130 K. The electric quadrupole interaction parameters of 101Ru were determined to be VQ= 5.72 MHz and v/= 0 at 1.3 K. Although URu2Si2 is in the antiferromagnetic (AF) state below 17.5 K, no broadening of NQR line was observed, indicating that transferred hyperfine field from U moments is cancelled at Ru site. The nuclear spin-lattice relaxation rate (I/TI) decreases drastically below 17.5 K associated with AF ordering. In the superconducting state, 1/T~ has no coherence peak just below Tc = 1.2 K, and decreases in proportion to T 3 with no deviation down to 0.2 K, which shows the existence of line nodes in the superconducting energy gap. Keywords: URu2Si2; Superconductivity; NQR
The nature of the superconducting state in highly correlated electron systems as CeCu2 Si2, UPt3, UBel3, UPd2AIs and URu2Si2 is of much current interest. These compounds show formation of heavy quasiparticles as the conduction electrons hybridize with the uranium 5f electrons. The hybridization leads to antiferromagnetic (AF) spin fluctuations on U sites. The presence of the spin fluctuations has led to the prediction that an unconventional Cooper pair state with non-s wave symmetry is realized in these systems. In URu2Si2, neutron diffraction experiment revealed that long-rang AF ordering with an ordered moment of (0.03 + 0.01)#B appears below the Nrel temperature (TN) of 17.5 K [1]. Since the anomalously small magnitude of the ordered moment is difficult to reconcile with the large jump of the specific heat at TN, this has led to a speculation that the ordering might have an exotic character. The origin of small moment is still a subject of lively debates. In URu2Si2, the superconductivity occurs below 1.2 K and coexists with the * Corresponding author.
AF ordering. Recently, we have succeeded in observing a l°lRu NQR signal in URu2Si2, which enables us to obtain the informaton of electric field gradient at l°lRu site and to measure 1/1"1 without external magnetic field both in the normal and superconducting states. NQR measurements were carried out by using a conventional phase-coherent pulsed spectrometer. 7"1 was obtained by the recovery of the nuclear magnetization after a saturation pulse. The measurements above 1.3 K were performed with 4He cryostat, and below 1.3 K with the 3He-4He dilution refrigerator. As the electric quadrupole moment of 99Ru is small, the 99Ru spectrum was obtained by NMR with 8 T superconducting magnet. Fig. 1 shows the 99Ru NMR spectra obtained in randomly oriented and aligned (tetragonal c-axisllHext) microcrystals. Each NMR spectrum consists of a center line and satellites induced by the first-order quadrupole effect. The magnitude of the electric quadrupole interaction (VQ) was deduced to be about 0.95 MHz from the separation of the first-order
0921-4526/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved Pll S0921-4526(96)00718-1
K. Matsuda et aL / Physica B 230-232 (1997) 351-353
352
f=14.3MHz T=I.3K
J"l
K=O , :
........
i
........
I
........
!
'
'
r" 7~
". i
.. • ,~ •
Z W }Z rr
'
iV 1/T'1 ~
(a)
. ~.".
t
or:,
10°.:
' 818 ' ;,12 ' ;,'6 ' r
z ..s
•
rr • °,
I
I
I
6.8
I
Tc
-
(b)
.:
1/T1°cT
•
'
I
I
7.2 H(T)
I
10 -2
7.6
,~
ol°lRu NQR o 29
Fig. 1. 99Ru NMR spectrum obtained at 14.3MHz and 1.3 K in (a) randomly oriented, and (b) aligned (c-axisl[Hext)powder sample. The positionof K = 0 was determinedby 99Ru NMR of Ru metal (K = 0.483% at 4.2 K). 11.8
~ . . . . . . . . . . . . . . .
Si N M R
O
¢ 1/'T'1 ~ T 3 10-
1
,I / . . . . . . . .
0_ 1
I
10 0
........
I
10 1
........
i
10 2
,
,,
T(N Fig. 3. Temperaturedependenceof I/T1 of ]°lRu. In the figure, 1/T] of Z9Si is also plotted.
~11 •
S
m '•e
11.4 11.211,4
11.6
f(M~:) i
0
.
.
.
.
.
i
,
i
T(N
i
I
i
i
i
,
i
100
Fig. 2. Temperature dependence of 2VQ. In the inset of the figure, l°lRu NQR spectrum obtained at 1.3 K is shown.
satellites of the randomly oriented powder pattern, and the direction of the electric field gradient (Vzz) was obtained to be the tetragonal c-axis by the field alignment of microcrystals. By comparing the respective electric quadrupole moments o f 99Ru and l°lRu [2], VQ(IO1Ru) was estimated to be about 5.5 MHz. Indeed l°]Ru NQR signals were observed at 5.72 and 11.44 MHz at 1.3 K, as shown in the inset of Fig. 2. From the spectrum, we evaluated the electric quadrupole interaction parameter precisely as vo = 5.72 MHz and r / = 0. Although URuvSi2 is in the AF state below 17.5 K, the NQR lines at 1.3 K are narrow, implying the
transferred hyperfine field from U moments being canceled at Ru sites. This explanation is consistent with the magnetic structure proposed by neutron diffraction experiment [1]. Above 20 K, the resonance frequency (2VQ) increases gradually with increasing temperatures, as shown in Fig. 2. The T-dependence of VQ (l°lRu) would be caused by the energy level splitting of uranium 5f-electrons induced by the crystal-field effect [3]. Since the sizable anomalies observed at TN in various thermodynamic quantities is hard to be reconciled with the extreme weakness of the magnetic moment, the possibility such as the quadrupolar ordering is proposed for the phase transition at 17.5 K. In this case, the change of electric field gradient should be expected, however, we could not observe any change of VQ at Ru site. Further study is still necessary to understand the origin of the sizable anomalies at TN. Using NQR signal observed around 11.44 MHz, the nuclear spin-lattice relaxation time (7'1) of l°lRu was measured in zero magnetic field both in the normal and
K. Matsuda et al. / Physica B 230-232 (1997) 351-353 superconducting states in the temperature range from 0.16 to 130 K. The T-dependence of 1/1"1 is shown in Fig. 3. In the figure, our previously reported 1/1"1 of 29Si is also plotted [4]. As seen in the figure, 1/1"1 of l°lRu is nearly T-independent above 60 K and varies in proportion to T at low temperatures, which implies that the crossover occurs from the localized state at high temperature to the Fermi-liquid state below 60 K. Below TN=17.5 K, 1/I"1 decrease markedly, whose T-dependence is fitted by the following form:
1/T1=O.28T
(l/s)
(17.5K
1/T1 = 0.048T + 14 500 exp(-A/kBT)
(I/s)
(1.2K < T < 17.5K), with A/kB = 150 K, where the first term in the ordered state represents the contribution from the residual density of states (DOS) and the second term from the thermal excitations above the energy gap of the magnitude, A. The behavior of 1/I"1 indicates the opening of gap at the Fermi surface below TN and DOS is reduced to about 40% of the value in the paramagnetic state. This T-dependence is nearly the same as that observed previously in Si NMR. In the superconducting state, l/T1 shows no HebelSlichter coherence peak just below Tc = 1.2 K and decreases in proportion to T 3 with no deviation down to 0.2 K. It should be noticed that the measurement was performed in zero magnetic field. Then, there is no contribution from the vortex cores. Owing to small gyromagnetic ratio of l°lRu spin, 1/I"1 of l°lRu is insensitive to the paramagnetic impurity. Hence, the relaxation of l°lRu is dominated by the excitations of
353
the superconducting quasiparticles down to 0.2 K. The T-dependence of 1/7'1 in the superconducting state is explained in terms of the anisotropic superconducting energy gap which has line nodes on the Fermi surface. This result supports the appearance of non-s wave superconductivity in URu2Si2. In Summary, the electric quadrupole interaction parameters of l°IRu were determined to be VQ = 5.72 MHz and r/-- 0 at 1.3 K. Although the system is in AF state below 17.5 K, no broadening of NQR line was observed, indicating that the transferred hyperfine field is cancelled at Ru site. l/T1 decreases drastically below 17.5 K associated with AF ordering. In the superconducting state, 1/T1 has no coherence peak just below Tc -- 1.2 K and decreases in proportion to T 3 with no deviation down to 0.2 K, which shows the existence of line nodes in the superconducting energy gap. This work is partly supported by a Grant-in-Aid from the Ministry of Education, Science and Culture of Japan, and also supported by Hyogo Science and Technology Association.
References [1] C. Broholm, H. Lin, P.T. Matthews, T.M. Mason, W.J.L. Buyers, M.F. Collon, A.A. Menovsky, J.A. Mydosh and J.K. Kjems, Phys. Rev. B 43 (1991) 12809. [2] A. Burgstaller, J. Voitl~inderand H. Ebert, J. Phys.: Condens. Matter 6 (1994) 8335. [3] See, for example, G.J. Nieuwenhuys, Phys. Rev. B 35 (1986) 5260. [4] Y. Kohori, K. Maysuda and T. Kohara, J. Phys. Soc. Japan 65 (1996) 1083.
Physica B 230-232 (1997) 351-353
101RuNQR study of antiferromagnetic superconductorURu2Si2 K a z u y u k i M a t s u d a , Y o h K o h o r i *, T a k a o K o h a r a Department of Material Science, Faculty of Science, Himeji Institute of Technology, Ako-gun, Hyo9o 678-12, Japan
Abstract
We have carried out I°IRu NQR measurement of URu2Si2 in zero magnetic field in the temperature (T) range from 0.16 to 130 K. The electric quadrupole interaction parameters of 101Ru were determined to be VQ= 5.72 MHz and v/= 0 at 1.3 K. Although URu2Si2 is in the antiferromagnetic (AF) state below 17.5 K, no broadening of NQR line was observed, indicating that transferred hyperfine field from U moments is cancelled at Ru site. The nuclear spin-lattice relaxation rate (I/TI) decreases drastically below 17.5 K associated with AF ordering. In the superconducting state, 1/T~ has no coherence peak just below Tc = 1.2 K, and decreases in proportion to T 3 with no deviation down to 0.2 K, which shows the existence of line nodes in the superconducting energy gap. Keywords: URu2Si2; Superconductivity; NQR
The nature of the superconducting state in highly correlated electron systems as CeCu2 Si2, UPt3, UBel3, UPd2AIs and URu2Si2 is of much current interest. These compounds show formation of heavy quasiparticles as the conduction electrons hybridize with the uranium 5f electrons. The hybridization leads to antiferromagnetic (AF) spin fluctuations on U sites. The presence of the spin fluctuations has led to the prediction that an unconventional Cooper pair state with non-s wave symmetry is realized in these systems. In URu2Si2, neutron diffraction experiment revealed that long-rang AF ordering with an ordered moment of (0.03 + 0.01)#B appears below the Nrel temperature (TN) of 17.5 K [1]. Since the anomalously small magnitude of the ordered moment is difficult to reconcile with the large jump of the specific heat at TN, this has led to a speculation that the ordering might have an exotic character. The origin of small moment is still a subject of lively debates. In URu2Si2, the superconductivity occurs below 1.2 K and coexists with the * Corresponding author.
AF ordering. Recently, we have succeeded in observing a l°lRu NQR signal in URu2Si2, which enables us to obtain the informaton of electric field gradient at l°lRu site and to measure 1/1"1 without external magnetic field both in the normal and superconducting states. NQR measurements were carried out by using a conventional phase-coherent pulsed spectrometer. 7"1 was obtained by the recovery of the nuclear magnetization after a saturation pulse. The measurements above 1.3 K were performed with 4He cryostat, and below 1.3 K with the 3He-4He dilution refrigerator. As the electric quadrupole moment of 99Ru is small, the 99Ru spectrum was obtained by NMR with 8 T superconducting magnet. Fig. 1 shows the 99Ru NMR spectra obtained in randomly oriented and aligned (tetragonal c-axisllHext) microcrystals. Each NMR spectrum consists of a center line and satellites induced by the first-order quadrupole effect. The magnitude of the electric quadrupole interaction (VQ) was deduced to be about 0.95 MHz from the separation of the first-order
0921-4526/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved Pll S0921-4526(96)00718-1
K. Matsuda et aL / Physica B 230-232 (1997) 351-353
352
f=14.3MHz T=I.3K
J"l
K=O , :
........
i
........
I
........
!
'
'
r" 7~
". i
.. • ,~ •
Z W }Z rr
'
iV 1/T'1 ~
(a)
. ~.".
t
or:,
10°.:
' 818 ' ;,12 ' ;,'6 ' r
z ..s
•
rr • °,
I
I
I
6.8
I
Tc
-
(b)
.:
1/T1°cT
•
'
I
I
7.2 H(T)
I
10 -2
7.6
,~
ol°lRu NQR o 29
Fig. 1. 99Ru NMR spectrum obtained at 14.3MHz and 1.3 K in (a) randomly oriented, and (b) aligned (c-axisl[Hext)powder sample. The positionof K = 0 was determinedby 99Ru NMR of Ru metal (K = 0.483% at 4.2 K). 11.8
~ . . . . . . . . . . . . . . .
Si N M R
O
¢ 1/'T'1 ~ T 3 10-
1
,I / . . . . . . . .
0_ 1
I
10 0
........
I
10 1
........
i
10 2
,
,,
T(N Fig. 3. Temperaturedependenceof I/T1 of ]°lRu. In the figure, 1/T] of Z9Si is also plotted.
~11 •
S
m '•e
11.4 11.211,4
11.6
f(M~:) i
0
.
.
.
.
.
i
,
i
T(N
i
I
i
i
i
,
i
100
Fig. 2. Temperature dependence of 2VQ. In the inset of the figure, l°lRu NQR spectrum obtained at 1.3 K is shown.
satellites of the randomly oriented powder pattern, and the direction of the electric field gradient (Vzz) was obtained to be the tetragonal c-axis by the field alignment of microcrystals. By comparing the respective electric quadrupole moments o f 99Ru and l°lRu [2], VQ(IO1Ru) was estimated to be about 5.5 MHz. Indeed l°]Ru NQR signals were observed at 5.72 and 11.44 MHz at 1.3 K, as shown in the inset of Fig. 2. From the spectrum, we evaluated the electric quadrupole interaction parameter precisely as vo = 5.72 MHz and r / = 0. Although URuvSi2 is in the AF state below 17.5 K, the NQR lines at 1.3 K are narrow, implying the
transferred hyperfine field from U moments being canceled at Ru sites. This explanation is consistent with the magnetic structure proposed by neutron diffraction experiment [1]. Above 20 K, the resonance frequency (2VQ) increases gradually with increasing temperatures, as shown in Fig. 2. The T-dependence of VQ (l°lRu) would be caused by the energy level splitting of uranium 5f-electrons induced by the crystal-field effect [3]. Since the sizable anomalies observed at TN in various thermodynamic quantities is hard to be reconciled with the extreme weakness of the magnetic moment, the possibility such as the quadrupolar ordering is proposed for the phase transition at 17.5 K. In this case, the change of electric field gradient should be expected, however, we could not observe any change of VQ at Ru site. Further study is still necessary to understand the origin of the sizable anomalies at TN. Using NQR signal observed around 11.44 MHz, the nuclear spin-lattice relaxation time (7'1) of l°lRu was measured in zero magnetic field both in the normal and
K. Matsuda et al. / Physica B 230-232 (1997) 351-353 superconducting states in the temperature range from 0.16 to 130 K. The T-dependence of 1/1"1 is shown in Fig. 3. In the figure, our previously reported 1/1"1 of 29Si is also plotted [4]. As seen in the figure, 1/1"1 of l°lRu is nearly T-independent above 60 K and varies in proportion to T at low temperatures, which implies that the crossover occurs from the localized state at high temperature to the Fermi-liquid state below 60 K. Below TN=17.5 K, 1/I"1 decrease markedly, whose T-dependence is fitted by the following form:
1/T1=O.28T
(l/s)
(17.5K
1/T1 = 0.048T + 14 500 exp(-A/kBT)
(I/s)
(1.2K < T < 17.5K), with A/kB = 150 K, where the first term in the ordered state represents the contribution from the residual density of states (DOS) and the second term from the thermal excitations above the energy gap of the magnitude, A. The behavior of 1/I"1 indicates the opening of gap at the Fermi surface below TN and DOS is reduced to about 40% of the value in the paramagnetic state. This T-dependence is nearly the same as that observed previously in Si NMR. In the superconducting state, l/T1 shows no HebelSlichter coherence peak just below Tc = 1.2 K and decreases in proportion to T 3 with no deviation down to 0.2 K. It should be noticed that the measurement was performed in zero magnetic field. Then, there is no contribution from the vortex cores. Owing to small gyromagnetic ratio of l°lRu spin, 1/I"1 of l°lRu is insensitive to the paramagnetic impurity. Hence, the relaxation of l°lRu is dominated by the excitations of
353
the superconducting quasiparticles down to 0.2 K. The T-dependence of 1/7'1 in the superconducting state is explained in terms of the anisotropic superconducting energy gap which has line nodes on the Fermi surface. This result supports the appearance of non-s wave superconductivity in URu2Si2. In Summary, the electric quadrupole interaction parameters of l°IRu were determined to be VQ = 5.72 MHz and r/-- 0 at 1.3 K. Although the system is in AF state below 17.5 K, no broadening of NQR line was observed, indicating that the transferred hyperfine field is cancelled at Ru site. l/T1 decreases drastically below 17.5 K associated with AF ordering. In the superconducting state, 1/T1 has no coherence peak just below Tc -- 1.2 K and decreases in proportion to T 3 with no deviation down to 0.2 K, which shows the existence of line nodes in the superconducting energy gap. This work is partly supported by a Grant-in-Aid from the Ministry of Education, Science and Culture of Japan, and also supported by Hyogo Science and Technology Association.
References [1] C. Broholm, H. Lin, P.T. Matthews, T.M. Mason, W.J.L. Buyers, M.F. Collon, A.A. Menovsky, J.A. Mydosh and J.K. Kjems, Phys. Rev. B 43 (1991) 12809. [2] A. Burgstaller, J. Voitl~inderand H. Ebert, J. Phys.: Condens. Matter 6 (1994) 8335. [3] See, for example, G.J. Nieuwenhuys, Phys. Rev. B 35 (1986) 5260. [4] Y. Kohori, K. Maysuda and T. Kohara, J. Phys. Soc. Japan 65 (1996) 1083.