Ga NQR relaxation rates in superconductor PuRhGa5

ARTICLE IN PRESS

Journal of Physics and Chemistry of Solids 68 (2007) 2103–2106 www.elsevier.com/locate/jpcs

Ga NQR relaxation rates in superconductor PuRhGa5 H. Sakaia,, S. Kambea, Y. Tokunagaa, T. Fujimotoa, R.E. Walstedta, H. Yasuokaa, D. Aokib, Y. Hommab, E. Yamamotoa, A. Nakamuraa, Y. Shiokawaa,b, K. Nakajimac, ¯ nukia,d Y. Araic, T.D. Matsudaa, Y. Hagaa, Y. O a

Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan b Institute for Materials Research, Tohoku University, Oarai, Ibaraki 311-1313, Japan c Department of Nuclear Energy System, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan d Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan

Abstract Nuclear quadupole resonance (NQR) measurements have been performed on the Pu-based superconductor PuRhGa5 with a transition temperature of 8:8 K. NQR lines ascribed to 69 Gað2Þ, 71 Gað2Þ, and 69 Gað1Þ have been found in zero field. Spin–lattice relaxation rate (1=T 1 ) data for these lines have been measured in the superconducting state. The temperature variation of 1=T 1 can be interpreted in terms of a line-nodal superconducting gap. Data for both the 69 Gað2Þ and 69 Gað1Þ NQR lines show a constant-T 1 T behavior between T c and T  30 K, which suggests that a coherent Fermi-liquid state sets in below T  . The modified Korringa relation using 1=T 1 and Knight shift data in an applied field indicates that the normal state of PuRhGa5 can be regarded as an antiferromagnetically correlated metal. r 2007 Elsevier Ltd. All rights reserved. PACS: 74.70.Tx; 74.20.Mn; 76.60.k Keywords: A. Superconductor; D. NQR

1. Introduction Recently, Pu-based superconductors PuCoGa5 with superconducting (SC) transition temperature T c ¼ 18 K [1] and PuRhGa5 with T c ¼ 8:5 K [2] have attracted a good deal of attention owing to their relatively high values of T c . Both PuCoGa5 and PuRhGa5 have the tetragonal HoCoGa5 (1 1 5) crystal structure. Recently, from NMR/NQR measurements [3–7], these Pu115 superconductors have both been found to show a dwave, line-nodal SC gap. In the isostructural CeMIn5 (M ¼ Co; Ir; Rh) series, unconventional d-wave SC states have been identified through various experiments, although their respective T c values are less than for the Pu115 systems, e.g. T c ¼ 2:3 K for M ¼ Co [8], T c ¼ 0:4 K for M ¼ Ir [9] under ambient pressure, and T c 2 K for M ¼ Corresponding author. Tel.: +81 29 282 6889.

E-mail address: [email protected] (H. Sakai). 0022-3697/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jpcs.2007.08.039

Rh under about 2 GPa [10]. On the other hand, the other actinide (Th, U, Np) 115 series have not been reported to show any superconductivity so far. They are usually Pauli paramagnets or antiferromagnets. From our study of the NMR/NQR relaxation rates for these actinide 115 compounds [11], the normal states of Pu115 systems have been found to be metals with correlations intermediate between a weakly correlated Pauli paramagnet and highly correlated systems showing long-range antiferromagnetic order. In order to further elucidate the spin fluctuation behavior of Pu115 systems, we have extended our NQR measurements on PuRhGa5 . In the tetragonal 115 structure, there are two crystallographically inequivalent, 4i and 1c sites for ligand Ga (or In) atoms. The 4i-Ga site is labeled as Ga(1), which is coordinated in the c plane with four nearest-neighbor (nn) actinide atoms, and the other 1c site is labeled as Ga(2), which is coordinated in the a plane with two nn actinide and two nn transition metal atoms. It should be noted that

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month from synthesis), the onset T c was 8.5 K. After these NQR experiments, when about three months had elapsed after the annealing, the onset T c had decreased to 7:7 K by the self-irradiation effect.

this Ga(2) site has lower local symmetry than the Ga(1) site. To our knowledge, in Pu115 systems all the NQR measurements have been performed using the Ga(2) resonances. The site dependence of T 1 between Ga(1) and Ga(2) should give us the information about the anisotropy of spin fluctuations. NQR measurements and analysis for Ga(1) are now in progress. On the other hand, since the SC properties (e.g., T c , H c2 , J c , and so on) are well known vary through self-irradiation aging effects in 239 Pu115 systems. Recently, the rate of T c decrease through aging has been reported to be   0:39 K=month for 239 PuRhGa5 [13,14]. Moreover, this aging effect is enhanced at low temperatures, because the damage incurred through self-irradiation is not dispersed microscopically. In this brief paper, we report the finding of NQR line for the Ga(1) site, and the effects of aging on 1=T 1 for Ga(2) in for PuRhGa5 .

3. Results and discussions Fig. 1 shows the temperature dependence of the NQR frequency (nNQR ) for 69 Gað1Þ and 69;71 Gað2Þ in PuRhGa5 . During our NMR experiment in Ref. [5], the 69;71 Gað1Þ NMR lines were very weak under applied field. Moreover, the center lines could not be distinguished from other NMR lines coming from residual Ga flux, while the satellite lines were barely observable. So we could not determine precise values for the 69;71 Gað1Þ NQR parameters from previous NMR experiments. One reason why Ga(1) NMR signals were weak may be due to a fast spinspin relaxation rate (1=T 2 ). However, in this experiment, the NQR line has been found near the frequency estimated roughly from NMR satellite lines. It is very likely that this NQR line near 13 MHz can be ascribed to 69 Gað1Þ. As shown in Fig. 1, the T-variation of nNQR is basically similar to the other NQR lines for PuRhGa5 , i.e., each NQR frequency decreases slightly as temperature increases. nNQR seems to vary with temperature as T 3=2 , which is often observed in paramagnetic metals. Moreover, 1=T 1 for this line is confirmed to decrease considerably in the SC state. The inset of Fig. 1(a) shows the putative 69 Gað1Þ line at 10 K in the normal state of PuRhGa5 . The signal-to-noise ratio was quite low compared with the 69;71 Gað2Þ NQR lines observed at higher frequencies, as shown in the inset of Fig. 1(b) and (c). These assignments of 69;71 Gað2Þ are also cross-checked by NMR under applied field. Further, the ratio of NQR frequencies is found to be consistently equal to the ratio of nuclear quadrupole moments (Q) in the whole temperature range. Next, let us discuss the T 1 in the SC state of PuRhGa5 . Fig. 2 shows the 1=T 1 vs. T plot for 69 Gað2Þ NQR. Our

2. Experimental Single crystals of PuRhGa5 were grown by the flux method [12]. The sample was prepared using pure 239 Pu isotope, which is an a-emitter (half life 2:4  104 years), giving a uranium recoil atom. The same sample batch of PuRhGa5 was used for this NQR experiment as used previously for NMR/NQR measurements [5,7]. NMR/ NQR measurements were performed using a standard pulsed spectrometer simultaneously with in situ ac susceptibility (w) measurement using the NQR coil in order to check the T c . NQR spectra were taken by the fast-Fouriertransform (FFT) technique of accumulated spin-echo signals. T 1 was measured by the inversion-recovery method. After 14 months of aging, the sample batch was reannealed just before this NQR experiment. By this annealing, the onset T c was fully recovered to 8.8 K. For example, in the previous NQR experiments (after one

18.35

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69Ga(1)

69Ga(2)

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12.6

28.9

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12.90

T = 10 K

28.8 28.7

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18

18.2 18.4 ν (MHz)

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50

100 T(K)

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Fig. 1. Temperature dependence of NQR frequency for (a) spectrum at 10 K in zero field.

T = 10 K

28.6

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29 29.2 ν (MHz)

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18.00 0

Echo FFT (arb. units)

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T (K) 69

Gað1Þ, (b)

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Gað2Þ, and (c)

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T(K) 69

Gað2Þ in PuRhGa5 . Each inset shows the respective NQR

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where Tc = 8.8 K

102

PuRhGa5 69 Ga(2) NQR

101

N 0E N s ðEÞ ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ; 2 E  D2 ðy; fÞ

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1 / T1 (sec-1)

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Ref. [5] This exp.

0·N0

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101 T(K)

Fig. 2. Temperature dependence of 1=T 1 for 69 Gað2Þ NQR in PuRhGa5 . The open and closed circles show the data for this experiment as well as previous data from Ref. [5]. Each onset T c determined by ac-w measurements is shown by an arrow. The solid curves are calculated assuming the SC gap D0 ð0Þ ’ 5kB T c (DðTÞ ¼ D0 ðTÞ cosðyÞ) with the ratio N res =N 0 ¼ 0; 0:15 with T c ¼ 8:8 K, N res =N 0 ¼ 0:25 with T c ¼ 8:5 K, respectively. The dotted lines are guides for the eye.

previous data from Ref. [5], which were taken after one month of aging, are also shown. In this experiment the onset T c was determined by ac w measurements to be 8:8 K, as shown by the arrow in Fig. 2. It should be noted again that the previously reported T 1 data were taken after one month of sample aging, at which time the onset T c was 8:5 K. In Ref. [5], the following features of the 1=T 1 vs. T plot have been reported: (i) there is no coherence-peak increase of 1=T 1 just below T c , (ii) 1=T 1 shows a T 3 -dependence below T c , and (iii) a deviation from T 3 behavior is also observed for T well below T c . These evidences (i) and (ii) indicate that the SC gap is line-nodal. The item (iii) may come from non-magnetic scattering centers introduced by self-irradiation. These features of 1=T 1 below T c can be reproduced tentatively assuming a line-nodal SC gap, DðTÞ ¼ D0 ðTÞg ðy; fÞ, here D0 ðTÞ is assumed to have BCS-type T-variation. In general, the T-dependence of 1=T 1 below T c can be calculated from the following integral, ) Z (* 2 + N s ðEÞ 2 ðT 1 ÞT¼T c =T 1 ¼ 2=kB T þ hM s ðEÞi f ðEÞ½1  f ðEÞ dE, N 20

Dðy; fÞ M s ðEÞ ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi , 2 E  D2 ðy; fÞ

and where N 0 is the density of states (DOS) in the normal state. f ðEÞ is the Fermi distribution function, and h  i indicates an angular average over the Fermi surface. In the case of s-wave SC gap, the both hN 2s ðEÞi and hM 2s ðEÞi diverge strongly around ED, and then 1=T 1 shows a coherence peak just below T c . In the line-nodal case, such a divergence around ED is strongly suppressed or quenched. From the best fit of the previous data with T c ¼ 8:5 K, we evaluated 2D0 ð0Þ ’ 5kB T c assuming polar-type gðy; fÞ ¼ cos y (if two-dimensional gðy; fÞ ¼ cosð2fÞ is assumed, 2D0 ð0Þ ’ 4.4kB T c ) with a residual DOS N res =N 0 ’ 0:25. On the other hand, for the present experimental data with T c ¼ 8:5 K, the best fit provides the same gap parameter ’ 5kB T c with N res =N 0 p0:15. Next, in the normal state, 1=T 1 shows a T-linear behavior above T c to T  30 K, as seen in Fig. 2. The temperature dependence of the Knight shift (K) also shows an anomaly at T  , i.e., K becomes temperature independent below T  in the normal state [7]. Both results indicate that a coherent state is established below T  . These results stand in contrast to the NMR/NQR results for PuCoGa5 [3,4]. In PuCoGa5 , both K and 1=T 1 T continue to increase as T decreases toward T c . In order to study the nature of the T 1 process in PuRhGa5 , T 1 has been measured for the 71 Gað2Þ NQR line. It was found that the isotope ratio of 1=T 1 for the Ga(2) NQR is very nearly equal to that of g2N in the whole temperature range up to 300 K. This is strong evidence that the T 1 process has magnetic dipolar character, rather than being quadrupolar. Using the isotropic parts of K and T 1 T obtained from NMR [6], the correlation factor Kðaq Þ can be estimated. In exchange enhanced metals, the Kðaq Þ works as a simple indicator to interpret whether spin fluctuations are ferromagnetic (Kðaq Þ less than 1) or antiferromagnetic (Kðaq Þ more than 1). The modified Korringa relation [15] in terms of random  phase approximation is given as ðT 1 TÞ1 ¼ Kðaq Þ=z K 2 =S, where z is the effective number of magnetic atoms coupling to the ligand nucleus and S ¼ ðgE =gN Þ2 ð_=ð4pkB ÞÞ is a numerical coefficient depending on gN (gE ; gN : the gyromagnetic ratio of the electron and the nucleus). Generally, the correlation factor can be defined as Kðaq Þ ¼ hð1  a0 Þ2 =ð1  aq Þ2 iF , where a0 and aq are given as a0 ¼ Iw0 ð0; 0Þ=2 and aq ¼ Iw0 ðq; 0Þ=2, here, w0 ðq; 0Þ is wavelength dependent susceptibility, and h   iF means an average over the Fermi surface. In PuRhGa5 , Kðaq Þ=z can be obtained as 20 using K iso ¼ 0:08 % and 1 ðT 1 TÞ1 for 69 Gað2Þ below T  . If z ¼ NMR;iso ¼ 3:05 ðs KÞ 2 is adopted for the number of the nn magnetic atoms, Kðaq Þ is much larger than 1, indicating that a large enhancement of w0 ðq; 0Þ occurs around a specific, nonzero wave vector. In such way, the normal state of PuRhGa5

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can be regarded as an antiferromagnetically correlated metal. Lastly, we mention the recent 69 Gað1Þ NQR results. It is noted that the temperature dependence of 1=T 1 for Ga(1) also shows constant-ðT 1 TÞ behavior below T  . This characteristic temperature variation is identical for the Ga(1)and Ga(2) sites. Based on the site dependence of 1=T 1 , the anisotropy of the spin fluctuations in this system will be discussed in near future. In summary, we have performed measurements of relaxation times T 1 using several NQR lines ascribed to 69;71 Gað2Þ and 69 Gað1Þ sites in the crystal. Here, let us note again that the re-annealing process was very useful for studying the low-T properties of the Pu compounds, since the damage caused by self-irradiation is fully relaxed and diffused microscopically. The temperature variation of 1=T 1 T for all the sites shows a characteristic temperature T  , below which 1=T 1 T becomes temperature independent. KðTÞ for 69 Gað2Þ is also found to be nearly temperature independent below T  . These results suggest that a condensed fermi-liquid state occurs before the SC state sets in. From the modified Korringa relation, the normal state of PuRhGa5 can be regarded as a antiferromagnetically correlated metal.

Acknowledgments The author (H.S.) was partially supported by the Ministry of Education, Culture, Sports and Science and Technology, Grant-in-Aid for Young Scientists (B), 18740217, 2006.

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