Ligand and Actinide NMR Studies in Actinide Oxides and Intermetallic Compounds
Russell E. WALSTEDT, Shinsaku KAMBEy, Yo TOKUNAGAz, and Hironori SAKAIx
Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195
(Received March 28, 2007; accepted April 13, 2007; published July 10, 2007)
In this paper we present highlights from a 6-year program of NMR/NQR/AFNMR studies carried out on both actinide and ligand nuclear spins in oxides and intermetallic compounds of the actinide elements U, Np, and Pu. We begin with the large family of actinide 115 compounds, consisting of metallic antiferromagnets, metamagnets, Pauli paramagnets, and the superconducting Pu-based systems. Short summaries are presented of69;71Ga NMR studies of the exotic metamagnet NpCoGa5, the surprisingly inhomogeneous UCoGa5, and the heavy-fermion ‘‘high-Tc’’ superconductors PuTGa5,T¼Rhand Co.
The case of microdomains in the metallic antiferromagnet UGa3is briefly reviewed. Next, we summarize the direct and indirect235U NMR studies on USb2and URh3. These are the first studies of their kind and the only studies of235U NMR in a metallic environment. Under the heading of actinide oxides we recap our original studies of235U and17O NMR in UO2, followed by a summary of our investigation of multipolar ordering in NpO2via17O NMR, in which the237Np NMR parameters were determined via cross-relaxation effects. And finally, we summarize our31P study of the ferromagnetic transition in the filled Skutterudite UFe4P12.
KEYWORDS: NMR, actinide compound, unconventional superconductivity, multipolar ordering DOI: 10.1143/JPSJ.76.072001
1. Introduction
In the spring of the year 2000, under the directorship of Professor H. Yasuoka, a new research group was created at the Advanced Science Research Center of the Japan Atomic Energy Research Institute for the purpose of NMR/NQR/
AFNMR studies of actinide oxides and intermetallic com- pounds. The facilities for synthesis and characterization of such materials, often containing high concentrations of radioisotopes, were already at hand. The group’s assigned program was already auspiciously under way with a study of the235U NMR in the antiferromagnetic (AFM) state of UO2, the first-ever direct NMR study of an actinide nucleus in a solid. Subsequent research projects were to produce other
‘‘firsts’’ for the group as well in a wide-ranging investigation of hyperfine (HF) effects by resonance methods in actinide oxides and intermetallic compounds.
In this paper we offer a survey of actinide-related projects which our group has carried out in the six years since the group’s inception. Actinide intermetallic compounds offer a wide panorama of interesting properties, including heavy- fermion effects, metallic antiferromagnetism, metamagnet- ism, multipolar ordering, and unconventional, 5f-electron superconductivity at relatively high temperatures. In each of these areas, this paper offers a summary of recent research.
Moreover, these researches were accomplished not only through studies of ligand NMR effects, but also through direct and indirect study of the actinide nuclear resonances as well. These are the first results ever reported on NMR studies of actinide nuclear spins.
In §2 we present a survey of 115 actinide compounds, which offer a broad tableau of properties in themselves. We give more detailed summaries on (i) NpCoGa5, a sharply anisotropic magnet which is antiferromagnetic with field applied in theabplane and an exotic metamagnet dominated by in-plane ferromagnetism when field is applied along the c-axis; (ii) UCoGa5, which is Pauli paramagnet with surprisingly inhomogeneous properties; and (iii) the PuTGa5
superconductors, T¼Co and Rh, which haveTc values of 18 and 8.5 K, respectively. The latter are both heavy-fermion systems with superconducting (SC) states which offer no coherence peaks, but exhibit regions with 1=T1/T3 characteristic of energy gaps with line nodes. On the other hand, these two isomorphs have strikingly different properties in the normal state, which we shall describe along with results from our study of theT¼Rhsystem.
In §3 we give a brief summary of NMR studies of the (67 K) AFM ordered state of UGa3. This system exhibits strong evidence of disorder apparently caused by small domains and/or broad domain walls. Nonetheless, the spectrum of internal fields from the AFM state has been analyzed in detail.
Section 4 reviews direct and indirect studies of235U NMR in several compounds.235U has an extremely small nuclear gyromagnetic ratio n’0:76MHz/T, which makes direct studies of 235U NMR difficult. Ironically, it also makes them possible, since the more ‘‘normal’’ values of n for
237Np and 239Pu mean that, given the enormous HF couplings of such heavy ions, ultra-fast relaxation precludes any possible direct study via spin echo techniques. In the AFM state of USb2a resonance peak at’217MHz has been identified as the central (1=2$1=2) transition of the
235U AFNMR spectrum. Relaxation time studies have not yet been completed. Meanwhile, indirect studies of 235U in the Pauli paramagnet URh3 via the 103Rh NMR line
Present address: Physics Department, The University of Michigan, Ann Arbor, MI 48109, U.S.A. E-mail: [email protected]
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have yielded the first-ever measurements ofT1for235U in a metallic environment. This novel technique will be describ- ed in some detail.
In §5 we make a brief summary of our flagship project, the combined 235U and 17O study of AFM ordering and relaxation effects in UO2. Following that, we describe our
17O probe of the exotic octupolar–quadrupolar ground state of NpO2, finding good accord with symmetry-based pre- dictions of HF effects therein. A field-induced octupolar moment is found to have a marked effect on the measured spectrum in the ordered state. StudyingT1, cross-relaxation effects from the 237Np nuclear spins allow a complete characterization of their dynamic properties both above and below the ordering temperature.
In §6 we close with a summary of our 31P study of the properties of the ferromagnetic filled skutterudite UFe4P12. The NMR spectrum shows clear evidence of hybridization effects at all of the 31P nuclear spin sites. The relaxation rates vary in an interesting way with applied field, showing the expected increase in the spin-wave energy gap for this semiconducting ferromagnet.
2. Actinide 115 Compounds
The AnTGa5 series (An: actinides and T: transition metals) is frequently referred to as the ‘‘Actinide 115’’
(An115) compounds. In recent years, discovery of the ‘‘high- Tc’’ Pu superconductors, that is, PuCoGa5withTc¼18:5K1) and PuRhGa5 with 9 K,2) has added special interest to research on the An115 materials. On the other hand, other actinide (Th, U, Np) 115 series have not been reported to show any superconductivity up to now.3–10) The latter systems are usually Pauli paramagnets or metallic antiferro- magnets. As a rule, the Np115 systems show a tendency to have complicated AF magnetic order, e.g., canted magnetic moments, double AF transitions, and/or additional magnetic moments on the transition metal elements.9–15) Theoretical considerations suggest that peculiar magnetic behavior such as that found in the Np115 systems may be related to 5f quadrupolar interactions or orbital correlations.16,17) Corre- spondingly, in order to study the exotic magnetism in these Np115 systems, it is important to elucidate the nuclear HF parameters. We note in passing that An115 compounds have the same crystal structure as the well-known systems CeMIn5 (M¼Co, Ir, and Rh), which are often referred to as ‘‘Ce115’’ compounds.
The AnTGa5series crystallizes in the tetragonal HoCoGa5
(115) structure (space group,P4=mmm), which is shown in Fig. 1. This crystal structure is quasi-two-dimensional in character, i.e., can be regarded as a sequential stacking of AnGa3 and TGa2 layers along the c-axis. For site-selective NMR/NQR experiments, we note that there are two crystallographically inequivalent, i.e., 4i and 1c sites for the ligand Ga (or In) atoms. The4i-Ga site is labeled Ga(1), which is coordinated in the c-plane with four nearest- neighbor (nn) actinide atoms, and the 1c sites are labeled Ga(2) and are coordinated in the a-plane with two nn actinide and two nn transition metal atoms. It should be noted that the Ga(2) sites have lower local symmetry (orthorhombic) than the Ga(1) site, which is tetragonal.
For some time now the isostructural cerium-based Ce115 systems have been in the limelight, since they are heavy-
fermion superconductors. In the isostructural Ce115 series, unconventionald-wave SC states have been also identified through systematic NMR/NQR experiments.21–23) Further- more, AF spin fluctuations are thought to play an active role in the SC pairing,24–27) although their respective Tc values are smaller by nearly an order of magnitude than for the Pu115 systems, e.g., Tc¼2:3K forM¼Co,18)Tc¼0:4K for M¼Ir19,20) under ambient pressure, and Tc2K for M¼Rh under about 2 GPa.28)
Very recently, NMR and NQR experiments have been reported for PuCoGa5by Curroet al.29)and for PuRhGa5by our group.30) In both cases, measurements of spin-lattice relaxation rates (1=T1) using NQR have revealed that the Pu115 superconductors show unconventional superconduc- tivity with an anisotropic gap. TheT1results of Curroet al.
have also been analyzed in terms of d-wave superconduc- tivity, finding a SC gap value 20’8kBTc (cf. 5kBTc for PuRhGa5). It should be noted that the site assignment, as Ga(1), for the NQR line used forT1measurements in ref.29 may be unsound, in which case the corresponding shift data may need to be reinterpreted. On the other hand, our NQRT1 data for PuRhGa5 has been measured on the 69Ga(2) line.
In this section, we will briefly review our NMR/NQR studies for An115 compounds. Owing to the lower site symmetry, analyses for the Ga(2) site generally provide more detailed information, including the anisotropy, than those for the tetragonal Ga(1) or T site. Therefore, we focus here on the NMR/NQR results for the Ga(2) site.
2.1 Static magnetic responses and nuclear quadrupolar parameters
Figure 2 shows static susceptibilities for the para- magnetic states of several 115 actinide compounds with applied field Hk c-axis ([001]). In AFM UPtGa53) and NpCoGa5,10,31)the static susceptibilityobeys Curie–Weiss (CW) behavior at high temperatures. In AFM NpFeGa5 theT-dependence ofis somewhat peculiar,10,31)which may be due to its semi-metallic nature.
Effective moments obtained from analysis of the CW behavior are 1.1B and 2.6B for UPtGa5 and NpCoGa5, respectively. In NpCoGa5 the effective moment is near to that of an Np3þ ion (2.68B), but is reduced in UPtGa5
compared with 3.62B for a U3þ ion, indicating that localized character is more prominent in NpCoGa5. In
a a c
Ga(1)
Ga(2)
An: Actinide element
T : Transition metal VZZ
VZZ
VYY
VXX
Fig. 1. (Color online) Crystal structure of AnTGa5(An: actinides and T:
transition metals). The EFG principal axes for both the Ga(1) and Ga(2) sites are indicated.
contrast, the ordered moments are considerably smaller, i.e., 0.3B for UPtGa5, 0.86B for NpFeGa5, and 0.74B for NpCoGa5,32)reflecting their itinerant nature. These data imply that the latter AFM compounds show localized character at high temperatures, but become itinerant at low temperatures, where they finally exhibit an itinerant ordered state.33)
In UPtGa5 and NpCoGa5, the magnetic structure of the ordered state has the propagation vector Q¼ ð0;0;1=2Þ with the ordered moment parallel to [001]. In contrast, in NpFeGa5 one has Q¼ ð1=2;1=2;0Þ, with the ordered moment parallel to [110].32)
In UFeGa58) is small and has the weakT-dependence characteristic of an itinerant Pauli paramagnet.
In the SC PuRhGa5 compound, it may be difficult to estimate the intrinsicT-dependence of, particularly at low temperatures, owing to the possible presence of magnetic impurities.34)At least above 50 K, CW behavior is observed.
NMR studies have led to the determination of HF parameters for a variety of AnTGa5 materials.35)Individual site symmetries are reflected in their respective electric field gradient (EFG) tensors. Using conventional notation, the quadrupole frequency parameter is defined as Q 3e2qQ=½2Ið2I1Þh, where eQ is the nuclear quadrupolar moment, I is the nuclear spin quantum number, and eq VZZ is the principal component of the EFG tensor. Here, Vii denotes EFG tensor components in the principal axis coordinate system, such thatjVXXj jVYYj jVZZjfor each ionic site. The EFG components satisfy LaPlace’s equation, i.e., VXXþVYYþVZZ¼0. The EFG asymmetry parameter is defined as ðjVYYj jVXXjÞ=jVZZj. If¼0, as for the Ga(1) and Co sites, then the NQR frequencyNQR is simply equal to Q. Otherwise, NQR¼Qð1þ2=3Þ1=2 for the Ga(2) site. The principal EFG axis (VZZ) for the Ga(2) site is perpendicular to the a-plane, as shown in Fig. 1. With the external field (H0) applied along the crystallographica-axis, the Ga(2) sites divide into two magnetically inequivalent sites, i.e., Ga(2a) and Ga(2b), where (2a) and (2b) meansH0
parallel and perpendicular to the EFG principal (a) axis,
respectively. In the case of H0kc, such a breaking of equivalency does not occur. Under this definition of coordination, we have obtained the HF parameters K, Q, andfrom NMR experiments using an external field.
The transferred HF coupling constants are determined straightforwardly in the paramagnetic state from the slopes of Knight shift (K) versus static susceptibility () plots, where temperature is an implicit parameter. For example, the temperature dependence of Knight shifts and the K–plots for the 69Ga(2) site are shown for NpCoGa5 (ref.36) and PuRhGa5 (ref.37) in Figs. 3 and 4, respectively.
For NpCoGa5 the Knight shifts Ki, where i is the field axis, increase in the paramagnetic state as temperature approaches TN. This temperature variation of Ki scales with that of i, which obeys a modified Curie–Weiss law:
ðTÞ ¼0þC=ðTÞ. As shown in Fig. 3(b), eachKi–i
plot shows good linearity from TN¼47 up to 200 K.
The transferred HF coupling constantsAi(i¼a;b;c) can be determined from the slopes of the dashed lines shown.
It is noted that linear K–plots in the paramagnetic state have also been obtained for other An115 compounds, e.g., UCoGa5, UFeGa5, UPtGa5, UNiGa5, and NpFeGa5. The HF coupling constants for the Ga(1), Ga(2) and transition metal sites for several An115 compounds are summarized in Tables I–III.35)
On the other hand, in the case of PuRhGa5, a bend is seen in the K– curve around T30K. This means that the temperature dependence of K deviates from the CW-like behavior which is followed by the static susceptibility. To our knowledge, PuRhGa5is the first example of a nonlinear K–relation among An115 compounds. Tables II and III list HF coupling constants determined above T. As seen in Tables II and III, the c-axis HF coupling constants do not
2 4 6
10-38 2 4 6
10-28 2 4 6
10-18
χ ( emu / mol )
300 200
100 0
Temperature ( K ) NpCoGa5
UPtGa5 NpFeGa5
PuRhGa5 H // c
UFeGa5 UCoGa5
Fig. 2. (Color online)T-dependence of the static susceptibilityfor a selection of 115 actinide compounds for the case ofHkc-axis.
20 15 10 5 0
K ( % )
3x10-2 2
1 0
χ ( emu / mol ) NpCoGa5
69Ga(2)
Kc Ka
Kb 20
15 10 5 0
K ( % )
300 200
100 0
Temperature ( K ) NpCoGa5
69Ga(2)
Ka Kb
Kc TN = 47 K
Fig. 3. (Color online) (a) Temperature dependence of Knight shifts Ki
(i¼a;b;c) in NpCoGa5. (b) K– plots for 69Ga(2) site in the para- magnetic state of NpCoGa5.
vary widely in these An115 compounds. However, in PuRhGa5, the coupling constants along a- and b-axes are different from those in the other 115 compounds, indicating that the hybridization between Pu and the Ga(2) orbitals is somewhat different in this compound.
K–bending anomalies, such as that seen in PuRhGa5, have been observed in many heavy-fermion systems: As examples we may cite CeCu2Si239)and CeCoIn5.40)Recent- ly, an interpretation in terms of a two-fluid description of the Kondo lattice41) has been proposed.42) In this scheme, the susceptibility and Knight shift can be resolved into two components, one term coming from the localized spin on the magnetic site and another term from the coherent fermi liquid. In this scheme, the characteristic temperature of the K–anomaly corresponds to the condensation temperature of the heavy Fermion liquid. Regarding PuRhGa5, the temperature dependence of the NQR relaxation rate 1=T1
also shows an anomaly around this characteristic temper- ature T 30K, and shows nearly constant T1T behavior betweenT andTc, as described below, which suggests the emergence of a Fermi liquid state below T. On the other hand, suchK–bending has also been explained by thermal depopulation of crystalline electric field (CEF) levels.39,40) According to this mechanism, theK–anomaly in PuRhGa5
suggests that the CEF energy splitting would be smaller than that in the other An115 compounds like NpCoGa5, UPtGa5, UNiGa5, etc, where the linear K– behavior extends to 300 K or more. It should be noted that, throughout the
An115 compounds, the transferred HF constants deduced for the Ga(2) site are highly anisotropic. Such anisotropic HF couplings are related to hybridization effect between An5f and Ga4pbands, as predicted from band calculations.
Next, we consider the nuclear quadrupolar parametersQ
and for the An115’s. Figure 5 shows the temperature dependence of Q and for 69Ga(2) in PuRhGa5, which have been determined by analysis of NMR spectra. At the predicted frequency NQR, we have succeeded in observing an NQR signal in zero field. The results from this NQR experiment are also shown in Fig. 5. The observed temper- ature variation exhibits typical features seen in many paramagnetic compounds, i.e., (i) Q (or NQR) varies as 1T3=2, (ii) the temperature variation levels off the lowest temperatures, and (iii) is almost T-independent.
Such features for Q and are confirmed in the other paramagnetic An115 compounds, and would be associated with the temperature variation of lattice volume. Unfortu- nately, owing to the lack of lattice parameter data at low temperatures, the couplings between the lattice and EFG parameters are as yet undetermined.
0.3
0.2
0.1
0
K ( % )
200 150
100 50
0
Temperature ( K ) Ka
PuRhGa5
69Ga (2)
Kb Kc
0.3
0.2
0.1
0
K ( % )
2x10-3 1.5
1 0.5
0
χ ( emu / mol ) Ka Kc
Kb 30 K PuRhGa5
69Ga (2)
(a)
(b)
Fig. 4. (Color online) (a) Temperature dependence of Knight shifts Ki
(i¼a;b;c) in PuRhGa5. (b)K–plots for69Ga(2) site in the normal state of PuRhGa5.
Table I. Nuclear quadrupole resonance frequenciesQin MHz for69Ga and59Co in actinide 115 compounds, with asymmetry parameter given for the Ga(2) site. The asymmetry parameteris zero by symmetry for the Ga(1) and Co sites.
Ga(1) Ga(2) (Ga(2)) Co
UFeGa5 18.0 29.7 0.35 —
UCoGa5 10.2 32.5 0.10 0.93
UNiGa5 18.1 25.7 0.15 —
UPtGa5 14.5 27.5 0.20 —
NpFeGa5 17.3 27.4 0.41 —
NpCoGa5 16.4 28.9 0.36 1.0
PuRhGa5 13.2 28.2 0.42 —
Table III. Hyperfine coupling constantAin kOe/BforHk ½001at Ga, Co, and Pt sites in actinide 115 compounds.
Ga(1) Ga(2) Pt or Co
UFeGa5 54 14 —
UCoGa5 33 20 18
UNiGa5 55 13 —
UPtGa5 42 10 87
NpFeGa5 57 30 —
NpCoGa5 71 25 30
PuRhGa5 — 21 —
Table II. Hyperfine coupling constantAin kOe/BforHk ½100at Ga, Co, and Pt sites in actinide 115 compounds.
Ga(1) Ga(2a) Ga(2b) Pt or Co
UFeGa5 17 17 19 —
UCoGa5 16 12 12 4
UNiGa5 21 27 22 —
UPtGa5 10 17 20 41
NpFeGa5 10 16 21 —
NpCoGa5 33 44 38 7:5
PuRhGa5 — 3 1:5 —
On the other hand, it has been found that the coupling between magnetism and the EFG parameters is non- negligible in the magnetic An115 compounds, i.e., that the nuclear quadrupolar parameters are very sensitive to such interactions and charge states reflecting the Fermi surfaces.
As a typical case, let us consider the antiferromagnet NpCoGa5. NpCoGa5exhibits AFM order belowTN¼47K.
Neutron diffraction measurements have revealed that the AF wave vectorQisð0;0;1=2Þ, and that the ordered moment is 0.8B/Np parallel to thec-axis.38)This magnetic structure is illustrated in the inset to Fig. 6(a). Similar AF magnetic structure is found in the related system UPtGa5.4)The AFM phase of NpCoGa5has been found to be metamagnetic along thec-axis, i.e., becomes a field-induced ferromagnet (FIF) at fields higher thanHm40kOe.38,43)As shown in Fig. 6(a), a crossover line [the broken line in Fig. 6(a)] at TN from paramagnetic to FIF states has also been suggested by the magnetization43)and specific heat38)measurements. On the other hand, for the case of Hka, such metamagnetic behavior does not appear.
In the same manner, nuclear quadrupole parameters have been determined from the NMR/NQR experiments.36)Using the internal field of the AFM state, NMR spectra have been observed in order to obtain the EFG parameters. The EFG parameters in the AFM state have been computed from the NMR positions using numerical diagonalization of the Zeeman and nuclear quadrupolar Hamiltonians. As seen in Fig. 6(b), the nuclear quadrupolar parameters in NpCoGa5 vary strongly with temperature below TN. Variation of the EFG between the FIF and AFM states suggests an effect from the ordering of nearby 5f orbitals, but also may indicate the existence of coupling between the lattice and magnetic polarization, as well. By empirical calculations based on point charge model, such a change of EFG would be involved with the emergence of a huge magnetovolume effect. In near future, thermal expansion or low-T x-ray diffraction experiments will supply critical information for
these EFG changes below TN. At this point we can only reiterate that the nuclear quadrupolar parameters show striking changes at TN and that they are quite sensitive to magnetovolume effects and changes in the charge state (hybridization between the Ga4pand Np5f electrons).
2.2 Dynamic magnetic responses: measurements of relaxation rates in An115 materials
In order to determine the SC gap symmetry, the NQR relaxation rates 1=T1 in PuRhGa5 have been measured above and belowTc. In ref.30, the following features of the 1=T1 vs T plot for PuRhGa5 have been noted: (i) there is no coherence-peak increase of1=T1 just belowTc, (ii)1=T1 shows a T3-dependence below Tc, and (iii) deviation from T3behavior is also observed forT well belowTc. Evidences (i) and (ii) indicate that the SC gap is line-nodal. Item (iii) may come from non-magnetic scattering centers introduced by self-irradiation. The reduction of the Knight shift below Tchas also been measured,37)corresponding to the decrease of the spin susceptibility. This reduction of Knight shift belowTcindicates spin-singlet SC pairing in PuRhGa5. Both 1
0
η
200 150
100 50
0
Temperature ( K ) 30
29
28 νQ, νNQR ( MHz )
νQ
η
νNQR under zero field PuRhGa5
69Ga(2)
Fig. 5. (Color online) Nuclear quadrupolar parameters, Q and for
69Ga(2) in PuRhGa5, extracted from NMR spectra, are plotted vs temperature (open circles and open squares, respectively). The temper- ature dependence of the experimental value of NQR frequency, NQR
under zero field is also shown (solid circles).
60
40
20
0
External Field ( kOe )
100 80 60 40 20 0
Temperature ( K ) AF P
FIF
NpCoGa5 H0 // c-axis
35
30
ν, ν ( MHz )QNQR 25
200 150
100 50
0
Temperature ( K )
1
0
η
NpCoGa5
69Ga(2) TN = 47 K
P νNQR
νQ
νQ, AF
νQ, FIF
ηAF η ηFIF
(B) Zero Field NMR / NQR (A) NMR
(b) (a)
Fig. 6. (Color online) (a)H–Tphase diagram of NpCoGa5for the case of Hkc-axis. The arrows (A) and (B) denote schematically the different experimental routes to obtaining the nuclear quadrupolar parameters. The inset illustration shows the antiferromagnetic structure determined by neutron experiments.38) (b) Temperature dependence of nuclear quad- rupolar parameters,Qandfor69Ga(2) in NpCoGa5. The data for the antiferromagnetic (AFM) and field-induced ferromagnetic (FIF) phases below TN were obtained from NMR/NQR analyses with or without external fields, as illustrated by the arrows (A) and (B) in the upper panel (a). The temperature dependence of the experimental value of NQR frequency in the paramagnetic state,NQRin zero field is also shown.
1=T1 and the Knight shift in the SC state strongly suggest that PuRhGa5 has anisotropic, even parity (most probably, d-wave) superconductivity.
In Pu115 superconductors, the SC properties (e.g.,Tc,Hc2, Jc, and so on) are well known to vary through self-irradiation aging effects in 239Pu115 systems. Recently, the rate of Tc
decrease through aging has been reported to be0:39K/
month for 239PuRhGa5.44,45) Moreover, this aging effect is enhanced at low temperatures, because the damage incurred through self-irradiation is not dispersed microscopically. In Fig. 7, two data taken using samples with one month aging and with one week aging are plotted together. The aging effect onTcis rather slight, so thatTcafter one month aging had only decreased toTc¼8:5K, where same sample after one week of aging showed an onset Tc¼8:8K, by ac susceptibility measurements. Judging from the respective relaxation rate curves below Tc, the difference between samples with different aging appears only far belowTcas the effect of a residual density of states (Nres) in the SC state.
It is noted that the gap values obtained from the differently aged samples are not so different under the assumption of an empirical d-wave gap ¼0cos or ¼0cos 2 . The 1 month aging data provides Nres’0:25N0, where N0 is the density of states at the Fermi energy just above Tc. On the other hand, the fresh, 1 week aging data gives us Nres<0:15N0. The finite Nres in the d-wave SC state is mostly caused by potential scattering associated with non- magnetic impurities, crystalline disorder, and contamination with secondary phases.46,47)In Pu compounds, the influence of unavoidable potential scattering coming from self- radiation damage is also expected. In the literature, the
relationship between the magnitude ofNresand the reduction rate ofTchas been calculated on the basis of an anisotropic SC model, where the scattering is treated in the unitary (strong) limit.48) Using such a theoretical formula, we can estimate the maximum (intrinsic) Tc0¼9:0K, where Tc0 is the intrinsic value ofTc without potential scattering effects.
Next, let us discuss the normal (paramagnetic) state of the An115 superconductors. Recently, the relation between Tc and crystallographic tetragonality (c=a), which may reflect on the strength of antiferromagnetic spin correlations, has been discussed for the layered compounds. PuCoGa5 and PuRhGa5 have been classified in this way as intermediate between CeTIn5 and the high-Tc cuprates.49) However, owing to the lack of experimental evidence, it is unclear whether such antiferromagnetic fluctuations exist in these Pu compounds. Nuclear magnetic resonance (NMR/NQR) is also a suitable tool for probing low-energy magnetic excitations via nuclear relaxation rates. Ifis not too large, the spin-lattice relaxation time T1 is related to the spin- fluctuation densities perpendicular to the quantization axis, and can be expressed as
ð1=T1TÞHk¼n2kB 2
X
q
AðqÞ2H?Imðq; !nÞH?
!n
; ð1Þ
where ¼a-, b-, or c-axis, Imðq; !nÞ is the dissipative magnetic susceptibility, !n is the NMR/NQR resonance frequency andAðqÞis theq-dependent HF coupling constant [A¼Að0Þ]. Regarding the NQR relaxation rates at the Ga(2) sites, the quantization axis is parallel to the a-axis, so the spin fluctuations along c (inter-plane) and a (in-plane) are effective. Since theq-dependence ofAðqÞis different at each site, theq-dependence ofImðq; !nÞcan be estimated from the difference in T1 behavior between different sites. The behavior of1=T1Tmost is sensitive to the maximum point of AðqÞ2 at each site. For the Ga(1) site, although AðqÞ2 has a maximum at qa ¼qb¼0, it becomes zero at qa¼qb¼, i.e., antiferromagnetic fluctuations are almost filtered off in 1=T1T by this HF form factor. For the Ga(2) site, contributions from a rather large range of q-space are expected, except for the in-plane antiferromagnetic fluctua- tions. So we focus on theT1at the Ga(2) site, which covers a large amount of q-space compared with the Ga(1) and transition-metal sites, owing to lower site symmetry.
In order to estimate non-5f contributions in the Pu115 systems, LuCoGa5can be considered as a candidate because the Lu atom has a fully occupied4f shell, and also, it has the smallest atomic radius in the lanthanide series. It is closer in size to the actinide elements than the La ion, which also has no4f electrons. One may consider a Th115 compound having no 5f electrons to be more suitable reference.
However, up to now, there are no Th115 (nor La115) compounds with Ga ligands.
In Fig. 8, the69Ga(2) relaxation1=T1T is plotted vs T for several An115 compounds: Superconductors PuRhGa5 and PuCoGa5, paramagnets LuCoGa5, UFeGa5, and UCoGa5, and antiferromagnet NpCoGa5. The data for PuCoGa5
was taken from ref.29. Regarding the superconductors, for PuRhGa51=T1T increases with decreasing temperature, and becomes constant below 30 K. This means that the formation of the heavy fermion state occurs below 30 K, as described in the previous section. Estimates of magnetic correlation 10-2
10-1 100 101 102 103
1 / T1 ( sec-1 )
100 101 102
T ( K )
∝ T 3
∝ T
Tc = 8.8 K PuRhGa5
69Ga(2) NQR
~1 week of aging ~1 month of aging 0.15N0
0.25N0
8.5 K
0·N0
Fig. 7. (Color online) Temperature dependence of 1=T1 for 69Ga(2) NQR in PuRhGa5. The open and closed circles show the data for one month aging and one week aging samples, respectively. Each onset Tcdetermined by ac-measurements is shown by an arrow. The solid curves are calculated assuming the SC gap 0ð0Þ ’5kBTc [ðTÞ ¼ 0ðTÞcosðÞ] with the ratio Nres=N0¼0;0:15 with Tc¼8:8K, Nres=N0¼0:25withTc¼8:5K, respectively. The dotted lines are guides for the eye.
effects have been obtained from K–1=T1T analyses. As a result, the normal state of PuRhGa5 can be considered as an antiferromagnetically correlated metal. The occurrence of superconductivity after the formation of a heavy-fermion state is also observed in many U-based superconductors such as UPt3,50) URu2Si2,51,52) UPd2Al3,53,54)and UBe13.55) In general, a heavy-fermion formation temperature T can be estimated with the electronic specific heat coefficient [J/(mol K2)]: T ðKÞ 1=.56) This relation indicates T’10K in PuRhGa5, in rough agreement with 30 K. In contrast, 1=T1T in PuCoGa5 increases with decreasing temperature down to Tc,29) where the superconductivity appears before the heavy-fermion state is formed. The considerable difference of Tc between PuCoGa5 and PuRhGa5 might be related to this difference in behavior in the normal state.
These 1=T1T values in the normal state of the Pu superconductors are intermediate between those in weakly correlated Pauli paramagnets and in highly correlated systems showing long-range antiferromagnetic order. For example as a highly antiferromagnetic case, 1=T1T for NpCoGa5 is shown in Fig. 8. In this case, the temperature dependence of 1=T1T shows CW-like behavior at high temperatures, which indicates an exchange-narrowing en- hancement. Moreover, critically divergent behavior toward TN in the paramagnetic state is also seen.
On the other hand, regarding the paramagnets, the values of 1=T1T are down by nearly one order of magnitude, two orders for UCoGa5, relative to the SC Pu115’s and the antiferromagnet NpCoGa5. The values 1=T1T for An115 paramagnets are nearly temperature independent. One may consider it strange that the value of 1=T1T for UCoGa5 is much smaller than that for non-f LuCoGa5. The origin of weak relaxation in UCoGa5 is the small density of states on
the Fermi surface. As for UCoGa5, from band calculations and de Haas–van Alphen (dHvA) experiments, it has been found that these Fermi surface sheets are all small in size and closed in topology, whereas the other An115 paramagnets, including Pu115, have large Fermi surface volumes and similar topologies. In this way, 1=T1T of LuCoGa5 rather than UCoGa5 can be considered as better background estimate for the 5f electronic contributions to assess the enhancement of spin fluctuations in the Pu115 systems.
Indeed, there appears to be a small enhancement in 1=T1T from the case of LuCoGa5 for the paramagnet UFeGa5, which has similar Fermi surface topologies.
From our studies, it is highly plausible that the SC mechanism for PuRhGa5 would be antiferromagnetic spin fluctuations. In order to test another possible SC channel such as valence/orbital fluctuations, the isotope ratio of relaxation rates between69;71Ga isotopes has been measured.
Generally, if the relaxation mechanism is not magnetic, the isotope ratio of relaxation rates will not equal the squared ratio of nuclear gyromagnetic ratios, but veer toward the squared ratio of nuclear quadrupolar moments. Indeed, in the related cubic mother compound UGa3, such a shift of isotope ratio in relaxation rates has been observed.57) However, so far, in the An115 compounds, including PuRhGa5, the isotope ratios verify that the relaxation mechanism is magnetic from LuCoGa5 to PuRhGa5.
In order to elucidate the origin of ‘‘high-Tc’’ in Pu115 systems, further experimental efforts will be required, in spite of the difficulties stemming from high radioactive internal damage in these compounds. At the present, we are left with open questions as to what are the key differences between Ce115 and Pu115 systems, between PuRhGa5 and PuCoGa5, or between Pu115 and high-Tccuprates.58)
2.3 UCoGa5: A case of multiple bands in a semi-metal In this particular compound 1=T1T and decrease with decreasing T, as shown in Figs. 2 and 8. In addition, the value of1=T1T for this compound is fairly small compared with the other 115 actinide compounds. Figure 9 shows a plot of1=T1T for the Ga(2) site vs that for the Ga(1) site in UCoGa5 for H kc-axis, where temperature is an implicit parameter. It is remarkable that the extrapolation of the
Fig. 8. (Color online) Temperature dependence of1=T1Tof the69Ga(2) NQR line for various actinide 115 compounds. Regarding data for UCoGa5, UFeGa5, and the antiferromagnetic state of NpCoGa5, equivalent NMR data with applied field alonga-axis are plotted. The NQR data for PuCoGa5were taken from ref.29.
0.20 0.15 0.10 0.05
-1-1 1/TT at Ga(2) site (sK)1 0
0.5 0.4 0.3 0.2 0.1 0
1/T1T at Ga(1) site (s-1K-1)
UCoGa
5H//c
Fig. 9. (Color online)1=T1Tat the Ga(2) sites vs that at the Ga(1) sites in UCoGa5forHkc-axis, with temperature as the implicit parameter.
The solid line is obtained by a linear regression.
fitting line in this plot does not intersect the origin, as it does in other An115 systems studied such as UPtGa5.59)
Considering eq. (1), such a plot interesects the origin when a unique term in Imðq; !nÞ is dominant, in which case the slope of the plot would be the square of the ratio of the HF coupling constant at the Ga(2) and Ga(1) sites ðAGa(2)=AGa(1)Þ2. The plot indicates that there are multiple bands in UCoGa5, one or more of which do not behave in a Fermi liquid-like fashion. This picture is consistent with band calculations60)and dHvA measurements,6)which show a semi-metallic nature for UCoGa5, with small hole and electron bands. The observed small 1=T1T value is also consistent with the low carrier density of this compound, which is confirmed by the band calculations mentioned and by dHvA measurements. A plot of 1=T1T vs for the Ga(2) shows a straight line for the whole temperature range (not shown). This strongly suggests that the band which dominatesðTÞand1=T1Tfor the Ga(2) develops an energy gap, whereas the one which relaxes the Ga(1) is more Fermi liquid-like. In the case of UPtGa5, the density of states and 1=T1T are evidently dominated by one (main) Fermi liquid-like band.
3. UGa3: An AFM with Microdomains
UGa3 is an itinerant 5f-electron system with the cubic AuCu3 structure which undergoes AFM ordering, (TN 66K), with a small ordered moment (0:7B) and a type-II AFM structure62) with the propagation vector Q¼ ð1=2;1=2;1=2Þ. Magnetization measurements have revealed another crystallographic phase transition at 40K.62,63) Since the electronic specific heat coefficient ¼50mJ/
(K2 mol)64) is relatively large, this compound is regarded as a simple example of a heavy fermion system with AFM order and has been studied intensively.
Figure 10 shows the field sweep spectrum of Ga NMR for H kthe cubic axis at 45 K in UGa3.61) In spite of the simple AFM structure, the Ga NMR spectrum is quite broad, indicating large AFM HF fields which may lie parallel or antiparallel to the applied field at different Ga sites. The lines drawn in the figure indicate such a scheme
which has been identified. The spectra also indicate a major wipeout effect for the NMR intensity from certain Ga sites,61)which gives evidence for AFM domain structure on a short length scale. The occurrence of such domains is consistent with pressure-dependent neutron scattering re- sults.65) Small domains of this sort have not been found in the AFM ordered states of the tetragonal 115 compounds, indicating that their occurrence here may be related with the cubic symmetry of UGa3. In such a case there would be a small magnetic anisotropy energy, thus a wide domain wall.
Within the small domain scenario, NMR, neutron-scattering, and119Sn Mo¨ssbauer results are all consistent with an AFM moment orientation along½110axes atT¼45K.
Below 40 K, splitting of the Ga NMR peaks occurs,66) indicating a lowering of the symmetry of the AFM state, e.g., from [110] to [; ; ] direction. It is difficult to identify the symmetry change from NMR spectra alone. Investiga- tion of the origin of the low-temperature, complex phase in this cubic compound remains as a future topic for investigation.
4. Direct and Indirect Study of 235U NMR 4.1 Direct235U NMR in USb2
The NMR of235U in solids is difficult because of the low abundance of this isotope (<1%), and because it possesses a dismally small nuclear magnetic moment, albeit a large quadrupole moment. The former difficulty can be overcome by isotopic enrichment, in which case one must employ advanced techniques for the handling of radioisotopes.
The second problem can only be dealt with, we now believe, by restricting consideration to compounds containing ordered, 5f-electron magnetism, which then provides an internal HF field typically of order 300 T, and thus a resonance frequency around 200 MHz.
USb2is known to be a5f itinerant antiferromagnet with a relatively high Ne´el temperature of 203 K and a large ordered moment of 1.88B.67–69) In spite of the small gyromagnetic ratio n of 235U nuclei (¼0:784MHz/T),70) the large HF field originating from the ordered moments enables us to observe a235U NMR signal under zero applied field. To our knowledge, this is the first observation of the
235U NMR signal in an itinerant5f electron system, which follows the previous report of a 235U NMR study on a localized 5f electron system, UO2.71,72)
The NMR spectrum at 4.2 K is shown in Fig. 11.73)Here, the amplitude of the NMR signal near 217.2 MHz is calibrated relative to the Sb signal intensity. It is shown that the amplitude of the NMR peak in question scales in rough proportion to the enrichment level for 93 and 20%
235U enriched samples, giving good evidence that the NMR signal at 217.2 MHz originates with the235U nuclei. Further, if we assign the observed peak to the center (1=2$1=2) transition of the235U spectrum,Hhffor the uranium nuclei is then estimated to be277:00:1T, in good agreement with the previously reported value (27020T) from Mo¨ssbauer studies on USb2.74)Accordingly, the observed line at 217.2 MHz can be identified as the center line of 235U AFNMR in USb2. Using the relation Hhf¼ jAhfMordj in the ordered state, where the ordered moment Mord is 1.88B,68) the magnitudejAhfjof the HF coupling constant is evaluated to be 1473 kOe/B in this system. This value of jAhfj is
Echo Intensity (a.u.)
80 70
60 50
40
External Field (kOe)
69Ga(1)
71Ga(1)
69Ga(2)
71Ga(2)
69Ga metal
71Ga metal
Fig. 10. (Color online) AFM ordered-state (T¼45K) UGa3single-crys- tal69;71Ga field-sweep NMR spectrum taken with applied field nominally oriented along a cubic axis. The NMR frequency is 79.0 MHz.61)
comparable to that in other uranium intermetallic com- pounds except for URu2Si2.71,72,74–76)
From the NMR spectrum in an applied magnetic field, the Knight shiftKhas been evaluated asK¼ 26:7%.73)In the present case, this shift originates primarily from Hext- induced-magnetization of the5f electrons, which is related to the5f-electron susceptibilityf. Thus,
K¼Ahf
f NB
: ð2Þ
Since f >0, the sign of Ahf is actually negative, thus Ahf ¼ 1473kOe/B. To our knowledge, this is the first experimental determination of the sign of Ahf for 235U nuclei. Although there is no available theory for the HF couplings of5f electrons, the only plausible mechanism for such a large, negative coupling would be core polarization.
From the values determined for K and Ahf, f is thus estimated to be 1:0103emu/mol. This is comparable to the observed magnetic susceptibility withHextparallel to the c-axis of the crystal, obs¼1:32103emu/mol.69) Non- zero f is a characteristic feature of an itinerant system, where the magnitude of ordered moments originates from band polarization and may be substantially modified by an external field. Hence, our NMR measurements probe the itinerant character of the5f electrons in USb2, as suggested by other experimental results.69,77)
4.2 Indirect235U NMR in URh3
Experimental estimates of theT1of 235U (235T1) are very important for gauging the observability of direct235U NMR in uranium compounds. ForT1values less than a few tens of ms, detection of 235U NMR signals becomes quite difficult by standard pulsed NMR techniques. Recently, we have proposed a new method to estimate the235T1‘indirectly’’ in uranium intermetallic compounds which contain ligand nuclei observable by NMR.78,79) Spin–spin couplings be- tween235U and ligand nuclei play a key role in the method.
By applying this method to URh3, using the 103Rh NMR line, we have found235T1T 2s K. This is, to our knowl- edge, the first such estimate for the metallic state of a uranium compound.
Two polycrystalline samples of URh3 were prepared for the experiment, one with natural abundance uranium and the other with an enrichment of 20% 235U. In the non-enriched
sample, the integrated 103Rh spin–echo intensity MðÞ, which was recorded as a function of the time between the excitation pulse and the refocusing pulse, was observed to exhibit a simple Gaussian decay throughout the temper- ature region studied. Thus the Gaussian decay rate 1=T2G
was obtained by simply fitting the 103Rh echo decay to a Gaussian function. On the other hand,MðÞin the enriched sample showed a deviation from Gaussian decay above 80 K. In this temperature range,MðÞwas well fitted by the functionMðÞ ¼M0exp½ð2=T2GÞ2=T2L. Consequent- ly, two different decay rates1=T2Gand1=T2Lwere obtained at each temperature.
As shown in Fig. 12, the1=T2G observed in the enriched and non-enriched samples were found to be nearly identical, even though they were extracted using different fitting functions. This indicates that the T2G decay process comes entirely from the like-spin second moment for the 103Rh nuclei, which is, in principle, independent of the 235U concentration in the samples. On the other hand, the additional1=T2Ldecay only observed in the enriched sample was identified with a cross-relaxation process driven by the
235T1-modulated 235U spins.80) 1=T2L shows a strong T dependence with a significant peak around 180 K.
Since URh3 is a metallic compound with simple Pauli paramagnetism, it is natural to consider that the235U spins would exhibit a Korringa-likeT1behavior, i.e.,1=T1 /T in the whole temperature range. In such a case, 235T1 at very high (low) temperatures will be extremely short (long) compared with the time scale ofT2G, and thus the decay will be governed by the like-spin (103Rh–103Rh) coupling alone.
234 232 230 228 226
Sb signal
Echo Intensity ( a. u. )
219 218 217 216 215 214
235U-NMR signal
93% 235U-enriched 20% 235U-enriched
Frequency ( MHz )
× 1/5
Fig. 11. (Color online) 217 MHz AFNMR peaks observed at 4.2 K in both 20% and 93%235U-enriched samples of USb2, showing amplitudes in rough proportion to their respective enrichment levels.
1.0x10-1
0.8
0.6
0.4
0.2
0.0
1/T2L ( msec-1 )
300 250 200 150 100 50 0
Temperature (K)
235U enriched (20%) 1.0x10-1
0.8
0.6
0.4
0.2 1/T2G ( msec-1 )
235U enriched (20%) Non-enriched
(a)
(b) URh3
Fig. 12. (Color online) The temperature dependence of (a) the Gaussian decay rate, which is unchanged from the unenriched sample to the 20%
235U-enriched one, and (b) the Lorentzian decay term, which only occurs in the enriched sample. The latter term peaks at about 180 K, and varies in a fashion consistent with aT1T’2s KT-variation of the235UT1
process.78,79)
In between, 235T1 will cross the time scale of T2G, and if the unlike-spin second momenth!2iU{Rh is comparable to the like-spin second moment h!2iRh{Rh, there will be a peak in the spin–echo decay rate at or near the point where h!2iU{RhT121. The value of 1=T2L at the peak temper- ature roughly corresponds to the square root of the unlike- spin second moment, i.e., 1=T2Lpeak h!2i1=2U{Rh.78) The observed cross-relaxation effect is consistent with this premise. Correspondingly, from1=T2Lpeak80s1we obtain, in addition, the value h!2iAB6:4103s2. These results yield, finally, 235T1T 2s K. This value suggests that the 235T1 in URh3 would be enough long to detect the
235U NMR signal directly at a low temperature.
Note that a cross-relaxation effect like the foregoing will automatically occur if enough235U spins are present to drive it and if the background relaxation of the ligand nuclei is not too strong. We thus suggest that the indirect 235U studies mentioned here could be feasible with many non-magnetic uranium compounds and possibly in the paramagnetic state of some magnetic ones.
5. AFM and Multipolar Ordering in Actinide Dioxides Actinide dioxides (AnO2:An¼U, Np, and Pu) represent possibly the most intensely studied series of any actinide compounds. However, their surprisingly varied physical properties continue to be of interest for both theory and experiment. Although these actinide dioxides are all cubic insulators (the CaF2 structure) with rather well-localized 5f electrons, their CEF ground states vary significantly:
These are suggested to be a5 triplet for UO2 (U4þ: 5f2), a 8 quartet for NpO2 (Np4þ: 5f3) and a 1 singlet for PuO2(Pu4þ:5f4), respectively. These CEF ground states are believed to be responsible for their varied physical proper- ties at low temperatures.
5.1 235U and 17O studies of UO2
UO2 exhibits an AFM phase transition at TN¼30:8K.
The magnetic structure is the transversetriple-qtype, with an ordered moment of 1.74B/U atom.72,81–84) This phase
transition also causes an internal distortion of the oxygen cubes that surround the U cations.85,86)Furthermore, recent resonant x-ray scattering (RXS) measurements have reported that long-range antiferro-quadrupolar (AFQ) ordering coex- ists with the ‘‘primary’’ AFM ordering belowTN.87)
In UO2, we have succeeded in detecting the direct
235U NMR signal in the AFM ordered state.71,72) This was the first observation of NMR on ions of a magnetic actinide compound. In the AFM ordered state, we have observed a quadrupole-split 235U AFNMR spectrum over a range of 40MHz from a center frequency near 200 MHz, as seen in Fig. 13. This quadrupole-split spectrum reveals the presence of a quadrupole moment at the U sites due to AFQ ordering and/or the distortion of the oxygen. At this frequency, with 93% enrichment of 235U, there was ample signal strength for spin echoes to be observed up to 14 K or so, and for the spin–lattice relaxation timeT1measurements to be performed as well. Above T’14K, T1 becomes unmanageably short.
Figures 14(a) and 14(b) show the temperature dependence of 17O NMR spectra obtained at H010T using a 17O- enriched UO2 powder sample.72)In the paramagnetic state [Fig. 14(a)], a narrow, symmetric spectrum has been observed. There is neither a quadrupole splitting nor an appreciable anisotropic NMR shift at the O sites, reflecting
Echo Intensity (a.u.)
Frequency (MHz)
UO2 235U-AFNMR
T=1.5 K
Fig. 13. The235U AFNMR spectrum atT¼1:5K in 93%235U-enriched UO2.72)
-8000 -4000 0 4000 8000
H0 - Hext (Oe) T= 28 K
800 400 0 -400 -800
T= 125 K
NpO2
800 400 0 -400 -800
H0 - Hext (Oe) T= 17 K 600
400 200 0 -200 -400
UO2
T= 300 K (c)
-400 -200 0 200
PuO2
-200 0 200
-400
H0 - Hext (Oe) T= 8 K
T= 6 K
(a) (e)
(d) (f) (b)
paramag.
paramag.
paramag.
paramag.
AFM AFO
Fig. 14. The temperature dependence of17O NMR spectra obtained atH010T for UO2[(a) and (b)],72)NpO2[(c) and (d)],89)and PuO2[(e) and (f)], respectively.