Intermetallic compounds with special properties

GdAI2

5. Intermetallic compounds with special properties

5.1. Van Vleck paramagnets

As was discussed by Andres and Bucher (1968), the intermetallic compounds with rare-earth ions in the singlet ground state, such as praseodymium

(141pr),

turned out to be rather suitable for the production of very low temperatures by means of nuclear adiabatic demagnetization. Since the pioneering studies of Jones (1967, 1969) on the Pr and Tm intermetallic compounds, it has been known that the (effective) resonance field at the nucleus of these van Vleck paramagnets may be several times the applied magnetic field H 0. All the main points of interest for cooling applications, i.e., the interaction of the lanthanide nuclei with the magnetizing field, the static nucleus-nucleus interactions and the static and

100 E. DORMANN

dynamic nucleus-electron interactions can be studied with the help of NMR (Kaplan et al. 1980).

Mostly, the low-temperature lanthanide 'Knight' shifts could only be measured.

Weaver and Schirber (1976a) (see Schirber and Weaver 1979) analysed the pressure dependences 0(ln K)/Op and the temperature dependences of the NMR shifts in compounds such as PrP, PrAs or TmP (and others) with the N M R of 14~pr, 169Tm and the nuclei of the non-magnetic partners! From the temperature dependence, one c a n - a t least in principle- distinguish between crystal-field and exchange effects. The 14~pr NMR study of Kaplan et al. (1980) on a PrNi 5 single crystal gave an upper limit of the zero-field quadrupolar-like nucleus-electron interaction and provided accurate values of the magnetic field enhancement factors as a function of the crystal orientation and of the temperature. Satoh et al.

(1981) measured the 141pr NMR in the singlet ground state system Pra_xLaxIn3 and analysed the field dependence of the resonance frequency and the composi- tion dependences of the nuclear spin-spin and spin-lattice relaxations. The nuclear relaxation rate 1/Ta has been studied theoretically in substances with a singlet ground state such as PrNi5 by Ishii (1988). He showed that 1/T 1 deviates from the Korringa law with decreasing temperature and vanishes at the nuclear ordering temperature.

5.2. Itinerant-electron ferromagnets

Already two decades ago, the effect of localized lanthanide magnetic moments on the conduction electron ferromagnet ZrZn 2 was analysed by Asanuma and Yamadaya (1968) with 91Zr NMR in Zrl_xGdxZn 2 (x ~ 0.015), using a K~--~X analysis. The value obtained for a, i.e., a ~ - 3 8 kOe p~l, was small and essen- tially independent of the Gd concentration. Moriya (1977) explained how the spin fluctuations of itinerant-electron magnets can be studied with the help of N M R spin relaxation. Sc3In is a weak band-magnet that orders ferromagnetically with T c ~ 6 K and /.tsc~0.07 ~B. N M R and T 1 for 45Se in the itinerant-electron ferromagnet Scfln was studied in both the ferromagnetic and paramagnetic states by Hioki and Masuda (1977). The correlation of K(T) and x ( T ) gave a hyperfine coupling constant of a = +58.4 kOe la~ 1 per Sc atom. This was interpreted as an indication of strong 3d admixture in the wavefunction at the Fermi surface and of the d-spin contribution to the susceptibility. Yoshimura et al. (1988) analysed the nuclear spin-lattice relaxation rates, 1/Ta, of various kinds of metallic magnets, and 1 / T 1 w a s found to be independent of temperature. They ascertained that the values of 1/Ta in the weak itinerant ferromagnets like Y(Co-A1)2 were explained by the self-consistent renormalization theory taking into account spin fluctuations only around q = 0.

5.3. Hydrogen in intermetallic compounds

Hydrogen in rare-earth intermetallics has been an area of minor NMR activity in the last decade, compared with the period covered by Barnes (1979) in chapter

NMR IN INTERMETALLIC COMPOUNDS 101 18 of this Handbook. However, several interesting recent investigations are mentioned in the tables of the appendix, e.g., for the N M R probes 139La (A3), 159Tb (A9), 167Er (A12), 1U, 2H (B1) and 59C0 (B12), where the letters and numbers in parentheses refer to the table numbers.

5.4. ' Conventional' superconductors

Frequently, N M R has been applied for the study of 'simple' superconducting intermetallic compounds. We refer to the review of MacLaughlin (1976) for a general introduction. Occasionally, N M R has also been applied to tackle more complicated systems, like heavy-fermion superconductors (sect. 5.5.1) or systems, where the eventual coexistence between magnetism and superconductivity was of interest (sect. 5.4.1). N M R has made important contributions to a better under- standing of the high-To oxide compounds, as well. The latter, growing, field of activity has to be covered in a future volume of this Handbook.

Nuclear spin-lattice relaxation (l/T1) has frequently been used to study the nature of the superconducting state, because it gives information about low- energy excitations (and the so-called coherence factor). Zero-field N Q R is generally more reliable for investigations of superconductors, since only the rf field, and not the static magnetic field as well, must penetrate the sample. If due care is taken in the analysis, the rf penetration need not even be homogeneous.

T1, T 2 (T~) and the spectrum can be used as information sources. The necessary requirement is, however, that a nucleus with I > 1 and a reasonable quadrupole moment resides in the intermetallic compound on a site with a symmetry lower than cubic, resulting in a large enough N Q R frequency v o. 27A1, 63Cu and 139La turned out to be useful N Q R probes. If spin-lattice relaxation times are long enough, field-cycling N M R experiments are also appropriate for the analysis of superconductors. Relaxation experiments are less susceptible to experimental problems than Knight shift measurements, which require the application of an external magnetic field, which is in conflict with superconductivity. At least the accuracy suffers severely under the influence of the internal-field distribution in the field range//ca ~ H 0 < He2 in type-II superconductors.

Several authors have analysed the influence of paramagnetic impurities on the relaxational behaviour of conventional superconductors. MacLaughlin et al.

(1973) analysed zero-field nuclear spin-lattice relaxation rates in superconducting magnetic pseudobinary compounds (LaGd)AI 2 in terms of direct impurity and conduction electron contributions. The temperature dependence of the Korringa rate exhibited the effect of impurity pair breaking near the superconducting transition. MacLaughlin et al. (1976) found that the 139La spin-lattice relaxation times in Laa_xCexA12 agree with the theory based on weak exchange coupling between conduction electrons and paramagnetic impurities. Matsui and Masuda (1977) studied the 27A1 relaxation in (La(Gd, Ce))3AI , both in the normal and the superconducting states. Here too, the impurity-induced relaxation rates were found to play an important role.

102 E. DORMANN 5.4.1. Superconductivity and magnetic order?

The coexistence of superconductivity and magnetic order is an exciting problem for many researchers. We refer to the review of Roth (1978) for an introduction.

Experiments on magnetically ordered superconductors were also reviewed by Maple (1983). There are several rare-earth intermetallic compounds in which NMR has been applied to investigate the details of an eventual coexistence between magnetism and superconductivity. Unfortunately, in this area the chances are high that one may jump into a pitfall with the N M R analysis, because many of the interesting intermetallic compounds are not easy to prepare in single-phase form; the risk is thus imminent, that N M R is observed in a magnetic phase, but superconductivity occurs in the other phase of a two-phase sample.

The RRh4B 4 structure allows sufficient separation between the magnetic lanth- anide ion and the superconducting electron. Ferromagnetism is observed for R = Gd, Tb, Dy, Ho or Er; for R = Er, the long-range ferromagnetic order destroys the superconductivity. For R = Nd, Sm and Tm long-range antiferromag- netic order and superconductivity coexist. Superconductivity is also found for R = Lu (Kohara et al. 1983). After the discovery of 're-entrant' superconductivity in the ternary compound ErRh4B 4 by Fertig et al. (1977), where long-range ferromagnetic order quenches superconductivity below TVM < To, there have been a number of NMR investigations dealing with the question of superconductivity and magnetic order in rhodium-boride compounds containing a lanthanide ion with a localized magnetic moment.

liB NMR of Tse et al. (1979) in Yl_xErxRh4B4 (x ~<0.1) indicated that the conduction electrons in this system couple strongly to the local moments, despite the extremely weak influence of x on the superconducting transition temperature To. The presence of large hyperfine fields was claimed for the boron sites in the superconducting state (for He1 ~ H 0 < He2 ) from the pronounced loss of the 11B signal below the transition temperature Tc(H0). In contrast, Kumagai et al.

(1979) found only a small polarization of the conduction electrons at the B site in the magnetically ordered compounds RRh4B 4 (R = Tb, Dy, Ho and Er) via 11B NMR. The hyperfine field at the Gd nuclei in GdRh4B 4 was observed to be largely anisotropic (forming a powder pattern in the N M R wall spectrum).

Kumagai et al. (1980) observed T 1 anomalies for ErRh4B 4 (T~ = 8.15 K) in low magnetic fields (2.2 kOe). Johnston and Silbernagel (1980) found by laB N M R in GdRh4B 4 and LuRh4B 4 that in both examples the anisotropic part of the Knight shift was larger than the isotropic one. The absence of any detectable temperature dependence for Kis o and Kan i in LuRhgB 4 between 90 and 300 K, in spite of a large variation of the static susceptibility of the material, indicated a weak interaction of the liB with the Rh d-like electrons responsible for the T- dependence of the susceptibility. The authors suggested that the decoupling between certain classes of conduction electrons might be important for the unusual superconducting and magnetic properties. ~*B NMR was also measured in the paramagnetic and ordered state of GdRh4B 4 (TFM = 5.6 K) by Kohori et al.

(1983a, 1984). Kumagai and Fradin (1983b) studied the 11B spin dynamics in (Y1 xRx)Rh4B4 for R = Gd and Er with the adiabatic demagnetization-remag-

NMR IN INTERMETALLIC COMPOUNDS 103 netization field cycle method. 11B NMR was measured for SmRh4B 4 in the paramagnetic, antiferromagnetically ordered and superconducting state (T c 2.5K, T N = 0 . 8 7 K ) by Kohori et al. (1983a, b). Kohori et al. (1985) also analysed liB NMR in R(Rhx_xIrx)4B 4 for R = Tb, Dy and Ho. They observed the decrease of TFM with increasing Ir concentration x and the appearance of antiferromagnetic long-range order coexisting with superconductivity for larger values of x, with Tc > T N at the Ir-rich side.

(Cel_xGdx)Ru 2 is another rare-earth intermetallic compound suspected of showing coexistence between superconductivity and magnetic order for pseudo- binaries with x ~ 0 . 1 . Speculatively, Kumagai and Asayama (1975) concluded from Gd NMR on a coexistence between superconductivity and ferromagnetism.

Kumagi et al. (1978) measured Gd NMR at T = 60 mK in zero field down to x = 0.105 and with field down to x = 0.095 (even at 1.2 K). From the variation of the hyperfine field and T~ with composition, they concluded that the NMR signal should n o t originate from a precipitated ferromagnet. They discussed the possibi- lities of spin-glass type and short-range order. A sharp superconducting transition was observed for x ~ 0.110. The temperature dependences of T 1 for x = 0.105 and 0.110 were considered suggestive of a small energy gap associated with a superconducting state at the ferromagnetic sites. Matsumura et al. (1982) meas- ured the temperature dependence of T1 for the zero-field NMR signal as a test for the coexistence between superconductivity and ferromagnetism. They reported that T 1 increases exponentially with lowering of the temperature due to the energy gap. In addition, Kohori et al. (1983b) inferred the coexistence from the zero-field NMR and T 1 reflecting the superconducting energy gap in (Cel_ x Gdx)Ru 2 for x ~ 0.12, where superconducting and magnetic ordering tempera- tures roughly coincide.

Y4Co 3 was regarded as a new type of magnetic superconductor, because experiments indicated the interplay between itinerant electron ferromagnetism and superconductivity. This is different from the rare-earth rhodium borides or the Chevrel phases, where magnetism is associated with localized lanthanide moments (Takigawa et al. 1983c). NMR results dealing with this question for Y4Co3 were reported by three different groups in 1983: Lewicki et al. (1983), Takigawa et al. (1983c) and Wada et al. (1983). Y4Co3 is a compound that is difficult to prepare at least 'close to single phase' and was sometimes considered to be Y9Co7 . Its magnetic ordering temperature T M ~ 4.5-5 K is larger than the superconducting transition temperature T~ ~ 2.5 K. The saturation magnetization is small, corresponding to an average moment of 0.01-0.037 P~B per Co atom.

Pulsed 59Co NMR and NQR have been performed by Wada et al. (1983) in the paramagnetic and ferromagnetic states. They analyzed two sites with small positive Knight shift, corresponding to nearly non-magnetic Co sites. The effect of spin fluctuations was seen in an enhancement of the 59Co relaxation rate around the ferromagnetic ordering temperature. They suggested that the magnetic mo- ment of the compound should mainly be carried by the d electrons of the Co atoms at the remaining (linear-chain) site. Takigawa et al. (1983c) observed three kinds of 59Co resonance signals, corresponding to the three (6h, 2d and 2b) sites

104 E. DORMANN

of the hexagonal structure (the 2b sites being occupied once per unit cell in Y4Co3, but four thirds per unit cell in Y9Co7). They did not find the resonance line with large positive shift that Figiel et al. (1981) and Lewicki et al. (1983) attributed to 2d sites. A zero-field Co line observed at 18 MHz indicated a Co moment of 0.23 txB, corresponding to an average moment of 0.11 ix B for the Co 2b sites.

5.5. Intermediate-valence, Kondo-lattice and heavy-fermion systems

This is an area of solid state physics that has been intensely studied in recent years. Other chapters of this Handbook are devoted to this subject: chapter 11, volume 1, chapters 62-66, 68 and 71, volume 10; chapters 76 and 78, volume 11;

chapter 83, volume 12; and chapters 95, 96 and 97 in this volume. There have also been several recent reviews for this field- as far as N M R applications to inter- mediate-valence compounds are concerned, one might get the impression that there are more reviews than original work! For a review of unstable-moment phenomena in rare-earth compounds, including key thermodynamic experiments, such as susceptibility and lattice constant, spectroscopic experiments and theoreti- cal work, we refer the reader to Lawrence et al. (1981). A general overview was also given by Parks (1985). NMR and relaxation experiments in rare-earth compounds, which exhibit unstable 4f magnetism and related effects, were reviewed by MacLaughlin (1985). He concluded that in several systems paramag- netic NMR shifts indicate a modification of the electronic band structure below the characteristic temperatures, found from the classical experiments like suscep- tibility and specific heat (i.e., shift anomalies as compared to eqs. (9) and (10c) are observed). Shift anomalies are small or absent in compounds with low characteristic temperature and integral or nearly integral valence, like CeCu2Si 2 and CeRu2Si 2. Nuclear spin-lattice relaxation rates yield estimates of spin fluctuation rates and are sensitive to the onset of correlated near-neighbour fluctuations. Crisan (1986) reported a formula for the NMR relaxation rate of heavy fermion systems. In their recent review, Asayama et al. (1988a) pointed to the fact that in several heavy-fermion materials an antiferromagnetic type of ordering is observed to appear in the ground state. The anisotropic superconduc- tivity coexists or competes with the magnetic ordering. Recently, MacLaughlin (1989) has reviewed the use of NMR and related techniques in the study of the magnetism of 'unstable magnets', i.e., intermediate-valence and heavy-fermion materials. He mentioned that for temperatures below the characteristic or 'Kondo' temperature T O the experiments give evidence for:

(i) modification of the transferred hyperfine field (non-linear K(X));

(ii) onset of spatial correlations between f spin fluctuations:

(iii) strong energy-gap anisotropy, with zeros of the gap along lines on the Fermi surface in heavy-fermion superconductors;

(iv) very weak static magnetism, with average moments of about 10-1-10 -3 P~B per 4f atom in CeA13 or CeCu2Si 2. In addition, Panissod et al. (1988) reviewed the NMR study of electron spin fluctuations in intermediate-valence, Kondo and

NMR IN INTERMETALLIC COMPOUNDS 105 heavy-fermion compounds. They pointed to the fact that a universal thermal dependence of the f-electron fluctuation rate 1/%ff is observed. 1/re~ ~ is constant for T ~ T o in the Fermi-liquid regime and 1/%~f- T 1/2 for T >> T 0.

The dense Kondo system CeB 6 was studied by Kawakami et al. (1981, 1982, 1983) and Takigawa et al. (1983a, b). It seems to have three magnetic phases. In the highest temperature phase I ( T > 3 . 1 K), a pronounced Kondo effect is observed, with a log T dependence of the resistivity and negative magnetoresist- ance. Here the N M R spectrum was characteristic of the paramagnetic phase, and quadrupolar splitting was observed at 77K (Kawakami et al. 1981). In an intermediate phase II, an antiferromagnetic component seems to be induced by the external field, increasing with field and being zero in zero field. N M R line splitting into two lines for the magnetic field in the [111] direction (and more for the other directions) is observed. Whereas the 11B splitting behaves like that observed in antiferromagnetic ordered compounds (Kawakami et al. 1981, Takigawa et al. 1983a), no long-range order is detected by neutron scattering in phase II. From an analysis of the orientation, field and temperature dependence of the 11B N M R line splitting in a single crystal for phase II, possible anti- ferromagnetic structures could be inferred. The change in the N M R spectrum from phase II to III (T ~< 2.3 K) seems more drastic with decreasing temperature (or increasing field). In this phase, long-range order with multiple q-structures is detected by neutron scattering.

Shimizu et al. (1985a) analysed the spin-lattice relaxation time, T1, of Cu nuclei for a CeCu 6 single crystal. The N M R spectrum is complicated due to the presence of four formula units per unit cell and five groups of inequivalent Cu sites. However, from the temperature dependence of T~ an effective value for the relaxation rate of the Ce moments, 1/Zeff, could be estimated, which would be the largest in the series C e C u 6

(h/q"

⁼ 9 meV, T K = 2-3 K), CeCu2Si 2 (hl'r = 0.8 meV, T~: = 11-14 K) and CeAl3(h/7 = 0.5 meV, TK = 5 K). The transition from the magnetic regime to the non-magnetic Fermi-liquid regime of the typical Kondo- lattice compound C e C u 6 w a s explored by Kitaoka et al. (1985b) with the help of the 63Cu N Q R from a microscopic point of view. They had a large single crystal available, giving narrow N Q R lines. They concluded that C e C u 6 shows heavy- fermion properties at low temperatures, T <~ T* = 0.2 K. In the Fermi-liquid state below T* the Korringa law T 1 T ~ 0 . 0 1 1 s K = const, was obeyed, whereas for T i> 6 K, 1/T~ ~ const, ~ 150 S -1.

Kitaoka et al. (1985a) showed with 29Si N M R (K(T), 1/T1) that CeRu2Si 2 is a non-magnetic Kondo-lattice compound below Trc--12 K. They found that KII depended on temperature, while K± did not. KII/K l was about 30 at 4.2K, and the anisotropy about one order of magnitude larger than the dipolar contribution.

1/Txi was independent of temperature for 1 2 K < T < 7 0 K , whereas for T <

T* = 8 K as a Korringa relaxation T i l T = 1 . 0 s K was observed indicating a Fermi-liquid state, T~T of 63Cu was analysed by N M R or N Q R in CeCuzSi 2 (Tr: -- 10 K) in the temperature range above T c (in the normal coherent state of the Kondo-lattice system), as well as in the Kondo-lattice compounds CeRu2Si 2 (T K = 12 K) and C e C u 6 ( r K = 6 K) by Kitaoka et al. (1986). T1T was considered

106 E. DORMANN

to be almost constant below T* = 2.5 K for CeCu2Si2, T* -~ 6 K for CeRu2Si 2 and T* = 0.2 K for C e C u 6.

The magnetism of CeA13 was probed with NMR by Lysak and MacLaughlin (1985) at temperatures T > T* ~ 0.5 K, below which the system can be described as a degenerate Fermi fluid. Magnetism and NMR at high temperatures could be described well by a model of independent Ce 3+ ions. A change of slope in the relation between the 27A1 isotropic frequency shift Ki~ o and the bulk susceptibility X has been found below about 10 K and was attributed to a temperature- dependent transferred hyperfine field in this temperature range. This hyperfine field anomaly was believed to be probably not the same as that previously noted at T-~ T* in other lanthanide compounds, where the moment instability is associated with intermediate valence. The temperature range was rather charac- teristic of crystalline electric field splittings. In CeA12 an anisotropic hyperfine interaction in the presence of CEF splitting has been invoked to explain a similar shift anomaly. The temperature dependence of the effective Ce spin fluctuation rate, obtained from measured spin-lattice relaxation rates

1/T1,

indicated the onset of near-neighbour spatial correlations between dynamic Ce spin fluctuations at low temperature.

Nakamura et al. (1988c) pointed to the fact that conventionally, the heavy- fermion systems have been classified into three types of ground states: paramag- netic, antiferromagnetic and superconducting. More recently, several of the c o m p o u n d s - e . g . , CeA13, TN = 1.2K, Nakamura et al. (1988a)-were found to be ordered antiferromagnetically at low temperature, suggesting a close correla- tion between superconductivity and antiferromagnetism. They questioned whether the normal Fermi liquid was stable at low temperatures or whether long-range ordering might set in eventually at low temperatures. Also the heavy fermion system CeInCu 2 was reported to show antiferromagnetic-like ordering behaviour at 1.1 K.

Sampathkumaran et al. (1979c) showed that the quadrupole coupling constant

eZqQ

for 63Cu in EuCu2Si 2 has a strong temperature dependence, in contrast to YbCuzSi 2 or SmCueSi 2. Sampathkumaran et al. (1985) observed a strong anoma- ly in the expected linear relationship between the 31p NMR Knight shift and the bulk magnetic susceptibility at low temperatures for the intermediate-valence compound EuNi2P 2. They showed that this anomaly should not be caused by the CEF or lattice volume effects. Instead, they believed that it results from the formation of the hybridized 4f conduction electron ground state.

For the intermediate-valence compound YbCuAI, MacLaughlin et al. (1979) observed a linear relationship between

27K

and X only for temperatures above the maximum of the bulk susceptibility. For T < Tma x --~ 27 K, this relation was no longer obeyed. This was tentatively attributed to a temperature-dependent effect of intermediate valence on the transferred hyperfine coupling between the Yb moments and the

27A1

nuclei. The T 1 relaxation data yielded a 4f spin fluctuation rate via

(K2T1 T ) - I x ~-- 2 ' Y i k B 2 "reff, (21)