GdAI2
3. NMR information about the electronic structure of intermetallic compounds with non-magnetic partners
3.2. Analysis of the conduction electron spin polarization 1. Uniform polarization model
3.2.5. Anisotropy of the transferred magnetic hyperfine interaction
NMR IN INTERMETALLIC COMPOUNDS 85
1 00, v .... 39,,,,,-,zA Lo99 0000 ,0,,I
. ~ T = 4.2 K I
c-
O
,ll!~,l~,rl,,f,,~,r~Fi,,,llll,r,,r,l,ll,lll rlWl,ll[l~,,~rllllr ~1JJ i
t'- cD
1:3 __1
O3
5 8 6 0 62
H0/k0e
Fig. 6. t39La echo heights plotted against external magnetic field for a sin- gle crystal of La0.995Gd0.005Ag for differ- ent orientations (q~ is the angle between H 0 and the [001] direction in the (110) rotation plane). For Ure S = 39 MHz, T = 4.2K the main 139La line is at H 0=
64.4 kOe; only that part of the spectrum is shown, where satellite 'A' is located.
The solid lines show the calculated satel- lite splitting due to a Gd moment in the third nearest R shell. (Adapted from Goebel and Dormann 1979).
special 'a priori' assumptions for the distance dependence. The conditions are somewhat m o r e favourable in paramagnetic c o m p o u n d s with a small concen- tration of magnetic moments. Three to four distinct neighbour contributions were derived for the R h site in G d R h , the Z n site in G d Z n and for the lanthanide sites of G d Z n , L a A g , G d I r 2 and G d R h 2 by D o r m a n n and Buschow (1976), Eckrich et al. (1976), Goebel et al. (1977) and D o r m a n n et al. (1976, 1977a).
86 E. DORMANN
the transferred hyperfine field HN(A1 ). Such 'pseudodipolar' contributions have to be explained by the influence of polarized non-s-like electrons, e.g., p electrons at the aluminum site. Similar indications of pseudodipolar contributions were ob- tained from the analysis of the line splitting in Y- or La-diluted GdZn, for the
67Zn NMR line that originates from Zn atoms surrounded by seven Gd and one La or Y ion, instead of, as originally, eight Gd nearest neighbours in the cubic CsC1 structure. Here, as well, a 30% larger splitting than that corresponding to the classical dipole field was observed (Eckrich et al. 1976). These experiments give the additional information that the respective pseudodipolar contribution originates from the nearest neighbours.
A more clear-cut proof of anisotropic contributions to the transferred hyperfine fields was the detailed analysis of the angular dependence of the 27A1 N M R in a single-crystal sphere of GdA12 by Fekete et al. (1975). This investigation gave the unequivocal proof that the anisotropic contribution to the hyperfine field has the same anisotropy as the classical dipolar field, but that outside the error bar it is clearly larger than the classical point-dipole contribution. Barash et al. (1983) measured the N M R of 27A1 in a spherical single crystal of DyA12 in the paramagnetic state. The well split spectrum yielded a quadrupole frequency v o = 561 kHz and an isotropic hyperfine coupling constant a = - 3 . 1 7 kOe p~a _ in agreement with the data in the ferromagnetic state. In this case, the anisotropy of the spectrum was 10% stronger than is predicted by the classical dipole contri- bution.
We have mentioned already, t h a t - via the dipolar part of the anisotropy of the hyperfine interaction-with 139La NMR in a paramagnetic single crystal of La0.995Gd0.005Ag a third nearest Gd neighbour was identified as the one with the largest contribution to the hyperfine field (Goebel and Dormann 1979). Figure 6 shows the interesting part of the a39La NMR spectra in comparison with the line profiles calculated by considering a dipolar form of the anisotropy:
AHre s = AHis o + AHani(3 COS20 -- 1). (15)
It is important to note that in this case of an unequivocal site assignment the line splitting (AHani) was four times larger than could be explained by a classical dipole interaction with the Gd moment of 7 ix B. This is an especially clear proof for the presence of pseudodipolar or orbital contributions to the indirect inter- action, even in intermetallic compounds containing only S-state lanthanide ions.
3.2.6. Evidence for magnetically induced nuclear quadrupole interaction
Further evidence for non-s, especially orbital contributions to the hyperfine interaction in magnetically ordered intermetallic compounds is obtained from a closer inspection of nuclear quadrupole interactions. For an electric field gradient (EFG) of axial symmetry eq = V~¢ caused, e.g., by the low-symmetry arrangement of ionic charges in the crystal lattice, the quadrupole interaction of the nuclear spin I with the quadrupole moment eQ (Barnes 1979, McCausland and Mackenzie
N M R IN I N T E R M E T A L L I C C O M P O U N D S 87
1980) is
3e2qO [ i ~ _ 1 I ( I + 1 ) ] Y(o - 4•(2•- 1)
o r
(16a)
YEo = hP[I~ - 11(1 + 1)]. (16b)
For the predominating magnetic dipole term in the hyperfine interaction and for half-integer spin I > 1, as usually encountered in magnetically ordered rare-earth intermetallic compounds, 2 1 - 1 quadrupole satellites of the main (Zeeman) resonance (rn I = + ½ ~-> -½ ) are observed with frequency separations of
VQ = P(3 cos20 - 1). (16c)
Here 0 is the angle between the axis of the EFG, ~, and the direction z of the magnetic resonance field Hres, eq. (3d). In addition to the direct resolution of quadrupolar splitting or the resolution by double-resonance techniques introduced recently (Pieper et al. 1986), the technique of analysing the spin-echo modulation caused by the quadrupole interaction (in addition to multiple echoes), as intro- duced by Abe et al. (1966), was applied in particular. It allows one to derive the weak unresolved quadrupolar interaction in the presence of the larger magnetic hyperfine interaction. Shamir et al. (1971), Degani and Kaplan (1973) and later on many other groups applied this technique for the study of the 27A1 quadrupolar interaction in RA12. In addition to the well known lattice EFG at the axially symmetric site, Degani and Kaplan (1973) observed a contribution to the EFG that was linearly proportional to the magnetization. The strength of a possible magnon-induced pseudoquadrupole interaction in ordered systems was analyzed by Zevin and Kaplan (1975). Within the framework of the long-wavelength magnon approximation, they showed that this contribution is indeed linear in the magnetization and that it could account for the 27A1 results for GdA12. However, the explanation with the pseudoquadrupole effect is not yet without controversy.
Gehring and Walker (1981) showed that this effect can be related to the difference between the transverse and longitudinal magnetic susceptibilities. They concluded-while agreeing for the linear magnetization d e p e n d e n c e - f r o m the model calculations that they performed for GdAI2, that the pseudoquadrupole effect appears to be too small to be observed. Recently, Dumelow et al. (1988) reinvestigated the 27A1 quadrupolar interaction for GdA12 with the help of powder samples. They analysed signals from domains and walls and also used holmium substitution and external fields. They found that their results were incompatible with a significant magnetic contribution to the EFG at the A1 sites unless such a contribution had its principal axis along the (111) axis of the lattice EFG at the A1 site in both the domains and the domain walls, i.e., independent of the direction of the magnetization. Thus an orbital polarization of p-like conduction electrons at the A1 site of the magnetically ordered compound might be at the origin of this puzzle.
88 E. DORMANN
The magnetically induced electric quadrupolar interaction was recently ob- served in several cubic, ferromagnetically ordered intermetallic compounds at the nucleus of the rare-earth S-state ions Gd 3+ and E u 2+, despite the fact that the nuclei are residing on nominally cubic lattice sites: e.g., nuclear quadrupole splittings v o of 0.6-0.8 MHz were derived for 155Gd and ~SVGd in GdA12, GdIr 2 and GdRh 2 or of 0.7 and 1.5 MHz for a53Eu in EuPd 2 and EuPt2, respectively, all at 4.2K. Figure 3 showed an example ( I = 3); see Kropp et al. (1979a, 1983), Barash and Barak (1984), Dormann et al. (1984, 1986), Dormann and Dressel (1989), Dressel et al. (1988), and Dressel and Dormann (1988) for further details.
For GdA12 and EuPt 2 the temperature dependence of vQ was measured and found to vary roughly as [Ms(T )/Ms(O K)] 2, as is expected for a magnetically induced EFG at a cubic site. In addition to the relativistic single-ion quadrupolar interaction that should always be observed in magnetically ordered Gd and Eu intermetallic compounds, the lattice contribution caused by the magnetostriction and an eventual contribution of orbitally polarized conduction electrons at the lanthanide site have been identified as the most important contributions to the EFG.
3.3. Crystal-field effects and orbital contributions to the hyperfine interactions 3.3.1. Extensions of the R K K Y framework
In addition to the evidence from the analysis of the angular dependence of the transferred hyperfine interaction, which indicated that orbital contributions to the hyperfine interactions should be taken into account, further hints were obtained.
If the contributions of the conduction electrons to the magnetic order and hyperfine field at the rare-earth site, as discussed in sect. 3.2.3, were considered for the whole lanthanide series, analyses based on the isotropic bilinear exchange interactions between 4f and conduction electrons have generally not been able to explain the systematic variation of these contributions across the lanthanide series satisfactorily. Therefore, several theoretical papers have studied the indirect exchange and hyperfine interactions in more detail. Indirect exchange via spin- orbit-coupled states was considered by Levy (1969), who found the resulting new terms in the interaction Hamiltonian necessary in order to fit the Curie point data on several series of intermetallic rare-earth compounds. Numerical results by Ray (1974) indicated that d electrons contribute predominantly to both the isotropic and anisotropic exchange. Belorizky et al. (1981) developed the model frame- work necessary to explain the variations within the lanthanide series by taking the full 4f-conduction electron exchange interaction (higher-rank coupling) and the crystallographic symmetry of the rare-earth site into account. They also included spin-orbit coupling of the conduction electrons. (As discussed before, the con- duction electrons in the lanthanide intermetallic compounds of principle interest are primarily of 5d and 6s character.) They derived the expressions for the orbital and spin polarizations of these conduction electrons and for their contribution to the hyperfine field and the magnetization. The 'ab initio' calculations of indirect multipole interactions for DyZn by Schmitt and Levy (1984) are another example
NMR IN INTERMETALLIC COMPOUNDS 89
of such improvements. These results underscored again the predominant effect of the d electrons in the conduction band: their orbital character is the origin of the strong tetragonal quadrupolar interactions observed in the rare-earth CsCl-type intermetallic compounds.
Recently, Orlov (1985, 1986) suggested a 'crystal potential model' for the interpretation of crystalline electric field effects in intermetallics and used it for a discussion of these effects in PrA13 or of the sign and magnitude of the magnetic crystal anisotropy for RX 5 and R2X15 compounds. This effective crystal potential
V(r)
has the crystal symmetry and is constructed from experimental data or calculated from first principles; it oscillates and decreases rapidly with distance.Generally the agreement between experiment and calculation for each series of intermetallic compounds is improved decisively with the improved theoretical models at the cost, however, of an increased number of free parameters or a less convenient form of the relations.