Crystal-field splitting, magnetic order and the hyperfine interaction

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

3.3.3. Crystal-field splitting, magnetic order and the hyperfine interaction

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.

90 E. DORMANN

direction of magnetization has been observed as mentioned before and a calcula- tion, in agreement with the observations, has been developed. The isotropic exchange parameters J4f-s were determined and were observed to decrease in the lanthanide series by almost a factor of three.

For a general introduction to the field of N M R in magnetically ordered compounds with non-S state lanthanide ions, we refer the reader to Taylor (1971) or McCausland and Mackenzie (1980), where the interplay of the exchange and crystal-field interactions has been analysed. Generally, for cubic systems like RAI 2 at least a three-parameter mean-field model is adopted, based on a single-ion Hamiltonian comprising a crystal field of cubic symmetry [CEF parame- ters W, x; Barnes (1979)] and an isotropic molecular field constant (A):

= ~CEF(W, X) + ~MF(A) + ~ z e ( H o ) . (17)

In addition to the magnetic dipole and electric quadrupole an octupolar contribu- tion (w) of the hyperfine interaction at the lanthanide site has also to be considered. The transition freqeuncy is described by (McCausland and Mackenzie 1980)

1]mz,rni_ 1 -~- a ~- ( 2 m I -- 1)P + (3m 2 - 3 m I + 1)w. (18a) The nuclear quadrupole frequency parameter P contains second-order corrections p(2) to the first-order part,

p ( 1 ) _~ ( 3 J 2 - J ( J + 1))

J ( 2 J - 1) P0, (18b)

(with the free-ion value P0) that generally can not be neglected (Waind et al.

1983). Along these lines McMorrow et al. (1986) performed recently for the first time a complete analysis of the hyperfine interactions for 165Ho in a s i n g l e c r y s t a l of H0.01Gd0.99A12 with an applied external field ( H 0 ~ 80 kOe).

In the past, there were several reports of lanthanide-site N M R for ferromag- netically ordered RA12, based on powder samples. Berthier et al. (1977) analysed the variation of the 163Dy NMR with x in Dyl_xYxA12. They observed satellite lines, which showed the modification of H4~ (after separation of the various contributions in eq. (13a)). This modification is caused by the variation of the molecular field, which influences the angular momentum ( ( J z ) ) of the ground state wavefunction, and hence the 4f moment. Berthier et al. (1978b) also analysed the conduction electron spin and orbital polarization effects in RAI 2 compounds with R = Nd, Dy, Tb and Er. The hyperfine fields were separated into their various components [eq. (13a)]. They deduced the variation of the self- polarization field H s with the lanthanide element. The observed behaviour indicated a strong dependence on the lanthanide o r b i t a l moment and was accounted for by including both the spin and the orbital polarizations of the conduction bands. From a comparison with the transferred hyperfine field at the A1 nuclei, they concluded that the large orbital polarization did not extend to these sites. Magnetic hyperfine and electric quadrupole interactions were analysed

NMR IN INTERMETALLIC COMPOUNDS 91 for 159Tb and 167Er in Rl_~GdxA12 by Berthier and Devine (1980b). They found that the effective molecular field, seen by the lanthanide ions, varies in these compounds less than predicted from a simple scaling according to the Curie temperatures. The required change of the orbital polarization of the conduction band was correlated with a modification of the band structure. The hyperfine parameters of holmium in RA12 (at 1.4 K) have shown to be strongly anisotropic;

Waind et al. (1983) in their analysis of

165Ho

NMR in pseudobinary compounds, could also reproduce the observed directions of the spontaneous magnetization.

An extensive analysis of 165Ho NMR in HoA12, in which the exchange and crystal-field parameters were optimized together, was performed by Prakash et al.

(1984), giving detailed information about the crystal-field ground state.

Summarizing the development of the different NMR investigations, it seems that orbital contributions of the conduction electrons are existing, but were probably overestimated in earlier work. A reasonable derivation of the exchange and crystal-field parameters can only be achieved if the magnetic dipole hyperfine interaction at the lanthanide site-giving access to (Jz) -and the electric quad- rupolar contributions-indicating ( J ~ ) - are analysed together (as well as the conduction electron and neighbour ion contributions to Hh~ and P).

3.3.4. The quadrupolar interactions for lanthanide nuclei

Devine and Berthier (1981) used NMR measurements of the quadrupolar splitting at the lanthanide sites in RAI2- , RFe 2- and RZn-ordered compounds and determined the value of (Jz) for the 4f electrons. Extended discussions of this technique were presented by Berthier and Belorizky (1984), Belorizky et al.

(1984), and Belorizky and Berthier (1985). They considered both the possibilities and the difficulties (e.g., possible errors in p(2)) in the determination of the 4f-shell magnetic moments in cubic lanthanide intermetallic compounds by per- forming a zero-field NMR quadrupolar hyperfine splitting analysis and compared these with the other, more standard techniques like magnetization measurements, polarized neutron diffraction, elastic and inelastic neutron spectroscopy. Since the 4f electronic moment can be obtained directly via zero-field NMR, with good accuracy, this procedure allows a much easier separation of the magnetic effects arising from localized 4f electrons of the lanthanide ion from those arising from the conduction electrons or other atoms.

3.3.5. Analysis of the self-polarization field

Earlier, Belorizky et al. (1979) analysed the contributions to the self-polariza- tion field H s from orbital, magnetic dipole-dipole, contact or core polarization with group symmetry arguments in order to determine the independent parame- ters of the problem for cubic compounds. The recent progress in the accuracy of the determination of the 4f part of the hyperfine field in cubic intermetallic compounds, H4f [eq. (13a)], by using NMR quadrupolar splitting results, has enabled a more accurate determination of the self-polarization field H s (Berthier and Belorizky 1986, Belorizky and Berthier 1986). It was shown by these two authors that, for the cubic ferromagnetic RA12 and RZn series, H s increases

92 E. DORMANN

roughly proportional to (S z ), the total 4f

spin

of the lanthanide ion

H s : as(Sz) +

aL(Lz),

(19)

with as = 5 1 . 7 k O e and 15.7kOe for RA12 and RZn, respectively, and a L = 4 -+ 8 kOe or 12 --+ 19 kOe for RA12 or RZn, respectively. The orbital effects in the RA12 series are present, but relatively weak - at most 30% of the spin-polarization field. Orbital effects are more important in the RZn series (for ErZn they are three times larger than the spin-polarization part). For the RA12 series Berthier and Belorizky (1986) obtained estimates for the local orbital, spin and quadrupo- lar polarization of 5d-like conduction electrons: (l~) d ~<0.06, (s~) d ~<0.09 and (lz 2 -- 2)d ~ 0.05.