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
3.2.3. Correlation of magnetic ordering temperatures and transferred hyperfine fields
As is evident from a comparison of eqs. (11d) and ( l l e ) , there is also a direct empirical access to the conduction electron spin polarization, if magnetic ordering temperatures and transferred hyperfine fields at the R site are compared. Both quantities contain the spin polarization at the R site, induced by all the other R electronic spins
9./rZ 2 R
{ s z ) c e - 4EF J(0)(Sz)R,,~m ~]
F(2kvrnm)"
(11f)82 E. DORMANN
The eqs. ( l l d ) and (11e) can thus be generalized, not implying anymore the special distance dependence of the RKKY model [eq. (llf)] and allowing the experimental distinction between the influence of 6s-(6p-) and 5d-like conduction electrons to be made:
SR(S R + 1)
r c "~---'Op -- 3 k B ( S z ) R (J4f_s(Sz)s 21- J4f_d(Sz)d) (12a) and
HN(R) = - 2 ( a s ( S z ) s + aa(sz}d). (12b)
Whereas both exchange coupling constants are assumed to have the same sign and comparable magnitude, opposite signs and different strengths for the hyperfine coupling constants for conduction electrons with 6s or 5d character at the lanthanide site are considered (a d ~ -0.1as). For more details and references for the coupling constants see Dormann (1977) and Kropp et al. (1979b).
The ordering temperature is directly accessible; the contribution of the neigh- bours H N to the hyperfine field at the magnetic rare-earth ion's site is, however, only one of the three components of the hyperfine field //he, which itself is conveniently accessible to NMR measurements:
Hh~ = H4f + H s + HN, (13a)
for a lanthanide ion in general, and
Hhf = Hcp + H s + HN, (13b)
for Eu z+ or Gd 3+ ions with half-filled 4f shells and thus a 8S7/2 ground state. Due to the large orbital contributions to H4~ for non-S state ions, only in favourable cases-see sections 3.3.4 and 3.3.5-is it possible to separate HN from the influence of the lanthanide ion's own conduction electron spin polarization H s - the so-called self-polarization field - and the 4f-shell contribution, H4f , in eq.
(13a). The situation is more agreeable for the S-state ions, eq. (13b), because in the absence of a 4f-shell orbital moment, the remaining core polarization contri- bution Hcp is small, assumed to be constant and known experimentally-e.g., Hcp(Gd ) = -(332 -+ 6) kOe (Koi 1969). Nevertheless it was a precondition for the usefulness of eqs. (12a) and (12b), that it could be proved that non-magnetic rare-earth ions such as Sc, Y, La or Lu, introduced in small concentrations in pseudobinary intermetallic compounds, could serve as excellent direct NMR probes for H N. For example, the 139La NMR spectrum in Gd 1 xLaxRh 2 has been measured for 0.5 i> x/> 0.01 (Dormann et al. 1977a), Hhf(La ) for a vanishing La concentration has been determined by extrapolation (see, e.g., fig. 5) and
Hhf(La )
could be converted to HN(Gd) by use of the known hyperfine coupling constants.
[The required outer-electron coupling constants for the various elements were interpolated between the values given by Campbell (1969)].
Such an NMR analysis for ferromagnetic Gd intermetallics revealed that the s-like conduction electrons predominate only in those compounds investigated that have a weak coupling-or low ordering t e m p e r a t u r e - , i.e., GdRh, GdRh2,
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 83
- I , -
o t- O
_J
lID
°..~ N
E °
t,..
o r- 1
0 40
G d t - x L a x R h 2
T = 4 . 2 K o o
x = 0 . 0 1
I
0 0
o 0 0
0 0
0 0
0 0
j °
0x = 0 . 0 5
o
0 0
0 0
O 0
00 0 0
o 0
%
I I
5 0 6 0 7O
V r e s
/MHz
Fig. 5. Zero-field 139La NMR spectra from Gdl_xLa~Rh 2 with a small non-magnetic dilution x at T=4.2K (adapted from Dor- mann et al. 1977a). The main line originates from La with four Gd nearest neighbours, the satellites from La with three Gd/one La or two Gd/two La nearest neigh- bours. The shoulder of the main line indicates the influence of sec- ond and third nearest neighbours (N 2 = N 3 = 12).
GdPt2, GdNi, GdNi 2 and G d I r 2 ( D o r m a n n 1977). In the compounds that have high ordering t e m p e r a t u r e s (GdAI2, G d Z n ) , the 5d-like conduction electrons are clearly essential. A corresponding analysis for the antiferromagnetic G d A g by G o e b e l and D o r m a n n (1979) proved that if the contribution of d-like conduction electrons predominates then this can also lead to antiferromagnetic coupling. In Eu interrnetallics ( E u 2+) Kropp et al. (1979b) found that coupling via non-s conduction electrons is important in many compounds even including those with low magnetic ordering temperatures.
In the above analysis, only the spin polarization of the conduction electrons was considered. This seems permissible: Berthier et al. (1978b) analysed the mechan- ism of magnetic coupling in RA12 and R Z n ( T c and H N for the whole lanthanide series). T h e y concluded that, although strong orbital polarization of the conduc- tion band is present in the vicinity of the 4f electrons, it does not propagate between them.
3.2.4. Distance dependence of the transferred hyperfine interaction
N M R investigation of non-magnetically diluted, ferromagnetically o r d e r e d intermetallic compounds like Gda_xLaxZn allows one to analyse the distance d e p e n d e n c e of the transferred hyperfine interaction at the sites of the lanthanide and the non-magnetic partner. Usually, a statistical occupation of the different
84 E. DORMANN
neighbour shells is assumed. In this case, for a La concentration x and a neighbour shell i with N i sites (e.g., N 1 = 8 for the Zn site in GdZn, of CsCl-type structure), the probability for the occurrence of ni La ions in the ith shell is
Ni! xni(1 - x) u~-nl . (14)
W ( n i , Ni, x) - ni!(N, " _ n~)[
With these probabilities and a RKKY-like distance dependence (adjusting k'v and a(0)), the 27 AI NMR line profiles m Gdl_xLaxA12 or Gdl_xY~AI 2 could be • • explained qualitatively (Dormann et al. 1973). Such experiments can be in keeping with an RKKY-like oscillatory distance dependence; however, they cannot prove or disprove it in detail. In more favourable situations the contribu- tion of distinct magnetic neighbours to the transferred hyperfine field can be derived by zero-field NMR of pseudobinary compounds with powder samples.
The contribution of one nearest magnetic Ln (Ln = lanthanide) neighbour to the hyperfine field at the eighffold-coordinates Zn in the CsCl-type structure was easily derived by
67Zn
zero-field NMR measurements in Gdl_xRxZn (R = Sc, Y, La, Ln) by Eckrich et al. (1972, 1976) because the eight nearest-neighbour Gd ions contribute 82.5% of the total Zn hyperfine field. Despite the occurrence of a large broadening of the zero-field 139La NMR lines, the appearance of satellites to the main 139La resonance line could also be observed in Gdl_~La~Ir 2 by Dormann et al. (1976) and in Gdl_~LaxRh 2 by Dormann et al. (1977a), see fig. 5 for an example. This means that the predominant neighbour contribution could be read directly from the NMR spectrum.The predominating contributions of the nearest neighbours (nn) to H N were observed in many intermetallic compounds: the six nn Gd atoms contribute to the hyperfine field at the non-magnetic sites (78-+ 5)% in GdP (Myers and Narath 1973a) or up to 100% in GdIr2, 92% in GdPt 2 and 85% in GdAl2, whereas the four nn Gd atoms already contribute to HN for the magnetic site 60% in GdRh2, 56% in GdIr 2 and 80% in GdPt 2 (Dormann 1977).
The decision, as to which lanthanide neighbours are responsible for the dominant hyperfine field contributions observed, is not always unequivocal-at least if it is based on the concentration dependence of the line intensities in the zero-field spectra of powder samples, relying on statistical site occupation, and suffering from the errors in the determination of the relative intensities. A clear-cut assignment can be obtained through an analysis of the angular depen- dence of the NMR spectrum in an external magnetic field, performed with a single crystal. For example, from such investigations on paramagnetic Lal_ x Gd~Ag with a small Gd concentration (x = 0.005), it could be determined that the third-nearest Gd neighbour gives the largest contribution to the 139La hyperfine field (Goebel and Dormann 1979). This neighbour was identified via the dipole part of the anisotropy of the hyperfine interaction- see fig. 6. (It is the neighbour along the [111] diagonal of the CsCI unit cell, along a L a - A g - G d 'bond' direction.)
In general it is difficult to derive more than three distinct neighbour contribu- tions by NMR line shape analysis in magnetically ordered compounds, without
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).