GdAI2
2. Microscopic information about the macroscopic properties of magnetically ordered intermetallic compounds
NMR can be used to obtain information about different macroscopic properties of magnetic intermetallic compounds, such as the temperature dependence of the magnetic susceptibility of the main phase and of impurities (or impurity phases), ordering temperatures
(Op, Tc),
magnetic phase transitions with and without an external field, type of magnetic order, influence of deviations from stoichiometry and annealing treatments and others. As examples, we select here information arbitrarily about the temperature dependence of the spontaneous magnetization (sect. 2.1) and on the direction of easy magnetization ('easy direction') (sect. 2.2) of magnetically ordered compounds.74 E. DORMANN
2.1. Temperature dependence of the spontaneous magnetization
NMR presents a convenient local probe for the temperature dependence of the spontaneous magnetization. Evidently, the measurement of the temperature dependence of the zero-field resonance frequency is much easier than the careful analysis of the variation of the resonance frequency with orientation and strength of an external field and with temperature in a single crystal. It has, however, always to be kept in mind that the zero-field N M R analysis of a multidomain powder sample can only yield information about the phenomena in the Bloch wall if the zero-field signal originates from nuclei in the Bloch wall. This variation should not be compared with the temperature dependence of the magnetization in the domain. Only a careful N M R analysis is thus worthwhile for a discussion of the eventual differences in the variations of V~es(r)h%s(0K), h ( r ) = Hhf(T)/
Hh~(0 K) and re(T) = Ms(T )/Ms(O K), that could prove the temperature depen- dence of the hyperfine coupling constant (after correction for the volume vari- ation!). Narath (1967) has already given different examples proving that the temperature dependences of the zero-field resonance frequencies for domain and domain wall signals may be different (e.g., 53Cr in C r X 3 with X = Br, C1, I).
Generally it is easy to follow the temperature dependence of zero-field NMR spectra in the ferromagnetically ordered state up to about (0.5-0.7)T~. This was done, e.g., for
67Zn
and ~55'157Gd in GdZn (T c = 267 K), and 27A1 and I55'157Gd in GdA12 (T c = 172 K), by Herbst et al. (1974), and for 153Eu in EuPt 2 (To = 105 K) by Dressel et al. (1988). Short relaxation times T 1 and T 2 and the strong influence of temperature instabilities-via large O v~es/OT for T approaching T~- are obsta- cles to an extension of the temperature range, which can be, however, overcome.For example, Barash and Barak (1984) measured the NMR of 27A1, 155Gd and 157Gd in ferromagnetic GdA12 and of 27A1 in ferromagnetic DyA12 over a wide temperature range in zero external field. [The temperature dependence of the NMR frequencies for GdA12 agreed with Bloch's T 3/2 law up to 0.5Tc, while that for DyA12 was explained in terms of molecular fields (MF) and crystal electric fields (CEF).] They were able to follow the temperature dependence up to T = 0.94 To, using the temperature variation instead of the frequency variation to record the NMR lines.
If spin-wave excitations are dominant, the magnitude of the hyperfine field decreases as the temperature is raised like
Hhf(T)
h(T) - Hh,( 0 K~ - 1 - (;3/2 T 3 / 2 - Cs/2T 5/2 . (7a) Edwards (1976) showed that - at constant volume - the coefficient C3/2 in eq. (7a) is identical to that of the reduced magnetization
Ms(T) r t T3/2
C;/2 T5/2
(7b)m ( T ) - M~(OK) - 1 - ~ 3 / 2 - -
i.e., Ca/2 = C;/2 (if spin-wave excitations are dominant). The explicit temperature
NMR IN INTERMETALLIC COMPOUNDS 75 dependence of the normalized hyperfine coupling constant contains a T 5/2 term in the lowest order:
A ( T ) r ' " T 7/2 (7c)
A(O K~ - 1 - C~/2 T5/2 + ~7/e~ "
Thus the values of the coefficient C3/z for different sites in the same crystal should also be the same. Nagai et al. (1976) found different coefficients C3/2, ranging from (5-8.5) x 10 - 6 K -3/2 for different Co sites from a constant-pressure N M R analysis of G d 2 C o 1 7 [omitting, however, the C5/2 term in eq. (7a)]. Oppelt et al.
(1976) observed different temperature dependences of h(T) for the two non- equivalent Y sites (with 18 and 12 nearest Fe neighbours) in YFe3, as well. Riedi and Webber (1983) reinvestigated the normalized hyperfine fields at the two Y sites in YFe 3. No difference was observed up to T = 35 K, the limit of the r 3/2
law. Differences evident at temperatures above 100 K were shown to arise from higher-order spin-wave terms. Riedi and Webber (1983) also analysed the pres- sure dependence of Hhf up to p = 15 kbar, as is necessary for a more precise comparison of the temperature dependences in eqs. (7a) and (7b). The pressure dependence was in agreement with the picture that the yttrium hyperfine field results predominantly from polarization of s-like conduction electrons, with only a small d-band contribution.
2.2. Easy direction of the magnetization
The characteristic line profile caused by the contribution of the dipolar field //dip, which depends on the orientation of the magnetization, to the resonance field at a non-cubic lattice site can be used to dismantle the easy direction of magnetization. An early N M R example was the 27A1 line shape analysis in ferromagnetically ordered RAI~ (R = rare earth) by Kaplan et al. (1973).
This is an area of N M R applications where the probability of pitfalls is especially high: frequently, the experiments are performed with powder samples containing walls and magnetic domains. Then the zero-field N M R spectrum may reflect the direction of magnetization in the center of the Bloch wall, where only a small number of nuclei are situated, which encounter, however, the largest rf field and signal enhancement factor. In the way, an interesting piece of information for the understanding of the wall type may be obtained, but evidently it does not reveal the easy direction of the magnetization. Only if the necessary experimental tests (e.g., variation of the N M R spectrum with the strength of the rf field or the external field, determination of the enhancement factor, dependence on sample preparation) are performed, proving that the signal originates from wall edges or domains, can the easy direction be derived reliably. For a discussion of related problems also see Bowden et al. (1983).
With the help of NMR, spin reorientations-with temperature in HoCo 2 (Guimar~es et al. 1987) or with concentration x in pseudobinary compounds like Gdx_xDyxA1: (Ichinose et al. 1984a) or Tbl_xDy~Co 2 (Hirosawa and Nakamura 1982b) - were also analysed. We have compiled many other examples for this type
76 E. DORMANN
of application in tables B6 (27A1), B10 (55Mn) and B12 (59Co) in the appendix.
The anisotropy of the quadrupolar interaction and especially the interplay between the magnetic dipole and electric quadrupole interactions may be used for the derivation of the easy direction of the magnetization, as well. Both extremes -
electric quadrupolar interactions that are weak or strong compared with the magnetic hyperfine interaction- are useful. The [100] direction was derived, using NMR on Ir in GdIr 2 for the portion of the sample from which the N M R signal stems from, by Dormann and Buschow (1973) and Dormann et al. (1976)- this is an example, where the electric quadrupolar contribution is much larger than the magnetic dipolar one. There are many examples, where the 3cos20- 1 depen- dence of the quadrupolar splitting (McCausland and Mackenzie 1980) or of the quadrupolar echo modulation (Abe et al. 1966) could be used for the derivation of the direction of the magnetization in the case of a 'weak' quadrupolar interaction. We mention Gdl_xDyxA12 by Miles et al. (1977), DyA12 by Bowden et al. (1982) and GdA12 by Dumelow et al. (1988) as examples.
In some intermetallic compounds, such as RZn with the simple cubic CsC1 structure, no lattice sites with a low enough symmetry are available in order to use the techniques discussed above for the derivation of the easy direction.
Eckrich et al. (1976) showed that, nevertheless, N M R can be applied in this case:
a small concentration of non-magnetic a t o m s - s u c h as Sc, Y or L a - w a s intro- duced. The 67Zn NMR line profile for Zn atoms with seven Gd and one Sc, Y or La nearest neighbours in pseudobinary compounds of the general form Gdl_x(Sc/
Y/La)xZn was analysed. It indicated the orientation of the magnetization in this portion of the sample via the 3cos20 - 1 dependence of the dipolar field contribu- tion of the 'magnetic hole' to the resonance field. By the use of different non-magnetic ions and extrapolation to vanishing concentration (x--> 0) one can determine the easy direction, but one has to make sure, however, that the easy direction of the system under study is not influenced by the non-magnetic dilution.
3. NMR information about the electronic structure of intermetallic compounds