Frustration of magnetic order in GdAl3 (and in CeAl3?)

. Electron spin resonance measurements of 4f7 Gd moments confirm the suggestions of susceptibility measurements that the onset of antiferromagnetism in GdAI, is strongly frustrated. This raises the possibility that the isostructural heavy fermion compound CeAI, fails to order magnetically, unlike CeAI2, because frustration has depressed the temperature of long-range ordering.

It is well known that in certain types of crystal lattices the existence of nearest-neighbour antiferromagnetic interactions between magnetic moments on lattice sites can frustrate the onset of long-range antiferromagnetic order. The most obvious examples are twodimensional triangular lattices or face-centred cubic lattices where nearest neighbours of one moment are nearest neighbours of one another and receive competing instructions on the direction in which they should point. In MnO, for example, an average strength of the exchange interaction is indicated to be about 500 K from a value of that order for 101 in a high-temperature fit of the susceptibility to the Curie-Weiss expression C/(T-0). Since the final onset of antiferromagnetic order, in a structure governed by the relative strengths of second-neighbour and first-neighbour interactions, is at 100 K, long-range order is said to be frustrated in the temperature range -100-500 K, and only short-range order is seen in neutron scattering experiments at room temperature.
The intermetallic compound GdA13 with the Ni3Sn structure (DOl9) has a Nee1 temperature that is surprisingly low (17 K) compared with the value of 101 (-90 K) obtained from fitting the Curie-Weiss law ( x = C / ( T -0 ) to its susceptibility above 20 K (Buschow and Fast 1966). It is also low compared with the strength of interactions in its neighbouring ferromagnetic Laves phase GdA12 (T, z 6 z 170 K).
Such large ratios of l6l/TN have been noted Coles 1975, Fisk et a1 1971) in a number of other Gd intermetallic compounds, and have been shown to correlate with deviations from the a + b T form of temperature dependence for the linewidth of the electron spin resonance of the well known S-state Gd 4f7 resonance. In all such compounds the linewidth passes through a minimum at a temperature somewhat above 101, broadening rapidly as T is reduced towards TN. This pattern of behaviour was ascribed to the frustration that can arise, as pointed out above, for antiferromagnetic interactions in some geometries. Figure 1 shows the linewidth data for GdA13 at X band ( eutectic and therefore does not prevent the growth of the XA13 phase here, as unfortunately the high peritectic temperature of Ce3Al11 prevents the growth of CeA13 by this technique.) At 300 K the g value of GdAl3 was 2.00 k 0.01, remaining unchanged down to about 50 K, below which temperature it seems to increase, reaching 2.03 i 0.03 at 30 K. However, the rapid increase in linewidth below 50 K, which has already begun below 100 K and which is firm evidence for frustration, makes the g value increasingly uncertain at lower temperatures. The ESR results are thus in strong agreement with the suggestion that GdAl3 possesses competing interactions which suppress long-range order from an expected onset temperature of -100 K to the observed Nee1 temperature of 17 K. The apparent enhancement of p ,~ to 8.3 p B may also be a consequence of short-range order effects below 100 K.
In the DOl9 structure the Gd atoms, which form a hexagonal lattice, lie in close-packed planes in which they are separated from one another by A1 atoms. The stacking of the planes is such that each atom has six Gd neighbours out of its plane at -4.4 A and six other Gd neighbours within the plane at -6.3 A. For ferromagnetic interactions with the latter group the onset of order is clearly not frustrated, being simple ferromagnetic for ferromagnetic interactions with the former group and planar antiferromagnetic for antiferromagnetic interactions with them. If the 6.3 8, interaction is antiferromagnetic, however, the result must be frustration whatever the sign of the 4.4 A interaction, and experiment indicates that this situation holds. It can be noted, without too much significance being attached to it, that for a free-electron Fermi surface with kp = 1.75 x lo8 cm-' both these separations correspond to negative values of the R K K Y coupling, lying between the fifth and sixth and between the seventh and eighth zeros respectively, and give inevitable frustration of the in-plane interactions.
Current interest in the heavy fermion problem (Fisk et a1 1986) makes these results of slightly more than passing interest, since CeA13, isostructural with GdA13. is one of the heavy fermion compounds that (unlike CeA12 in spite of its very similar value of pen) fails to give a magnetically ordered ground state, but also fails (unlike CeCulSi2) to become superconducting. Thus, if the ratio Tc(GdA12)/T~(GdAl,) is any guide, the long-range order that is found below 3.8 K in CeAI2 could not be expected above about 0.35 K in CeA13, by which temperature the Kondo compensation of the Ce moments is likely to have made a non-magnetic Kondo lattice more stable. The delicate question of how 'nonmagnetic' this lattice has to be for a superconductive state to be stable is still not clear. It must also be borne in mind that the ordering of CeA12 is of an incommensurate character, and its Nee1 temperature may not be a good guide to what one would expect of CeA13 in the absence of frustration, especially if the Fermi surface geometry that leads to its characteristic ordering has been reconstructed (relative to that of GdAl2) by its own fconduction band hybridisation.