70 Journal of Magnetism and Magnetic Materials 63 & 64 (1987) 70-72 North-Holland, Amsterdam MAGNONS IN CeAl2 R OSBORN**, M LOEWENHAUPT #, B D RAINFORD* and W G STIRLING ~ *Department o[ Phystcs, The Umversity, Southampton S09 5NH, UK # Insatut fur Festkorperforschung, KFA-Juhch, D-5170 Juhch, Fed Rep Germany ~ Insatut Laue-Langewn, 156X, 38042 Grenoble, France The low energy magnetic excitation spectrum in the ordered phase of CeAl2 has been measured by inelastic neutron scattering The results are discussed in the hght of recent theories of magnetic excitatmns in slnusoidally modulated systems, and it is shown how they lead to a new explanation for the large value of the linear specific heat coefficient Below 3 8 K, CeA12 is a sinusoldally modu- lated antlferromagnet, the magnetic moments are constrained to he along (111) directions while their magmtudes are modulated in the perpendtcular (110) direction with a periodicity Incommensurable with the lattice [1] It is, therefore, an example of a transverse spin den- slty wave There is a sertous problem in treatmg theoretically the dynamics of such systems because the wavevector, q, IS no longer a good quantum number [2] Modes with a particular q are coupled to those of wavevector q± O,, where Q, IS the wavevector of the incommen- surable modulation, so that linear spin wave theory leads to an infinite set of coupled equa- ttons The magnetic excitation spectrum does not consist of a set of discrete modes but of a broadened intensity dlstrtbutlon, not easily related to the exchange and anlsotropy parameters stablhzmg the structure There have been a number of recent attempts at calculating the transverse dynamtc susceptlblhty of spin density waves, by truncating the set of infinite continued fraction [3], by using a Green's func- tion expanston [4] and by numerically diagonal- izing an equivalent one-dlmenstonal quast- periodic Hamfltonlan [5] The first two methods predtct magnon bands with dispersion stmilar to that calculated for a commensurable system but broadened by the spattal fluctuattons of the + Present address Neutron Division, Rutherford Appleton Laboratory, Chilton, Dtdcot, Oxon OX 11 0QX 0304-8853/87/$03 50 © Elsevier Sctence Pubhshers (North-Holland Physics Publishing Divtslon) moments The last study, however, predicted qualitatively new features such as a broad quaslelasUc line, energy gaps and a sharp dts- perslonless band at htgher energy None of these authors have treated the problem of phase modes whtch, in the models chosen, are a fea- ture of the longitudinal suscepttblhty So far the calculattons have been restricted to simplified models and no detailed comparison with experiment has been possible The observation of magnon bands in neutron time-of-flight spectra of CeAI2 [6] has prompted the current mvestlgatlon of the magnetic excita- tion spectrum in a large single crystal Thts was mounted wtth the (112) axts vertical The measurements were performed on the cold- source triple-axis spectrometer, IN12, at the In- stitut Laue-LangevIn, which gave energy resolutton of 0 12 meV at an incident wavelength of 4 05/k The sample was main- tained at 1 3 K during a series of "constant- O" scans performed along various symmetry direc- tions Elastic magnetic satellite peaks were seen at (1 392, -0 392,0 5) and (1 608,-0 608,0 5) corresponding to q= ~'± Q,, where ~" is a nuclear reciprocal lattice vector and Q,= (1/2+8, 1/2-6, 1/2) 6=0108, confirming that the modulatton pertod is approximately nine unit cells The spectra conststed of broadened bands, with strongly q dependent intensities At every q examined, the data could be charac- terized by two overlapping Gaussian peaks sug- gesting that the spectra are divided into two BV