linear spin-wave dispersion (D fa 250meV-A) for wavevectors up to w 1/2 of the Brillouin zone and a strong .... don, Oxford, 1984) chap. 9. [2] M. J. Gillan, J. ... [5] T. M. Holden, K. Mikke, E. Fawcett, and J. A. Fernandez-Baca, Proceedings of the.
C0NF-921201--5 DE93 001634
HIGH-ENERGY MAGNETIC EXCITATIONS IN Mn90Cu10
J. A. Feinandez-Baca Solid State Division, Oak Ridge National Laboratory, Oak Ridge, TN 378S.- H393
M. E. Hagen Department of Physics, Keek University, Staffs. ST5 5BG, United Kingdom, and ISIS Science Division, Rutherford Appleton Laboratory, Didcot, Oxon. 0X11 OQX, United Kingdom
R. M. Nicklow Solid State Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6393
T. G. Perring ISIS Science Division, Rutherford Appleton Laboratory, Didcot, Oxon. 0X11 OQX, United Kingdom
and
MASTER Faculty of Science, University of Osaka. Osaka, Japan DISCLAIMED
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Abstract The study of the magnetic excitations in Mn-rich alloys should be a good test of the multiband calculations of the spin dynamics of pure 7-Mn, which is a prototypical itinerantelectron antiferromagnet. In this paper we report the results of recent neutron inelastic scattering measurements performed on MngoCuio at room temperature (T = 0.63 T/v) and up to 300 meV of energy transfer. These measurements were performed using the HET chopper-spectrometer at the ISIS spallation neutron source, Rutherford Appleton Laboratory, U.K. The results have been compared with calculations using a model scattering function convoluted with the full HET resolution function. In this model there is a steep linear spin-wave dispersion (D fa 250meV-A) for wavevectors up to w 1/2 of the Brillouin zone and a strong damping which is linear in the wavevector q . For larger wavevectors the spin-wave energies are constant at about 190 meV. These features are qualitatively similar to the predictions of Cade and Yeung for pure 7-Mn.
PACS 75.50.Ee, 75.30.Ds, 75.10.Lp
1
Introduction
The study of the magnetic excitations in Mn-rich alloys is of interest because these alloys provide the best examples of 7-phase itinerant-electron antiferromagnets (pure 7-Mn would be the best but it is metallurgically stable only at temperatures around 1100°C ). The best technique to perform such a study is neutron inelastic scattering, which provides a direct measurement of the imaginary part of the generalized susceptibility x{
q*
and up to the Brillouin zone boundary the spin-wave energy and damping are assumed to remain constant at the values E{q*) and F(, between the (0 10) reciprocal lattice direction and the direction of the incident beam is 22.6°. In this figure the full circles are the reciprocal lattice points, and the radial lines are the loci of the wavevector transfers measured by each of the detectors in the 4m bank. Each point along the length of these loci corresponds to a different energy transfer and in this figure the circular contour levels are lines of constant energy transfer, in 10 meV steps from 0 to 250 meV. The double lines indicate the 0,50,100,150 and 200 meV energy transfer levels. For the high energy transfers we have examined in 6
these measurements the scattering is very weak, and it is necessary to add together the spectra from the different detectors in the 4m bank in order to obtain a significant signal. This corresponds in figure 1 to integrating along the direction of the circular contours of constant energy transfer. In the configuration shown in figure 1 the measuring locus passes over the (110) zone center at an energy transfer of ss 120 meV. Altogether we have measured 5 configurations in this scattering plane which had E{ and values of (86.4 meV, 35.3°), (156.6 meV, 29.7°), (262.2 meV, 23.1°), (442.6 meV, 22.6°) and (813.4 meV, 11.9°) and which corresponded to energy transfers of 50, 70, 90, 120 and 150 meV at the (110) zone center. In each case we expected to observe scattering which originated from the spin waves around the (110) position. However as can be seen from figure 1 the loci also pass close to the (010) zone center, which in figure 1 occurs at an energy transfer of 30 meV. The (010) lattice point is not a zone center and the observation of spin-wave excitations from this point would not be expected if the sample consisted of a single magnetic domain. As explained above, however, the three domain structure of the sample means that the (010) lattice point coincides with the (001) lattice point from another domain. The (0 0 1) point is a zone center and therefore we expect to observe spin-wave excitations from this center at energies in the vicinity of 30 meV. Figures 2a to d show the data measured with £, = 156.6, 262.2, 442.6 and 813.7 meV respectively. The upper two data sets are plotted with respect to the axis at the top of the figure and the bottom two with respect to the axis at the bottom. In each case a
background has been subtracted from the original data. This background was obtained using a detector bank that was also located at 4m from the sample but out of the scattering plane. This out-of-plane detector bank covered the same solid angle and scattering angles as the in-plane 4m bank but their measuring loci in reciprocal space did not pass close to any magnetic zone centers.
3
Analysis and Discussion
In order to analyze the data collected we have compared the measured spectra with the lineshapes calculated for two different spin wave dispersion relations. The lineshapes have been calculated by assuming that the dynamic structure has the DHO form given in equation( 1), convoluting this structure factor with the resolution function for the HET spectrometer [7], and integrating along the constant energy transfer contour levels. We have included DHO structure factors for the scattering from both the (110) and (010) domains, with the relevant 1 + (Q-S)2 orientation factors and assumed equal population factors for the two domains. The magnetic form factor and the thermal population factor have also been included. Initially we tried holding the parameters in equations( 1), ( 2) and ( 3) fixed at the values found previously [4] for all wavevectors q within the magnetic Brillouin zones. However we were unable to obtain satisfactory representations of the data in this way. Therefore we used a model which is a highly simplified version of the theoretical results of Cade and Yeung [3]. In their multiband calculations Cade and Yeung predict the existence of five spin-wave modes, the energy of the lowest of these increases
roughly linearly with wavevector out to about as 1/3 of the Brillouin zone where it turns over and carries on with a relatively flat dispersion relation out to the zone boundary. In our model we have assumed that for wavevectors q < q" we can use equations( 1), ( 2) and ( 3) with the values obtained previously [4]. However for wavevectors from q* up to the Brillouin zone boundary the spin wave energy E(q), damping V(q) and the Lorentzian pre-factor are kept fixed at the values they had at q*. The best description of the data is then obtained with q* « 0.8A
, ie. E(q*) « 190meV as shown in figures 2a to d by the
solid lines. The implication of this is that the spin wave dispersion relation in Mn
