Relaxation and Renormalization of Spin Waves in EuO. Page: 4 of 14
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Horizontal and vertical divergences of the collimators between
reactor and detector were 0.33*-0.35*-0.68*-0.66* and 0.9*-1.9*-1.4*-1.4*
respectively. The energy resolution was approximately 0.10 meV.
3. EXPERIMENTAL RESULTS
Figure 1 st ows the spin-wave line shapes observed at IqI - 0.201
in the temperature rahge 0.15 < (T -T)/T < 0.005. Both renormalization of
the spin-wave energies and line broadening are evident.
In Figure 2 we have shown how spin-wave line shapes observed at
a fixed temperature (T.-T)/Tc = 0.05 vary with (q . Dispersion effects
are apparent and there is also significant q-dependent line broadening.
Figures 1 and 2 represent only part of the data collected but the behavior
is illustrative of all of our results. It should be noted that the sta-
tistical uncertainty of the individual data points is not the square root
of the plotted intensity. The data have been normalized to a common count-
ing time shorter than that actually used.
Casual inspection of the observed line shapes is sufficient to
establish that there are limits on the.extent to which- the characteristics
of the actual excitations can be determined from-the data. The spin-wave
peaks merge and broaden as T approaches Tc and the spin-wave energies ob-
viously become less and less well defined. Further, although the line
widths of the spin waves decrease more rapidly than their energies, we can-
not resolve peaks much narrower than our instrumental energy resolution
which is 0.10 meV. Thus our line width measurements were limited for in-
strumental reasons to values of q * 0.1211 and to temperatures greater
than - 60*K.
The line shapes of Figures 1 and 2 show no evidence of a three-
peaked structure such as was observed in both the isotropic Heisenberg
antiferromagnet RbMnF3  and in the anisotropic Heisenberg ferromagnet
MnP . As was the case in iron [101 and nickel , while transverse
propagating modes are clearly visible, nothing identifiable as a longitu-
dinal mode appears even near Tc'
Although our energy resolution was about the same as that used
for the iron and nickel measurements, our observations were limited.to some-
what larger values of the wave vector q. This is simply because in both
iron and nickel the energy of a spin wave with a givpn value of q is con-
siderably larger than that of an equivalent mode in Au0. Thus energy reso-
lution, not q resolution, represented the limiting factor in our measure-
4. ANALYSIS OF THE DATA
4.1. Form of the Cross Section
The inelastic magnetic scattering cross section is customarily
expressed in terms of the scattering function S(f,w) representing the
Fourier transform of the spin pair correlation function. S(q,w) is defined
as the product of three terms; a Boltzmann population factor, the static
response function X(q) describing the magnetic moment response to a hypo-
thetical static applied field varying sinusoidally in space with wave vec-
tor 4, and the dynamic spectral shape function F(q,;) whose Fourier
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Passell, L.; Als-Nielsen, J. & Dietrich, O.W. Relaxation and Renormalization of Spin Waves in EuO., report, October 31, 1972; Upton, New York. (digital.library.unt.edu/ark:/67531/metadc1028165/m1/4/: accessed January 24, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.