Relaxation and Renormalization of Spin Waves in EuO. Page: 3 of 14
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essentially isotropic almost to the Brillouin zone boundary. This unus-
ual isotropy, which also is a property of iron [10 and nickel , is, in
EuO, Ed to a combination of factors. First, the S7/2 ground state of
the Eu ion has a spherically symmetric spin distribution. Further, Eu0
is unique among the divalent chalcogenides in that both the nearest and
next nearest neighbor exchange constants are of the same sign. In addition
the europium ions form an fcc lattice with 12 nearest neighbors which is
spatially very isotropic. As a result of this combination of characteris-
tics the magnetic environment of an Eu+ ion in Eu0 is isotropic to a
A brief consideration of neutron scattering in powders will show
why the isotropy of spin-wave dispersion in Eu0 is essential for line width
measurements. When neutrons of wave vector ti are scattered to wave vector
If, energy and momentum conservation require that
hW =. (h2/2m) (k -k )
Only the reciprocal lattice vector .at the origin, i- (000), is well de-
fined in a powder; all other t's are distributed uniformly over spheres
surrounding the origin. If, as in EuO, the scattering cross section de-
pends only on the modulus of 4, the small angle scattering from a powder
will be identical to that observed in a single crystal at the same , pro-
vided the observations are restricted to values of t1- ' well within the
first Brillouin zone. More commonly, however, the cross section depends
on the direction of as well as its magnitude. In this case, even well
within the first Brillouin zone the scattering from a powder will show a
finite energy width simply because of the random orientation of indivi-
dual crystallites. For example, in EuS this "powder broadening" is large.
enough to almost completely obscure the effects of relaxation processesl9].
Fortunately, in Eu0 "powder broadening" of the lines is small and broad-
ening due to relaxation processes can clearly resolved.
Aside from the limitations outlined above, which affect line
width measurements on powders, small angle scattering itself also intro-
duces certain experimental complications which should be.mentioned. First,
the range of energy transfers accessible with a given value of -I is much
more restricted. This is not a problem in EuO where the spin-wave energies
are small, but it can become important in materials in which the excitation
energies are larger. Second, at small scattering angles (in practice less
than about 2 ) background variation across the scans is sufficient to in-
troduce unwanted distortions in the observed line shapes. Thus the access-
ible i range in powders is limited on the one hand by the requirement that
ki-If be well within the first Brillouin zone and on the other by the re-
quirement that the .scattering angles be large enough to avoid background
distortion of the line shapes.
2.2. Experimental Methods
All of our measurements were made in the constant-q node with a
triple-axis spectrometer using pyrolytic graphite monochromating and ana-
lyzing crystals. The incident neutron energy employed was 4.8 meV. Pyro
lytic graphite and polycrystalline Be filters were used to insure against
higher order contawination of the beam.
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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/m1/3/: accessed January 20, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.