Spin-Waves in Ferromagnetic Dysprosium Metal Page: 4 of 11
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The agreement between the calculation and the neutron data would be diffi-
cult to improve, but it is likely fortuitous since other choices for the con-
stants involved are possible. In addition according to Brooks [12] there is
theoretical evidence that the temperature dependences assumed here may not be
correct. Assuming that K2 is well determined by existing macroscopic data,
about all we can conclude at present from these neutron measurements is that
the dominant contribution (whatever its source) to the square brackets in
Eq. (1) varies between 40 and 80 K approximately as on with n - 20. Thus,
for example, if K6 dominates as we have assumed, the a36 variation of this
constant deduced by Brooks [12] would not be satisfactory.
The data obtained for the [001] and the [110] directions are shown in
Fig. 2 for 4.7 K and in Fig. 3 for 77*K. At 4.7 K evidence is seen for mag-
non-phonon interactions for both of the crystallographic directions studied.
In the [001] direction the results are qualitatively similar to those re-
ported for Tb [13], except that for Tb the optical magnor, branch lies above
the optical phonon branch. In the [110] direction the magnon acoustic
branch (MA in Fig. 1) appears to interact with both the longitudinal and
transverse acoustic phonon branches. Such interactions were not possible in
Tb where the acoustic magnon branch lies entirely above the acoustic phonon
branch in this symmetry direction. There is no evidence in these data of an
interaction between the magnon optic branch (MO) and the acoustic phonon
branches or between the magnon acoustic and the phonon optic branches.
Calculations based on Jensen's [14] theory for magnon-phonon interactions
in the rare-earth metals indicate that an energy splitting of approximately
1.0 meV could be expected at the nominal crossing point of the acoustic mag-
non and the transverse acoustic phonon branches in the 1110] direction. This
is in good agreement with the splitting of approximately 0.8 meV observed at
both 4.7* and 77*K. In making this comparison we have assumed, as indicated
in Figs. 2 and 3, that the interaction is between the magnon and the TALI
phonon. The theoretical prediction for the splitting associated with the
magnon interaction with the [110]-longitudinal mode at 4.7*K is about 0.4 meV
again in reasonable agreement with the experimental results. The theory
also predicts a linear dependence of the splitting on the q corresponding to
the point of crossing. Thus the absence of an observable magnon-phonon
interaction associated with either the [110]-longitudinal and the 1001]-
transverse modes at 77 K is probably due to the fact that the corresponding
crossing points have changed with increasing temperature so as to occur at a
q that is too small to result in a splitting which could be resolved in
these experiments.
The absence of a degeneracy between the acoustic and optic spin-wave
branches at the K-symmetry point in the [110] direction at 4.7"K indicates
the existence of a significant anisotropic magnetic interaction in Dy in
addition to those mentioned above. Similar results found in Tb have been
explained by introducing a dipolar interaction into the spin-wave theory [15].
We have not yet carried out similar calculations for Dy. Also in the
vicinity of K at 4.70K, neutron scattering by both acoustic and optic modes
was observed at locations in reciprocal space where the neutron scattering
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Nicklow, R. M. & Wakabayashi, N. Spin-Waves in Ferromagnetic Dysprosium Metal, report, January 1, 1972; Oak Ridge, Tennessee. (https://digital.library.unt.edu/ark:/67531/metadc1031012/m1/4/: accessed May 6, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.