  The all-temperature magnon (ATM) theory [J. Phys. Condens. Matter 21,
336003/1-14, 2009] has been used to analyze the temperature dependence of
magnetization as well as the internal energy components of a mono-domain
ferromagnetic solid. The critical exponents have been in better agreement with
experiment than their mean-field theory and critical phenomenon theory
counterparts, and unlike in the latter theories, vary from one ferromagnet to
another. Expressions have been derived for the thermally averaged spin-center
force constants and their break-up in terms of the base-line related (solid)
and exchange-cum-field mediated (magnetic) components. These components give
rise to expressions for phonon frequencies and their modifications by
magnon-phonon coupling. The derived expressions are suitable for a correct
quantum chemical evaluation of the involved properties. A detailed numerical
calculation using spin configurations at varying crystal geometries is hardly
possible even today and beyond the scope of the present work. The focus here is
on the correctness and explaining the trends of properties. It has been shown
that the frequency modification by magnon-phonon interaction can be negative
for certain phonon branches near the ferromagnetic transition temperature.
Also, the ratio of frequency modification and phonon frequency is approximately
proportional to the ratio of curvatures of the involved energy surfaces.
