  Order-by-disorder, whereby fluctuations lift an accidental classical ground
state degeneracy to stabilize a subset of ordered states, is a recurrent and
prominent theme in the field of frustrated magnetism where magnetic moments, or
spins, are subject to competing interactions. Thus far, such a phenomenon has
been discussed in systems where the quantum ground state is not a product
state. In this circumstance, both thermal and quantum fluctuations act to lift
the accidental classical degeneracy, begging the question whether one mechanism
of order-by-disorder is possible without the other. In this paper, we present
results exposing a novel route to order-by-disorder, without quantum zero-point
fluctuations, in a family of ferromagnetic Heisenberg materials with the
Dzyaloshinskii-Moriya (DM) interaction as the leading perturbation. We prove
that any colinear ferromagnetic state is an exact eigenstate, even in the
presence of the anisotropic DM interaction, while thermal fluctuations give
rise to a preference in the magnetization direction. Here, we present in detail
an example of the pyrochlore Heisenberg ferromagnet with DM interactions. Using
both linear spin-wave theory and classical Monte Carlo simulations, we find
that the magnetization can spontaneously rotate at intermediate temperature(s)
within the colinear ferromagnetic phase when the DM interaction is large.
Additionally, we find that in the large DM regime, the ferromagnetic ground
state becomes unstable within the framework of non-linear spin-wave theory. Our
results show that thermal order-by-disorder is possible even in the absence of
quantum zero-point fluctuations.
