  The feasibility of creating a Bose-Einstein condensate of magnons using a
dense ensemble of nitrogen-vacancy spin defects in diamond is investigated.
Through assessing a density-dependent spin exchange interaction strength and
the magnetic phase transition temperature ($T_c$) using the
Sherrington-Kirkpatrick model, the minimum temperature-dependent concentration
for magnetic self-ordering is estimated. For a randomly dispersed spin
ensemble, the calculated average exchange constant exceeds the average dipole
interaction strengths for concentrations approximately greater than 70 ppm,
while $T_c$ is estimated to exceed 10 mK beyond 90 ppm, reaching 300 K at a
concentration of approximately 450 ppm. On this basis, the existence of
dipole-exchange spin waves and their plane-wave dispersion is postulated and
estimated using a semiclassical magnetostatic description. This is discussed
along with a $T_c$-based estimate of the four-magnon scattering rate, which
indicates magnons and their condensation may be detectable in thin films for
concentrations greater than 90 ppm.
