  The coercive field and angular dependence of the coercive field of
single-grain Nd$_{2}$Fe$_{14}$B permanent magnets are computed using finite
element micromagnetics. It is shown that the thickness of surface defects plays
a critical role in determining the reversal process. For small defect
thicknesses reversal is heavily driven by nucleation, whereas with increasing
defect thickness domain wall de-pinning becomes more important. This change
results in an observable shift between two well-known behavioral models.
  A similar trend is observed in experimental measurements of bulk samples,
where a Nd-Cu infiltration process has been used to enhance coercivity by
modifying the grain boundaries. When account is taken of the imperfect grain
alignment of real magnets, the single-grain computed results appears to closely
match experimental behaviour.
