  We investigate the effects of magnetic inhomogeneities and thermal
fluctuations on the magnetic properties of a rare earth intermetallic compound,
Nd$_2$Fe$_{14}$B. The constrained Monte Carlo method is applied to a
Nd$_2$Fe$_{14}$B bulk system to realize the experimentally observed spin
reorientation and magnetic anisotropy constants $K^{\rm A}_m (m=1, 2, 4)$ at
finite temperatures. % Subsequently, it is found that the temperature
dependence of $K^{\rm A}_1$ deviates from the Callen--Callen law, $K^{\rm
A}_1(T) \propto M(T)^3$, even above room temperature, $T_{\rm R}\sim 300\rm\,
K$, when the Fe (Nd) anisotropy terms are removed to leave only the Nd (Fe)
anisotropy terms. This is because the exchange couplings between Nd moments and
Fe spins are much smaller than those between Fe spins. % It is also found that
the exponent $n$ in the external magnetic field $H_{\rm ext}$ response of
barrier height $\mathcal{F}_{\rm B}=\mathcal{F}_{\rm B}^0(1-H_{\rm ext}/H_0)^n$
is less than $2$ in the low-temperature region below $T_{\rm R}$, whereas $n$
approaches $2$ when $T>T_{\rm R}$, indicating the presence of
Stoner--Wohlfarth-type magnetization rotation. This reflects the fact that the
magnetic anisotropy is mainly governed by the $K^{\rm A}_1$ term in the
$T>T_{\rm R}$ region.
