  We have investigated the escape rate of the nanospin particle with a magnetic
field applied along the easy axis. The model studied here is described by the
Hamiltonian $\hat{\cal H} = K_1 \hat{S}_z^2 + K_2 \hat{S}_y^2 + g\mu_b H
\hat{S}_x $, $(K_1 > K_2 > 0)$ from which the escape rate is calculated within
the semiclassical approximation. We have obtained a diagram for the orders of
the phase transitions depending on the anisotropy constant and the external
field. For $ K_2 / K_1 > 0.85$ the present model reveals, for the first time,
the existence of the first-order transition within the quantum regime.
