  We have presented dynamic phase transition features and stationary-state
behavior of a ferrimagnetic small nanoparticle system with a core-shell
structure. By means of detailed Monte Carlo simulations, a complete picture of
the phase diagrams and magnetization profiles have been presented and the
conditions for the occurrence of a compensation point $T_{comp}$ in the system
have been investigated. According to N\'{e}el nomenclature, the magnetization
curves of the particle have been found to obey P-type, N-type and Q-type
classification schemes under certain conditions. Much effort has been devoted
to investigation of hysteretic response of the particle and we observed the
existence of triple hysteresis loop behavior which originates from the
existence of a weak ferromagnetic core coupling $J_{c}/J_{sh}$, as well as a
strong antiferromagnetic interface exchange interaction $J_{int}/J_{sh}$. Most
of the calculations have been performed for a particle in the presence of
oscillating fields of very high frequencies and high amplitudes in comparison
with exchange interactions which resembles a magnetic system under the
influence of ultrafast switching fields. Particular attention has also been
paid on the influence of the particle size on the thermal and magnetic
properties, as well as magnetic features such as coercivity, remanence and
compensation temperature of the particle. We have found that in the presence of
ultrafast switching fields, the particle may exhibit a dynamic phase transition
from paramagnetic to a dynamically ordered phase with increasing ferromagnetic
shell thickness.
