  The ferrimagnets, such as GdxFeCo(1-x), can produce ultrafast magnetic
switching and oscillation due to the strong exchange field. The two-sublattices
macrospin model has been widely used to explain the experimental results.
However, it fails in describing the spatial nonuniform magnetic dynamics which
gives rises to many important phenomenons such as the domain walls and
skyrmions. Here we develop the two-dimensional atomistic model and provide a
torque analysis method to study the ferrimagnetic oscillation. Under the
spin-transfer torque, the magnetization oscillates in the exchange mode or the
flipped exchange mode. When the Gd composition is increased, the exchange mode
firstly disappears, and then appears again as the magnetization compensation
point is reached. We show that these results can only be explained by analyzing
the spatial distribution of magnetization and effective fields. In particular,
when the sample is small, a spatial nonuniform oscillation is also observed in
the square film. Our work reveals the importance of spatial magnetic
distributions in understanding the ferrimagnetic dynamics. The method developed
in this paper provides an important tool to gain a deeper understanding of
ferrimagnets and antiferromagnets. The observed ultrafast dynamics can also
stimulate the development of THz oscillators.
