  Quantum Fisher information is a key concept in the field of quantum
metrology, which aims to enhance the parameter accuracy by using quantum
resources. In this paper, utilizing a representation of quantum Fisher
information for a general unitary parametrization process, we study unitary
parametrization processes governed by su(2) dynamics. We obtain the analytical
expression for the Hermitian operator of the parametrization and the maximal
quantum Fisher information. We find that the maximal quantum Fisher information
over the parameter space consists of two parts, one is quadratic in the time
and the other oscillates with the time. We apply our result to the estimation
of a magnetic field and obtained the maximal quantum Fisher information. We
further discuss a driving field with a time-dependent Hamiltonian and find the
maximal quantum Fisher information of the driving frequency attains optimum
when it is in resonance with the atomic frequency.
