  Magnetic excitations in a Ni$_4$ magnetic molecule were investigated by
inelastic neutron scattering and bulk susceptibility ($\chi_\text{bulk}$)
techniques. The magnetic excitation spectrum obtained from the inelastic
neutron scattering experiments exhibits three modes at energy transfers of
$\hbar\omega=0.5$, 1.35, and 1.6 meV. We show that the energy, momentum, and
temperature dependences of the inelastic neutron scattering data and
$\chi_\text{bulk}$ can be well reproduced by an effective spin Hamiltonian
consisted of intra-molecule exchange interactions, a single-ionic anisotropy,
biquadratic interactions, and Zeeman term. Under a hydrostatic pressure, the
bulk magnetization decreases with increasing pressure, which along with the
biquadratic term indicates spin-lattice coupling present in this system.
