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The tunneling splitting in biaxial ferrimagnetic particles at excited stateswith an explicit calculation of the prefactor of exponent is obtained in termsof periodic instantons which are responsible for tunneling at excited statesand is shown as a function of magnetic field applied along an arbitrarydirection in the plane of hard and medium axes. Using complex timepath-integral we demonstrate the oscillation of tunnel splitting with respectto the magnitude and the direction of the magnetic field due to the quantumphase interference of two tunneling paths of opposite windings . Theoscillation is gradually smeared and in the end the tunnel splittingmonotonously increases with the magnitude of the magnetic field when thedirection of the magnetic field tends to the medium axis. The oscillationbehavior is similar to the recent experimental observation with Fe$_8$molecular clusters. A candidate of possible experiments to observe the effectof quantum phase interference in the ferrimagnetic particles is proposed.Comment: 15 pages, 5 figures, acceptted to be pubblished in Physical Review

Tunnel splitting and quantum phase interference in biaxial ferrimagnetic particles at excited states