Abstract
We investigate the heterotrinuclear trigonal spin cluster (each particle with S = 1/2) driven by a time-dependent magnetic field. Using an algebraic dynamics method, we solve the time-dependent Schrodinger equation of the spin-cluster system and give an alternative expression for the nonadiabatic geometric phase or the Berry phase when the magnetic field rotates around the Z axis. Based on the exact analytical solutions, we show how the Berry phase depends on the external magnetic field parameters ω (the angular velocity of the rotating magnetic field) and θ (the angle between the magnetic field and the Z axis), and we discuss the changing diagram of the Berry phase of the system in the ground state.
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