Crossover of the magnetic levels and adiabatic magnetization of the mesoscopic cluster V₁₅

The magnetic three spin-1/2 model for nanometer-scale molecular cluster V₁₅ is analyzed with the emphasis on the origin of the mixing of different spin levels in the resonance fields that is generally important for the problem of single molecular magnets. The zero-field splitting in the ground quadruplet (two S=1/2 levels) is shown to depend mainly on the normal component of AS exchange meanwhile the zero-field splitting in the excited S=3/2 multiplet is a second order effect with respect to in-plane components of AS exchange. The normal component of the AS exchange is shown to lead to the exact crossing of the magnetic sublevels at the arbitrary direction of the field. The positions of two crossing/anticrossing points in the ground manifold depend mainly on the isotropic exchange and normal component of AS exchange meanwhile the gap in the avoided crossing point in parallel field is affected only by the in-plane component. We discuss the role of AS exchange in the field and temperature dependence of the adiabatic magnetization. We predict a specific field dependence of the magnetization vs. field caused by AS exchange.