Phase transition between quantum and classical regimes for the escape rate of dimeric molecular nanomagnets in a staggered magnetic field

We study the phase transition of the escape rate of exchange-coupled dimer of single-molecule magnets which are coupled either ferromagnetic ally or antiferromagnetically in a staggered magnetic field and an easy z-axis anisotropy. The Hamiltonian for this system has been used to study molecular dimer nanomagnets \[Mn₄\]₂. We generalize the method of mapping a single-molecule magnetic spin problem onto a quantum-mechanical particle to dimeric molecular nanomagnets. The problem is mapped to a single particle quantum-mechanical Hamiltonian in terms of the relative coordinate and a coordinate dependent reduced mass. It is shown that the presence of the external staggered magnetic field creates a phase boundary separating the first- from the second-order transition. With the set of parameters used by R. Tiron, textit{et al}, \prl {\bf 91}, 227203 (2003), and S. Hill, textit{et al} science {\bf 302}, 1015 (2003) to fit experimental data for \[Mn₄\]₂ dimer we find that the critical temperature at the phase boundary is T^(c)₀ =0.29K. Therefore, thermally activated transitions should occur for temperatures greater than T^(c)₀.