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We derive a simple system of equations to describe the magnetizationrelaxation of a molecular spin in weak interaction with a thermal bath for thewhole temperature domain. Using this for the intermediate temperature domainwhere the transition from coherent to incoherent relaxation occurs, we findthat the slowest relaxation mode shows a first-order phase transition.Associated with this transition, an unusual non-monotonictemperature-dependence of the relaxation rate of this mode is alsodemonstrated. Contrary to the popular belief, this non-monotony gives rise to apeculiar but observable behavior where increasing temperature will not onlyresult in a smaller rate of the slowest relaxation mode but also may lead to aslower decaying of the magnetization after some relaxing time. Additionally, itis also shown that magnetization relaxation in this intermediate temperaturedomain can only be accurately described by a bi- or tri-exponential form. Thephysical reason underlying these features can be attributed to the role of thequantum tunneling effect and different but comparative relaxation modes. Asimple experiment to confirm our findings on the first-order phase transitionand the non-monotony of the relaxation rate is accordingly proposed.

Non-monotonic temperature dependence and first-order phase transition of relaxation times in molecular spin