The Raman exponent of single-molecular magnetic relaxation may take various unexpected values because of rich phonon spectrum and spin-phonon coupling of molecular crystals. We systematically examine the origins of different abnormalities, and clarify misunderstandings in the past, particularly the appropriateness of the fitting procedures for the exponents. We find that exponential laws raised by optical phonons can yield spurious power laws with low exponents. This observation indicates long-standing misunderstandings for origins of low Raman exponents in a large bulk of single-molecule magnets. Resulting from spin-lattice coupling with optical modes, presence of these exponents suggests the importance of the local dynamical environment for the magnetic relaxation in this regime.
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