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The nuclear spin-lattice relaxation rate 1/T_1_ is calculated for magneticring clusters by fully diagonalizing their microscopic spin Hamiltonians.Whether the nearest-neighbor exchange interaction J is ferromagnetic orantiferromagnetic, 1/T_1_ versus temperature T in ring nanomagnets may bepeaked at around k_B_T=|J| provided the lifetime broadening of discrete energylevels is in proportion to T^3^. Experimental findings for ferromagnetic andantiferromagnetic Cu^II^ rings are reproduced with crucial contributions ofmagnetic anisotropies as well as acoustic phonons.Comment: 5 pages with 5 figures embedded, to be published in J. Phys. Soc.  Jpn. 75, No. 10 (2006

Spin Dynamics in Molecular Ring Nanomagnets: Significant Effect of Acoustic Phonons and Magnetic Anisotropies