The spin-spin relaxation time is usually shorter than the spin-lattice relaxation time, at least at not too high temperatures. so the spin waves, absorbing the energy of rf field, come into equilibrium with other spin waves in a short time. Therefore, we can treat the spin-lattice relaxation process in the thermal equilibrium between the spin system.
Recently, Kittel-Abrahams calculated the spin-lattice relaxation time, introducing the macroscopic magneto-elastic energy.
Here we estimate the spin-lattice relaxation time at extremely low temperature, starting from the microscopic point of view and is indicated that the transverse component of the lattice vibrations is predominant.
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