Data are presented on the paramagnetic spin-lattice relaxation times in concentrated erbium ethylsulphate. The results, above 4 K, can be described by means of an Orbach process: (τ L) H c = 0.5 kOe = 1.55 × 10 −10 exp( 54 T ) s. In a single crystal with H c ⊥ c axis double relaxation processes have been observed at the temperature of liquid helium at external magnetic fields above 3 kOe. This behaviour is studied extensively on several samples. It is noticed that the double relaxations become less pronounced if the crystal size decreases and this suggests the double relaxation behaviour is related to phonon bottleneck effects. The relaxation time in the powdered sample, at low temperatures and high external magnetic fields, is found to be proportional to T -1.8 H c -1.8; this may indicate that relaxation dependences have been observed intermediate between that of an Orbach process and that of a direct process. The b/ C value is found to be 9.7 x 10 4 Oe 2 if H c ⊥ c axis and 1.5 x 10 6 Oe 2 if H c c axis.
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