In this paper we review the work done on magnetic relaxation during the las
t 10 years on both single-domain particles and magnetic molecules and its c
ontribution to the discovery of quantum tunneling of the magnetic moment (C
hudnovsky and Tejada, Macroscopic Quantum tunneling of the Magnetic moment,
Cambridge University press, Cambridge, 1998). We present first the theoret
ical expressions and their connection to quantum relaxation and secondly, w
e show and discuss the experimental results. Finally, we discuss very recen
t hysteresis data on Mn-12-Ac molecules at extremely large sweeping rate fo
r the external magnetic held which suggest the existence of quantum spin-ph
onon avalanches. (C) 1999 Elsevier Science B.V. All rights reserved.