Mesoscopic systems provide a unique opportunity for the study of the p
henomenon of quantum tunneling of magnetization (QTM). This phenomenon
is a macroscopic quantum tunneling effect in which the magnetization
vector undergoes quantum underbarrier transitions which manifest thems
elves as temperature independent magnetic relaxation. The study of thi
s relaxation at very low temperatures affords the opportunity to study
the phenomenon experimentally. Low temperature relaxation will be dis
cussed in a variety of mesoscopic systems. Data will be presented for
logarithmic and exponential relaxation to demonstrate the occurrence o
f QTM. At high temperatures the relaxation shows the temperature depen
dence. Below a certain temperature, called the crossover temperature,
T-c, the relaxation becomes independent of temperature. These data agr
ee qualitatively with the recent theoretical work on QTM. We will conc
lude the paper with the recent work on polynuclear high spin molecules
where we have observed thermally assisted resonant tunneling processe
s between degenerate spin levels of opposite orientation. (C) 1997 Act
a Metallurgica Inc.