We have used ballistic Hall micromagnetometry to study the magnetizati
on of individual submicrometer nickel disks (80 nm high, 0.1-1.0 mu m
diameter). At low temperatures, hysteresis loops of the disks no longe
r show inversion symmetry in a magnetic field, as if the time reversal
symmetry were broken. Furthermore, the magnetization of the smallest
disks can be ''frozen'' in two possible states that are characterized
by hysteresis loops which are each other's inverse. At temperatures be
low 19.5 K a magnetic field as high as 2 T cannot switch between the s
tates, proving that it is extremely difficult to fully polarize a smal
l ferromagnetic particle. On the other hand, at slightly higher temper
atures (only T>19.8 K), a field as low as 0.1 T appears to be enough t
o fully polarize the disks. We attribute this extraordinary behavior t
o the glass-liquid transition experienced by spins at the particle sur
face. [S0163-1829(98)06542-4].