We report the results of magnetoresistance and magnetization measurements o
n single crystal EuB6 for temperatures above and below the ferromagnetic or
dering temperatures T-C(+) = 15.3 K and T-C(-) = 12.5 K, in magnetic fields
as large as 30 T. Shubnikov-de Haas and de Haas-van Alphen oscillations we
re observed with four fundamental frequencies. By comparison to band-struct
ure calculations, we ascribe the orbits to small pockets of electrons and h
oles, centered at the X points. The effective masses and extremal areas of
the pockets are in good agreement with the predictions of band-structure ca
lculations. We conclude that EuB6 is an intrinsic semimetal and not a doped
insulator. The intrinsic carrier concentration is 1.2x10(20) cm(-3), altho
ugh our sample is somewhat uncompensated, with a 65% surplus of holes. Ther
e is no appreciable modification to the Fermi-surface dimensions or carrier
masses with the onset of ferromagnetism. [S0163-1829(99)01907-4].