We present a study of the structural and magnetic properties of single
-crystalline EuB6. Temperature-dependent x-ray diffraction found no si
gnificant anomalies at the onset of ferromagnetic order. The resistivi
ty, de susceptibility, magnetization, and specific heat prove the crys
tal to be of extraordinarily high quality. Two ferromagnetic transitio
ns at T-cl=15.3 K and T-c2=12.5 K are observed in all investigated pro
perties. The ordered state displays an unexpected anisotropy, and we d
erive the magnetic phase diagrams for the three principal cubic direct
ions. We argue that the two magnetic phases are connected by spin reor
ientation, enabled by a reduction of the crystalline symmetry from cub
ic. An additional anomaly in the specific heat is observed at low temp
eratures, which we interpret as arising from the splitting of tile Eu
ground-state multiplet in internal magnetic fields.