A new anisotropic magnetic fluid is obtained using a colloidal suspension o
f magnetic particles of nanometric size (ferrofluid) as a component of a sw
ollen lyotropic hexagonal phase. This doped hexagonal system exhibits speci
fic behaviors when submitted to a magnetic field of weak intensity. The fie
ld-induced instabilities are described and interpreted; they result from a
high anisotropy of the magnetic susceptibility of the medium, which is meas
ured. It is finally shown that the magnetic properties of the doped hexagon
al phase allows one a determination of the compression modulus of the syste
m.